Effects of Heat Treatment on Microstructure and Mechanical Properties of a Near-a Titanium Alloy

This thesis is concerned with the effect of heat treatment on the microstructure of the near-a titanium alloy IMI 834. Furthermore, it investigates the crack growth rate behavior in two microstructures of this alloy differing in their primary alpha ( ap) volume fractions. IMI 834 is an aerospace high temperature material that possesses the highest creep resistance of duplex near-alpha alloys at temperatures up to 650°C. A series of heat treatment experiments are carried out to examine the influence of recrystalization temperature, cooling rate, aging time and over-aging time, on the volume fractions of the primary alpha as well as the corresponding hardness characteristics. It is shown that for ap volume fractions up to 20%, colony size decreases with increasing the volume fraction. For higher ap volume fractions, the colony size remains relatively constant. Results show that between approximately 10% and 30% ap volume fractions, the material has a constant hardness, defined by the cooling rate. On the other hand, the hardness decreases significantly for volume fractions lower than 10% and for volume fractions higher than 30%. It is also found that element partitioning effects are most dominant in volume fractions above 30%. Over-aging specimens with 5%, 23% and 39% ap volume fractions at 650°C shows that only S2 type silicides precipitated in IMI 834. Furthermore, results show that the critical silicide size is achieved at about the same over-aging period, 2,000 minutes, for ap volume fractions greater than 23%. Over-aging the material with 5% ap volume fraction results, however, in precipitation of S2 type silicides after a shorter time, 80

minutes, and a noticeable increase in hardness is observed when compared with that of the other two microstructures. The influence of two selected CX.p volume fractions, 20% and 30%, on the fatigue crack growth rate (FCGR) is examined at 650°C for three different loading frequencies, 10 Hz, 0.05 Hz, and 0.003 Hz. It is shown that for the 10 Hz and 0.05 Hz tests, the FCGR is similar in the two microstructures. The fracture mechanisms under these two test conditions involves transgranular cracking of both the a!P colony and the CX.p particles. For the loading frequency of 0.003 Hz, the fatigue crack growth is higher in the 30% ap volume fraction than in the 20%. For this loading condition, the fracture mechanism involves transgranular cracking in the ex.IP colony accompanied by interboundary cracking in the CX.p particles. These fracture mechanisms are discussed and explained in terms of phase strength and toughness as well as silicide density and size in each of these two microstructures. 111 Firstly, I would like to extend my gratitude and appreciation to Dr.
Hamouda Ghonem for the opportunity he gave me to work on this thesis. His perseverance on excellence has driven me to new heights in my studies.
In addition, I would like to thank Dr. Frederic Sansoz who helped me in every step of this thesis and continuously provided me with ideas, guidance and support.   Table 3-1: Average size of silicides after oil quenching different solution treatments for 2-hours followed by aging at 700°C for 2-hours on IMI 834 (from reference [44]). *(Size determination from projected images a and b refers to major and minor axes of the projected ellipsoid  Table 3-2: Average size of silicides after water quenching solution treatments at 1050°C and aging for 24-hours followed by air-cooling at various temperatures on IMI 829 (from reference [19]). *(Size determination from

Chapter 1: Introduction
Titanium and its alloys are extensively used in aerospace and industrial applications due to their lightweight, high ability to withstand extremes of temperature and excellent resistance to corrosion. For instance, titanium is lighter than steel with equivalent strength, and heavier than aluminum, but twice as strong.
Pure titanium metal promotes an allotropic solid phase with very slow transformation at 883°C. Below 883°C, its crystalline form is hexagonal close packed (HCP), or alpha (a), whereas at temperatures above, its form is body centered cubic (BCC), or beta (~) [1]. The manipulation of these crystallographic variations is performed by the addition of alloying elements and the thermomechanical process. Alloying elements are classified according to their ability to change the temperature of either alpha or beta phase transformation [2]. Alpha stabilizing elements in titanium alloys are usually non transition metals, such as aluminum (Al) or gallium (Ga), as well as non-metals, such as oxygen (0) and nitrogen (N). Transition metals, such as molybdenum (Mo), niobium (Nb) and vanadium (V) are beta stabilizers [3,4]. Based on its chemical composition and the predominant room temperature constituent phase(s), titanium alloys can be classified as a, near-a, a/~, or ~-alloys [5][6][7] . Alpha alloys usually have creep resistance superior to that of beta alloys [8], but beta alloys offer increased fracture toughness at a given strength level [9]. Alpha alloys cannot be strengthened by heat treatment because the alpha structure is a stable phase, whereas beta alloys have excellent hardenability and response to heat treatment [2,10]. The principal 1 alloying element in alpha alloys is aluminum. When these alloys contain small amounts of beta-stabilizing elements [10], they are classified as super alpha or near alpha alloys. Near-alpha titanium alloys are processed to achieve either equiaxed alpha microstructures, acicular transformed beta microstructures, or a mixture of equiaxed grains embedded within transformed beta matrix, so-called duplex microstructures. Acicular microstructures possess better creep resistance than duplex microstructures. On the other hand, the latter has excellent fatigue strength, crack initiation resistance and higher ductility [11][12][13][14][15][16][17][18][19][20][21][22][23].
The increase in performance requirements for use in turbine engines and other high temperature applications has led to demands of titanium alloys with combined high creep and fatigue resistance. In order to achieve that objective, a considerable amount of research has been carried out over the past decades to enhance the creep resistance of near-a Ti alloys with duplex rnicrostructure. One of these alloys, IMI 834, is an advanced near-a titanium alloy designed for high temperature applications that exhibit a good compromise between creep and fatigue properties [26,29,31,[34][35][36][37] at temperatures up to 600°C [24][25][26][27][28][29][30][31][32]. In some applications, however, the alloy is already used for high-temperature components where temperature excursions reach 650°C [33]. Among the chemical changes in IMI 834, the addition of silicon has a major effect on the creep resistance and rnicrostructure of the alloy. Silicon raises the creep resistance in titanium alloys by reducing dislocation movement [29]. Furthermore, silicon lowers the molybdenum content of the ~-phase and consequently, for lower cooling rates, the ~ transforms to orthorhombic martensite instead of al~ colonies [23 , 38]. The most effective concentration of silicon in high-temperature alloys is governed by its tendency to form zirconium silicides. These are undesirable since studies have shown that the precipitates remove silicon from solid solution in the a phase and reduce ductility of the alloy [10]. Typically, silicides precipitate slowly at the aging or service temperatures of the alloys, resulting in a reduction in material stability. In addition to silicides, Ti 3 Al precipitates, or a 2, also form during high temperature applications. Studies show, however, that a 2 stability is achieved after aging at 700°C for 2 hours only [22]. In order to understand the effects of alloying additions in titanium alloys, a large amount of studies have been carried out to relate the heat treatment [6,9,13,32,[38][39][40][41][42][43] and the aging [20,23,[44][45][46][47][48][49] with the associated mechanical properties up to 600°C. In particular, studies by Madsen and Ghonem [47,49] on near-a Ti-1100 with basket-weave microstructure showed that the combined effect of creep and fatigue at 593°C and low loading frequency changed the fracture mode from quasi-cleavage to intergranular fracture. This change results in a significant increase in the fatigue crack growth rates. When the material was aged, however, the appearance of silicides in the a/~ colonies altered the slip process and the crack tip mechanism becomes transgranular with lower crack growth rates. These results suggest that aging is an important factor on the creep-fatigue effects in near-a alloys. However, in duplex rnicrostructure, such as IMl834, this relationship has never been established and the effect of aging is not fully understood. Moreover, Maier et al [28], in their study of the thermo-mechanical fatigue behavior of IMI 834 with a bimodal microstructure of a grains and lamellar a/~ colonies, have shown that at test temperatures above 600°C, dislocation slip changes from a planar slip mode within the primary alpha grains, to a more wavy type that leads to critical cracks in the lamellar a/~ colony. These results suggest that temperature selection is also an important parameter in the damage process.
It is the purpose of the present investigation to explore the role of heat treatment on the microstructure and high temperature fatigue crack growth behavior of the near-a titanium alloy IMI 834 at a single temperature. The next chapter of this thesis reviews the role of alloying elements as well as the thermomechanical processing and mechanical properties of near-a alloys. Additionally, heat treatment and hardness tests performed on the material under study, IMI 834, to explore the effects on phase morphology and yield stress at room temperature are discussed. The effects of long-term exposures at 650°C on the thermal stability of IMI 834 are presented in the third chapter. Background is given in the significance of aluminide and silicide precipitations on the yield stress of near-a alloys during over-aging. Testing and analysis of over-aged IMI 834 conclude the chapter. In the fourth and final chapter the controlling crack tip mechanisms are examined in water-quenched IMI 834 with two different duplex microstructures as a function of the loading frequency through fatigue crack growth testing at 650°C. These tests will be achieved with loading conditions of lOHz and 0.05Hz. The effect of a 300second hold time imposed at peak stress level of the loading cycle will be also 4 addressed for the lower frequency; 0.05 Hz. Results of this study will be discussed and a generalized hypothesis of the crack tip mechanisms at elevated temperature in near-a duplex microstructures will be presented.

