DYNAMIC BEHAVIOR OF ADDITIVELY MANUFACTURED METAL ALLOYS

The dynamic behavior of additively manufactured metal alloys is investigated. For 17-4PH stainless steel (with H1100 heat treatment) and a nickel-copper alloy, the dynamic constitutive behavior is tested at various rates of compressive and tensile loading at both room and high temperatures. Experiments are conducted using an Instron 5582 Universal Tester and a Shimadzu AGX Universal Test Frame for quasi-static compression and tensile tests, respectively, and a Split Hopkinson Pressure Bar for all dynamic tests. An induction coil heating system is used for the high temperature (HT) experiments. Strain rates of 10 s to 10 s are studied. At the dynamic strain rate of 2500 s, the effects of HT are investigated for temperatures ranging from 22 oC to 1000 oC for compressive loading and for temperatures from 22 oC to 600 oC for tensile loading. Johnson-Cook models (one for compressive loading and one for tensile loading) are established to determine the dynamic plastic response of the 17-4PH H1100 stainless steel for various strain rates and temperatures. The dynamic response of additively manufactured nickel-copper alloy corrugated panels is studied using a shock tube. By keeping areal mass density and face sheet dimensions the same for all panels, hexagonal and sinusoidal corrugation geometries are tested to determine the effect of corrugation geometry on shock response. The panels have four layers of corrugation allowing for an equal number of contact points between the corrugations and the face sheets on both the front face (shock side) and back face of the panel, as preliminary tests demonstrated the importance of equal contact. Corrugation buckling and back face panel deflection are tracked using high speed photography and 3D Digital Image Correlation (DIC).


Introduction
A widely used alloy, traditionally manufactured 17-4PH SS is a common and practical choice for many industries, including aerospace, chemical and food processing, due to its high strength, good corrosion resistance and good mechanical properties at high temperatures. This metal can also be easily heat treated to suit a variety of applications [1]. With the recent advent of additive manufacturing, which can fabricate complex geometries as well as reduce waste and save money, much research has been conducted to determine if AM 17-4PH SS is a suitable replacement for traditionally manufactured 17-4PH SS. Cheruvathur et al. (2016) analyzed the effect of post-processing heat treatment on the microstructure of AM 17-4PH SS, noting that the as-printed material often has a dendritic structure with a large percentage of austenite. Through homogenization heattreatment, they were able to obtain a microstructure with 90% martensite and only 10% austenite, which more closely resembles that of wrought 17-4PH SS than the as-built condition [2]. Lum et al. (2017) investigated the effect of additive manufacturing on the material properties of 15-5PH stainless steel, a similar material to 17-4PH SS, and found that the additive manufacturing process left behind unmelted regions and a small percentage of austenitic structure [3]. Rafi et al. (2014) examined the effect of argon and nitrogen atmospheres during the laser sintering process to determine the effects and also found that post-process heat treatment is required to obtain better tensile material properties, as the phase content is greatly influenced by multiple factors besides the AM atmosphere [4]. Multiple studies have been conducted to examine the fatigue and tensile properties of AM 17-4PH SS for a variety of heat treatments [5][6][7]. Yadollahi et al. also noted that, during tensile testing, the build orientation of the AM 17-4PH SS affected the material properties and concluded that defects such as pores from entrapped gas, as well as regions where the 17-4PH powder did not melt or fuse sufficiently, played a noticeable role in why the AM material was inferior to its wrought version [7]. However, to the best of the authors' knowledge, no studies have been conducted on the high temperature dynamic characterization of AM 17-4PH SS. Therefore, this paper will evaluate the thermomechanical response of this material and will provide the Johnson-Cook model parameters to describe obtained results.

