Flow Strength Measurements of Wrought and AM SS304L via Pressure Shear Plate Impact Experiments

Abstract

Pressure-shear plate impact experiments were performed to quantify flow strength of wrought, as-built additively manufactured (AM), and heat-treated and recrystallized AM 304 L stainless steel (SS304L) under combined loading. Impact velocities spanned between 0.03 and 0.24 mm/μs, resulting in corresponding pressures of 0.62–5.93 GPa. Flow strength measurements are comparable for the sample variants across the studied loading conditions; however, shear wave structures significantly differ between sample type. Microstructurally aware simulations indicate local strain differences attributed to anisotropic elastic constants of large grains ($\sim$1 mm) in the as-built and heat-treated AM may impede the ability to uniformly transmit a shear wave.

Appendix A Modeling of Inelastic Materials Subjected to Pressure-Shear Loading

To aid in visualization of the described dispersive phenomena, CTH simulations were performed for a simple impact between a molybdenum impactor and anvil at impact velocities of 0.1, 0.5, and 1.0 mm/μs with a skew angle of 20°. Pertinent equation of state (EOS) parameters are listed in Table 2. A constant yield strength of Y=1.1 GPa and Poisson’s ratio $\nu$=0.31 were prescribed. Note that the configuration simulated is akin to that of the rear anvil in a PSPI experiment without the added complexity of a front anvil and sample. Understanding the wave dynamics in this configuration helps to provide a simplified example of the described physics needed to assess the wave dynamics recorded in an inelastic PSPI experiment.

Figure 13F illustrates the simple two-dimensional simulation domain, where initial velocities $u_{0}$ ($Vcos\theta$) and $v_{0}$ ($Vsin\theta$) were prescribed. Upon collision, the longitudinal and shear waves propagate into the anvil. In-material wave dynamics of the simulation were captured at 0.7$\mu$s and plotted in Figures A, C, and E. Images are intended to provide context regarding the influence of Eqs. 9–13 on the dispersive features and wavespeeds at an instance in time.

It is important to note that thickness of the impactor as well as the transverse velocity in the impactor in Figure C have been clipped from the image due to scale. Figures B and D present the free-surface velocities after the stress waves propagate through the anvil. Results of Figures B and D are akin to experimental interferometry measurements. Utilizing the figures, focus is directed towards the following topics: dispersive features, stress deviators, wavespeeds, shear wave amplitudes, and the influence of a free surface.

Fig. 13

Demonstration of wave propagation for the case of inelastic pressure-shear loading. F Representative simulation domain. A Longitudinal and C shear wave propagation through the material at time $t=0.70$μs. E Corresponding spatial stress deviators pertaining to Eq. 9. B Longitudinal and D transverse free surface velocities akin to an interferometry measurement of an experiment

Illustration of spatial deviatoric stresses in the material at time 0.7 μs can be seen in Fig. 1E. The bolded black line at 0.4 GPa$^{2}$ represents the yield strength ($1/3Y^{2}$) of Eq. 9. Unbolded black and red lines represent $S_{xx}$ and ${\tau }_{xy}$. As the longitudinal wave front propagates through the material, it is apparent that the yield criterion is satisfied by the Hugoniot elastic limit (HEL) (i.e. $3/4S_{xx}^{2}=1/3Y^{2}$). Coupling behavior (Eq. 9) and dispersive features (Eqs. 10, 11), however, can be seen between the longitudinal and shear stress deviators spatially from 0 to 2 mm. These manifest due to propagation of the shear wave, and the dispersive features are additionally observed in the free surface transverse velocity profiles of Fig. 1D.

Wavespeeds and transverse velocity amplitudes also are dependent on the stress state. Shear wavespeeds increase with stress as seen in Fig. 13C and D. It should be noted that amplitude of the transverse particle velocity diminishes with increased compressional stress. As the shear wavespeed increases, material impedance changes (i.e., $\rho _{0}C_{S}$). Therefore, if the yield strength is constant the transverse particle velocity, v, must reduce assuming $Y=\sqrt{3}\tau _{xy}$ and $\tau _{xy}=\rho _{0}C_{S}v$. This is a product of the prescribed constant yielding. A dynamic yield surface will likely differ.

Additional complexities also arise due to the free surface of the anvil. Free surface release of the longitudinal wave will perturb the shear wave as it propagates towards the free surface of the anvil. Release will reduce the compressive stress in the material, altering wavespeeds. This can be noted in the arrival time of the shear wave in Fig. 1D. Additionally, recall idealized constant yield strength was prescribed in this example. Strain hardening, strain-rate, thermal influences, and other phenomenological dependencies all may influence the yield strength, further complicating wave dynamics. Therefore, the need for a methodology which accurately incorporates the described effects is imperative to extract material strength for an inelastic pressure shear experiment at high pressures. Additionally, it is critical to have a well characterized anvil material, such that the rear anvil does not attenuate the shear wave propagation due to deviatoric limitations at a given state.