Chapter 2: Role of Heat Treatment in Titanium Alloys
Introduction: This chapter describes the role of heat treatment on the morphology and associated mechanical properties of near-a Ti alloys. It is divided into three sections. The first section is a review on general aspects of physical metallurgy of near-a titanium alloys. Attention is given to the role of the a and ~ stabilizing elements as well as the thermomechanical processing on the mechanical property changes of near-a titanium alloys. The last two sections will detail experiments and analysis related to the effects of heat treatment on the microstructure and yield stress of IMI 834.

Review of Near-Alpha Titanium Alloys
As previously discussed, a wide range of titanium alloy microstructures may be attained through routes involving manipulation of alloying additions and thermomechanical processing [1]. In this section, a detailed description is given for the role of the aforementioned processes on the mechanical properties of near-alpha alloys.

Role of Alloying Elements
Typical alloying elements and corresponding phase diagrams for titanium are shown in Figure 2-1. This figure shows that the addition of alpha stabilizing elements, in particular nitrogen and oxygen, significantly raises the temperature of 6 the a ~ a+P phase transformation. On the other hand, beta stabilizers, especially elements such as vanadium, niobium and molybdenum, lower the a+p ~ P phase transformation -also called P-transus.
Understanding the role of alpha and beta stabilizers is of primary interest as their additions significantly influence the mechanical properties of the alloy. Alpha alloys promote better mechanical properties at high temperatures and off er easier welding in complex components such as turbine blades [2]. On the other hand, Palloys have higher formability especially in the form of foils. Figure 2-2 shows that a and near-a alloys have better high temperature strength and flow stress compared to a+ p, near-p, and P-alloys [12]. However a+ p, near-p, and P-alloys have better room-temperature strength and less strain rate sensitivity. In addition, a and near-a alloys have better welding ability, yet a + p, near-p, and P-alloys make forming and heat treatment easier.
Aluminum and molybdenum equivalent concentrations, respectively, are used to give the relative effect of alpha and beta stabilizers in titanium alloy. The two equivalencies are calculated using the following equations [7]. ''er" and "/3" are hep and bet solid-solution alloys, respectively, and "y" represents an interrnetallic compound.  [ 12]

10-25%
The role of each alloying element on the mechanical response of titanium alloys is described as follows [ 16]: • Aluminum (Al) ---+ The addition of aluminum, an a stabilizer, increases tensile and creep properties while reducing Ti-alloys density. Aluminum addition is however limited, as concentrations above 7% promote ordering as well as the formation of Ti3Al (a2) alurninides. This precipitate class is the subject of some interest, as at elevated temperatures, it often leads to severe post-exposure embrittlement due to decreased cross slip energy and sheared particles. A decrease in cross slip energy and sheared particles cause the slip to intensify and promote crack nucleation sites that lead to creep failure.
Details on the effects of alurninides in titanium alloys are discussed in chapter 3.
• Molybdenum (Mo) ---+ Molybdenum is the prime beta stabilizer in near-a alloys and is preferred for its substantial solid solution strengthening at high temperature and for its weight.  high-temperature alloys is governed by its tendency to form zirconium silicides, which will be detailed in chapter 3.
• Carbon (C), Tin (Sn) and Zirconium (Zr) -----+ Carbon, tin and zirconium are neutral as a or ~ stabilizers concern, but they are used to strengthen the alloy and to provide thermal stability of the phases.   Differences in elongation as seen in Table 2-3 could be the result of aluminum and molybdenum equivalence in addition to variations in their material microstructure.