Experimental Details Additive Manufacturing of Test Specimens
Samples are additively manufactured using a 3DSystems ProX300 machine with powder supplied by North American Höganäs High Alloys LLC. This powder is vacuum melted and then gas-atomized in argon gas. A typical composition is shown in Table 1. Argon is used to operate the ProX300 machine. During the additive manufacturing process, the oxygen level in the build chamber is limited to less than 1000 ppm. The laser settings are summarized in Table 2. The powder layer height before laser melting is approximately 50 m. Following the additive manufacturing process, samples are solution heat-treated in air at 1,038 °C for one hour, air-cooled to room temperature, and subsequently aged at 593 °C for four hours to achieve an H1100 condition. The microstructure of a longitudinal section of both an AM (A) and a wrought sample (B) in H1100 condition is shown in Fig. 1. and wrought 17-4PH in H1100 condition (B) In the as-built condition, additively manufactured samples reveal significant microstructural differences to their wrought counterparts: Extended columnar grains are typically observed for additively manufactured samples while wrought samples reveal typically an equiaxed martensitic microstructure. Solution heat treatment then occurs in a temperature range that establishes an austenitic microstructure. During the subsequent air cooling, the austenite then transforms to martensite. The final ageing treatment then induces nanoscale precipitates that significantly contribute to the strength of the heattreated alloy. Despite the significant microstructure differences between as-built additively manufactured sample and wrought sample, the heat-treatment steps induced comparable microstructures in prior work [8]. As in the prior work, the comparison between the two images in Fig. 1 suggests a slightly smaller grain size for the additively manufactured sample than for the wrought counterpart. Figure 1A reveals second phase particles at grain boundaries and it is likely that these particles are carbides or inclusions that inhibit grain growth of the additively manufactured sample during the ageing treatment.

Compressive Quasi-static Characterization
An Instron 5582 Universal Tester is used to determine the compressive quasi-static behavior of H1100 AM 17-4PH SS at RT. The specimen dimensions (see Table 3) and testing procedure are determined from ASTM standard E9-19. During testing a compression rate 1.524 mm/min is used to achieve a strain rate of 10 -3 s -1 up to 25% strain.
To reduce interfacial friction between the Instron compression platens and the specimen, molybdenum disulfide is used as a lubricant.

Compressive Dynamic Characterization
A Split Hopkinson Pressure Bar (SHPB) is used to determine the dynamic behavior of H1100 AM 17-4PH SS at 22° C, which will be referred to as RT, and at HT's of 400 °C, 600 °C, 800 °C and 1000 °C. Strain rates varying from 10 3 to 10 4 are investigated. The SHPB is comprised of an incident bar, a transmitted bar and a striker bar, all made of 350 maraging steel, as shown in Fig. 2. These bars are aligned along a horizontal axis to ensure uniform specimen deformation and one-dimensional elastic waves during testing.

