Microstructure-Dependent Dynamic Flow Stress in Metallic Alloys

A constitutive relationship for the dynamic flow stress in metallic alloys has been derived as a function of strain, strain rate, temperature and microstructure parameters. The microstructural features of interest in this study are the secondary phase and the grain size in dual and single phase materials, respectively. The role of the secondary phase has been investigated in Carbon steels by determining the relative contribution of pearlite colonies to the evolving flow stress. In this regard, several steels have been studied including as-received A572 steel, composed of α-ferrite matrix phase and pearlite colonies, and a heat treated A572 comprised of carbide particles dispersed within a ferrite matrix. In order to investigate the role of grain size being a strengthening mechanism on the flow stress, a fine and coarse grained Al6061 alloy have been investigated. An Equal Channel Angular Press was designed and built as a tool to refine the grain size of a coarse grained Al6061 material. Testing in the dynamic loading level was completed using a Split Hopkinson Pressure Bar at strain rates of 10 2 to 10 4 s -1 at temperatures of 20, 300, 500 and 650°C for the carbon steel and 20, 50, 100 and 200°C for the aluminum alloy. Result of the experimental testing in the form of true stress-true strain curves were used to model the stress-strain relationship as the sum of two independent components; athermal and thermal. The athermal stress component, which is due to the interaction of dislocations with stress fields generated by long range barriers has been described as a function of strain as well as relevant microstructural features. Sources of long range barriers include grain boundaries, large second phase particles, and dislocations on parallel slip planes. The thermal component of the flow stress as described as a function of strain rate and temperature and is the result of dislocation interactions with thermally activated barriers or short range barriers; dominant sources include Peierls-Nabarro barriers in BCC metals and forest dislocations in FCC metals. The presence of the dislocation forest as a short range barrier requires the inclusion of strain in the derivation of the thermal component of stress. These two stress components, thermal and athermal, are derived as explicit functions of loading and microstructure parameters. For the carbon steel it is determined that the thermal stress is a function of strain rate and temperature while the athermal component is dependent on the pearlite phase measured in terms of its volume fraction. For the single phase aluminum alloys, both the athermal and thermal stresses are shown to be grain size dependent. Upon reaching a critical grain size, the thermal component becomes increasingly sensitive to grain size refinement thus indicating a change in the deformation mechanism. This increased influence of the grain size on the thermal stress is accounted for by considering the evolution of the short range barrier source. This treatment, furthermore, provides knowledge of the different grain size scales encompassing, coarse, fine and ultra-fine each of which is defined by a deformation mechanism that reflects the specifics of dislocation/barrier interactions. These mechanisms are identified and numerically simulated. A validation procedure of the final form of the proposed dynamic flow stress model which was derived as explicit function of loading and microstructure has been carried out though a numerical simulation using loading and material conditions that were not involved in the generation of the model parameters. A comparison of the simulation results and those experimentally obtained are described and discussed.

the secondary phase has been investigated in Carbon steels by determining the relative contribution of pearlite colonies to the evolving flow stress. In this regard, several steels have been studied including as-received A572 steel, composed of α-ferrite matrix phase and pearlite colonies, and a heat treated A572 comprised of carbide particles dispersed within a ferrite matrix. In order to investigate the role of grain size being a strengthening mechanism on the flow stress, a fine and coarse grained Al6061 alloy have been investigated. An Equal Channel Angular Press was designed and built as a tool to refine the grain size of a coarse grained Al6061 material. Testing in the dynamic loading level was completed using a Split Hopkinson Pressure Bar at strain rates of 10 2 to 10 4 s -1 at temperatures of 20, 300, 500 and 650°C for the carbon steel and 20, 50, 100 and 200°C for the aluminum alloy. Result of the experimental testing in the form of true stress-true strain curves were used to model the stress-strain relationship as the sum of two independent components; athermal and thermal. The athermal stress component, which is due to the interaction of dislocations with stress fields generated by long range barriers has been described as a function of strain as well as relevant microstructural features. Sources of long range barriers include grain boundaries, large second phase particles, and dislocations on parallel slip planes. The thermal component of the flow stress as described as a function of strain rate and temperature and is the result of dislocation interactions with thermally activated barriers or short range barriers; dominant sources include Peierls-Nabarro barriers in BCC metals and forest dislocations in FCC metals. The presence of the dislocation forest as a short range barrier requires the inclusion of strain in the derivation of the thermal component of stress. These two stress components, thermal and athermal, are derived as explicit functions of loading and microstructure parameters. For the carbon steel it is determined that the thermal stress is a function of strain rate and temperature while the athermal component is dependent on the pearlite phase measured in terms of its volume fraction. For the single phase aluminum alloys, both the athermal and thermal stresses are shown to be grain size dependent. Upon reaching a critical grain size, the thermal component becomes increasingly sensitive to grain size refinement thus indicating a change in the deformation mechanism. This increased influence of the grain size on the thermal stress is accounted for by considering the evolution of the short range barrier source. This treatment, furthermore, provides knowledge of the different grain size scales encompassing, coarse, fine and ultra-fine each of which is defined by a deformation mechanism that reflects the specifics of dislocation/barrier interactions. These mechanisms are identified and numerically simulated.
A validation procedure of the final form of the proposed dynamic flow stress model which was derived as explicit function of loading and microstructure has been carried out though a numerical simulation using loading and material conditions that were not involved in the generation of the model parameters. A comparison of the simulation results and those experimentally obtained are described and discussed. x

Statement of Problem
The study of material performance for use in structural designs must consider loading conditions spanning a range of parameters including strain, strain rate and temperature. The case of high strain rate loading, above 10 2 , has been of great interest as the material response is known to change significantly in this dynamic loading regime as opposed to lower rate loading conditions. In order to investigate a materials behavior subjected to high strain rate loadings, several models have been developed for identifying the corresponding stress-strain relationship as a function of the loading parameters mentioned above. These models include the well-known Johnson-Cook (JC) and Zerilli-Armstrong (ZA) relationships [1,2] which, while shown to accurately predict the dynamic response, their parameters lack a direct correlation with microstructure characteristics.
The absence of this correlation, limits the predictive ability of these models to materials and loading conditions for which the model parameters are determined experimentally. ii) The second microstructure feature to be considered in relation to the dynamic flow response of materials is the grain size which is known to influence the athermal stress component via the Hall-Petch relationship, in which the flow stress is inversely proportional to the grain size [5]. The validity of this relationship breaks down as grain size is refined, particularly below 10μm [6], where dislocation/barrier interaction may no longer be the dominant source for deformation accommodation. Different grain size scales have therefore been identified in terms of the corresponding deformation mechanism [7]. These scales include coarse grain (>1μm), ultra-fine grained (20nm-1μm) and nano-grained (<20nm). The transition between each of these scales while is not well defined, is expected to be a material dependent. It is therefore, important that a mechanistic based flow stress model to not only take into account a direct grain size parameter but also have the capability of transitioning through the different grain size scales. This type of model could provide insight into deformation mechanisms associated with each of these scales as well as a procedure to determine the grain size at which transition between the different scales would occur. In order to achieve grain refinement of a coarse grained material, a severe plastic deformation method, Equal Channel Angular Pressing (ECAP), is applied on an aluminum alloy, Al6061. Similar to the work on LCS, the model parameters for both the thermal and athermal stresses as a function of the grain size, are determined by conducting a series of high strain rate compression tests using SHPB in a range of strain rate and temperature.
The experimental testing and numerical modeling which is carried out to investigate the role of second phase particles and grain size in low carbon steel (BCC) and aluminum alloy (FCC) are detailed in chapters 2 and 3 of the thesis, respectfully. The significance of constitutive equations to model the stress-strain response of a material at high strain rates and a range of temperatures is reviewed in the following sections, followed by the justification of the research presented and carried out in this thesis.

Models of Dynamic Flow Response of Metals
Material models are utilized in order to predict a materials response under different loading conditions in order to simulate mechanical responses which generally include yield strength, strain hardening, and strain rate and temperature effects.
Typically, yield strength defines the level of stress at which linear elastic properties no longer exist and a plastic behavior is defined. Strain hardening is the rate at which a material increases in flow stress with an increase in strain. Temperature effects, in a general sense, include thermal softening, where an increase in temperature results in a decrease in flow stress, until a saturation of this relationship occurs at a critical temperature and flow stress. Strain rate effects in most metals include an increase of flow stress with an increase in strain rate. There exist two separate and distinct linear relationships between flow stress and strain rate, usually a less sensitive region that exists from very low strain rates (10 -12 s -1 ) to approximately 10 0 -10 1 s -1 . The other distinct region includes a relatively high degree of sensitivity, usually above 10 2 s -1 , considered to 5 medium/high strain rate testing regime. The increase in sensitivity has been shown to be due to an enhanced rate of dislocation generation [8][9][10] The equation predicts the high temperature material characteristics considering isotropic hardening, temperature softening, strain rate hardening and coupled effects of temperature and strain and strain rate and temperature.  is the dynamic flow stress,  is the plastic strain,  is the strain rate of a given condition and similarly for T, the temperature. The parameters of C 1 , C 3 , C 4 , C 5 and n are material constants that must be determined using experimental data and a procedural analysis. By assuming that the portion of the equation of , is independent of temperature and therefore an athermal component of stress, one can plot flow stress versus temperature for multiple strain levels and strain rates. It can be seen that at a critical temperature, the flow stress will saturate with temperature and strain. This value of stress is determined to be C 0 .
With C 0 determined and assuming the yield stress at zero plastic strain and taking the natural logarithm, equation 1-6 is simplified to equation 1-7, and n can be determined. The utilization of these models is prevalent throughout literature. This is most likely due to not only the proven accuracy of the models, but also the relative ease of model parameter generation, through the use of experimental stressstrain curves in a range of strain rates and temperatures and followed by the procedural analyses as presented. More recently a model has been developed by Nemat-Nasser et al [19][20][21] in which the flow stress is expressed as the sum of two separate stress components each of which is dependent on the corresponding barrier sources to dislocation motion. The model has been applied to predict materials' responses considering effects of strain, strain rate and temperature. In these works, the authors point out to the fact that their model formulations allow the incorporation of microstructure related parameters, such as grain size, secondary phase particles, alloying content, dislocation density as well as crystalline structure. Results of the JC and ZA models, as discussed above, show that these microstructural characteristics have a direct effect on the model prediction response.

Thesis Justification
In the past several decades, a large amount of research efforts has been carried out to examine the dynamic response of materials with particular emphasis on the hardening characteristics and related flow stress patterns. These studies have shown that the evolution of the flow stress is affected significantly by strain, strain rate and temperature.
Many attempts have been made to quantify these relationships through models that account for both loading and material conditions. These models are generally required as a design tool to predict materials performance under real-life scenarios including dynamic loadings with or without temperature. Examples of high strain rate loadings, among others, are explosive detonation, automobile crashes or ballistics. Additionally, these dynamic flow models are employed to investigate deformation mechanisms that occur during loading events considering effects of strain and strain rate hardening, and temperature sensitivity. Successful models in this regard would provide a tool to develop materials with tailored microstructures suitable for dynamic loading resistance. An important outcome of these studies is the observation that the strain rate sensitivity of the flow stress changes significantly at strain rates higher than 10 2 s -1 . This strain rate sensitivity transition is attributed to the distinct increase of the dislocation generation rate when compared with that at lower rate loadings (<10 0 -10 1 s -1 ). The increase in dislocation generation rate has been shown to be due to the competition between dislocation generation and annihilation, in which the increase in strain rate decreases the time available for annihilation (recovery) and dislocation rearrangement processes, such as 13 cross-slip, to occur. This transition phenomenon is illustrated in Figure 1-1 for three different materials; aluminum [22], stainless steel [10] and copper [23].
Furthermore, it was shown that the flow stress is strongly dependent on microstructural characteristics such as grain size, secondary phases, alloying content, dislocation networks and crystalline structure [10,22,23]. At high strain rate levels, this dependency is explained in terms of the dislocation motion, being a source of deformation accommodation, as it is affected by interactions with microstructure related stress barriers. This correlation between flow stress and microstructure indicates that an accurate dynamic flow stress model must account for these dislocation interactions by considering the governing microstructure features. Development of such a model is the primary goal of this thesis with a focus on two strengthening microstructure characteristics; secondary phases and grain size. The two materials used to study the roles of these characteristics are carbon steel in relation to the second phase pearlite volume fraction and an aluminum alloy in relation to grain size refinement. Carbon steel is selected due to its dual phase microstructure in which the strength is governed by its carbon content. The proposed dynamic flow stress model presented in this thesis will be applied to A572 grade 50 low carbon steel which consists of alpha ferrite matrix with secondary phase pearlite colonies in the form of a lamella structure of alternating platelets of cementite and alpha-ferrite. The relative contribution of pearlite, being a strengthening phase, has been studied by D. Edmonds [24], where the quasi-static tensile strength of steels was measured as a function of the carbon weight percent which determines the pearlite volume fraction of the alloy. In addition, Campbell [25] has shown that the strength of low carbon steel is the sum of contributions due to grain size, pearlite and solid solution, see Figure 1-2. For the same material, while the role of the grain size is generally modeled by the Hall-Petch law [2,5], a constitutive relationship between the dynamic flow stress and pearlite content has yet to be established. This type of relationship, as discussed above, would need to be based on physical parameters that represent events taking place during the dynamic deformation process, specifically dislocation/barriers interactions.