Example of Near-a Alloys and their Mechanical Properties
Ti-1100, for example, is a near-a alloy with a Widmanstatten microstructure, which is less ductile than the duplex microstructure of the other two alloys.  [11]   Although aluminum and molybdenum equivalences are useful tools in analyzing titanium alloys, other factors must also be considered. Creep deformation, which is a measure of evolving strain as a function of stress, time and temperature, is often analyzed by methods such as the Larson-Miller parameter [17]. Data in figure  shows that for high temperature applications, there is a limit to the amount of silicon that can be added before creep resistance decreases. The presence of a limit is due to the tendency of the alloy to form Zirconium Silicides, (Ti,Zr) 5 Si 3 -S 1 and/or (Ti,Zr) 6 Si 3 -S 2 , on the a platelets of the transformed ~-phase as well as on the martensite boundary between ex/~ colonies and ap. On studies done by Sridhar and Sarma it is shown that the size of silicides increases with aging temperature [19].  and /3 processing as indicated (from ref [8]).

Processing and Heat Treatment of Duplex Microstructures
The processing and heat-treatment of near-alpha titanium alloys leads to two distinct microstructures: Widmanstatten microstructures, made of lamellar colonies embedded within large P grains; and duplex microstructures, composed of fine equiaxed particles of alpha phase, called primary alpha (ap), and a!P colonies, containing a lamella or needles in retained beta phase.  Typical processmg of duplex alloys consists of four steps as shown schematically in figure 2-7. The first step is comprised of a solution heat treatment or homogenization in the P-phase field. In this step, the alloy temperature is raised above its P-transus to be homogenized. The rate at which the material is cooled following solution treatment dictates the size of the primary alpha particles, making this an important treatment step [13]. Hot working in the a+P phase field, or deformation process, is the second step in processing and it introduces dislocations in the alloy, so that a and p can be recrystalized later. The third processing step consists of recrystalization of the material in the a+p phase field. Recrystalization in this field has a significant effect on the alloy mechanical properties. The recrystalization temperature, indicated by Ts in figure 2-7, determines the volume fraction of the primary alpha, which forms as equiaxed grains at the "triple points" of the recrystalized P-grains. The cooling rate at the end of the recrystalization process determines the width of the individual lamellae or needles formed within the al~ colonies [13] .
Depending on the cooling rate following recrystalization, more or less nucleation and growth of a-crystals occurs as ~-phase material passes through the al~ phase field [48] . As the alloy cools down, alpha phase nucleates at sites on the prior beta grain boundaries and grows as parallel platelets or as needles towards the interior of the prior beta grain. Needle or platelet formation becomes more coarse with decreasing cooling rates as the driving force for nucleation within the grain is reduced. Platelets tend to grow in an aligned manner, with all platelets having the same crystallographic orientation. Needles grow in several intertwining orientations forming the so-called "basket weave" morphology. Needle formation is mostly found with high cooling rates (greater than 10°C/min).   During the recrystalization phase, a and ~ stabilizers partition into the corresponding material phases. The alloy elements that are strong a-stabilizers, such as aluminum and oxygen, or strong ~-stabilizers, such as molybdenum and vanadium, partition into the a and ~ phases, respectively. This alloy partitioning effect also causes the a-lamellae, or a', to have a lower concentration of a stabilizing elements compared to ap [13) . This process is detailed later. The final processing step is an aging treatment. Aging is used to precipitate TbAl particles for strengthening and thermal stability of the alpha phase.

Ts
Depending on the titanium alloy, different aging time and temperature are recommended. For example, IMI 834 is aged for 2-hours at 700°C. At temperatures above 750°C, Ti3Al starts dissolving [9] . In addition to Ti 3 Al, the aging phase also precipitates silicides. S 1 and S2 type silicide precipitates usually form at temperatures below approximately 600°C, with small temperature variations depending on the chemical composition of the alloys. Aging above 600°C, such as aging of IMI 834, forms only S2 type silicide precipitates (20].

Effects of Heat Treatment on Mechanical Properties
Important parameters in each of the aforementioned processing steps are related to material microstructural features and mechanical properties in figure 2-10 [13]. This figure shows that the cooling rate is the most important parameter in the solution heat treatment phase, step I. Microstructural features such as texture type and texture symmetry are attained during the hot working phase, or step IL Step III shows that changes in the recrystalization temperature, as well as recrystalization time and cooling rate cause significant changes in the material mechanical properties. Finally, figure 2-10 shows that in step IV the aging temperature influences the ThAl content, as well as the formation of a' in the a/~ colony.
Based on this figure, manipulation of the processing in steps III and IV causes important changes in the mechanical properties of the material. For this reason, these steps are analyzed in detail throughout this thesis.
Step  In the study by Ltitjering [13], it is suggested that one of the influential microstructural features on the mechanical properties of duplex microstructures is the effective slip length controlled by the size of the a/~ colony. The colony size, 00 the other hand, is dependent on the recrystalization time and cooling rate, as shown in Fig. 2-10. Plastic deformation of HCP alpha-titanium occurs by both slip and twinning processes; however, slip appears to be the dominant deformation mode [3].    Another microstructural feature that is influential in the mechanical properties of duplex titanium alloys is the alloy element partitioning effect [13].
Zhang et al have reported element partitioning in the Ti-6-22-22 alloy, particularly of the a-stabilizer Al and the P-stabilizer Mo [ 40] . In addition, the concentration of Al in a' is lower than that in the ap but about twice as high as those in the P-phase, see table 2-4. Baxter et al [36] found that the aluminum equivalency in the primary and secondary alpha is influenced by the a-stabilizing interstitial elements, carbon and oxygen. Sn and Zr have extensive solid solubility in both a and p phases and partition to both phases occurs at similar degrees. Element partitioning in alpha favors slower cooling rates [38] and higher ap volume fractions [13]. Increases in ap volume fraction cause a-stabilizer elements in the wp colony to lessen, which results in a much lower basic strength region as compared with ap. This alloy partitioning effect has a negligible influence on ductility and on the growth of short and long term cracks, including the fracture toughness. However, the partitioning effect shows dependence between ap volume fraction and yield stress as well as creep.

Material of the Study
The material selected for this study is the near-a titanium alloy IMI 834, with a nominal composition Ti-5.8Al-4.0Sn-3.5Zr-0.7Nb-0.5Mo-0.35Si-0.06C.
The aluminum and molybdenum equivalences for this alloy are 7.49 and 0.56, respectively. Although near-a titanium alloys offer a wide range of microstructures through thermo-mechanical treatments, IMI 834 is usually processed in the a.IP field, which results in a duplex microstructure. In this study, IMI 834 is heat-treated and aged following the steps III and IV previously discussed (see figure 2.7). A micrograph of the material with 23% ap volume fraction after recrystalization and aging treatments was shown previously in figure 2-6. The experimental procedure used to determine the effect of heat treatment on the phase morphology of this alloy, as well as the heat treatment results and analysis will be presented.

