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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 its strain rate exceeds 106 s–1. The initial sinusoidal perturbation exhibits the phase inversion trend of forming spike and bubble structure, 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 show that the maximum value of the spike velocity which can be directly measured can 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 investigated. Tin is a critical material in the study of dynamic mechanical behavior under extreme conditions. Currently, the experiments of dynamic strength on tin usually combine various effects such as strain rate, pressure, and phase transitions. So far, no research has been found on the Richtmyer-Meshkov (RM) instability experiment, which is a method to separate high strain rate effect on tin free surface. The characteristics of tin dynamic strength behavior under extremely high strain rates are still unclear. This study conducts numerical simulations on the Richtmyer-Meshkov instability experiment of a tin sample with a pre-imposed sinusoidal perturbation with an amplitude 0.15 mm and a wavelength 0.8 mm under a shock pressure of 5.5 GPa. Using our 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 measurements. The equivalent strength of tin can be evaluated by obtaining a consistent maximum spike velocity of free surface perturbation between the calculation with elastic-perfectly plastic model and measurements. It is found that the strength increases by about 64 times at a strain rate of ~106 s–1 compared with that at a quasi-static strain rate of ~10–4 s–1, indicating that the strain rate hardening is extraordinarily significant. By adjusting model parameters, both the elastic-perfectly plastic model and Steinberg-Cochran-Guinan model can capture the maximum spike velocity but fail to reproduce the unloading process observed in experiment. Compared with the experimental results, the calculated spike velocity decreases too rapidly. In contrast, stress relaxation model due to considering strain rate effects achieves excellent agreement with the entire experimental spike velocity evolution, not only capturing the peak velocity but also solving the problem of overly rapid velocity decay. This demonstrates that the strain rate effect on material strength not only suppresses the maximum spike velocity but also affects the deceleration stage, revealing that the influence of strain rate effect persists throughout different stages of perturbation development. This study indicates that the experiment data available for dynamic constitutive model research extend from a single peak velocity value to the complete velocity evolution. The utilization efficiency of experimental data is greatly improved, providing important values for studying the dynamic constitutive models under extremely high strain rates.
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图 1 计算模型示意图
Figure 1. Schematic diagram of calculation model.
图 2 不同YEP的弹性理想塑性模型计算的尖钉速度历程与实验结果的比较
Figure 2. Comparison of spike velocity history calculated by elastic-perfectly plastic model with different YEP and experimental results.
图 3 (a) YEP = 0.9 GPa时扰动发展过程的压力分布; (b) YEP = 0.9 GPa时扰动发展过程的等效塑性应变率分布
Figure 3. (a) Pressure distributions of preturbation evolution as YEP = 0.9 GPa; (b) effective strain rate distributions of perturbation evolution YEP = 0.9 GPa.
图 4 锡材料强度随应变率的变化关系
Figure 4. Variation relation between strain rate and strength of tin material.
图 5 不同Y0的SCG模型计算的尖钉速度历程与实验结果的比较
Figure 5. Comparison of spike velocity history calculated by SCG model with different Y0 and experimental results.
图 6 不同τ的应力松弛模型计算的尖钉速度历程与实验结果的比较
Figure 6. Comparison of spike velocity history calculated by stress relaxation model with different τ and experimental results.
图 7 自由面扰动附近强度、应变率随时间的变化关系
Figure 7. Distributions of strength and strain rate varing with time near the perturbation of free-surface.
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