Figure 1-2:
Quasi-static flow stress versus carbon weight. This shows that pearlite, outlined in blue, is the most effective manner to increase the strength of the steel. Grain size, outlined in red, also being a source of strength, but relatively insensitive to carbon weight percent [24].
Models such as Johnson-Cook or Zerilli-Armstrong [26], are widely used in predictions of the dynamic flow stress. Parameters of these models, while include temperature and strain rate sensitivities, lack physical representations and are phenomenological in nature. To overcome this deficiency, other approaches, such as the thermal activation theory [4,8,20,21,[27][28][29] has been used to derive constitutive models capable of expressing the mechanical response of metals over a broad range of strain rates and temperatures on the basis of deformation mechanisms evolving due to dislocation motion. This theory is based on the thermally assisted movement of dislocations reaching, penetrating and passing through a barrier; thus leading to plastic deformation. Barriers to dislocation motion are described as two types; short range and long range. Short range barriers include phonons, forest dislocations, dislocation jogs and kinks and Peirls-Nabarro stress. Long range barriers include grain boundaries, large second phase particles and dislocations on parallel slip planes [3,8]. features such as grain size, microstructural phases and alloy elements [20]. The summation of these two stress components is shown graphically in Figure 1-3, in which the larger low frequency hills represent the long range stress fields, while the smaller more frequent hills represent the stress fields due to short range barriers. Here it can be seen that the maximum stress due to short range barriers, σ o , will occur at 0K, known as the mechanical threshold stress at which no thermal fluctuations aid in the passing of the barrier. With the addition of thermal fluctuations caused by an increase of temperature, the mechanical stress, σ, that is needed to overcome the short range barrier and its stress field, σ th , is lowered. With further increasing of the temperature, the totality of this hill 18 will diminish (shaded area in the Figure 1-3) and thus the mechanical stress becomes athermal in nature, σ ath , at which any further increase of temperature will not lower the stress required to overcome the barrier. A third component of stress that can be included into this summation is due to viscous drag of dislocations moving through the solid solution from barrier to barrier during plastic deformation [8,21]. This only occurs at very high strain rates (>10 4 s -1 ) where the plastic deformation of the material is no longer dominated by stress-assisted thermally activated processes as previously expressed, but rather dominated by the 19 viscous drag of dislocations and the duration in which it takes for mobile dislocations to move from barrier to barrier [4,10]. Since strain rates above 10 4 s -1 are not considered in this thesis, stresses due to viscous drag has not been taken into account. This restriction represents an upper limit of the applicability of the constitutive flow model presented in this thesis.
Ogawa et al [28] used quasi-static data to generate model parameters for a constitutive model based on thermally activated motion of dislocations that is capable of predicting high strain rate response that would be seen in SHPB testing. These results showed that using thermal activation theory, and the separation of flow stress into components to explain mechanical behavior, is an accurate method to generate a constitutive model with physically based parameters. Nemat-Nasser et al [21,27] has extensively studied the dynamic response of several materials including vanadium,

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of their work showed, as in many BCC metals, their exists an inverse relationship of flow stress with increasing temperature and an increase in flow stress with increasing strain rate. Results also showed that there exists an increasing relationship with carbon content in which flow stress increases with increasing carbon content, and an increase in temperature sensitivity with increasing carbon content. Lee and Lin [10] studied the effect of pre-strain on 304 stainless steel, and results showed that there is a sensitivity to the dynamic response of the steel to adjustments in the microstructure of the steel via prestraining, which adjusts the dislocation network and density inherent in the material.
They too noted the relationship of increasing flow stress with strain rate and decreasing with increasing temperature, but also showed that there is a sensitivity with these properties with the microstructure of the material, this case dislocation network and density. Bardelcik et al [30] studied the effect of cooling rate on the high strain rate response of steel, showing that the changes in microstructure with phases including martensite, bantite, pearlite and ferrite, had a noticeable effect in the dynamic response of the steel, showing the microstructure sensitivity to dynamic response.
As discussed above, the second strengthening microstructure feature to be considered in the current analysis is the role of grain size. Grain refinement in materials has been of research interest for several decades as it is considered a means by which the strength of a material can be enhanced, which in combination with post-processing heat treatments, allows for the material to retain much of its original ductility [6,[31][32][33][34][35][36][37][38][39][40][41][42][43]. The ability to accurately model the flow response of a material as a function of grain size is of great importance in order to further understand the corresponding dynamic deformation mechanisms. K. Muszka et al [44] has studied the effect of grain size on the dynamic mechanical properties of micro-alloyed steels and showed that the mechanical response strongly depends on the grain size. The work of Q.Wei [6] has shown that the strain rate sensitivity of UFG BCC metals to be highly reduced compared to that of coarse grain microstructures. On the other hand, the strain rate sensitivity of FCC microstructures was shown to increase with decreasing the grain size.
The understanding of mechanisms that occur during the deformation of materials with refined granular structures has proved to be difficult, as this requires models capable of expressing the evolving deformation mechanisms as the grain size changes from coarse (<10μm) to ultra-fine (>10μm important parameters that will be investigated in this thesis are the role of a second phase in dual phase materials such as carbon steels and the role of grain size in single phase materials such as aluminum alloys.

Thesis Approach
As discussed above the goal this thesis is to identify the dynamic flow stress as a The SHPB is a widely used testing system for generating high strain rate stressstrain curves [45][46][47][48][49]. The SHPB designed and built in this thesis has several unique capabilities including the ability to test materials at temperatures ranging from the liquid nitrogen level, using a liquid bath method, to above 900°C using an induction heating system. Included in the extreme temperature testing setup is the use of a specially designed actuator for automatic positioning of loading bars. The system is precisely timed using an Eaton timing relay that also controls the firing of the gas gun projectile used as a means in causing the dynamic loading event. The timing relay is capable of timing the entire system to a millisecond resolution. By use of a data acquisition system in conjunction with strain gauge measuring techniques and Matlab coding, experimental stress-strain curves can be generated.
In order to investigate the role of pearlite colonies on the dynamic flow stress of low carbon steel through the derivation of a constitutive model and its parameters, In order to investigate the effect of grain size of the flow stress of dynamically loaded Al6061, an ECAP system was designed and built, in which a total of 400% strain has been applied to the Al6061 material in order to refine its coarse granular structure from 100μm, in the annealed condition, to a fine grain scale of 5μm. The ECAP system consists of a high strength tool steel die equipped with heating, displacement control and a data acquisition system and is mounted within a 100 ton hydraulic press. The Al6061 material generated by the severe plastic deformation processing as well as that of the annealed condition is further analyzed using SHPB testing techniques under different high strain rates and temperatures.
The model utilized to describe the dual phase carbon steel in chapter 2 and the single phase Al6061 in chapter 3, is based on the thermal activation theory which defines the thermal resistance of barriers to dislocation motion. Barrier sources and its resultant stress field that allow a thermally-assisted dislocation to pass through are short range in nature and have stress fields that are less than 10 atomic distances. The flow stress that results from the interaction of dislocations with these types of barriers is thus termed, the thermal component of stress and is generally a function of strain rate and temperature.
Barriers in which thermally assistant has no affect in whether or not a dislocation can pass, have resultant stress fields greater than 10 atomic distances. The resultant flow stress generated by dislocations interacting with short range barrier types is termed the athermal component of stress, due to its inherent temperature insensitivity. The athermal component is defined as being strain dependent, while also being sensitive to microstructural characteristics such as grain size or volume fraction of large precipitates.
The summing contributions of athermal, a  , thermal, th  , and also the inclusion of dislocation drag, D  , stress components, each arising from individual mechanisms involving dislocation interactions with different types of barriers, is given as in equation [1][2][3][4][5][6][7][8][9]. The drag stress is not included further in this derivation due to the lack of flow stress dependency until above 104s -1 , not within the scope of this work.  The thermal stress component, as can be seen from equations 1-13 and 1-14, depends on the dislocation spacing, l . To include this into the derivation of the equation for a more general sense to include FCC metals where the dominant short-range barrier is dislocation forests, means that l must be an evolving function of the average dislocation spacing. This is expressed as [20]; where o l is the initial average dislocation density. From this relation it can be expressed that: It is reasonable to assume that the average dislocation spacing increases with further straining in a manner similar to work-hardening effects and decreases with increasing temperature as in annealing effects. These trends are written as By substituting equations 1-17a,b and 1-18 into equation 1-15, the thermal stress can be expressed as:, From this the constitutive relationship for flow stress as a function of strain, strain rate, temperature and grain size can be assembled in the following form:, It is noted that this relationship still remains true for BCC metals, where from

Thesis Overview
The thesis is divided into four chapters and two appendices. Chapter 1 is an introduction which summarizes the goals of the thesis and presents a review of dynamic flow responses of metals which lead to thesis justification. This chapter also reviews the modeling and experimental approach utilized in the thesis to achieve its objectives.
Chapter 2 describes the determination of parameters used within a constitutive relationship for carbon steel. Model parameters are generated as a direct function of the microstructural characteristics, specifically the volume fraction of pearlite being the 29 second phase strengthener, as well as strain, strain rate and temperature. Chapter 3 describes the development of a dynamic flow stress model and identifies the model parameters for the transition through multiple grain size scales each of which is characterized by a distinct deformation mechanism. The material of concern is the single phase aluminum Al6061 in both coarse and fine grain size. The model formulations include effects of grain size, strain, strain rate and temperature.
Chapter 4 presents the major conclusions obtained in the thesis work as well as gives recommendations for future studies in the dynamic flow stress of metals.
Additionally the thesis includes two appendices describing in details the design and operation of the two experimental tools used in the thesis. Appendix A describes the Split Hopkinson Pressure Bar (SHPB) which is used for the generation of high strain rate stress-strain curves, with the ability to test within a large range of temperatures.

Appendix B describes in details an Equal Channel Angular Press (ECAP) designed and
built to generate materials with refined granular structure, through sever plastic deformation of coarse grained microstructure,

Introduction
Low carbon steel (LCS), is the primary reinforcing phase in civil structures due to its diverse nature of mechanical properties relative to its economical feasibility.
Consideration of this material in structural designs must account for its effective properties under conditions resulting in abnormally high loading rates and elevated temperatures. These properties are generally studied utilizing models which incorporate strain, strain rate and temperature dependent parameters. Several models exist for calculating the stress-strain response under these conditions. One of the common models is that of Johnson-Cook (JC) [1] in which the material constants are determined from empirical fitting of experimental dynamic flow stress obtained from at various strain rates and temperatures. These constants do not include microstructure related parameters such as the grain size, phases and dislocation homogeneity and density which are known to influence the material dynamic response [2][3][4][5]. Another model is the Zerilli-Armstrong (ZA) that includes the effect of grain size by utilizing the Hall-Petch relationship for both the BCC and FCC crystal structures [6]. A third widely used phenomenological model is the Mechanical threshold stress (MTS) [7,8] which is based on a physical mechanism of thermally activated dislocation motion and focuses on the determination of mechanical threshold stress. The flow stress is expressed in terms of an athermal component due to barriers of thermally activated dislocation motion, the strain hardening due to dislocation accumulation, and strain-rate and temperature dependent scaling factors based on normalized activation energies. The model parameters do not include explicit microstructure dependent terms [9]. DeMange et al, [10] utilized the JC model to simulate the dynamic response of Inconel-718 in the annealed and precipitate-hardened 38 states. The hardening parameter in the model is written as a strain rate independent which could explain the fact that the model outcomes over predict the flow stress response at high strain rates. The model also did not accurately predict the saturation of the flow stress with increasing strain, a feature that was observed in the experimental results.
Daridon et al [11], studied effects of adiabatic shear band spacing on the dynamic response of HY-100 steel and Ti-6Al-4V alloy and concluded that the physically based MTS model was in better agreement with experimental results than that of the JC model.
The authors reasoning being that the adiabatic shear bands act as thermal activation barriers for dislocation motion, a physical phenomenon that the JC model does not account for.
Lee and Liu [2] studied the dynamic behavior of different steels with varying weight percent of carbon with respect to effects of temperature and strain rate. Results of their work showed that the flow stress and temperature sensitivity increase with increasing carbon content. Lee and Lin [3] studied the effect of pre-strain on the 304 stainless steel where results showed that the dynamic deformation response is sensitive to pre-straining. They interpreted this effect in terms of the role of pre-straining in modifying arrangements and density of the dislocation network within the microstructure.
Bardelcik et al, [12] studied the effect of cooling rate on the high strain rate response of steel, showing the changes in microstructural phases including martensite, bantite, pearlite and ferrite, had a noticeable effect on the dynamic response of the steel by adjusting the UTS and hardening rate. Odeshi et al [13] examined effects of the high rate loading of low alloy steel and showed that the plastic deformation is governed by two occurring processes. In the early stage, strain hardening which is strain rate dependent, is dominant. As deformation progresses, adiabatic heating occurs causing thermal softening to dominate. Zhang et al [14] and Lee and Chen [15] have recently investigated the role that Al 3 Sc precipitates have on the dynamic response of the material. It was shown that the secondary particles had a significant effect on the microstructural evolution during dynamic loading conditions. Zhang studied the condition of high speed projectile impacts while Lee and Chen utilized SHPB techniques to characterize the dynamic response.
They similarly concluded that the particles had two effects; the first is related to the stabilization of the matrix and the second is due to effect of the particles acting as a major source of dislocations, thus resulting in an increase in the strain-induced hardening.
DeMange et al [10] studied the dynamic deformation response due to blunt projectile penetration, dynamic compression and top-hat dynamic shear testing of annealed and precipitate-hardened Inconel-718. During blunt projectile testing, using plate impacts, the annealed material had a higher resistance to penetration than that of the precipitatehardened state. During dynamic compression tests, the annealed state resulted in a much lower over-all flow stress than the latter material, but showed considerably superior work hardening than the precipitate-hardened Inconel. The reason for the lowered work hardening in altered state of the Inconel was validated by top-hat geometry dynamic shear tests. Results of these tests showed that the precipitated hardened material readily forms shear bands, leading to localization which lowers the load capacity as compared to the annealed state of the material.
Ogawa et al [16] studied the high strain rate of low carbon steel employing a model based on the concept of separating the flow stress into two physically-based components. The first is an athermal component which is only a function of strain and is modeled as a simple power law relation. The second is a thermal component that is a function of temperature and strain rate and is modeled assuming that deformation obeys a single thermal activation process. The combined dependence of the stress on strain rate and temperature is based on the Larson-Millar parameter. In a similar approach, Nemat-Nasser et al [4,5,17] has studied the dynamic response of several metals and alloys including vanadium, tantalum alloys, titanium alloys, aluminum alloys, OFHC copper,  [18,19]. The pearlite colonies are a harder secondary phase than that of its ferrite matrix and would thus act as an effective long range barrier to dislocation motion [20,21]. In order to examine this effect, the flow stress of the as-received microstructure (9% volume fraction of pearlite), is assessed along with three other steels having 0%, 20% and 72% of pearlite volume fraction. The first part of the paper describes the materials used in the study followed by details of a dynamic flow stress model. The third part is the experimental program for determining parameters 41 required for the identification of the stress components. The last part of the paper is a discussion of the role of the pearlite volume fraction on the basis of the model outcomes.

Material
The material of study is A572 Grade 50 LCS which consists in the as-received condition of equaixed alpha-ferrite grains with evenly dispersed pearlite colonies of a lamella structure of alternating alpha-ferrite and cementite platelets as shown in Figure   43 In order to study the effect of pearlite volume fraction in relation to the dynamic flow stress, an attempt is made to generate a microstructure with no pearlite colonies. This is achieved by a heat treatment carried out on the as-received condition in order to disperse the carbon in speriodized form evenly throughout the alpha-ferrite matrix. In the initial stage of this procedure, as-received specimen is heated to 750°C, above the eutectic point, for one hour followed by rapid quenching in an ice-brine solution. This

Dynamic Flow Stress Model
Modeling the flow stress as the sum of separate stress components is based on the concept that stresses developed in the material as a result of dynamic loading are related to the different mechanisms associated with dislocation/barrier interactions. This sum is written as; This stress is shown to be strain dependent [2][3][4][5]. The thermal component, th σ , arises due to stress generated by short range barriers mainly that due to Peirls-Nabarro stress but also includes phonons, forest dislocations, dislocation jogs and kinks [4,5,21,24]. This stress is a function of thermal dependent effects mainly the strain rate and temperature.
The viscous drag stress component D  is due to the resistance of dislocation motion through a lattice by the lattice potential as well as interactions between phonons, electrons, radiation and point defects. In BCC metals, viscous drag effects are significant only at strain rates above 10 4 s -1 , which is higher than those applied in this study [25,26].
As such the drag stress component will be neglected in the current analysis.