Effect of Heat Treatment on Phases Morphology
The effect of heat treatment on the phase morphology of IMI 834 is addressed in this section. As shown before, primary alpha volume fraction and aJP colony size are major factors in changes of the mechanical properties of titanium alloys. Therefore, a series of experiments have been performed to determine the relationships between the heat treatment and the volume fraction of ap as well as the size of aip colonies in IMI 834. Analyses of these tests are detailed in the following sections.

Experimental Procedure
The material of study, Titanium alloy JMI 834, was supplied by TJMET in the form of 2.5-in.-diameter I 0.5-in.-thick forged pancakes; as shown in figure 2-l3. As-received JMI 834 pancakes were cut into quarters using a water-jet machine and subsequently cut into Y2 -inch cube specimens using a diamond precision saw.
To obtain different ap volume fractions in the desired duplex microstructure, the specimens were recrystalized at temperatures ranging from 920°C to 1055°C for two hours and aged at 700°C for 2-hours. All heat treatments were performed in an air-furnace. Four thermocouples were placed inside the furnace at different locations before and during heat treatments. Temperature changes showed less than a 3°C error. Prior to inserting the test specimens, stabilization of the furnace at the required treatment temperature was carried out for a minimum of one hour.
Heat treatment time started following stabilization of temperature after placing specimens in furnace, usually not taking more than two minutes. Cooling was done by air or by water quenching. After the aging treatment, a surf ace layer of 1 mm was removed from all specimens using a diamond precision saw. Mechanical polishing using 400, 600, 800, and 1200 grid water sand paper followed by 5, 3 and 1 micron diamond solution was performed after surface layer removal. The test specimens were then etched by immersion in Kroll's reagent for periods ranging between 10 and 35 seconds. SEM and optical microscopy examinations were performed afterward. Alpha primary volume fraction was measured from SEM images with 370X resolution to better capture the overall content of the phase.

34
Sigma Scan Pro image analysis software was used to calculate the ap percentage.
The error in measuring the volume fraction using this method was less than 2%.
Twenty-five colony size measurements were taken from each specimen using the linear-intercept method for two-phased microstructures described in reference [22].
Results of these observations are given in the following section. 35

Results and Analysis
The microstructure of specimens that were water-quenched and air-cooled after the recrystalization step as well as aged at 700°C for 2-hours are shown in Fig. z-14 and 2-15, respectively. shows that for volume fractions above 15%, aging resulted in an additional increase in ap volume fraction. Below 15% ap, however, volume fractions are not affected by aging. This outcome may be the result of element partitioning effects. As the volume fraction of ap increases, more aluminum is available in the particle to form the ThAl precipitate. When the material is aged, the increase in volume fraction is a result of a 2 growth in the primary alpha sites. This figure shows that maximum ap volume fraction is reached at higher recrystalization temperatures for the water-quenched microstructure compared to that of the air-cooled microstructure. Maximum water-quenched ap volume fraction, 40%, is obtained at recrystalization temperatures lower than 1000°C, whereas the maximum air-cooled ap volume fraction, 54%, is obtained at recrystalization temperatures lower than 970°C. Figure 2-17 also shows that below a critical volume fraction, referred to as CVF, corresponding to 35 %, the cooling rate has little effect on the growth of ap. It can be assumed that a phase growth also occurs in the a/~ colony, but no quantitative measurements have been performed in this thesis to corroborate this assumption. At ap volume fractions below 15%, the curves of the two cooling rates are slightly different. One reason for this difference may be that in the higher cooling rate material, a phase in the primary alpha sites is not allowed to diffuse into the colonies.       • OQ from reference [32] • AC from reference [30] 0

IMI 834
The influence of heat treatment on the hardness characteristics of IMI 834 was studied by performing Rockwell "C" hardness (Re) tests on selected specimens. Hardness value changes are generally correlated to changes in the yield stress (cry) behavior in a material. The following section describes the experimental procedure and discusses the results obtained when measuring the hardness of IMI 834 at room temperature.

Experimental Procedure
Macro-hardness measurements were performed at room temperature on the heat-treated and aged specimens of both water-quenched and air-cooled conditions.
These tests were performed using a semi-automatic Rockwell "C" testing frame A specific heat treatment, designated as Post-Age Heat Treatment (PAHT) [53] , was made on the water-quenched material to remove the existing Ti 3 Al particles.
Studies by Madsen and Ghonem [49] and by Zhang et al [40] show that a 2 is not present in titanium alloys when the material is heat treated above the solvus temperature of the particle. The PAHT, illustrated in figure 2-19, corresponds to an additional annealing at 850°C for 2-hours of IMI 834 specimens followed by aircooling.

Summary and Conclusions of Chapter 2
The physical metallurgy of titanium alloys has been discussed in this chapter, with emphasis on near-alpha materials. A description of the different alloy elements used with titanium and their influence on the material mechanical properties was presented and commented. Details on the phase morphology of the material of study, IMI 834, as well as the heat treatment process and its effect on the mechanical properties were also given. Heat treatments of IMI 834 using different recrystalization temperatures and cooling rates led to the following conclusions: I.
Maximum ap volume fraction values for air-cooled specimens were higher than that of the water-quenched by approximately 12%.
2. Regardless of the cooling rate following the recrystalization process, aged IMI 834 shows the same ap volume fraction when recrystalized between 1010°C and 1035°C.
3. In general, material recrystalized and aged has higher ap volume fraction than material only recrystalized.
4. Colony size decreases as ap volume fraction mcreases. Above 20% ap volume fraction, the colony size remains constant.

1.
Hardness measurements showed the following features: For the same ap volume fraction, air-cooled specimens have lower hardness than water-quenched specimens. 56 2.

3.
All heat treated material shows constant hardness between 15% and 33% ap volume fraction.

Chapter 3: Long Term Exposure Effects at 650°C on the Structural Stability of Near-a Alloys
Introduction: This chapter describes the role of over-aging on the structural stability of near-a Ti alloys. For the purpose of this study, over-aging indicates that the material is submitted to long-term exposure at 650°C following various heat treatments and aging at 700°C for 2-hours. The first section is a review on the effects of over-aging on aluminide and silicide precipitation and their implication on room temperature yield stress. In the second and last section, experiments are performed that show the significance of over-aging at 650°C on IMI 834. Results and analysis are also provided.