Fig. 2 SHPB compressive loading configuration
Before a test, the cylindrical specimen is positioned between the incident and transmitted bars. The specimen geometry is determined from length to diameter ratios chosen to ensure a state of uniaxial stress, minimal interface friction and reduced specimen inertia in both the radial and longitudinal directions.  positioned before the steel (0.375" diameter (9.5 mm), 0.25" length (6.4 mm)), which is affixed to the striker end of the incident bar with petroleum grease. This dual pulse shaper decreases the sharpness of the initial rise time and shapes the compressive pulse to match that of the specimens [9]. Additional details about the SHPB can be obtained from Kolsky [10]. Axial strain gages mounted on the incident and transmitted bars connect to a dynamic signal conditioning amplifier and oscilloscope system that record the experimental data.
Two strain gages are mounted on each bar at least one striker length from the specimen to prevent superposition of the stress waves and at 180 o offsets to negate possible bending of the bars. Each strain gage is connected in a quarter Wheatstone bridge configuration. A typical strain profile is shown in Figure 3. It is clear that the dual pulse shaping technique reduces the Pochhammer-Chree waves in the incident and subsequent pulses. Thus, from the strain measured in the incident and transmitted bars, the specimen strain and strain rates can be determined. From the strain data, using one-dimensional wave theory, the engineering strain rate, engineering stress and engineering strain can be determined from the following equations, respectively, where is the longitudinal wave speed in the incident and transmitted bars ( = √ ⁄ , where Eb is the elastic modulus of the incident and transmitted bars and is the their density), is the thickness of the specimen, is the reflected bar strain, is the crosssectional area of the bars, is the cross-sectional area of the specimen, is the incident bar strain and is the transmitted bar strain [11]. In SHPB tests, for ductile materials such as metals, a constant true strain rate is difficult to achieve, thus the engineering strain rate is typically considered. However, it is important to use the true stress and true strain rather than the engineering stress and strain because adiabatic heating can contribute to softening of the material, thereby negating the strain hardening, which may be inaccurately represented by engineering stress-strain curves [9]. Thus, the true stress and true strain may be determined from the following equations, respectively, For the HT tests, the SHPB setup is modified to include an induction coil heating system placed over the specimen, as shown in Fig. 5 [12]. Two pumps circulate water through two independent copper coils that are positioned over the ends of the incident and transmitted bars that are in contact with the specimen. This is to prevent a heat gradient in the bars, which would affect their modulus, and thus the wave speed, and to protect the heatsensitive strain gages. A tungsten carbide insert is placed between the specimen and the incident bar and another between the specimen and the transmitted bar to additionally prevent heating of the bars. The impedance of the tungsten carbide inserts is calculated so as to prevent the compressive stress wave from being altered before reaching the specimen.
Therefore, the inserts are 50% smaller in diameter than the incident and transmitted bars.
In order to reach the desired experimental temperature in the specimen, calibration experiments are first conducted to determine the relation between induction heating time at certain amperage levels and desired temperature. The calibration relation is developed Time (µs) by spot welding a chromel-alumel thermocouple onto a calibration specimen and its temperature is monitored until the desired temperature is reached and maintained.

Tensile Quasi-static Characterization
A Shimadzu AGX Universal Test Frame is used to determine the tensile quasi-static behavior of H1100 AM 17-4PH SS at room temperature. The specimen dimensions and testing procedure are determined from ASTM standard E8. Strain is recorded using a 1 megapixel camera at a frame rate of 10 fps and a random speckle pattern is applied to the specimen so that 2D Digital Image Correlation could be used to measure strain in the vertical direction.

Tensile Dynamic Characterization
A tensile SHPB setup is used to determine the tensile dynamic behavior of H1100 AM 17-4PH SS at RT and at HT's of 400 ºC and 600 ºC [13]. Strain rates on the order of magnitude   The one-dimensional wave theory used for compression (Eq.'s 1, 2 and 3) remains valid [12]. However, Eq.'s 4 and 5 must be modified to describe tensile behavior. Thus, the true stress and strain may be described as ( ) = ln(1 + ( )).
As in the case of compressive tests, during tensile SHPB tests, force equilibrium verification is undertaken, validating the use of Eq.'s 6 and 7. Figure 7 shows the strain- For the HT tests, the tensile SHPB setup is modified to include an induction coil heating system placed over the specimen, as in the case of the HT compressive setup. Similarly, two pumps circulate water through two independent copper coils that are positioned over the ends of the incident and transmitted bars that are in contact with the specimen. The same calibration method as described in the compressive HT configuration is used to determine the correct settings and time to reach the required temperature in the specimen before a test is conducted. Due to the fact that the tensile specimens are threaded into the incident and transmitted bars, boron nitride is used a lubricant to ensure that the specimens could be removed after testing without damage to the threaded sections of the bars. The threaded nature of the tensile SHPB also determined that 600 ºC was the upper testing limit before bars began experiencing a level of heating that could no longer be controlled by the copper cooling coils, thus altering the modulus of the bars [14].