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The athermal component is indirectly affected by temperature through the temperature dependency of the elastic and shear moduli. To account for this, a  is normalized by the elastic modulus function as expressed in equation 2-2. E o is the reference elastic modulus at room temperature and E(T) is the shear modulus at a given temperature.
In the remaining of the paper, Turning attention to the thermal stress component, it is, as mentioned above, a product of interactions between dislocations and short range barriers, mainly Peierls-Nabarro barriers. Here it is assumed that the activation energy, G  , required for a dislocation to surpass a barrier by a single thermally activated process is written as: where G o is the activation energy of 1eV/atom, and p and q are parameters that represent the profile of the dislocation barrier [17]. Furthermore, the strain rate,  , is related to ΔG by the following relationship: The model parameters of equation 2-10 are determined using experimental dynamic stress strain curves generated each of the materials with varying pearlite volume fraction using SHPB tests performed at a range of strain rates up to 5.4E3 s -1 and temperatures up 650°C. The experimental procedure and related analysis are described in the following sections.

Experimental Dynamic Flow Stress and Model Parameters
Dynamic testing has been carried out using a SHPB system capable of strain rates from 10 2 -10 4 s -1 . High temperature testing utilized Tungsten inserts with the impedance matched to that of the maranging steel split Hopkinson bars assuming that no effects are induced to the loading pulse. The specimens were heated using a 5kW induction system.
Cylindrical SHPB specimens with an L/D ratio of 0.5 for all tests where used and loading surfaces are ground to ensure parallelism while also to achieving a smooth, defect free surface, and reducing frictional effects. High temperature graphite lubrication was used in between the loading bars and specimen to reduce friction and ensure little to no barreling of the specimen will occur, resulting in an undesirable unsteady loading. Pulse    This transition from a low sensitivity to a high sensitivity with strain rate has been attributed to the increased rate of dislocation generation [3,27], which would cause the barriers that impede the motion of the dislocations to become a significant factor in the deformation of the material. The increase in dislocation generation is the cause in the increase in flow stress, or increase in strain rate sensitivity. Figure 2-7 shows that that there is a approximately 81% change in strain rate sensitivity between the loading regions at 20°C, and similarly at 500°C.

Athermal Flow Stress Parameters
The flow stress is extracted at constant values of strain for the as-received and heat treated A572 conditions from the dynamic stress strain curves and is plotted versus temperature in Figure 2-5 for three different strain rates for the as-received and heat treated conditions discussed above. These results show that the flow stress decreases rapidly with the increase in temperature, until saturation at a critical temperature, T cr . The trends in this figure indicate that the curves corresponding to the three different strain rates would converge to a single value of stress. This saturated stress represents the athermal stress component, see [2,4,5].  considering values from literature as well [28,29].

Thermal Flow Stress Parameters
Since the flow stress is presented as the sum of two components, the thermal stress can be calculated as: Where  is the normalized flow stress, it is shown in equation 2-9 that th  is a function of T p/q . This relationship is plotted in Figure 2-8, by selecting p/q to be 3/2 to obtain a simplified linear correlation [2,4,5].

Model Simulations
Parameters generated from the analysis detailed in the last section were numerically optimized and are presented in table 2-1 and can be used in conjunction with equation 2-10 to simulate the flow stress-strain curve as a function of pearlite volume fraction for different strain, strain rate and temperature.
where ρ is mass density which is assumed to remain constant at 8065 kg/m 3 , η is a constant representative of the amount of energy converted into heat, and C v is the temperature dependent heat capacity of the material, initially 0.420 J/gK. The variation of ΔT is taken in consideration during simulation steps of the flow stress calculations carried out at different strain rates and temperature conditions. Results of these simulations for isothermal and adiabatic stress-strain curves compared with those experimentally obtained but were not utilized in parameter identification, are shown in Figure 2-9. This figure shows the good agreement between these simulated and experimental curves for the as-received (9% volume fraction of pearlite) and heat treated conditions (0% volume fraction of pearlite) at all loading conditions. The comparison between the experimental and modeled stress-strain curves shows that the parameters generated, Table 2   increase in contribution of pearlite to flow stress, in just over a 30% decrease in grain size. The pearlite volume fraction becomes an increasing contributor as a strengthening phase within the low carbon steel. These figures show that the pearlite colonies are more effective as long-range barriers to dislocation motion, in that they provide an increase in the o  -parameter with increasing volume fraction of pearlite than that of a greater increase due to a decrease in grain size would cause. The pearlite colonies are there for a stronger barrier to dislocation than that of grain boundaries themselves.

Conclusions
The role of pearlite colonies of the dynamic flow response has been studied for -A heat treatment procedure is carried out on the as-received A572 LCS to modify the ferrite-pearlite microstructure into a ferrite-speriodized LCS. This was carried out in order to compare the dynamic flow stress as a function of pearlite volume fraction.
-A series of SHPB dynamic loading tests were conducted on 1018 (20% VFP), 1060 (72% VFP), as-received A572 (9% VFP) and heat treated A572 (0% VFP) steels. The as-received and heat treated conditions were tested at temperatures: 20°C, 300°C, 500°C and 650°C for strain rates ranging from 7E2 to 5E3 s -1 . The 1018 and 1060 steels were tested at 500°C and 650°C at 1.5E3s -1 -A procedural analysis is performed in order to generate model parameters for the athermal and thermal components of stress of the steels mentioned above. It is shown that only the athermal component of stress is affected by the volume fraction of pearlite.
-A parameter representing the stress contribution due to pearlite within the athermal component of stress is derived as a function of volume fraction of pearlite. In addition, a weighted average of the Hall-Petch type relationship with respect to volume fraction of pearlite is generated. Furthermore the Hall-Petch constants for pearlite and ferrite are generated.
-The constitutive model has been applied for different microstructure, strain, strain rate and temperature. Results compared well with those experimentally generated.

70
-The effectiveness of pearlite as a strengthening phase in steel is evaluated as a function of volume fraction of pearlite. A parametric study is carried out to examine the role of pearlite as a strengthening phase in low carbon steel. It is shown that this role is more effective as grain size decreases.

Introduction
Grain refinement of a material, its generation, performance and microstructural characteristics has been of great interest of researchers for the past few decades. This is due the enhancement in mechanical properties with refinement in grain size. Severe plastic deformation methods are used for the manufacturing of fine (FG), ultra-fine (UFG) and nano-crystalline (NC) materials; these include equal channel angular pressing (ECAP) [1], high pressure torsion (HPT) [2,3], accumulative roll bonding (ARB) [4], tubular channel pressing (TCP) [5] and dissimilar channel angular pressing (DCAP) [6].
These methods lead to effective manner in which the process can be scaled from the laboratory level into full-scale production modes, with the ECAP method receiving the highest level of interest. With the increased production and future use of such a material, it is important to have the ability to derive constitutive relationships that can predict the corresponding mechanical stress-strain response in a wide range of strain, strain rate and temperature loading conditions. In addition, microstructure parameters, particularly the grain size, phases and dislocation configuration including density and homogeneity, are shown to have a significant influence on the refined material response [7][8][9][10]. A widely used model is the Johnson-Cook relationship in which material constants are derived from empirical relations of experimental dynamic flow stress carried out under varying strain-rates and temperatures [11]. These constants are general in nature and microstructure independent. Zerilli-Armstrong (ZA) model includes the effect of grain size by utilizing the Hall-Petch relationship. The model is applied with different formulations tailored to BCC and FCC microstructures [12]. A third model is the mechanical threshold stress, which is a phenomenological model based on the 76 consideration of thermally activated flow stress. This model does not include explicitly dependent microstructure terms [13,14]. A recent study by Spirdione et al. [15] has developed microstructure-sensitive flow stress formulations that have shown promising ability to predict the stress-strain response in a wide range of strain rates and temperatures for both FCC and BCC crystalline structures. This model, similar to the work of Nemat-Nasser et al [9], is based on the separation of the total flow stress into separate components, athermal and thermal, that are resultants of different physical barriers to dislocation motion. The athermal component is due to long range barrier sources such as grain boundaries and second phase particles, that generate stress fields that are 10 atomic diameters or larger. The thermal component on the other hand is attributed to the stress that arises as dislocations interact with short range barriers, stress fields generated less than 10 atomic diameters, mainly Peierls-Nabarro stress in BCC materials and dislocation-forests in FCC structures [16,17].
May et al [18] investigated UFG aluminum and aluminum alloys in regards to its mechanical properties, dislocation density and grain structure. This work showed that the precipitate and alloy content in the course grain (CG) state of the material contributes to the ability of the material to be refined into UFG; with an increase in alloying elements, the grain size decreased after ECAP processing, along with an increase in dislocation density within the grain interior. This effect is due to the inclusion of impurities that hinders dynamic recovery and re-crystallization during processing. Similarly, Chowdury et al, [19] showed that Al2024 and Al5056 had an increase in strength with an increase in the number of passes through an ECAP system. While with an increase in alloy content in Al7034, there was an initial decrease in strength with the number of passes, then 77 subsequent increase in strength with further processing. This is attributed to the effect that precipitates have on the texturing of the grain structure during UFG processing. This effect is due to the rate at which low angle boundaries, which are at a weaker nonequilibrium states, convert into the more equilibrated high-angle grain boundaries that do not allow dislocation transport as readily. Kahn et al [20] studied the thermo-mechanical response of Al6061 with and without ECAP processing. It was found that in the quasistatic loading regime, the strain rate sensitivity (SRS) increases with the increase in the number of ECAP passes. The increase in the flow stress while is directly dependent on the number of passes as well as the strain rate, reaches a saturation at 125°C. For the same number of passes, SRS was observed to increase with an increase in temperature.
Kunimine et al [4] have investigated the temperature and strain rate sensitivities in UFG copper. The work shows that there is an increase in SRS in a FCC material with a decrease in grain size but also shows that there is a SRS increase with an increasing temperature testing condition. Lee et al [21] showed that in the CG state of Al606-T6 the relationship with SRS and temperature is similar to the of Kunimine et al and Wei et al.
Also that temperature sensitivity increases with both an increasing strain rate and temperature in CG Al6061-T6.
Wei et al [22] investigated effects of the crystalline structure at the NC and UFG scales would have on the mechanical response, including the strain rate sensitivity. It is observed that SRS increases with the decrease in the grain size of the FCC microstructure while the opposite trend occurs in the BCC structure This response is attributed to the fact that in the FCC microstructure, the thermally activated barrier that interacts with mobile dislocations is mainly in the form of dislocation forests. As a decrease in the grain 78 size occurs, reaching a critical transitional grain size, defined as when the grain size is equivalent to the inverse root of dislocation density, the grain interior becomes nearly dislocation free, while the grain boundaries exhibit an increase in the dislocation density.
As such, dislocation forest cutting is no longer the rate controlling deformation The first part of the paper describes the materials of study, an annealed Al6061 and an FG Al6061. The FG Al6061 is generated using an ECAP system which is discussed in detail. Secondly the flow stress is formulated in a constitutive equation

UFG Material and Processing
Aluminum 6061 was received in the T6 temper with a composition of (wt%) Al-  2 cot cosec 2 2 2 2 3 where n  is the total strain applied during ECAP pressing and N is the number of passes.
The die accepts a 4.5 inch long specimen having a half inch square cross-section. The exit channel of the die is tapered from the interior outward to allow for the relaxation of elastic stresses within the specimen on exit. A schematic of the die detailing the dimensions is shown in Figure 3 [20,27] has shown that route B c , in which the specimen is rotated 90° about the Z-axis after every pass, is the most effective in generating equaixed low-angle fine grained structures. This route was chosen in the processing of Al specimens for this study. The FG material obtained after four passes in the ECAP system described, is shown in Figure   3  From the micrograph in Figure 3-3, it can be seen that the initial average grain size before ECAP processing of the annealed 6061 in Figure 3-1 is approximately 100μm, in an equaixed form. Similarly, the average grain size of the FG material is shown to be approximately 5μm.

Microstructure Dependent Dynamic Flow Stress Model
The flow stress as a result of dynamic loadings has been shown to be the The thermal stress component, as can be seen from equations 3-6 and 3-7, depends on the dislocation spacing, l . In FCC metals where the dominant short-range barrier is dislocation forests, means that l must be an evolving function of the average dislocation spacing. This is expressed as in [9]. From this the constitutive relationship for flow stress as a function of strain, strain rate, temperature and grain size can be assembled in the following form:, Examination of the validity of the flow stress as expressed above requires the identification of the material parameters, * a  , n, G  , o  , p, q, a and m. These will be determined using experimental flow stress curves generated for each of the materials described above; FG and CG materials having grain sizes of 5 and 100μm, respectfully.
These curves will be obtained using SHPB tests performed at strain rates up to 5.0E3s -1 and temperatures up to 200°C. The analytical procedure and model parameters determined are described in the following section.

Model Parameters Determination
Testing the CG and FG conditions of the Al6061 are carried out at strain rates ranging from 1.0E3 to 5.0E3s -1 , and temperatures ranging from 20°C to 200°C.
Experimental flow stress curves were generated and smoothed using a curve fitting procedure in order facilitate data analysis. decreases. These observations which are supported by the previous work [22], will be discussed later in this paper.  Kd . Using the known grain size of the annealed CG Al6061 to be 100μm, the K parameter can be determined.
Also noted is the variance in the hardening parameter, n, with grain size. This parameter is will be discussed further at a later time.

Thermal Flow Stress Parameters
The  [9]. In order to determine the a-parameter from equation 3-11, the relationship between l and  c , is assumed to be [9,22].
The work of Mujica et al [29] on commercially pure aluminum provided the dislocation densities at three different strain levels at room temperature (circles in Figure   3-10a). These densities were utilized, in addition to the assumption that m=0.5, to generate a three parameter power law (solid curve in Figure 3-10a) by which the constant a is determined to be 2.963 for the CG condition. To carry out similar calculations for the FG material, the dislocation density, as will be discussed later in this paper, is expected not to vary drastically with strain. An initial dislocation density for FG Al6061, determined as 2E11/mm 2 [29], is used to normalize the solid data points in Figure 3-10a.
These normalized dislocation densities are then fitted into a power law relationship (solid curve in Figure 3-10b) and utilized to determine the parameter a for FG material, which is calculated as 0.0266.
To determine the parameter o  , the relationship given in equation 3-2 is rearranged as:

Grain Size Dependent Flow Stress Parameters
In order to accurately model the flow stress as expressed in equation 3-13, it is important to investigate each of its parameters in relation to grain size. To start with, the hardening parameter, n, of the athermal stress component is shown to be inversely related with the grain size following a Morrison type law in UFG steels [30].