Structural Stability of Titanium Alloys
Near-alpha titanium alloys are not usually in a state of equilibrium after initial processing due to the relatively fast cooling rates from the forging and annealing treatments. Among the elements added to titanium alloys, aluminum and silicon are the most influential in material mechanical properties at elevated temperatures. Low concentrations of aluminum are used in these alloys as strengtheners and alpha-phase stabilizers [13], whereas silicon is added to technical titanium alloys to improve material creep resistance [23]. The formation of coherent ordered Ti 3 Al particles (see figure 3-1) and incoherent (Ti,Zr)sSi3 I (Ti,Zr) 6 Sh during the aging and averaging phases accounts for the biggest changes in the near-alpha titanium alloy mechanical properties, such as hardness, UTS, and creep-fatigue behavior [13,20,23,47,49). However, changes in the material microstructure as a function of the thermo-mechanical exposure during high temperature (550°C-650°C) applications can lead to material failure. Liu et al [55) described Based on the binary Ti-Al phase diagram, it is predicted that the a 2 -phase will form in titanium alloys containing over 8.0 wt% Al [57]. However, the interstitial oxygen impurity level may have a significant effect on the a 2 precipitation behavior since this element is a strong a 2 -stabilizer. Increases in oxygen content have been shown to shift the a ~ a + a 2 boundary in Ti alloys with lower aluminum content by raising the a 2 solvus temperature [58,59]. In fact, studies performed on the near-alpha Ti-1100, with 6.0 wt% Al and 0.078 wt% 0, show that a 2 was present when aging at 593°C [49]. Furthermore, Partha et al found when studying the near-a titanium alloy JMI 834, with only 5.86 wt% Al but 0.1 wt% 0, that a 2 particles are present when the material is aged at 600°C [44].
Alloying elements such as V, Sn, and Zr have been determined to have a detrimental influence on the oxidation behavior of titanium alloys. In contrast, additions of Mo, Nb, Si and Al reduce the oxidation rate [60]; however, the addition of these elements to high temperature near-alpha titanium alloys is relatively low since the aluminum equivalent has to be kept below about 9% to avoid embrittlement [60].
Studies have shown that a2 precipitation behavior is sensitive to the heat treatments and aging temperatures applied to the alloy [ 44]. Zhang et al [ 40] showed that when the microstructural morphology of the titanium alloy Ti-6-22-22 consisted of martensite plates (when cooled at rates 2: 5.5°C/s), neither a 2 nor retained p-phase were observed. On the contrary, when cooling rates are lowered to form a relatively fine Widmanstatten/aciculate structure, a2 started to precipitate.
Qualitatively, the same authors observed that the relative intensity of the a 2 superlattice reflections with respect to the fundamental a reflections, increased with decreasing cooling rates.
Aging temperatures have also been shown to have an effect on the precipitation of a 2 • Studies on IMI 834 with approximately 5%, 15% and 25% CXp [44] show that when aging at 600°C Ti 3 Al precipitates within the primary alpha only, whereas aging at 700°C causes ordering in .both primary and the a!P colony.
In these studies, it is also shown that aging at 700°C for 2-hours was sufficient to reach stability of the a 2 precipitates. The later result suggests, therefore, that the aging treatment conducted in the current study, as mentioned in chapter 2, is sufficient to precipitate all a 2 phase in the material. Furthermore, studies on IMI 834 at 650°C and 750°C indicate that oxygen becomes more soluble and mobile at high temperatures, which further stabilizes the a 2 phase [25,42].
Finally, when in the precipitation temperature range, a 2 particles show changes in size with aging [40]. The ratio of lattice parameters aafaa2 in both Ti-6-22_22 and IMI 834 alloys have a value of approximately 0.5 and have been considered to cause negligible misfits between the two phases [36,40). The lattice parameters for a found in Ti-6-22-22 were a = 29.7 nm, c = 46.9 nm and for a 2 they were a= 59.3 nm, c = 46.9 nm. However, aging of the Ti-6-22-22 alloy for 1,000-hours at 650°C showed the lattice parameters of a and a 2 to be a= 28.9 nm, c = 46.9 nm and a = 58.7 nm, c = 46.9 nm, respectively. This suggests that the clattice parameter is not affected by long time aging treatment, whereas the a-lattice parameters decreases by about 2.6% for the a-matrix and about 1 % for the a 2 precipitates [40), thus maintaining the aalaa 2 ;:::: 0.5 seen before long term aging. It has also been shown that aging causes significant changes in aluminide size [40).
When exposed to 600°C for 30-hours, a 2 precipitates in Ti-6-22-22 grew from a spherical shape, with sizes of about 1-2 nm, to much more stable a 2 precipitates, with sizes up to 5-10 nm in diameter and 20-50. nm in length. Zhang et al [ 40) explain this change based on the lattice mismatch between a 2 precipitates and the a matrix (about 1.5% in this case) and the resulting strain fields generated at their interface.

Effects of Over-Aging on Silicides
Like aluminum, silicon also stays in solid solution after rapid cooling following the initial heat treatment of the alloy. Madsen and Ghonem [47) showed that when aging Ti-1100 at 593°C, silicides start forming before aluminides, however, they add, silicide stability is reached after that of the aluminide.
Incoherent silicides are found predominantly on the a' platelet boundaries in the al~ colonies of lamellar microstructures alloys [25]. However, in duplex microstructures, silicides are found at the interfaces of a' and at the martensite boundaries of the primary a and the colonies [20,29,44]. Silicides change in size and shape depending on a number of factors including: the concentration of ~ stabilizers, heat treatment, aging temperature and aging time of the alloy [40,56].
These factors and their influence on the formation of silicide precipitates during long term exposure at elevated temperatures will now be discussed.
Two types of hexagonal silicides, S 1 with lattice parameters a= 0.78 nm, c = 0.54 nm, and S 2 with lattice parameters a = 0.70 nm, c = 0.36, have been identified by Ramachandra and Singh [61] to form in silicon bearing titanium alloys. They were found to coexist in the water quenched, 650°C to 800°C aged conditions in the alloy Ti-5Zr-1Si using X-ray and electron diffraction techniques [45]. ill the water quenched near-a titanium alloy 685, which contains smalls amount of ~-stabilizers, S 1 and S 2 silicides were found when the material was aged below 650°C [61]. However, aging of IMI 829, where ~-stabilizing elements are higher than in IMI 685, showed the presence of both silicides at temperatures lower than 625°C [19]. Between 625°C and 950°C only S 2 type silicides were found. In the alloy IMI 834, only silicides S 2 precipitated following aging in the temperature range of 600°C to 700°C [20].      at 80(f C (from ref [ 19] ).