Compressive Dynamic Constitutive Response (Room Temperature)
The compressive dynamic material properties of H1100 AM 17-4PH SS were determined for four different dynamic strain rates (1000 s -1 , 2500 s -1 , 5000 s -1 and 10000 s -1 ) at RT and each experiment was conducted five times for consistency. For this data, and all subsequent data, the yield strength is taken as the 0.2% offset. In Fig. 8, the RT true stress-true strain curves are plotted for one representative trial for the dynamic strain rates of 1000 s -1 , 2500 s -1 , 5000 s -1 and 10000 s -1 and for the quasi-static strain rate (10 -3 s -1 ). Figure 8 shows that H1100 AM 17-4PH SS is strain rate dependent in compression from quasi-static to dynamic strain rates, since yield strength increases by 8% as the strain rate increases from 10 -3 s -1 to 1000 s -1 . A 12% increase in yield strength is observed as the strain rate increases from 10 -3 s -1 to 2500 s -1 , a 27% increase is observed from 10 -3 s -1 to 5000 s -1 , and a 31% increase is observed from 10 -3 s -1 to 10 4 s -1 . The average dynamic compressive flow stresses are approximately 50 MPa, 100 MPa, 150 MPa, and 225 MPa greater than the average quasi-static compressive flow stress, respectively for the 1000 s -1 , 2500 s -1 , 5000 s -1 and 10000 s -1 strain rates.

Tensile Dynamic Constitutive Response (Room Temperature)
The tensile dynamic material properties of H1100 AM 17-4PH SS were determined for three different dynamic strain rates (1000 s -1 , 2500 s -1 and 5000 s -1 ) at room temperature and each experiment was conducted five times for consistency. In Fig. 10, the room temperature true stress-true strain curves are plotted for one representative trial for the dynamic strain rates of 1000 s -1 , 2500 s -1 and 5000 s -1 and for the quasi-static strain rate of 10 -3 s -1 . Figure 10 shows that H1100 AM 17-4PH SS is strain rate dependent in tension from quasi-static to dynamic strain rates, since yield strength increases by 50% as the strain rate increases from 10 -3 s -1 to 1000 s -1 . A 62% increase in yield strength is observed as the strain rate increases from 10 -3 s -1 to 2500 s -1 and a 73% increase is observed from 10 -3 s -1 to 5000 s -1 . The average dynamic tensile flow stresses are approximately 325 MPa, 400 MPa and 475 MPa, greater than the average quasi-static tensile flow stress, respectively for the 1000 s -1 , 2500 s -1 and 5000 s -1 strain rates. The specimens all broke during testing at very low strains, indicating brittle failure. The strains to failure were approximately 2.6%, 3.3% and 3.9% for the dynamic strain rates of 1000 s -1 , 2500 s -1 and 5000 s -1 , respectively, while the quasi-static strain to failure was only approximately 1.2%. At dynamic strain rates, it is postulated that adiabatic heating softened the material, resulting in higher strain to failure values than were seen in quasi-static, thus indicating that the material is strain rate sensitive. It is also postulated that the porosity in the material leads to lower failure stresses and strains. This effect seems to be more dominant in quasi-static tensile failure of this material, where a yield stress of 600 MPa (consistent over five specimens tested) compares poorly with a value of 790 MPa for the wrought material [1].

Fig. 10
True tensile stress-strain curves for room temperature dynamic loading

Tensile Dynamic Constitutive Response (High Temperature)
The tensile dynamic material properties of H1100 AM 17-4PH SS were determined at 2500 s -1 for three different temperatures (RT, 400 °C and 600 °C) and each experiment was conducted five times for consistency. The corresponding true stress-true strain curves are plotted in Fig. 11

Johnson-Cook Constitutive Model
The Johnson-Cook constitutive model provides an effective method of predicting the plastic response of materials subjected to HT, high strain rates and large deformations [15].
This empirical model is widely used in the characterization of metals due to its simple and comprehensive form. The model states that the flow stress may be described as where σ is the flow stress, A is the yield stress at the reference strain rate, B and n are strain hardening parameters, is the plastic strain, C is the strain rate parameter, ̇ is the plastic strain rate, ̇ is the reference strain rate, m is the thermal softening parameter and T * is the normalized temperature and can be described where Tref is the reference temperature (RT), Tmelt is the melting temperature (1400 °C) and T is the experimental temperature.