Flow Stress Simulation
Throughout the previous section, the flow stress with its two components; thermal and athermal, is described in terms of material parameters that are determined through series of high strain rate tests. These parameters were numerically optimized using the Matlab function fmincon, which attempts to find a constrained minimum of a scalar function of several variables starting at an initial estimate. Results are presented in Table   3 These validated parameters, can be used to simulate the true-stress strain curve for FG aluminum alloy 6061 as a function of grain size for different strain, strain rate and temperatures.

Discussion
The work presented in this paper aimed at obtaining an explicit form of the flow stress components, thermal and athermal, at high strain rate as a function of loading parameters; strain, temperature and strain rate, as well as microstructural variables, Cheng et al [32], presented a deformation mechanism map for FCC metals, in which the differing deformation mechanisms with grain size are separated into four regimes. The smallest grain size regime occurs roughly at 10nm and denoted Nano-1 in which deformation occurs solely by grain boundary processes such as grain boundary sliding or Coble creep. The lack of dislocation based activities is assumed to be due to the absence of dislocations within the grain interior. The inclusion of grain boundary processes as the dominant deformation mechanism explains the inverse Hall-Petch, or grain size refinement softening, seen at this grain size scale [23,[33][34][35][36][37][38]. The second scale, Nano-2, exists with grain sizes larger than 100nm. At this range, grains are sheared by twining or by Shockley partial dislocations which are absorbed in the opposite grain boundaries, leaving intrinsic stacking faults behind. The third regime, Ultra-fine, consists of grains larger then 20-35nm up to 200-1000nm, depending on the material. Here grains are sheared by lattice dislocations which are nucleated within grain boundaries. A trailing partial can be nucleated before the entire grain is sheared by a leading partial. Therefore UFG deformation occurs by the motion of perfect dislocations that are emitted from grain boundary sources. The difference between the UFG and the final regime, coarse scale, in which classical mechanical response is expected, is that, in the UFG regime, the dislocation source can only be the grain boundaries. In the coarse grain scale, dislocation sources include grain boundaries as well as intra-granular sources, other dislocations, precipitates etc. Cheng concluded that little research has been conducted to identify the transition between grain boundary sources and mixed sources, so the exact UFG/coarse transition is not well defined.
This type of classification of materials based on grain size scale and associated source of dislocations, indicates that in the UFG regime, even with the removal of intragranular dislocation sources, the deformation remains thermally activated due to presence of grain boundary emitted dislocations. Dao et al [39] proposed several deformation mechanisms that can occur in UFG, provided that the mechanism must have a small activation volume, a condition seen in NC and UFG metals [22,32]. These mechanisms include the punching of a mobile dislocation through a dense bundle of excess grain boundary dislocations, defect assisted dislocation nucleation, and the de-pinning of dislocations that are pinned at boundary obstacles. Results presented in the current study assume that the transition from the traditional regime to the UFG must involve a transitional regime characterized by a fine grain scale. In this fine grain regime, deformation accommodation, which encounters a decrease of dislocation sources within the grain, would require an increase in dislocations originating from grain boundary sources. This could explain the observation, Figure 3-15a, that the thermal stress component in the aluminum material studied is inversely proportional to the grain size and the sensitivity of which increases with further refinement. This effect is possibly due to the increase of thermally activated barriers from grain boundaries sources with a decrease in grain size. The residual athermal stress with further refinement into the nanoscale, may be the reason in which dislocation activities cannot be utilized during the deformation and only grain boundary processes, as this stress would be too high to allow a dislocation to be emitted from the grain boundary. The athermal component of stress still depends on the grain size, Figure 3-15b, in both the fine and the UFG regimes due to the observed fact that Hall-Petch relationship maintains its validity in these two regimes. . This indicates that once the grain size drops below a critical transition size, the rate controlling mechanism is no longer forest cutting, but rather grain boundaries or sub grain boundaries acting as the dominant source of dislocations. This is explained by the fact that as a grain size is decreased the dislocation density within the grain is expected to become very low, thus removing sources of forest dislocations, whereas the obstacle density associated with grain boundaries becomes very high. It is thus possible that the controlling intersection obstacles are the grain or subgrain boundaries. It was shown experimentally in heavily deformed copper [22], that as grain size was decreased a sharp decrease was measured in the activation volume indicating a change in the rate controlling mechanism in the thermally activated process. This is supported by results of the current work, see Figure 3-6, which shows that as the grain size is decreased, there is an increase in strain rate sensitivity, m, which is inversely proportional to activation volume v*, by the relation, . This relationship is further expressed in terms of l, yielding strain sensitivity expressions for both the coarse grains, m co , and fine grains, m fg , written as: The parameters determined provide a manner in which for the model used in this work for the flow stress as function of strain, temperature, strain rate and grain size to be sensitive and capable of evolving with the transition in deformation mechanisms that occur with grain refinement. These transitions are shown by the resultant change in strain rate sensitivity due to the changing mechanisms of deformation, related to the activation volume.
The parameters determined provide a means by which the flow stress can be accurately predicted through transitional grain sizes, where rate controlling mechanisms evolve with differing grain size regimes. These transitional regimes are experimentally observed by the increase in SRS with grain refinement, and explained by the sharp change in activation volume, an indication of a change deformation mechanisms. An attempt has been made to add a defined transitional regime, fine grain, between the CG and UFG materials. In the CG, the traditional mechanical response is expected, and in the UFG the deformation mechanisms differ in which intra-granular dislocation sources are no longer present. This fine grain regime of deformation, shares mechanisms that occur in both the CG and UFG materials, but exists at a point in grain refinement at which the dominant rate controlling mechanism is evolving from intra-granular sources of 118 dislocations to mainly grain boundary sources. The change in dislocation sources results in the thermal stress component having an increased dependency with grain size as refinement moves from the CG into the UFG.

Conclusion
The Utilizing the experimental data in conjunction with the models analytical formulations, parameters were generated as functions of materials and loading variables.
For carbon steels, these parameters were defined in terms of pearlite volume fraction while for the aluminum alloy they were generated as functions of the grain size through Hall-Petch type laws. This law has been shown to breakdown during the transition from the coarse grain scale (>10microns) to the ultra-fine grain scale (1micron-10microns).
This delineation from the original Hall-Petch effect has been shown to be due to the change in the deformation mechanism associated with each of these scales. The twocomponent flow stress model presented in this thesis is developed to have the ability to bridge this transition by considering each grain scale and associated deformation mechanism.
A summary of conclusions made from the experimental, analytical and numerical work are listed.

Influence of pearlite volume fraction in the dual phase carbon steel
-A dual stage heat treatment of A572 was developed to obtain a microstructure free of pearlite colonies. This treatment consists of heating to 750°C which is well above the eutectic point of the steel at which a phase transformation would occur.
The alpha-ferrite and pearlite grains transform into a fully austenitic phase. The material was held at this temperature for one hour, followed by a rapid quenching in an ice-brine solution. This rapid cooling allows the material to revert back into the dual phase structure consisting of alpha-ferrite and pearlite, though the rapid quenching does not allow the pearlite to form into as well organized colonies as in the as-received condition. This material is then tempered below the eutectic, at 720°C for 72 hours. This process diffuses the fine cementite structure into speriodized carbides, mostly residing at alpha-ferrite grain boundaries.
-Optical and scanning electron microscopy was utilized to characterize the volume fraction of pearlite, as well as grain size. The as-received A572 steel was shown to have a volume fraction of 9% and a grain size of 25μm, with the heat-treated condition resulting in a 0% volume fraction and grain size of 38μm. The other two steels 1018 and 1060 showed volume fractions of 20% and 72% and grain sizes of 9μm and 7μm respectfully.
-A Split Hopkins Pressure Bar (SHPB) apparatus was designed and constructed in order to experimentally test metals at high strain rates. The system includes the ability to test in a wide range of temperatures ranging from the liquid nitrogen temperature to temperatures up to 900°C. The SHPB components include a loading gas gun which fires a projectile to create a dynamic event, the loading bars along which strain pulses are measured, a thermal heating system as well as a data acquisitions system which allows for data to be collected from strain gauges bonded to the loading bars.
-A series of SHPB dynamic loading tests were conducted on as-received A572  -The constitutive model has been applied for different microstructure, strain, strain rate and temperature. Results of these comparisons showed a good agreement 128 with experimental curves that have not been used in the generation of the model parameters.
-A parametric study is carried out to examine the relative contribution of pearlite as a strengthening phase and showed that this contribution increases with the decrease in the grain size.

Influence of grain size in the single phase aluminum alloy
 An equal channel angular press (ECAP) was designed and constructed in order to refine the grain size of an aluminum alloy (Al6061) through severe plastic deformation. The ECAP system includes a high strength tool steel die with a channel angle of 95° to apply approximately 1.0 strain per pass, a 100 ton hydraulic press as a loading system, a die heating system to allow for the ability of high temperature pressing and a data acquisition system for measurements of pressing force, displacement and rate.
 A fine grained (FG) Al6061 (5μm) was generated using the ECAP system using processing route B c , at a temperature of 150°C and at a rate of approximately 1inch/minute. The material in its original state from which it was refined was an annealed Al6061 coarse grain (CG) condition (100μm). Dynamic true stress-true strain curves were generated during these tests.
 Using a the same analytical procedure applied to carbon steel, constitutive model parameters for the athermal and thermal stress components are generated for both the FG and CG Al6061 material conditions. By comparing parameters obtained for each of the Al microstructures, it is concluded that both the athermal and thermal stress components are grain size sensitive.
 It is shown that the FG material produced in this work exists as a distinctive scale that lies between the coarse and ultra-fine grain size levels.

Future Recommendations
The work completed in this thesis provided a constitutive relationship that -The effect of grain size specifically in BCC metals would be of great interest the behavior of this crystalline structure has been shown to differe from that of the FCC material studied in this work. This change is flow stress behavior is the decrease in strain rate sensitivity, as opposed to in FCC metals, grain size reduction results in an increase in strain rate sensitivity. The application of the model produced could therefore provide insight as to why this response occurs.
132 APPENDIX A

A.1 Split Hopkinson Pressure Bar Apparatus
This appendix section will present an overview and background of the history of dynamic testing as it pertains to the use of the split Hopkinson pressure bar (SHPB) in the dynamic loading field. Also a general description of the conventional SHPB will be given to aid in the understanding of following material.

A.1.1 Brief History
The split Hopkinson pressure bar has become the most widely used tool in high strain rate mechanical testing (10 2 -10 4 s -1 ). This is true because of the accuracy and repeatability that the tests can achieve. Data obtained from these tests can be utilized in many different fashions, such as determining conventional material properties like yield strength, strain hardening and ultimate strength while also being used in more advanced manners to study temperature and strain rate effects or to generate material models, as it has become common knowledge that these mechanical properties will change at higher strain rates. Most material properties found within handbooks and design manuals are determined at the quasistatic testing regime, it is important in some cases, in order to ensure proper performance, that designs be based on the material response in the high strain rate regime, examples include vehicle collisions, explosive detonation or the inevitable dropping of an electronic device [1].

133
The development of the SHPB system was due to the collective work of several researchers over several decades. The first was Bertram Hopkinson [2] (1913) who developed a manner in which to determine pressure-time relationships due to an impact produced by a explosive. Components of the experiments included an explosive impactor, a long steel rod, a short steel billet and a ballistic pendulum. Impact occurs at the rod generating a compressive wave which travels to the far end where the short billet is in contact, and reflected at the free-end of this short billet as tensile wave. When this pulse returns to the long rod interface, the pulse wave is ended. The wave that was now fully-generated within the long rod impacts a ballistic pendulum, located at the other end of the long rod. The motion of the ballistic pendulum would lead to the determination of the maximum pressure and total duration as well as an ill-defined pressure-time curve.
Davies [3] (1948) greatly improve the accuracy of this system by the addition of condensers to measure the strain generated within the pressure bar, the long steel rod in Hopkinson apparatus. The output of the condensers is relatable to the pressure-time relation within the bars, as long as the elastic limit is not reached within the bars. Kolsky [4] (1949) the first person to utilize this system in order to determine the stress-strain response of a material under high strain testing conditions. The manner in which Kolsky measured the pressure within the bars was similar to Davies. The major addition to the setup was the adding a second bar, which sandwiched a specimen between the first loading bar. Kolsky noted the importance of specimen dimensions, lubrication of the specimen as well as a detailed analysis in determining the stress-strain response from data collected using the condenser microphones. The system has been mostly unchanged in its most basic compressive form with the addition of the use of strain gauges by Krafft [5] (1954) to measure the signals generated within the pressure bars, as well as the addition of a gas gun to propel a striker into the pressure bars rather than the explosive detonation.

A.1.2 General Compressive SHPB
The SHPB has become the tool of choice to characterize materials at strain rates typically between 10 2 -10 4 s -1 . The SHPB as explained has evolved over the past century from a simple explosively controlled apparatus to a complex, accurate and repeatable system that can precisely define a materials properties. There are several variants that have been developed which include a tensile form of the system, systems used for high and low temperature conditions as well as automation of the system, please see the following references for a comprehensive SHPB literature review, [1,[6][7][8][9][10][11][12][13][14]. To begin it is necessary to investigate the general compressive SHPB system. are what causes the initial unsteady state stress state of the specimen, thus making early elastic data of the specimen unreliable, and are also the source of oscillations within the pulses collected using the data acquisition system. These oscillation and the initial unsteady stress state can be mitigated using pulse shaping techniques, but will be ignored at this point. The pulse that is transferred into the transmitted bar, travels along its length where it meets a momentum stopper to capture the remaining energy of the pulse. The strain histories of the two loading bars, which include the incident, reflected and transmitted pulses, can be recorded using two strain gauges. One mounting on the incident bar, which collects the incident and reflected pulses. The other is placed on the transmitted bar for the transmitted pulse. Typical data acquisition systems include the before mentioned strain gauges, a manner in which to excite, filter and amplify the gauges and a recording system, usually a high-speed oscilloscope or computer. These three pulses as, defined by Kolsky, can be used to generate the stress-strain response of 136 the specimen that was sandwiched between the loading bars. A derivation and explanation of these equations is expressed in the following section.

A.2.1 SHPB Governing Equations
The compression form of the split Hopkinson bar has been well established in the dynamic testing field, where most compression machines are similar in nature with a few iterations being applied by different researchers depending on the application [7]. The theory of the wave propagation with detailed analysis is largely found in literature and with the level of common knowledge of the subject [15]. A short derivation of the major equations used in the SHPB analysis will be presented. The solution to the one dimensional wave equation, A-1, for the incident and transmitted bars, denoted by subscripts 1 and 2 respectfully is shown to be in equations A-2 and A-3 where c b is the longitudinal wave speed of loading bar material given by E  , where E is the elastic modulus and ρ is the density. u 1 and u 2 is displacement for the incident and respect to x is shown to be, where, ε, is the strain induced with the corresponding subscripts for the incident and Furthermore, assuming that the interface between the two loading bars is in a state of equilibrium during a given experiment, the forces F 1 and F 2 are therefore seen to be equal in which, where A and E are the cross sectional area and elastic modulus of the loading bars respectfully and therefore be equating these two equilibrium forces it can be shown that The strain rate, s  , of the specimen being loaded can be described as Continuing with the assumption that the specimen is in a state of equilibrium, F 1 =F 2 , then therefore F 2 is the force that is applied upon the specimen and the engineering stress, can be written as where A s is the initial cross sectional area of the specimen. To calculate the true stress and strain, (1 ) From equations A-32 -A-36 it is therefore shown that during a given experiment, the magnitudes of the three loading pulses, incident, reflected and transmitted can be used to characterize the material during high strain loading by the generation of the true stressstrain curve. The method and apparatus used for the work presented within this thesis is presented in the following sections.