Role of Over-Aging on Room Temperature Hardness
As discussed in the previous section, changes in the size and shape of alurninides and silicides occur as the alloy chemical compositions change as well as when the alloy is exposed to elevated temperatures for extended periods. One way to examine how these changes occur in an alloy is by performing hardness measurements. By changing the chemical composition while keeping all other variables fixed, hardness tests may help to separate the individual effects of elements. Likewise, by maintaining the same chemical composition and changing the temperature that the alloy is exposed to, conclusions may be drawn pertaining to the effects of temperature on the material hardness. In the following sections, studies performed on different alloys over a range of temperatures are shown and detailed analysis are performed to relate the changes in hardness to the changes in the size and shape of aluminides and silicides. When analyzing age-hardening results, attention is given in particular to the relative shape changes in the hardness curves, to maximum hardness points (peaks), and to decreases in hardness. Shape changes are normally considered to be caused by changes in the types of precipitate formed. Hardness peaks are associated with attaining a critical particle size.
Finally, precipitate growth beyond the critical particle size causes a decrease in hardness. Figure 3-7 shows changes in hardness when a Ti-5%Zr-l %Si alloy is aged over an extended period at 500°C, 550°C, and 650°C [45]. Applying the method of analyses previously described, it appears that between 500°C and 550°C, as well as between 550°C and 650°C, there are changes in the type of precipitate formed as 73 0 C urves differ in shape from each other. Furthermore, aging at 650°C shows the tW two hardness peaks, indicating the presence of two precipitates. In fact, both of these observations appear to be substantiated. As discussed in the previous section of this report, studies show that when aging titanium alloys with zirconium and silicone above about 500°C (depending on the chemical composition of the alloy), two types of silicides are formed, S1 and S2 [20,23,44]. Furthermore, the two silicides were found to coexist below a close range of temperatures, depending on the chemical composition of the alloy, but at higher temperatures, only S 2 type silicides were found. Some examples include the studies on IMI 829, IMI 685, IMI 834, and Ti-1100, where aging at temperatures below 575°C, 650°C, 550°C, and 593°C, respectively, resulted in the formation of both S 1 and S 2 precipitates. The same studies show that above those temperatures, only S 2 type precipitates were evident. , where the silicon concentration varies between 1.0% and 2.39%, shows the same general hardness curve shape with one hardness peak. In this figure, it is worth noting, however, the change on the rate of precipitate growth beyond critical size. For the Ti-2.39%Si alloy, the growth occurs at a much higher rate compared to the 1 % silicon alloy. This effect is supported by studies that show that changes in the volume fraction of a+~ titanium alloys, where concentrations of silicon vary between phases, cause changes in the size of the silicides precipitated for a given heat treatment [ 44]. One explanation could be that the higher concentration of silicon promotes faster precipitation of silicides, causing the critical precipitate size and grain growth to occur sooner. In figure 3-9, aging of the Ti-1 %Si at 500°C, 550 oc and 650°C shows that with removal of zirconium from the alloy, the silicide variants S 1 and S 2 are unable to form. Instead, the phase Ti 5 Si 3 is formed. Hence, the second peak found at 650°C in figure 3-7 does not appear in figure 3-9. One variation in figure 3-9 relative to figure 3-7 is that at 500°C, the figure shows a hardness peak after aging for approximately 60,000 minutes, which may be indicative of the formation of a different precipitate. As the alloy in figure 3-9 is aged at higher temperatures, the precipitate growth becomes more pronounced.
These results are in agreement with studies performed on silicon bearing titanium alloys aged over a wide range of temperatures that showed rapid increases in silicides precipitation with increasing temperatures [ 19].
The effects of aluminum content on the aging characteristics of Ti -5%Zr-1 %Si-Al alloy at 550°C are shown in figure 3-10. The most striking effect seen when aluminum is added to the alloy is the sharp decline in the precipitate growth rate. Whereas the Ti-5%Zr-1 %Si alloy shows a relative decrease in hardness of more than 50Hv, or 15%, after over-aging for approximately 3,000 minutes, the Ti-5.0%Al-5%Zr-1 %Si shows no drop after 100,000 minutes. This result is supported by studies that show that aluminum addition in titanium alloys containing silicon delays the precipitation of silicides, which is also apparent in figure 3-10 as the hardness curves slightly shifts to the right between the 0% and 5.0% aluminum content. The alloys containing 1.0% and 2.9% aluminum also show strong evidence that the addition of aluminum retards the formation of silicides, however, 75 the change in shape of the curves appears to be indicative of the formation of precipitates other than the ones previously discussed. One possible answer could be the formation of the aluminides, however, the author states that the alloys shows 00 evidence of ThAl formation and the aluminum concentration in the alloys are also too low to form ThAl, as discussed in the previous section. 5%Zr-1%Si-Al alloy at 55CfC (from reference [45]).
Other studies on the effects of aging on the mechanical behavior of the near-alpha alloy Ti-1100 carried out by Madsen and Ghonem [47,49] show the effect of aging at 593°C on the hardness of Ti-1100, see Fig. 3-11. The unaged condition shown in this figure corresponds to Ti-1100 heat treated above the ~ transus and air-cooled, followed by an 8-hour aging at 593°C (stabilization).

Summary on the Role of Aluminide and Silicide Formation in Titanium Alloys
Aluminum, zirconium and silicon bearing titanium alloys show defined aging responses to changes in alloy element concentration, temperature and time of exposure. It was shown that in the binary Ti-Si system, only Ti 5 Si 3 silicides were formed when aging at 500°C, 550°C and 650°C. However, additions of zirconium to the Ti-1 %Si alloy precipitate S 1 and S 2 type silicides when aging at 550°C and S2 type silicides only at 650°C. Furthermore, retardation of silicide precipitation by aluminum occurred with increasing aluminum content when aging Ti-5%Zr-1 %Si-Al alloy at 650°C. In the near-alpha titanium alloy Ti-1100, aging results following heat treatment in the ~-phase field and stabilization at 593°C for 8-hours, show two hardness peaks that appear to be caused by reaching the critical particle size of S 1 and S 2 type silicides.