Determination of Model Parameters for Compressive Loading
The Johnson-Cook model requires five model parameters to effectively describe the plastic response of metals. Parameter A is the yield stress of the material at the reference strain rate, which is commonly defined as the quasi-static strain. However, in order to fit this model to the compressive dynamic strain rates more effectively, the strain rate of 1000 s -1 is used as the reference strain rate for this case. Thus, the yield stress at the 0.2% strain offset from the reference strain rate true stress-strain plot is taken. Once parameter A has been determined, parameters B and n may be found. At the reference temperature (RT) and reference strain rate, the Johnson-Cook model may be simplified as and a linear regression may be used to fit the quasi-static data to determine the slope, n, and the y-intercept, ln(B). Once A, B and n have been determined, C may be found. Using dynamic SHPB results for strain rates of 1000 s -1 , 2500 s -1 , 5000 s -1 and 10000 s -1 at the reference temperature, the Johnson-Cook model may be simplified as and again a linear regression may be used to calculate C, given a y-intercept of 1. Because the linear regression is unable to completely capture all of the data from the various strain rates, as the resulting plot from Eq. 13 is non-linear, an average value of C is obtained.
Finally, to determine the value of m, experimental data at a strain rate of 2500 s -1 and temperatures ranging from RT to 1000 ºC are used. At the given strain rate, the Johnson-Cook model may be simplified as and a linear regression may be used to find the slope, m. The final step is to optimize the five parameters, given that the experimental data did not provide exact linear relations during their determination. As such, the model may predict some experiments very well with little relative error, while other predictions may be less accurate. Thus, it is important to minimize the error between the model and all experimental data [12]. This is accomplished using the following relation as described by where σexp is the experimental flow stress, σp is the predicted flow stress and N is the number of data points. The result of this optimization is that by decreasing the parameter A to 635, which is below the yield stress for the reference strain rate, the model better predicts the shape of the true stress-strain curves with larger errors at low strain, but with smaller errors at higher strain. The parameters for the H1100 AM 17-4PH SS under compressive loading may be found in Table 4.

Determination of Model Parameters for Tensile Loading
The method described in the previous section was used to determine the Johnson-Cook model parameters for tensile loading of H1100 17-4PH SS. Once again, the reference strain rate chosen was 1000 s -1 and the same optimization was conducted using Eq. 15.
The Johnson-Cook model parameters for H1100 17-4PH SS may be found in Table 5.

Johnson-Cook Model Comparison with Experimental Data for Tensile Loading
The comparative results of the Johnson-Cook tensile modeling versus the corresponding experimental data are shown in Fig. 13. As before, only the plastic region is shown. Table   7 gives the average relative error between the model and the experimental data using Eq.
15. For all RT strain rates, the model predicts well, with less than 10% average relative error for all cases. Additionally, the model predicts better for lower strain rates, as the average relative errors for 2500 s -1 and 5000 s -1 are only 4.38% and 5.89%, respectively, while the average relative error for 1000 s -1 is 3.74%. The model also predicts well for

Conclusions
The dynamic constitutive behavior of H1100 AM 17-4PH SS was investigated under compressive and tensile loading at strain rates ranging from 10 -3 s -1 to 10 4 s -1 . At the average strain rate of 2500 s -1 , temperatures ranging from RT to 1000 ºC were investigated for compressive loading, while temperatures ranging from RT to 600 ºC were investigated for tensile loading. Two Johnson-Cook models were developed for this material under these conditions.
The following conclusions were drawn under compressive loading: • From quasi-static experiments, the compressive yield strength of H1100 AM 17-4PH SS was determined to be 810 MPa and the Young's Modulus was determined to be approximately 150 GPa.