A.2.2 Design of SHPB Components
The components of the SHPB system and it's subsystems each consist of several different design considerations when the system is first begin conceptualized. For the loading bar system, incident and transmitted bars, a few of these considerations are the length and diameter and the ratio between them, the material to be tested, a mounting system, the available laboratory space, testing temperature and material of the bars themselves. Each of these parameters are interrelated making the design of the SHPB a complex, multi-variable problem, the most important of which is the material to be tested.
A system that is to be used mainly for testing plastics, composite or concrete would be very different then that meant for testing metals as in this case, in which the bar material, diameter and lengths would all be adapted for the material to be tested, and in turn the gas gun and data acquisition system would also have to reflect these differences. The gas gun has several design considerations as stated, that are based upon the material to be tested, maximum pressure and velocity, the bar material and dimensions, projectile design and barrel length. The data acquisition system is less affected by the other variable of the system, but still has a few design considerations that must be taken into account, mainly being the strain gauges used to measure the loading pulses and their positioning along the length of the bars based on the length of projectiles being used, the amplifierconditioning system and data capturing system also need to be capable of handling the high rate of data with loading pulses being in the hundreds of nanosecond time range.
The details in the design of the SHPB used in this research is expressed in this chapter.  A high rate data acquisition system is assembled using strain gauges, a Vishay signalconditioning amplifier with a built-in Wheatstone bridge and a Tektronix digital phosphorus oscilloscope for data recording. Mechanical drawings of each part generated for the construction and manufacture of the SHPB is shown in a following subsection of this appendix.

A.2.2.2 Gas Gun
The gas gun component of the SHPB system is used to propel a striker bar at the incident bar, creating the loading pulse that is used to load the specimen at a certain desired strain rate. A typical gas gun consists of a holding chamber, a firing mechanism, a manner in which to fill the chamber and barrel to direct the projectile or striker into the loading bars. In use, the gas gun chamber is filled to a desired pressure, held in a state of pressure by utilizing a valve, when the valve is released, this pressure is applied to the striker, thus propelling the projectile into the incident bar.
The chamber must be designed to be able to with stand the high pressures utilized to propel the striker. In order to safely fill and release the pressure within this chamber, a conservative safety factor is applied, making the chamber much stronger and resilient than would be necessarily needed. The chamber is composed of a cylinder caped with two end pieces and bolted together using 4 1"-20 grade 8 bolts. The cylinder that creates the main body of the chamber is machined from 316 stainless steel with an ID of 4.5" and OD of 5.5", resulting in a thickness of 0.5". Using classical pressure vessel analysis it was determined that this thickness would result in a safety factor of approximately 13 at 500Psi. The end caps are machined from stainless 440C, a high strength hardened steel 144 alloy. Again this piece is designed to ensure safety during use. A series of o-ring groves are machined to seal in the pressurized gas, preventing any leaking to occur. A set of brackets were created to fix the gas gun to the support structure, not allowing any movement during firing. Additionally a funnel was created that is set into the main body at the front of the chamber. This allows for the pressurized gas to have a smooth transition from the chamber and into the gas gun barrel. This is a 3" tall, solid funnel that tapers from the 4.5"ID of the chamber down to the 0.75" barrel diameter.
The gas gun barrel is 38" long with an OD of 1.5" with the ID of 0.75" was precisely bored and honed to a R16 smoothness. This allows for a smooth fit of the striker, not allowing for any gas to escape around the projectile during firing. Beginning A series of test firings where completed on several of the strikers to establish and validate theoretical curves for gas gun pressure versus striker velocity curves. These curves are then used to decided upon a pressure to achieve a desired strain rate testing conditions. The velocity was measured by using the measured stress in the incident bar during impact, measured by the data acquisition system. The theoretical model for the incremental velocity down the length of the barrel is described as

A.2.2.3 Loading Bars: Incident and Transmitted Bars
The loading bar system typically consists of a incident bar, transmitted bar, minimal friction mounting apparatus and momentum trap at the free end of the transmitted bar. The bars are typically the same diameters, lengths and material. They must be ideally straight and free to move in any supports they may have while being accurately aligned, sharing a common longitudinal loading axis to ensure one dimensional wave propagation. Based on length of pulses typical upwards of 20 inches, and ratios of length to diameter of the bars which are 80 or greater, in the 5 foot range in length. This is to ensure one dimensional wave propagation and no over-lapping of loading pulses during data acquisition.
The SHPB being designed is to be used to dynamically test metal materials, meaning that they are generally higher in strength as opposed to a system meant for testing plastics. Equations derived for SHPB analysis are based on the assumption that a generated elastic wave is being applied onto smaller, softer specimen to plastically deform the material. To ensure that the loading bars remains elastic, a high yield, linear elastic material must be used. This sets an upper limit at which the level of stress from the striker can be applied on the incident bar, with a safety factor to ensure that a plastic wave is not generated within the loading bars, causing damage to the system.
The incident, transmitted and striker bars are made from maranging 350 grade steel that has been hardened to have a high yield stress of 2GPa and linear elastic behavior with an elastic modulus of 207.7GPa. This high yield stress ensures that the bars can be loaded to the stress necessary reach strain rates up to 10 4 s -1 and has become a popular material choice for the loading bars of SHPB. The diameter of 0.75" was chosen using the ratio of 80 of length to diameter ratio ensure one dimensional wave propagation, using a length of 5ft, a common length used in SHPB design, but also based on laboratory space constraints. The small diameter also reduces the force necessary applied by the gas gun to achieve the strain needed to deform the specimen, but still allowing for the specimen to be substantial enough for deformation analysis post testing,  A momentum trap is utilized at the free end of the transmitted bar to catch the residual momentum from the test. The entire system is supported by a rigid structure that consists of a structural steel W-beam with welded steel leg supports to raise the system to a comfortable user height with adjustable feet for fine adjustment of the height. The structural integrity of this component is important to ensure that all energy within the system is utilized in the testing, and not lost to any undesirable motion of the system. A separate W-beam section of the same type is used to mount the gas gun, and it too is structurally adequate to handle the force caused from the gas gun firing. The separation of the gas gun from the loading bars, ensures that any vibrations caused from the release of pressure during firing is isolated from the loading bars and the sensitive strain gauges used to measure axial displacement of the bars, as well as allowing for accurate alignment with the rest of the system.

A.2.2.4 Data Acquisition System
The data acquisition system utilized in the SHPB has several important considerations. The typical components used to acquire data are a set of strain gauges, Wheatstone bridge, signal amplifier and a manner to save and capture data typical a high rate oscilloscope or A/D computer interface. Strain gauges are used to capture the displacements of the loading bars caused by the passing of the applied and resultant stress pulses during testing, with a gauge being bonded on either. The gauges must be capable of withstanding the high amount of strain induced, properly bonded for accurate measurement, and accurately placed an adequate distance from either ends of the bars, to ensure an overlapping of pulses is not measured. They must also be compatible with the Wheatstone bridge and amplifier system utilized. The amplifier and oscilloscope must have high frequency response in order to record the appropriate data, usually shorter than a millisecond in duration. To ensure all components used are capable of doing so, a minimum of 100kHz frequency response should be established.
The strain gauges used to measure axial displacement of the loading bars are 0.125" dynamic strain gauges. These gauges a designed for dynamic use and are fully encapsulated iso-elastic with high endurance lead wires. The iso-elastic constantan alloy, designated alloy D by the supplier has superior fatigue life desirable for dynamic use as opposed to other alloys used for static cases. The gauges also have a high gauge factor, 3.3, which improves signal to noise ratio, in which high noise levels are typically seen in dynamic use. The size of the gauge selection is of importance. A gauge of smaller size is desirable so that the strain across the gauge is less affected by averaging over the length and thus able to handle measuring of high frequency load, but to small of a size and the gauge becomes difficult to bond to the bars and handle in general. This averaging phenomenon is represented in Figure A-6 from Vishay micro-measurement group.
They strain gauge utilized in the apparatus is a half-bridge configuration and has resistance of 350Ω, a higher resistance than the other common resistance of 120 Ω. This was chosen due to the advantages that include decrease of lead wire effects, reduction of heat generation by a factor of 3 and an improvement of the signal to noise ratio.
Generally strain gauges work by having a constant supplied voltage, in which when a resistance change occurs, as occurs when a strain is applied, the voltage measured across the gauge can be related to the amount of strain applied as given, where V is the measured voltage, G C is the gain applied by the signal-amplifier, V S is the supplied voltage and GF is the gauge factor, 3.3 for these gauges. The resultant measured voltage is in the millivolt range, so a signal-conditioner system with a built in Wheatstone bridge is utilized, where a specified gain, G C , can be applied to amplifier the signal into the Volt range of measurement.
The placement of the strain gauges is a critical step in the experimental setup of the SHPB. Placement of the gauges should be placed as close as possible to the specimen loading bar interfaces. This is to reduce wave dispersion effects that are caused by the physics of wave motion in an elastic media. From the nature of SHPB testing, a short rise time and step nature of the impact loading pulse, the elastic wave produced is a superposition of high and low frequencies. The higher frequencies travel at slower velocities than that of the lower frequency that maintain a velocity approaching one dimensional elastic wave velocity. Due to this difference in velocities, the wave over a long length will begin to spread and disperse. There exists another condition though that makes the ideal case of placing the gauge close to the specimen-loading bar interfaces, and this is that the loading pulse has a finite length. If the gauge is placed too close to this interface, the reflected and incident pulse would overlap when measurement is to be taken. To ensure this does not occur, the gauges should be placed at minimum, a distance equal to the length of the loading pulse from specimen-loading bar interface, or twice the length of the striker used. Furthermore, another concern in placing the gauges is to ensure that they are only measuring in the axial direction, meaning they are accurately placed to be parallel with the longitudinal axis of the bars. This is carefully done during mounting of the gauges, using tick markings supplied on the gauge body and use of paper wrapped around the loading bars to mark a line that is perpendicular to the longitudinal axis to which the tick markings are aligned. To bond the gauges to the loading bars, a M-200 bonding kit from Vishay is used. This is a quick curing epoxy, which strongly adheres the gauges to the bars, leading to accurate measurement of the displacement caused by the loading pulses; also a protective coating is utilized to ensure no damage occurs to the gauges during use. It is important to use the proper epoxy for gauge bonding, this epoxy transfers the displacement from the bars into the gauge for measurement, if this epoxy is to stiff, the epoxy will crack causing failure during loading and if to flexible the epoxy will absorb a portion of the displacement leading to incorrect strain measurement.
The system used to control the excitation voltage and amplify the signal generated from the strain gauges during testing is the Vishay 2310B signal conditioning amplifier which is specifically designed for dynamic use, and has the capability to accept quarter or half bridge strain gauges and has maximum frequency response of 300kHz, well above the accepted minimum of 100kHz. The voltage data is sent via BNC outputs from the signal conditioning amplifier to the data recording system, a Tektronix DPO 3034 digital phosphorus oscilloscope. The oscilloscope has a maximum recordable frequency of 300MHz and a sampling rate of 2.5 giga-samples per second. A trigger function is utilized once a pulse is sensed, in which when there is a slope change above a certain voltage level, the system begins recording for a set period of time, this allows for a repeatable and reliable manner to record the data. A picture of the data acquisition system used is shown in Figure A-7. The data can then be saved onto a flash drive, or also sent 155 through a closed network, and moved to a computer where data can be analyzed and processed to generate the stress-strain curve. A series of Matlab programs written by the author are utilized to complete this process. Figure A-7: Showing data acquisitions system designed for SHPB experimental apparatus. System includes high rate Tektronix digital phosphorus oscilloscope, Vishay dynamic signal conditioning amplifier with built in Wheatstone bridge and firing system power supply

A.2.2.5 High and Low Temperature Testing
The deformation of metal is known to be dependent upon temperature, in which the flow stress decreases with an increasing temperature. In generating model parameters that take this temperature sensitivity into account and in order to qualitatively define this sensitive it is therefore important to have the ability to test the material of investigation within a wide range of temperatures. There arise some difficulties that come with testing at extreme temperature conditions, which include achieving a constant uniform temperature of the specimen, the mechanical properties of the loading bars with changing temperatures mainly the elastic modulus' sensitivity with temperature, ensuring that heat damage does not occur to the loading bars and the temperature sensitivity of strain gauges used to measure the strain pulses. There are many different manners in which researchers have handled this issue these include automatic specimen positioning systems which load the heated specimen just before testing, the use of replaceable impedance matched inserts on the loading bar-specimen interfaces that protect the bars from any damage, and localized heating systems that reduce the heat transfer into the rest of the system.
Considering all of these factors a sub-system was devised that would take these concerns into consideration.
As mentioned having the specimen at a precise constant temperature is of importance to ensure that the data collected is accurate and not changing during testing.
The difficulty in keeping the specimen at a constant temperature is heat loss, sources of which include the outside environment, causing heat convection loss to the surrounding air and also through heat conduction in which heat is transferred from the specimen into the loading bars. The heat loss through convective processes can be easily avoided by 158 constantly applying a source of heat to the specimen, that is equal to this loss. The source of heating in the SHPB system used is 5kW induction system, that includes a 240V power supply, a feed-back temperature control system, a copper induction coil to generate a magnetic field that excites electrons with-in the material, causing heating and a cooling system that cycles water through the copper coil ensuring melting of this coil does not occur. This system provides ample heating that can easily overcome any convective heat loss. The other major source of heat loss, conduction through contact with the loading bars can be alleviated through another manner.
To reduce the amount of heat loss through conduction, which in turn would cause heating of the loading bars, a pneumatic actuator bar positioning system was devised.
This system provides preciously timed motion to the loading bars, within a millisecond before striker impacts the loading bars and positioning them in contact with either side of the specimen. Figure A-8 shows a schematic of the piston/cylinder system which is attached to each loading bar. The programmable timing relay used to begin the firing sequence, in which the pneumatic actuators and gas gun solenoids are precisely timed. The sequence begins using the ignition switch shown on the right of the image.
Using a high rate solenoid valve, a burst of approximately 40 to 60Psi of Nitrogen is applied to the back of actuator pistons, on the transmitted and incident loading bars. This moves each bar approximately 1inch into contact with the specimen after specimen has reached the testing temperature.
In order to control the timing of the actuator system with the firing of the gas gun to apply the loading pulse, a programmable Eaton timing relay was used as shown in where ρ is the density of the material, c is the wave speed and r is the radius of the bar.