Significance of Over-Aging on IMI 834 at 650°C
A major concern when studying the mechanical properties of near-a alloys is the effect of long-term exposure at high temperatures. As discussed in the previous section, in this class of alloys, over-aging at high temperature promotes the precipitation of additional phases due to the high content of aluminum and silicon. In the present study, this effect is investigated in water-quenched IMI 834 with 5%, 23% and 39% volume fractions of ap for long-term exposure at 650°C.
This material was selected because, as discussed in chapter 2, its microstructure consists of primary alpha grains and fine platelets of martensite [23,38]. By forming a martensite phase instead of a.IP lamellar colonies, silicide precipitation is expected to occur primarily at the boundaries between primary alpha and martensite [23,38]. Consequently, any effects due to silicide precipitation on the fatigue crack-growth mechanisms that will be studied in chapter 4 can be identified.
Alpha primary volume fractions of 5%, 23% and 39% were selected because they represent the highest changes in global hardness seen in chapter 2. The over-aging temperature was chosen based on studies by Maier et al [28] that show that the themomechanical fatigue behavior of IMI 834 changes at 600°C. By over-aging at a higher temperature, the structural stability of IMI 834 can be accessed in the region where one themomechanical fatigue behavior is predominant. Following, experimental procedures and results are discussed.

Experimental Procedure
Water-quenched IMI 834 specimens with 5%, 23% and 39% volume fractions of Up, following heat treatment and aging at 700°C for 2-hours as described in chapter 2, were used in this test. These specimens (hereafter "aged" material) were then measured for Up volume fraction and colony size using the same method described in chapter 2 and the results were compared to ensure a good agreement with previously tested data. Prior to over-aging, hardness measurements were made on the three different aged microstructures. As in chapter 2, all hardness results reported are the average of a minimum of twenty-five tests. Overaging was done at 650°C, see figure 3-12. Hardness measurements of specimens over-aged and corresponding over-aging times are also plotted. only. This is due to the fact that 650°C is a much higher temperature than that at which S1 and S 2 type silicides have been reported to coexist in IMI 834.
Additionally, ThAl particles in IMI 834 reach stability after aging for 2-hours at 700°C, as previously discussed. This means that no hardness peak was expected in the over-aging plot resultant from critical aluminide precipitation. Based on these facts, it can be concluded that the peaks shown in Fig. 3 minutes, whereas critical silicide particle size for the 5% ap is achieved after only 80 minutes. The fact that critical silicide size is achieved at nearly the same time for the 23% and 39% ap vf is not very clear in terms of the aluminum concentration, but it can be explained in terms of colony size. As previously discussed, silicides precipitate at the colony and ap boundaries. In addition, this study showed in chapter 2 ( Fig. 2-18) that colony size for volume fractions greater than about 23% ap remains relatively constant. Based on these results, it may be concluded that silicide precipitation rate in the two microstructures would be similar. In addition, colony size can also explain the shorter over-aging time to reach silicide critical size for the 5% ap vf. The much smaller colonies as well as the smaller size of precipitates that form in this microstructure are strong reasons to 88 believe that silicide critical size is achieved earlier compared to the other two microstructures.
Changes in the hardness from the aged condition to the maximum over-aged peak can be explained in terms of silicide size. As shown in figure 3

Summary and Conclusions for Chapter 3
The effects of long-term exposure at elevated temperature on the structural stability of titanium alloys have been discussed in this chapter. Also, a detailed description was given on the formation of aluminides and silicides when titanium alloys are over-aged. Furthermore, significant material mechanical property changes when over-aging due to aluminide and silicide precipitation was discussed.
Finally, over-aging at 650°C was performed on the titanium alloy IMI 834 with three different microstructures and the results were analyzed in terms of hardness changes with over-aging time. The following conclusions can be derived from this chapter: 1. a 2 -phase precipitates in the a-phase.

2.
Addition of a-stabilizers, especially oxygen, increases a 2 precipitation and shifts the a -7 a + a 2 transition temperature in titanium alloys with lower aluminum content.

4.
In IMI 834, aging below 600°C precipitates a 2 in the ap regions only. At 700°C, a 2 precipitates in both the ap and a' phases.

5.
In Ti-Si-Zr alloys, S 1 and S 2 type incoherent silicides coexist at the lower precipitation temperatures. In the upper temperature range, 600°C-1050°C, (depending on the alloy chemical composition) only S 2 type silicides are found. 91 6 .
In lamellar microstructures, silicides form on a' platelet boundaries, whereas in duplex rnicrostructures, silicides form on a' platelet boundaries and martensite boundaries of ap and a!P colonies.

.
Silicides increase in size with decreasing recrystalization temperature (increase ap volume fraction).

8.
When aged, silicides increase in size with increase in temperature. They also change from ellipsoid to circular with increasing aging temperature.
. 10 and 30% ap volume fractions, the material hardness has a constant value in each cooling condition. On the other hand, the hardness decreased significantly for volume fractions lower than 10% and for volume fractions higher than 30%. It was also found that element partitioning effects are most dominant in volume fractions above 30%.
Based on these results, microstructures with 5%, 23% and 39% ap volume fraction were prepared to study the role of over-aging at 650°C in IMI 834. Each of the volume fractions corresponds to regions where colony size effect, no effect, and Partitioning element effect, respectively, were predominant. Analysis aluminide and silicide precipitation in titanium alloys indicated that during over-aging, only S2 type silicides precipitated. Furthermore, results showed that critical silicide size was achieved at the same over-aging period, 2,000 minutes, for ap volume fraction greater than 23%. On the other hand, over-aging the material with 5% ap volume fraction resulted in precipitation of S2 type silicides in a shorter time, 80 minutes, and in a significant increase of hardness as compared to the other two volume fractions.
In the present chapter, the role of microstructure and loading frequency on the fatigue crack growth of the near-a titanium alloy IMI 834 is studied at 650°C for ap volume fractions of 20% and 30% ap. Based on the results from chapters 2 and 3, microstructures with 20% and 30% ap volume fraction support the following particulars: 1.
For the same recrystalization temperature, the morphology of the two rnicrostructures can be achieved independently of the cooling rate; in the present study, only water quenching will be imposed.

