Strength Behavior of Tin at High Strain Rate in Richtmyer-Meshkov Instability

The strain rate effect on strength is a key issue in the study of dynamic constitutive models, and the Richtmyer-Meshkov instability experiment on the free surface of metal reflects the strength behavior under extremely high strain rates. After the shock wave propagates to the free surface and undergoes unloading, the metal enters a near-ambient pressure state and exceed 10<sup>6</sup>s<sup>-1</sup> strain rate. The initial sinusoidal perturbation exhibits phase inversion trend of forming spike and bubble structures, while the development of the perturbation gradually stabilizes under the suppression effect of material strength. In the initial research, equivalent strength of metal under high strain rate is usually estimated by total spike growth for perturbation evolutions. Subsequent studies found that the maximum value of the spike velocity which can be directly measured could be the metric to determine equivalent strength. However, the influence of the non-uniformity of strength on the development of spike velocity has not been explored. Tin is a critical material in the study of dynamic mechanical behavior under extreme conditions. Currently, the experiment of dynamic strength on tin usually couple multiple effects such as strain rate, pressure, and phase transitions. Richtmyer-Meshkov (RM) instability experiment, as a method to isolate high strain rate effect, at the free surface of tin have not been publicly reported. The characteristics of tin dynamic strength behavior under extremely high strain rates remain unclear. This study conducts numerical simulations on the Richtmyer-Meshkov instability experiment of a tin sample with a pre-imposed sinusoidal perturbation (amplitude 0.15 mm, wavelength 0.8 mm) under shock pressure 5.5GPa. Using a self-developed two-dimensional explicit finite element program for elastoplastic hydrodynamics, the simulation results of three constitutive models, including elastic-perfectly plastic model, Steinberg-Cochran-Guinan model, and stress relaxation model, on the spike velocity curves are compared with the measured one. The equivalent strength of tin can be evaluated by obtaining consistent maximum spike velocity of free surface perturbation between calculation with elastic-perfectly plastic model and experiment. It is found that the strength increases by about 64 times at strain rate ~10<sup>6</sup>s<sup>-1</sup> compared to the quasi-static strain rate ~10<sup>-4</sup>s<sup>-1</sup>, indicating strain rate hardening is extraordinarily significant. By adjusting model parameters, both the elastic-perfectly plastic model and Steinberg-Cochran-Guinan model could capture the maximum spike velocity but failed to reproduce the unloading process observed in experiments. Compared to the experimental results, the calculated spike velocity decreases too rapidly. In contrast, stress relaxation model due to considering strain rate effects achieve excellent agreement with the entire experimental spike velocity history, not only capturing the peak velocity but also resolving the issue of overly rapid velocity decay. This demonstrates that the strain rate effect on material strength not only suppresses the maximum spike velocity but also influences the deceleration stage, revealing that the impact of strain rate effects persists throughout different stages of perturbation development. The study shows that the experiment data available for dynamic constitutive model research are expanded from a single peak velocity value to the complete velocity history. The utilization efficiency of experimental data is greatly improved, presenting important values for the study of dynamic constitutive models under extremely high strain rates.