Figure A-10:
Photograph of the high temperature tungsten carbide insert setup, which includes an incident and transmitted insert and support system including bearings. This system is utilized in extreme temperature testing to protect loading bars 162

A.2.3 Mechanical Drawing and Specifications
This appendix section contains all drawings generated for the design and manufacture of the SHPB at the MMRL facilities.

Figure A-11:
A schematic representing the final assembly of the SHPB system. From right to left this includes the gas gun assembly, the loading bar systems and below is the I-beam used to support the entire system   Schematic representing the high temperature specimen holder. This system is used to isolate the high temperature of the specimen from the loading bars. This is done by using two tungsten rods mounted in this apparatus, with the specimen being placed in between the two tungsten rods

A.2.4 Testing, Data Processing and Software
This appendix section contains the description of the testing procedure for dynamic testing using the split-Hopkinson pressure bar system. This include specimen preparation, testing procedure and data processing. Data processing is completed using a series of Matlab codes, taking the raw data collected from the high speed oscilloscope and ending with the final true stress-strain curve for the given test.

A.2.4.1 Experimental Procedure
The procedure utilized during a experimental SHPB setup and testing is presented in the following section. The importance of following this procedure is to ensure repeatability and accuracy of each test. The specimen preparation, experimental and equipment setup, and data capture will be discussed in detail.
Proper specimen preparation will ensure that each test will perform in a repeatable manner, that can be successfully used for material characterization. With-in this study two classes of alloys were used, low carbon steel and aluminum alloy, both of which a prepared in the same manner. The major concerns in generation specimens for testing in a SHPB compression system are the accurate dimensioning of specimens for proper wave interactions (length to diameter ratio) as well as surface finish on loading surface of the specimen, to reduce any frictional effects, to ensure 1D loading condition. Specimens should be machined in batches to ensure the same procedure and conditions were the same to generate them. Specimens in this case where created using raw stock, where was turned cylindrically using a machining lathe, to a diameter of 0.475" ±0.001". It is important to use lubrication not only to keep the specimen cool during machining but also to achieve a defect free surface. Once the diameter is within the given tolerance, the specimens were rough parted using the lathe and then faced within the lathe, with great attention placed on the final surface finish, ensuring the highest reduction in frictional effects as possible. The length of the specimen was 0.3875" ±0.001". The tolerances are held at a high level to ensure repeatability between tests. Finally a high-grit (1200) sanding was completed to further smooth the specimen loading surface. Pulse shapers used during testing where generated the same manner.
The alignment of the entire system is of great importance for the accuracy of properly with the loading bar axis. This is done is a similar manner as the specimen loading surface alignment, in which a striker is used to match the continuity of the axis.
All mounting blocks of the gas gun should be tightened fully. This procedure is complete A collection offset of 10% is utilized, in which when triggered, 10% of the total data will include data before the event. This data is used later in data processing sequence. The data capturing system should be complete and armed by setting "single" on the oscilloscope.

184
The specimen should be lubricated using graphite, high pressure type lubrication.
This aids in the reduction of frictional effects. The lubricated specimen should be centered between the two loading bars or in the high temperature condition, in between the two tungsten rods. This can be done by using the specimen centering tool presented in previous section. This precisely places the specimen directly in the middle of the loading bars, important for uniaxial loading. The lubrication should aid in holding the specimen in place when lightly squeezed between the loading bars. For high temperature testing, a thermocouple needs to welded to the end of the incident tungsten high temperature rod, closet to the specimen loading surface. This thermocouple is used to control the induction heating system.
For the remainder of the procedure for purpose of brevity, the test will be assumed to be at an elevated temperature, as this is the most complex set of testing and therefore includes all necessary steps for a room temperature test as well. Room temperature testing does not include the induction system and the high temperature tungsten rod setup. A pulse shaper should now be placed at the incident bar striker interface, using the same lubricant that is used for the specimen. The striker should be pushed down the length of the barrel into its initial firing position. The incident and transmitted bars should be placed into their initial positions before they are to be mobilized using the pneumatic bar positioning system. Their position should be based on a 0.5" gap between each bar and their adjacent tungsten rods. The regulator for the pneumatic bar positioning system should be set to 40-60Psi. The gas gun chamber can now be filled to the desired pressure determined to provide a desired striker velocity and therefore desired strain rate. Once the chamber has been filled, the heating of the specimen can begin. This can be done using the induction system which includes the power supply, heating coil apparatus, coil cooling system and the temperature controller.
The temperature controller is set to the desired temperature. Once the specimen has reached its desired temperature, the testing can begin. To reduce noise in the data collection system, it is important to turn off the induction power supply just before firing of the gas gun. Once the induction system is shut off, the user should quickly being the firing sequence by using the timing relay switch. The system should first move the bars into position just before the gas gun is fired. Data will be automatically collected using the triggering system of the oscilloscope. Data should be saved via a flash drive where it can then be transferred to the computer for data analysis.

A.2.4.3 Typical Experimental Results
An example of the typical experimental results generated during a split Hopkinson pressure bar compression test is presented. The data collected will be presented in terms of the oscilloscope output, the typical SHPB data analysis codes production and the generated SHPB stress-strain curve. Figure

B.1 Introduction of Equal Channel Angular Press
The first equal channel angular press (ECAP) was developed by Segal et al [1] in the Soviet Union, in which work provided a manner to apply simply shear as the most optimum manner to achieve transformation of microstructures, in terms of refining the grain size. Sever plastic deformation (SPD) has long been known to be cause grain refinement in materials, defined as deformation that occurs in a material beyond a strain of 4.00. SPD systems include wire drawing, rolling, constrained-pressing and ECAP. The benefit of grain refinement in which abnormally high strength and ductility can be achieved within a material is characterized by the Hall-Petch relationship [2,3], in which with a decrease in grain size, a large increase in yield stress occurs. Therefore grain refinement processes have been of great interest of research for the past 50 plus years.
Wire drawing is a process in which a cylinder is pulled through a die with a reduced cross section. The material is pulled through the die, it is forced to deform at a high level of strain, in which when the process is completed several times the material reaches the level of severe plastic deformation as previously defined, and a thin-wire of material with a refined grain structure [4]. The process is use-full in some applications but a negative is that a large reduction in cross sectional is resulted, not allowing for a bulk material to be generated. This reduction in cross section is also the draw-back in rolling as a process of SPD. Rolling is a process in which a material is repeatedly compressed through rollers, reducing the thickness after each processing step, leaving a nearly 90% reduction in cross section [5]. Constrained pressing does result in a bulk material, in which a sample is repeatedly forced in to a designed cavity and rotated and pressed again into the same cavity [6]. The difficulty is that the material is allows to bulge and therefore deform inhomogeneously, leading to the repeatability of the process to be difficult. The use of an ECAP system to cause SPD upon a material has shown to be the most viable, repeatable manner in which to cause grain size refinement within metals [7][8][9][10][11][12][13]. This can be expressed due to its use of the main deformation mechanism of shear to deform the material, allowing for the most optimum effect of plastic deformation upon a material. Segal showed that there are several requirements a process of SPD must apply to deform a material most efficiently. These include the uniformity of the stress and strain states, accurate control of the intensity of deformation and stress state, spatial development and texture formation control of the deformation and finally the capability to apply a ultra-high amount of deformation without resultant fracture.
The fundamentals of an ECAP is to pass a billet through two intersecting channels of equal cross section. These channels intersect at an angle anywhere from 90 to 120°, dependent of the desired amount of strain to be applied per pass, as schematically shown in Figure and reduces to, The Von misses shear strain, or equivalent strain can be calculated by dividing the shear strain by the square root of three, and considering the case of multiple passes, the strain of one pass can be multiplied by N, the number of total passes. These inclusions lead to equation B-8 being shown to be.
Using equation 8 represents an estimated amount of strain applied during processing excluding strain hardening, frictional and strain rate effects. It has been shown by several authors [9,[15][16][17][18][19][20][21] that the application of different routes of ECAP processing has a direct effect on the final generated material microstructure and characteristics. Routes are defined as the pattern in which each subsequent pass after the initial pass is performed in terms of the initial orientation of the billet. The four principle routes of processing in an ECAP are defined at A, C, B c and B a . Figure B-4 [22] gives a simple representation of these four routes. The initial coordinate system of the billet is defined as the transverse, extrusion and normal directions are equivalent to the X,Y, and Z axis respectively. Route A is defined as having no rotations along the extruding direction axis between each pass. Route C is characterized by being rotated 180° along the extrusion direction between each pass. This applies shear strain along the same shear plane for each pass, in which the direction is reversed with each rotation. The reversal of direction results in a reversal of the shear strain applied in the previous pass, which occurs every even pass. The B a route 234 includes a 90° rotation in the clockwise direction with relation to the extrusion direction on even passes numbers and a 90° rotation in the counter clockwise direction with odd numbered passes. This processing route therefore applies a superposition of the shear strain onto X and Y planes. Route Bc includes a 90 clockwise roation between each pass, applying shear to each spatial plane equally. Route Bc in several cases has been shown to be the most effective in generating ultra-fine grained materials. This is true because it is the only route that does not apply the strain repeatedly on the same shear plane(s). This causes dislocations generated on more slip planes each pass, rather than just moving the dislocations previously generated during the opposite direction shearing on the same plane. Figure B-5 [23] represents the routes discussed, showing the effect of the cubic element of each plan up to 8 passes. It can be seen in the case of Route A and C, that the Z plane does not have strain applied, which cause it to be less efficient in grain refinement. Routes B a and B c have strain applied to each plane after a number of passes.
During processing using route B a causes subsequent passes in the same direction on each of the planes, which in turn does not generate equaixed grain structures. This will cause the material to by anisotropic in nature, have grain elongated in a preferential direction.
Route B c not only applies strain on each plane equally, but after 4 passes, the direction at which the initial strain on a plane was applied, is also reversed. This is beneficial in generating an equaixed grain structure and has been shown to be the most efficient in the refinement process.

B.2 Design of ECAP at Mechanics of Materials Research Laboratory
The following appendix sections will present an overview of the Equal Channel Angular Press (ECAP) system designed and built at the MMRL. This system is utilized to generate fine-fine grain materials for the research within this thesis. This sections will include Abaqus FEM modeling for the design of the die and heating components, as well as explanation of the final system completed including mechanical drawings as well as an experimental manual for utilizing the system as described.

B.2.1 Die Design: Abaqus Numerical Material Process Modeling
The previous section of this appendix described the multiple variables of the ECAP processing technique. These include the channel angles of the inner, ϕ, and outer, Ψ, frictional effects and the total amount of desired strain applied based on the characteristic angles. The analysis utilized to predict the strain applied omits known variables like surface effects due to friction, and material strain rate and strain hardening characteristics. Also not discussed previously is the effect of the bottom configuration of the billet, in which the geometry of the leading edge of the billet can affect the deformation characteristics in terms strain uniformity [24]. The different geometry types include tapered in either direction, squared, or rounded. For all of these factors it is valuable to model the ECAP process using FEA simulations where insight is given into the effect of these variables without the high cost of multiple design iterations and lessening of experimental testing. Once the overall processing is determined, in terms of design parameters, then simulations can be completed on the structural components of the die can be completed to insure that the die will be able to with stand the high loads seen 237 during ECAP processing. To do so, the commercially available Abaqus, a FEA simulation program, is utilized to aid in the design of the ECAP system at the MMRL. First a generalized model will be discussed, in which idealizations are made, and other complexities such effect of the channel angles, channel dimensions, addition of frictional effects, specimen dimensioning tolerances and specimen configurations can be investigated.
To develop the FEA model both the bottom (L-shaped region) and top (corner) die sections that make up the channel are modeled as 2D analytically rigid shells using a channel geometry of 90° for the inner and outer angles, and radius of 0.25" and 0.75" respectfully. These variables will be varied at a later point. The die sections are then assembled in their proper positions with reference to one another. A specimen is modeled as 2D planar deformable shell with exact dimensions of 4" long and 0.5" thick, with the assumption that it is perfectly fit into the die channel, and assembled in its initial position.
A figure of this assembly can be seen in Figure B-6. A dynamic-explicit step is generated, at which the material loading will take place. An interaction is created where the contact between the billet and die will be seen to be frictionless for a simplified case.
The analytical die will be fixed in all directions for the boundary condition of the die surfaces. This is a valid assumption as the die surface is expected to not deform during the pressing of the billet. The top surface of the billet will have a constant velocity boundary condition, to ensure that the specimen will move with a constant rate through the die, allowing for the resultant force that it would take to do so to vary freely. These boundary conditions can be seen in Figure B   In order to accurately model the deformation of the material as it moves through the die, a plastic constitutive model is used. This allows for strain and strain rate hardening characteristics to be considered, these will affect the overall strain uniformity of the deformation, more accurately predicting the response in the real-world scenario.
The built-in Johnson-Cook plasticity feature of Abaqus was used to do so, along with data obtained in literature [25]. A relatively coarse mesh was used on the specimen to improve computer simulation time, this mesh was held to be constant as to allow for proper comparison between each variable change. This mesh can be seen in Figure   represents the force that would needed to move the specimen through the die.
In Figure B- This can be attributed to lack of friction involved. From this analysis it can be shown that with a 5° change in the channel angles, the reduction of force can be very beneficial with the effect of this reduction being amplified when frictional effects would be added. The change in the strain by only a difference of 0.23% from the 90° case to the 95° attains a nearly 1% decrease in the force necessary to press the billet between the two angles. With this reasoning it was determined that the 95° inner and outer channel angles would be utilized in the remainder of the simulation for that fact that it gives the best relationship of a high degree of strain applied but the benefit of a decrease in load applied, as well as will be utilized in the actual ECAP system designed.
With the channel angles determined it is now possible to investigate a few of the other variables involved. First the effect of friction is investigate, in which the importance 243 of proper lubrication of the die will be investigated by systematically adjusting the kinetic friction coefficient, μ k , within the interaction properties. This effect will investigated using the shear strain distribution along the length of the specimen, on node in from the right surface. This is done because friction is known to cause surface effects that extend into the interior of the specimen [24]. All other variables remain the same from the previous analysis.
It can be seen from Figure B-10a that although the increase in friction does cause an increase in the shear strain applied which is desirable, the distribution of the shear strain becomes less continuous with an increase in strain. This discontinuity is undesirable as the material will therefore not see a constant deformation along its length.
The force necessary to move the billet is also affected by the increase in the friction coefficient, as shown in Figure B-10b. It can be seen that the deformation is most uniform in the tapered specimen, followed by the square and then radiused geometry. This is determined by the uniformity of the PE12 contours, where majority of the bulk material of the tapered geometry specimen remains in one contour regime. This is not the only determinate facet though when investigating which geometry is best suited for the ECAP processing. From the taper geometry specimen, it can be noted that a large amount of deformation occurred at the leading edge. This material would have to be discarded and the taper re-machined for every pass. This large amount of material loss is not acceptable, and therefore it is determined that the square geometry specimen will be utilized as it gives the most uniformly deformed while also providing the largest amount of material to be utilized in following pressings.
248 The final geometry of the die channel and summary of the above results is now given. It was determined by varying the inner and outer channel angles, that the 95° angle set would result in an acceptably uniformly distributed deformation while also lowering the force needed to extrude the billet compared to the more extreme channel angles.
Therefore the channel dimensions will be 95degrees, with radii of 0.25 on the interior and 0.75 on the exterior angle, this is done to retain a uniform cross-section throughout the channel, in which the channel thickness will be 0.5". The specimen must be heavily lubricated as well as the die walls, to ensure that friction is reduced. Friction can be advantageous in the sense that it result in a larger amount of stain applied caused by surface effects that transfer through the specimen but, these effect also cause a discontinuous deformation while also increasing the load to extrude the specimen.
Therefore to ensure a repeatable experiment, where each billet produced has undergone the same deformation, and therefore grain refinement, it is important to remove the frictional effects as much as possible. A high temperature/pressure graphite based lubricant will be used. Finally it was determined that the square geometry of the billet results in an acceptable balance between even deformation of the material and retainable quantity of material between each pass. This is important as the bulk generation of a fine grain material will be later utilized for mechanical testing to determine material characteristics.