2.
Colony sizes for the two microstructures are expected to be similar.

3.
Little difference in the partitioning effect is expected.

4.
When over-aged at 650°C, silicide critical size occurs at a similar time.

5.
Silicide precipitates are expected to be smaller in the 20% ap volume fraction than in the 30%.
Studies have shown that, in near-a Ti-1100, the high temperature fatigue crack growth rate is influenced by the interaction between creep and fatigue [47].
Furthermore, it has been shown that creep in near-a alloys is very sensitive to the precipitation of silicides [ 49]. Considering these results, it was important in the present study to have volume fractions that show similar aging effects. Since creep between the two selected microstructures is not dependent on the time of aging, the present investigation on the fatigue crack growth behavior of IMI 834 will only focus on the role of microstructure features.
This chapter is divided into four sections. The first section describes the heat treatment process used to obtain the two selected microstructures as well as the specimen preparation and geometry. Procedures for fatigue crack growth tests will also be presented. The second section deals with the experimental results. The effects of loading frequency and hold time on the fatigue crack growth rate will be investigated and discussed with the support of SEM examinations in the third section. The chapter concludes with a summary of the test results.

Experimental Procedure
The material used in this study is the same as that presented in the previous chapters. The chemical composition and morphology of as-received are given in chapter 2. Using figure 2-17, recrystalization temperatures of 10 l 5°C and 1030°C were selected to obtain ap volume fractions of 20% and 30% respectively. The design of this specimen is given in Fig. 4-1. Room-temperature pre-cracking was performed at a loading frequency of 20 Hz to obtain an initial crack length of 0.3 W. The crack growth was monitored using optical measurements taken from the two sides of the test specimen. In addition, the crack growth was monitored using the Potential Drop (PD) method, as described in the ASTM Standard book.
In this technique, a 3-Ampere current was imposed in the specimen through wires welded on the load train. The potential drop at the notch, V 1 , was measured and compared to the reference V 2 , as shown schematically in figure 4-1. The potential drop curve that relates V 1 N 2 to the crack length "a" was calibrated based on optical measurements. All FCG tests were conducted on a servo-hydraulic material testing system controlled by the Test Star ITS computer environment shown in figure 4-2.
Heating of the specimens was achieved using a clamshell furnace in which the 96 specimen temperature is controlled by two thermocouples spot-welded on the top and bottom sides of the specimen as shown in figure 4-3. Temperature variations in all tests were maintained within less than 5°C along the specimen height. The testing temperature was 650°C. The crack mouth opening displacements (CMOD) were measured using a high temperature clip gauge, see Fig. 4

Experimental Results
The microstructures resulting from the heat treatment procedure are shown in the micrographs represented in figures 4-4 and 4-5. The volume fractions on these microstructures were determined to be equal to 20% and 30%. Note also that the colony size between the two microstructures is not similar, contrary to expected based on chapter 2 results (Fig. 2-18). The slight difference could be explained by the fact that different IMI 834 pancakes were used in the FCGR tests. and 30% <Xp volume fractions tested at 10 Hz and 10s-10s loading frequencies.
Specimens tested at 10 Hz show lower FCGR than those tested at lOs-1 Os.
Furthermore, changes in microstructure appear to have no significant effect on the FCGR at these loading frequencies. Figure 4-6 al~o shows the result of a 300s hold time on the 10s-10s loading frequency, designated as 10s-300s-10s. In addition to a crack growth rate increase in the specimens tested with a hold time, the two microstructures demonstrate a prominent crack growth rate difference, with the 30% <Xp microstructure having the highest crack growth rate. Detailed analysis of these figures is done in the next section.
The fracture surfaces of tested specimens were also subjected to both optical and scanning electron microscopy.

Discussion
It is apparent in Fig. 4  Based on the aforementioned observations, it can be assumed that for high frequency loading, pure fatigue dominates the FCGR behavior. The different strengths between the colonies and the ap phase, seen in Fig. 2-21, can further account for the changes in fracture growth rates. At the higher loading frequencies, fatigue crack growth mechanism is transgranular in ap particles due to the lower strength of this phase compared to that of the martensite boundaries. For the higher ap volume fraction, the slightly lower crack growth rates in the transgranular fracture region indicate that higher volume fractions are more crack resistant compared to the lower ones. This effect can be the result of a higher ap density and/or size.
Contrary to the fracture mode seen in the higher loading frequencies, creep dominates the FCGR response for low frequency loading. For these lower loading frequencies, the tougher material, ap, allows for higher plastic strain without failing, as the particles have the ability to absorb energy. In this case, failure ought to occur, possibly by fast fracture due to stress built up, at the martensite boundaries of ap particles. In addition, the presence of incoherent hard silicide precipitates further supports the mechanism of boundary fast fracture, also know as zipping effect. As previously discussed, silicide precipitates grow larger with increasing ap volume fraction. As a result, ap boundaries weaken due to increasing silicide size and incoherency. Results in Fig. 4-6 reflect this behavior, as the FCGR for the 30% ap vf is much higher than that of the 20% for the 0.003 Hz loading frequency.
Similar results to those obtained from the FCGR tests in this thesis were obtained when the loading frequency was maintained constant and the operating temperature increased [26]. ,.

Summary of Chapter 4 Results
The following conclusions may be drawn from the obtained results:

Appendix A Basic Mechanisms of Creep and Fatigue Fracture
Creep and fatigue failure are critical degradation mechanisms that occur in turbine engine components. Cyclic fluctuating loading conditions at elevated temperature can ultimately cause failure at stresses considerable lower than those required under monotonic loading. Fatigue and creep crack growth occurs in three stages: (1) localized damage leading to crack initiation, known as primary creep; (2) crack growth, also called steady-state creep; (3) and final tensile rupture or tertiary creep. Figures A-1 and A-2 show the typical shapes of creep and fatigue crack growth curves, respectively. Factors that influence crack initiation include the material microstructure, the applied mean stress and the surrounding environment. During the second stage, microstructure and the thickness of the material may play a role, however, the major contributors in crack propagation involve combinations of environment, temperature, mean stress and loading frequency. Failure in the final stage can be caused by the material microstructure and/or thickness as well as by the applied mean stress.
To better understand the causes of failure, creep and fatigue must be looked at an atomic level. There are two mechanisms of creep: that gives the power-law behavior and diffusional creep that gives linear viscous creep. In dislocation creep, dislocation movement is opposed by the intrinsic lattice resistance or the obstructing effect of obstacles such as solute atoms, precipitates, and/or other dislocations. At elevated temperatures, diffusion of atoms can release dislocations from its obstacles, designated as dislocation climb, which in turn glide on the next slip. This process is called dislocation creep. Figure A-3 is a schematic representation showing dislocation climb followed by dislocation glide.
Linear-viscous or diffusion creep occurs when dislocations are not involved.
Instead, atoms diffuse from grain face to grain face due to grain elongation in response to the applied stresses. Figure  .,.,..

Steady-state
Log LlK