Experimental Details Compressive Quasi-static Characterization
An Instron 5582 Universal Tester is used to determine the compressive quasi-static behavior of the AM nickel-copper alloy at room temperature, 22 °C (RT). The specimen dimensions (see Table 1) and testing procedure are determined from ASTM standard E9-19. During testing a compression rate 1.524 mm/min is used to achieve a strain rate of 10 -3 s -1 up to 25% strain. To reduce interfacial friction between the Instron compression platens and the specimen, molybdenum disulfide is used as a lubricant.  Fig. 1.
These bars are aligned along a horizontal axis to ensure uniform specimen deformation and one-dimensional elastic waves during testing.

Fig. 1 SHPB compressive loading configuration
Before a test, the cylindrical specimen is positioned between the incident and transmitted bars. The specimen geometry is determined from length to diameter ratios chosen to ensure a state of uniaxial stress, minimal interface friction and reduced specimen inertia in both the radial and longitudinal directions. Table 1 details the specimen dimensions used in this study.
To minimize interfacial friction and prevent barreling, the specimen is well lubricated with molybdenum disulfide for RT tests and with boron nitride for HT tests. To conduct the SHPB test, a gas gun is mounted at the end of the incident bar and fires the striker bar, causing it to impact the incident bar. The striker velocity determines the magnitude of the stress wave, while the striker length determines the pulse length. A pulse shaper is positioned between the striker and the incident bar to optimize the strain profile. This pulse shaper allows for stress equilibrium and constant strain rate in the specimen for the duration of the test. In order to optimize the experiments, a dual copper/steel pulse shaper was used for all strain rates, with the copper (0.375" diameter (9.5 mm), 0.05" length (1.3 mm)) positioned before the steel (0.375" diameter (9.5 mm), 0.25" length (6.4 mm)),, which is For the HT tests, the SHPB setup is modified to include an induction coil heating system placed over the specimen, as shown in Fig. 2. Two pumps circulate water through two independent copper coils that are positioned over the ends of the incident and transmitted bars that are in contact with the specimen. This is to prevent a heat gradient in the bars, which would affect their modulus, and thus the wave speed, and to protect the heatsensitive strain gages. A tungsten carbide insert is placed between the specimen and the incident bar and another between the specimen and the transmitted bar to additionally prevent heating of the bars. The impedance of the tungsten carbide inserts is calculated so as to prevent the compressive stress wave from being altered before reaching the specimen.
Therefore, the inserts are 50% smaller in diameter than the incident and transmitted bars.
In order to reach the desired experimental temperature in the specimen, calibration experiments are first conducted to determine the relation between induction heating time at certain amperage levels and desired temperature. The calibration relation is developed by spot welding a chromel-alumel thermocouple onto a calibration specimen and its temperature is monitored until the desired temperature is reached and maintained.

Tensile Quasi-static Characterization
A Shimadzu AGX Universal Test Frame is used to determine the tensile quasi-static behavior of the AM nickel-copper alloy at room temperature. The specimen dimensions and testing procedure are determined from ASTM standard E8. Strain is recorded using a 1 megapixel camera at a frame rate of 10 fps and a random speckle pattern is applied to the specimen so that 2D Digital Image Correlation could be used to measure strain in the vertical direction.

Tensile Dynamic Characterization
A tensile SHPB setup is used to determine the tensile dynamic behavior of the AM nickelcopper alloy at RT and at HT's of 400 ºC and 600 ºC [13]. Strain rates on the order of

Experimental Results
Results will be presented during the oral defense.

Shock Tube Setup
A shock tube is used to provide planar shock waves to load the corrugated sandwich panels, as shown in Fig. 3.