B.2.2.1 Overview of ECAP at MMRL
To facilitate an understating of the ECAP system designed and built at the MMRL, a brief summary of the system is given. The ECAP consists of five subsystems which include the tool steel die used to apply a desired amount of geometric strain per pass, the plunger and plunger elevator used to stabilize the application of the load to the billet, the hydraulic press used to apply and control the rate of loading, a heating system used to heat the entire die to a desired temperature, aiding in the controlled deformation of the material and a data acquisition system which gives the ability to collect experimental data of pressing force and rate over the duration of the experiment. A photograph of the entire system can be seen in Figure B-13.

Figure B-13:
The ECAP system built at the MMRL in which major sub-systems are noted including the tool steel die, shown with heater plates attached, 100Ton hydraulic press, plunger and plunger elevator, heating system including control unit and heater plates and the LVDT apparatus used for data acquisition

B.2.2.2 ECAP Die
The ECAP die is easily the most important component utilized in the SPD system.
The die needs to be accurately designed to provide the desired result in the generated refined granular structure of the material. The die must be very resilient to extreme levels of applied stress during pressing, while also capable of performing at elevated temperatures. The die must be easy disassembled and reassembled in a repeatable manner in order to remove the pressed billet after every pass. Also it is desirable that the die be designed in a modular fashion that will ensure, if failure occurs, the part can be easily replaced, while also able to fit within the constraints of the hydraulic press used during apply the load to the billet.
The major design consideration for the die as expressed previously in this appendix, is the geometry of the channel. Mainly the inner and outer channel angles and radii. Given by equation B-8, the inner and outer channel angles determine the amount of geometric strain that is applied per pass. The effect theses variables was investigated in B.2.2.1 of this appendix, and resulted in the determination that an inner and outer angle of 95°, with radii of 0.25" and 0.75" respectfully, resulted in the most uniform deformation of the billet material. The thickness of the specimen to be pushed was determined to be 0.5" thick, as this size is adequate for the future testing of the generated material, therefore that determining the channel width and thickness. It is possible to scale the entire system to a larger billet size, though this would cause an increase in load required to press the billet, and in turn an increase in load applied on the die.
It was determined that tapering the exit channel from the inner to the outer of the channel would be very advantageous as this would allow for the elastic stresses generated within the material of the billet during shearing and push outward onto the channel walls.
The removal of these stresses allow for the ease of disassembly of the channel plates, as well as decrease the amount of friction. If the stress is decrease, due to their removal, then the force in turn against the walls of the die will increase, lowering the friction. The gradual widening of the channel was completed by flaring the upper and lower surfaces of the die a total of five thousands from beginning to end of the exit channel. This magnitude of flaring was determined to allow the full elastic strain to be released half way through the exit channel.
The entire die, in general is 9"x9"9.5" tool steel die, as these dimensions fit into the criteria needed to use the hydraulic press, which will be discussed at a later point. The die is designed in a modular fashion in which the channel is created by the use of three separate plates, the central plate contains the major die geometry characteristics, the inner and outer angles and radii. This includes a bottom section of this plate in an "L-shape" and a corner section, this can be seen in Figure B-24 of the appendix. The center plate sections are caped on either side with two plates that create the side walls of the channel.
To ensure that the two separate sections that create the center plate remain in the proper relation between one another, a set of pins and sleeves are used. The pins and sleeves are pressed into the stack of three plates, the holes of which are machined with high degree of precision using EDM machining techniques, in which 9 strategically placed pins are used and along with four sleeves. The sleeves are placed in 4 strategic holes, that are also allow for bolts to pass through them. In this configuration, the pin and sleeves are really 254 the source of strength of the die during pressing. As the billet is shearing and moving through the die, through Poisson's ratio, exerts a force against the die walls. This force therefore is transferred on to the pins and sleeves that connect the three inner plates. It is therefore important that theses pins and sleeves be made out of high strength material.
The pins are 3/8" center-less ground to within half a thousand and made from M42 tool steel, with a hardness of approximately 66HRC. The benefit of this material is that it retains this hardness at high temperatures. The sleeves where machined from annealed A2 tool steel, heat treated to a hardness of 62-63HRC and then ground to their final dimensions. The precision machining of the pins and sleeves are of great importance as any shifting of the center plates during pressing, would therefore change the geometry of the channel, and the resultant material would not be consistent from billet to billet. Also any shifting of these plates can cause a failure during pressing. Outside of the three plates that create the die channel, two 4-inch thick A2 tool steel blocks, of the same 9"x9" width and height of the three center plates, are used as bulk strength in the die assembly. These blocks allow for the stress that is generated during pressing within the channel and on the two capping channel plates, to be transferred out of those plates and into the large bulk material. This causes the two side plates of the channel, to remaining rigid and not bulge outward from the processing loads. Each plate of the die, was received in the annealed state, machined either using standard CNC or EDM methods depending on the tolerance and critical nature of the machining needed. All the plates' where then heat treated to an HRC of approximately 62-63, and subsequently surface ground on the mating surfaces.
The surface grinding was essential to ensure that all plates where in perfect contact and square, so all stresses could be efficiently transferred.

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The material that the die is to consist of is a critical design criteria in the survivability of the die. The material must be resilient to wear, able to with stand high loads and elevated temperatures, as well as easily machine-able. Through a literature search of other ECAP systems [26][27][28][29], it could be seen that tool steel has proven to be a suitable material for this application. Utilizing a 2D Abaqus simulation and material properties obtained for the D2 tool steel [30,31], simulations were completed to investigate whether the material would with stand the high loads applied to the die during an ECAP pressing. A schematic of this simulation can be seen below, in which all pins, Also from this analysis it can be seen that the placement of the pins and sleeves will not 256 affect the survivability of the die material, all though as expected, the pins and sleeves do act as sources of stress concentrations.
Another design consideration is the torque to be applied of the 6 grade 8 steel bolts that hold the die together, which includes the three inner plates that create the channel and the two four inch bulk material blocks. The purpose of these bolts is not to only hold these plates in place during a pressing, but also to place the die into a state of compression. The added state of compression, effectively adds an increase of load that the die plates can withstand, as the outward force generated during pressing must overcome the applied compressive load of the bolts before the load would be applied onto the plates of the die. Any bulging outward of these side plates would result in die separation, thus the billet material would extrude through these gaps. It was determined that a torque of 600ft-lb would be sufficient not to allow any plate separation, while also not exciding the bolt strength [28]. The use of high pressure/temperature anti-seize was used on each bolt and nut to ensure ease of disassembly as well as limiting the friction during the torque being applied.

Figure B-14:
Von-Mises stress contour plot of a 2D simulated ECAP die under pressure loads on both channel walls of 80ksi, in which die is modeled using D2 tool steel material properties, pin are modeled using M42 tool steel material properties and sleeves are modeled using A2 tool steel material properties

B.2.2.3 Plunger Elevator System
A plunger elevator system is used to precisely align the plunger with the die channel. This is important as any miss-alignment of the tight fitting plunger with respect to the die dimensions, will result in failure of the plunger. The systems consists of several different components which include a base plate that bolts to the top of the die, a center plate in which the plunger is bolted and a top plate that allows for the passing of the ram through this system and also a serves as a fixing point for the four rods that connect these three plates together. These rods serve as a track that the center plate can move up and down freely upon as the press ram applies a load during pressing. The elevator system can be seen in Figure B-15. The height of this system is also of importance as, it needs to have the ability to have the plunger moved out of position while the specimen is inserted into the die and then move back into pressing position once this done. Also the plunger must be long enough to move the biller entirely through the die per pass. From this is was determined that the plunger would be approximately 5 inches long, and the elevator would be approximately 12 inches high to allow for ample room for the 4-5inch specimen to be inserted. The plunger directly applies all the load on top of the billet. Therefore the plunger must be extremely strong and precisely machined. The plunger is made from the same material as the die, therefore it will not have the ability to gouge or damage the die surface, as it would be able to if it was a harder material. It is therefore machined from annealed D2 tool steel to rough dimensions, heat treated to 62-63HRC and then surface ground to its final dimensions. The final dimensions are 0.495"+/-0.0005" square. This allows for a minimal gap between the plunger and the die channel, in which to large of gap would allow material to extrude between the die and plunger. If this occurs it can cause failure of the system, as it would generate an extreme increase in load to move the billet, essentially binding the system. The plunger is bolted to the center plate of this elevator system. This center plate has four brass bearing pressing into each corner hole, that are lubricated and allows for smooth movement along the 1" ground rods. These bearings are initial pressed into the holes and undersized. They are then reamed to the precise dimension, therefore not allowing any wobble of this plate on the support/tracking rods, retaining its proper alignment with the die. The plates are machined from high strength 4041 chrome-moly steel. A high degree of care was taken to have these machined precisely using CNC methods so that the entire system would move as designed with the movement of the center plate being smooth and straight, with no binding of the center plate.

B.2.2.4 Hydraulic Press
The choice of a loading applying system is critical in the design of an ECAP system. Several design criteria include the maximum applicable load, the size of the workable area, the ram extension and the rate at which the load can be applied. It was 261 decided the most effect method would be to purchase a commercially available press.
Through the design of the die and the size of the press is somewhat an interrelated problem, as the die cannot be to wide or tall to fit on the load applying apparatus, but yet the die has to be large enough to withstand the high loads experienced during pressing.
Also to be able to have the die in place, insert a specimen into the die from the top and then have the plunger move into position to begin the pressing process, the press would need a relatively long stroke. From all these criteria it was determined that the Dake 100 ton hydraulic press would fit all the criteria needed, and can be seen in Figure B-16.
The hydraulic press used in the ECAP system is capable of applying 100 Tons (5074Psi) of pressure. This press has an adjustable table with a wide open base, suitable to be worked around. The press has a maximum ram travel of 19" which was very desirable as it gives the ability to assemble the die without the ram being in the way, but also is capable of extending enough to extrude the billet. It has a rapid advance speed of 52 inches per minutes and maximum pressing rate of 3 inches per minute. The rate of pressing can be varied by the used by use of a lever that when compressed further will move the ram with increasing rate, and when direction of this lever is reversed, the press will move in the opposite direction. The system comes with an analog pressure gauge, which is upgraded to an electronic pressure transducer to be used in the data acquisition system, which will be discussed later. All operating considerations of this system should refer to the operating manual, which should be reviewed before any new user of the system.

Figure B-16:
100 Ton hydraulic press utilized in the ECAP system in which major components include the pressing table which serves a mounting and support of the ECAP die, the rigid frame, the 19" stroke ram, and the control box and ram control lever

B.2.2.5 Heating System
Many researchers have shown that it is very beneficial that during the pressing process to have the die and billet at an elevated temperature, the exact temperature being material dependent [27]. The benefits include that having the die and billet at elevated temperatures makes the pressing "easier" with the fact that the shear yield strength will decrease with an increase in temperature. This is not the only result of heating the system; the final microstructure of the material will be affected by pressing at elevated temperatures. The temperature has been shown to, at above a certain experimentally determined material dependent level, will result in recovery of the grain size, thus not as efficiently refining the material. If the temperature of the system is to far below a certain processing temperature, the resulting microstructure will be in a non-equilibrated state, thus not allowing the material to be at its highest possible strength as well as having the possibility of cracking during processing. This important factor of the ECAP processing system, heating of the die and billet.
Design considerations such as the amount of heaters, wattage and the length of time at which it will take for the die to arrive at its desired, element size and placement are to be considered in the usage of the cartridge heaters. In order to solve the problem presented, a manufacturing specification and design handbook is utilized.  Figure B-17a. Such methods, although valid and functional, can be seen as inefficient, with increased sources of heat loss by indirectly heating, heating the environment in which the die is placed. More efficient methods include the use of heating bands and cartridge heaters, such as in the work of J.
Werenskiold [12], seen in Figure B-17b, in which the cartridge heaters are directly inserted into the ECAP die.
From the work of J. Werenskoid, it was concluded that the use of the cartridge heaters was a very accurate method of heating and controlling the temperature of the ECAP system. The benefit of utilizing cartridge heaters can be explained by the ability to have the source of heat be directly in contact with the material to be heated, where no loss of energy would occur, say from convection between the air and the heat source and then the air and the die. Another great benefit of cartridge heaters is the high level of wattage available commercially, this is desirable to increase initial heating time and ability to remain at a constant temperature. The manner in which the die is to be heated in this case is through the use of two heater plates which include the inserted cartridge heaters. These heater plates are fixed to two outer surfaces of the die to apply even heating to both sides. Examples of ECAP Die heating Techniques a) ECAP die is inserted into furnace using heating coils imbedded in ceramic b) ECAP die heated using cartridge heaters inserted directly into die In any system that is to be heated or is within the process of heat transfer, a major area of interest is the temperature distribution through the system whether in the steady state or transient condition. Due to the complexity of the system it would be difficult to determine an exact closed form solution of the temperature distribution through the material. Therefore the manufacture has provided a set of equations to determine the amount of wattage necessary to heat the given material to a desired temperature within a certain amount of time. The predicted results based on these equations are presented below, these results will be compared to an FEA model generated using the Abaqus platform.
The manufacture of the cartridge heaters have provided a selection guide to aid in design and specifications of cartridge heater utilization, the Omegalux Cartridge Heat Selection Guide [33]. Within this guide an equation for determining the amount of wattage necessary is given in equation B-9, where W T is the weight of the material to be heated, C p is the specific heat of the material, ΔT is the change in temperature from initial to desired final temperature, in this case it is desired that the die would heat from room temperature to 350C, 3412 is a conversion factor from US units of BTU-lb-F to SI units of kW, and H being the amount of time to reach final desired temperature. From refs [30,31] the material properties used in the analysis are given in Table B-1. Using these material properties and the equation B-9, the amount of wattage necessary to heat the die within 2 hours can be determined to 267 be approximately 4KW with a safety factor of 2. This safety factor is used to include any heat lose effects.
To achieve the 4kW of power necessary to heat the die, four 1kW cartridge heaters will be used, based on Omegas available heaters, it was determined that the cartridge heaters would be 3/8" in diameter and 5" long. With predicted values of temperature and time based on the input wattage, an FEA model can be generated and compared to ensure the proper selection of cartridge heaters is made. The Abaqus FEA platform is utilized to model the heating of a simplified ECAP die. As in any heat transfer problem a set of boundary conditions must be defined which also includes the loading conditions, in this case the cartridge heater output or heat flux.
For simplification all exterior boundaries are seen to be insulated, the default setting for Abaqus heat transfer models, unless overridden by another boundary condition.
In order to simulate the transient process of heating the die, an initial step and loading steps are created. The loading step designated Step-1, this a heat transfer transient step that will simulate constant heating from the cartridge heaters for a time period of 7200s or 2 hrs. The loading step will include increments that automatically change during the duration of the simulation, but have the initial conditions of 0.1secs and the minimum 268 and maximum set to 1E-5 and 100 seconds respectfully. In order to model the interaction between the surfaces of the plates as they are assembled in real world application, contact properties are set between each matting surface, plate to plate, with some assumptions made. Each contact pair has the properties of the tangential behavior being frictionless, normal behavior being as hard contact and for thermal conductance between the surfaces, the contact is represented by having perfect conductance between surfaces. This last contact property, perfect thermal conductance, is an assumption that can be seen as valid for several reasons, being that in real world application, the mating surfaces are surface ground to ensure that each surface will be completely parallel with in a thousandth of an inch and have a smooth finish. Also the die itself is to be bolted together with each bolt being under a prescribed torque to ensure that no separation between the plates will occur.
Within the initial step mentioned previously, a predefined field must be generated.
This pre-defined field is set as a temperature, simulating that the die begins its heating process in room temperature condition. The heat transfer transient step, Step-1, is where the loading condition is applied within four cylindrical holes representing the cartridge heaters. The chosen cartridge heaters to fit the application has a total wattage of 1000W/cartridge heater or a watt density of 170W/in^2. This loading has been applied to the parametrical surfaces of the cylindrical hole, not including the bottom surface as the cartridge does not supply heating power to this surface. This loading condition makes the assumption that all power supplied from the cartridge heater is perfectly transferred into the heater plates, this is valid as the cartridge heaters have a tight fit within these plates.
The transient step is also were any other boundary conditions would be set, in this case since any other forms of heat transfer are not considered, the outer surfaces of the die will be seen as insulated. This is a valid assumption because the actual setup will include an insulation system built around the entire die that should limit these losses.
The meshing used is a tetrahedral free type of mesh, with the element type being standard, linear heat transfer element, DC3D4, meaning it is a four node linear heat transfer tetrahedron. The Abaqus simulation was run to model and simulate the heating of the tool steel ECAP die, heated by 4-1000W cartridge heaters from the initial state of 20°C or room temperature for duration of 2 hours. The results in the form of a temperature contour plot can be seen in Figure B-19, in which the maximum temperature after 2 hours of this constant heating was found to be 835°C located at the source of the heat as would be expected.
The temperature contour plot results are as expected, noting the symmetry between either half of the die, which represents even heating and proper transfer of heat flux from the heating plates, where heating occurs moving into the center of the die. As  These two positions will be monitored during actually pressing using thermocouple probes inserted into the die, therefore it is desirable to know the simulation results at this point. The experimental temperature for a pressing is considered the temperature at the interior point, as this will be the temperature in which the billet will be experiencing.

B.2.2.6 Data Acquisition
The acquisition of data during an ECAP test is important to be able to refer back to, and establish a consistent production of refined granular material, it was noted that there was seemingly lack of this type of data in literature. There are several experimental variables of interest to collect and analyze, which include the pressing force, the rate of pressing and the temperature at which the billet was produced at, previously discussed. In order to facilitate the data acquisition several apparatuses where added to the ECAP system. First a pressure transducer was implemented directly into the hydraulic lines of the press, used in conjunction with the analog gauge that was already present. The pressure transducer gives the ability to measure the pressure within the hydraulic lines and to be recorded digitally. From the hydraulic pressure it possible to make a relation to the amount of tonnage being applied on the billet top surface, and therefore the ability to generate this over the duration of the entire pressing. To measure the rate of the pressing, a linear variable differential transformer (LVDT) was used. This gave the ability to measure the displacement of the ram head, and utilizing the duration that the displacement occurs within, one can measure the rate simultaneously. The data was acquired using a Matlab data acquisition system, denoted Softscope. This built-in coding essentially acts as an oscilloscope. The benefit of this system is that multiple plots or channels can be generated for each data set measured versus the same time domain, as can be seen in Figure B-21. Not only does it have this feature, but also it has the ability to take the data measured in one channel and convert it using a user defined equation, and thus generate a new channel or plot. This was utilized to convert the pressure transducer and LVDT raw data, both of which are initially in the form of a voltage. Using the provided conversions for the pressure transducer and LVDT from the manufactures, the data was converted into pressure measured in Psi and displacement in inches respectfully.
The data of the pressure transducer was further converted into tonnage by utilizing the surface area at which he hydraulic pressure is applied, or simply the circular surface area of the ram head. The data of the displacement from the LVDT can also be further converted into rate. This is done by simultaneously and continuously calculating the difference between a block of displacement data, in this case 25pts, and dividing this by the total duration the block of data is collected at, based on the sampling rate of 5Hz. This gives the ability to receive the real-time pressing rate.
An apparatus was designed to adapt the LVDT for the ECAP used. This was done by adding a plate onto the end of the press ram that would receive an arm that would stick out perpendicular to the motion of the ram, at the end of this arm or rod, the LDVT was securely mounted. Also a table with another arm was fixed to the press frame. The arm attached to this table gave a position for which the LVDT could press against and compress as the ram was moved down during pressing. A figure of this can be seen in  Oscilloscope function utilized in Matlab, Softscope, for data acquisition, in which real-time data is collected during ECAP pressings. Data includes raw data of the pressure transducer and LVDT, determined displacement from LVDT data, determined hydraulic press from pressure transducer data and determined resultant tonnage from the hydraulic pressure. Also outputted measurements of pressing rate can be made, as shown in the measurements module of the figure  table and LVDT table arm 275

B.2.3 Mechanical Drawings
This appendix section contains all drawings generated for the design and manufacture of the SHPB at the MMRL facilities Schematic of the ECAP system utilized in this work. The schematic shows the three inner plates that create the channel, the otter tool steel plates that add strength to the die, the 7 bolts, that are torqued to keep the die plates from separating during pressing and the elevator apparatus used to align the plunger and die. 95° channel used in the ECAP system, this generates the channel used to deform the material for each pass. Plates of D2 tool steel were received oversized and in annealed state, at which the holes were drilled and honed. Then the plate was heat treated to a HRC 62-63, surfaced ground to the final thickness, and finally the channel geometry was machined using EDM processes.

Figure B-24:
Side plates used to cap the outer sides to generate the full 3D channel of the ECAP system. Plates of D2 tool steel were received oversized and in annealed state, at which the holes were drilled and honed. Then the plate was heat treated to a HRC 62-63 and then surfaced ground to the final thickness.

Figure B-25:
Bulk material used on either side of the ECAP inner plates that form the channel. These two plates add strength to the ECAP system, in order to be able to with stand the extreme loads. Plates of A2 tool steel were received oversized and in annealed state, at which the holes were drilled and honed. Then the plate was heat treated to a HRC 62-63 and then surfaced ground to the final thickness.   Plunger plate used in the elevator system. The plunger is bolted to this plate, fixing its position. This plate has four brass slider bearings pressed into the plate allowing for the plate to ride on four rods during pressing.

Figure B-30:
Top plate of the elevator system, which supports the rods that allow the motion of the plunger plate, as well as allow the press head to move into the elevator system  The plunger shown is used to apply force to the specimen at a constant rate during ECAP pressing. The material of the plunger is annealed D2 tool steel, that was received over sized. The material was then machined oversized in the thickness and length, heat treated to a hardness of HRC 62-63, then surface ground to the final dimensions. The tolerances of the plunger is critical, not allowing any "blow-by" of the specimen material during pressing.

Figure B-33:
The LVDT table shown, is used in the data acquisition system as a manner to mount a stable platform to measure displacement of the plunger using a LVDT. The heater plate shown in this figure is used on the bold head side of the die. This plate includes two 1000W cartridge heaters that are pressed into the plate. When the heaters are turned on, heat is transferred from the cartridge heater into the aluminum heater plate and then the heat is evenly distributed into the full face of the die

B.2.4 Testing, Data Processing and Software
This appendix section contains the description of the experimental procedure for utilizing the equal channel angular press for generation of fine and ultra-fine grain material. This include specimen preparation, testing procedure and data processing. Data acquisition using the Matlab softscope oscilloscope code, with data collected from the pressure transducer and LVDT. An example of the typical experimental results is given

B.2.4.1 Experimental Procedure
The procedure utilized during a experimental ECAP setup and testing is presented in the following section. The importance of following this procedure is to ensure repeatability and accuracy of each test. The specimen preparation, experimental and equipment setup, and data capture will be discussed in detail.
The assembly of the ECAP system begins with the preparation of the channel plates. This includes the painting of high pressure/temperature lubricant on each of the die channel surfaces as well on the specimen surfaces, the specifics of the specimen preparation before lubrication will be discussed shortly. Ample time for this lubricate to dry should be given, from 1-6hrs depending on environmental conditions (temperature and humidity). The lubrication of these surfaces is of great importance as the resultant material produced and as well as the survivability of the system during the pressing, as shown in this appendix, is a function of the resultant friction during pressing. The frictional effects have a great deal of effect on the deformation uniformity and amount of tonnage necessary to press the billet. Next the 9-M42 tool steel pins and the 4-A2 tool steel sleeves should be pressed into their appropriate positions of the three plates that 294 make the die channel. It is important to use an arbor press, as opposed to other methods such as hammering. The hammering can shock the brittle pins causing micro-cracks, that will lead to premature failure of the pins or sleeves during pressing. These three plates should not placed between the 2-4" tool steel blocks, noting that the edges on each face as aligned. All the plates as well as the mounting plates, that mount and fix the die to the press table should be lightly pressed together to prepare for the placing of the 6- Next in the assembly of the ECAP system is the plunger elevator. Before this subsystem can be attached and aligned to the die, proper function of the subsystem should be checked. First the plungers attachment to the center plate should be checked, for any movement within this plate, if this exists, the bolt used to attach the plunger should be tightened and then rechecked. The center plate should freely slide along the 4-1"diametre rods, and lubrication can be applied to aid in this motion. The subsystem can then be placed upon the die and the bolts used to attach the elevator to the die lightly 295 hand tightened. The alignment of the plunger to the channel is of great importance, as any miss alignment can cause catastrophic failure of the plunger or die channels. The alignment can be completed by slowly sliding the plunger in and out the die, once a position that feel smooth, the attaching bolts should be slightly further tightened in a Xpattern, the alignment checked again and this process continued until the bolts can no longer be tightened and the plunger has free and smooth movement in and out of the die.
The next step is to attach the two heater plates, noting that each is machined specifically depending on the nut or head side of the bolts used to torque the die. The mounting bolts used to mount the die to the press table must be removed to place the heater plates onto the die. Proper contact with the die surface should be checked. Three straps are used to pull the heater plates tightly onto the die faces. The mounting bolts can now be placed back into their proper position, but not tightened as the alignment of the die and elevator should now be made with the press ram. This can be done by carefully moving the ram head close to the elevator, a feel gauge should be used to assure that the ram head is aligned in the hold atop of the plunger elevator, with the entire die and plunger elevator being shifted to make adjustments, once the alignment as be corrected, the mounting bolts can be tightened and alignment check a final time. The two thermocouple wires can be threaded into place and checked to be functioning correctly, by powering the heating system, which should at this point be reading room temperature.
The insulation system can then be placed around the die.
The ram head can be moved down beyond the top plate of the plunger elevator system so that the LVDT mounting arm can be threaded into the ram head. Once threaded into place the LVDT can be mounting into this apparatus, and the LVDT table arm placed 296 into position to make contact with the LVDT. The power supply that powers both the LVDT and pressure transducer must be powered using 120V AC -12V DC adapter located behind the ECAP system. The data acquisition system can be opened by powering the supplied computer, and accessing Matlab and using the softscope2('mcc.si ') function, which has been configured for the ECAP tests. Just before testing begins, the trigger button can begin and data acquisition will begin. The data acquisition and analysis will be discussed in the following section.
The specimen preparation is of great importance as it will affect the resultant material generated. Important factors include tolerance of fit into the die and the surface finish and proper lubrication, both of which will affect the friction between the specimen and die during pressing. The specimen must precisely be machined to the square dimensions of 0.500-0.495". This allows for a tight fit within the die, if specimen is at a smaller dimension then 0.495", the adverse effects such as cracking will occur. The surface of the specimen should be sanded to a high grit to remove any machining defects, and reduce friction. The specimen as mentioned must be fully coated with high pressure/temperature lubricant which is allowed to dry adequately. Each of these steps for the specimen preparation must be completed for each pressing through the die. After a pressing the ends must be machined to remove any deformation from the previous pressing, and return to a square configuration, as which was shown to be the most beneficial geometry for the ECAP pressing. The specimen can then be placed into the die, and the plunger slide into position to move the billet into its initial position, just before the radius of the channel.

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With all components in proper alignment and specimen within the die, the heating process can begin. This is completed by powering the heating control unit, and utilizing the thermocouple closets to the heat plates as the feed-back controlling measurement, the desired temperature can be set and heating will begin. Depending on the temperature desired, this can take from 1.5-4-hours. Once the desired temperature has been reach the ECAP system can be utilized to press the billet and extrude it through the die. A secondary specimen, placed behind the first may be utilized to attain full extrusion of the primary billet, in order to attain the most extruded material as possible. With the test complete, heating system should be turned off and the entire system allowed to cool before disassembly.

B.2.4.2 Data Analysis
Utilizing the Matlab program and the built in softscope oscilloscope code, data is collected during the ECAP pressing. The program has been explained previously in this appendix, so this section will deal with a secondary program that converts the raw data collected and generates an excel and text file to be saved and analyzed at a later point.
Once the press has be completed, using the file drop down menu, the captured data can be saved to the command window of Matlab. With the data now sent to the command window, a second program, ECAP_data_processing.m, can be utilized. This program creates a text file of the collected data, and also generates an excel file, both of which have the appropriate column labeling. The data can then be analyzed to determine the rate of pressing, total displacement and a force-time plot, examples of which will be shown in the following section. The data processing Matlab code is given as follows.