爆轰加载下弹塑性固体Richtmyer-Meshkov流动的扰动增长规律

研究了冲击波加载弹塑性材料扰动自由面的动力学演化过程,分析了高能炸药爆轰驱动时初始扰动与材料性质对扰动增长的影响.研究结果表明:初始扰动的振幅与波长之比越高,扰动越易增长,强度越高的材料扰动增长幅度越小;扰动增长被抑制时,尖钉的最大振幅与增长速度无量纲数之间存在线性近似关系,进一步理论分析表明尖钉的振幅增长因子与加载压力、初始扰动形态和材料强度有关,该理论关系作为扰动增长规律的线性近似在一定范围内适用于多种金属材料.

A growth study of the Richtmyer-Meshkov flow in the elastoplastic solids under explosive loading

In this paper, a theoretical analysis model is proposed for the linear growth of the Richtmyer-Meshkov instability in elastoplastic solid medium-vacuum interface under the explosion shock wave loading. The analysis of the dynamic evolution of small perturbations shows that after the initial phase inversion, some perturbations would stop growing after they have reached their maximum amplitude, some others would continue to grow and then form jetting from the solid-vacuum interfaces. Numerical simulations show excellent agreement with the experimental results of explosively-driven Richtmyer-Meshkov instability in the sample of copper. The effects of two physical factors on the maximum amplitude of spikes are also studied numerically. The first physical factor is the initial configuration of the perturbation, which is expressed as the time values of the initial wave number and initial amplitude. With increasing the value of the initial configuration, the maximum amplitudes of the spikes would become greater while the growth of perturbations is suppressed. On the other hand, the maximum amplitudes of spikes would become smaller in the solid which has a higher yield strength when the initial configuration keeps unchanged. Further investigations show that the boundary of the stage division between the stable growth and the unstable growth is revealed by a combination parameter form of the two physical factors, which is expressed as the ratio of initial configuration to yield strength. In the stable stage, the linear relation between the non-dimensional maximum amplitude and the non-dimensional maximum growth rate of the spikes is fitted with the coefficient value 0.30, which is very close to 0.29, a theoretical prediction based on the Newton's second law analysis. Considering the shock Hugoniot relations in the elastoplastic medium and the maximum growth rate equation of the Richtmyer-Meshkov instability in ideal fluid, the linear model is improved to add the effects of the loading shockwave pressure and the compression acoustic impedance of the material on the amplitude growth of the spike to the analytical model proposed by the former researchers. Extensive numerical simulations are performed to show that the linear model could accurately describe the growth factor of the spikes in the stable cases in different metal materials, such as copper, aluminum, and stain-less steels. In the numerical analysis of the scope of application of the linear model, a rough estimation of the stage division boundary between the stable and unstable growth is given as 0.8 GPa^-1. When the ratio of initial configuration to yield strength is lower than the division boundary, the perturbation growth would be stable and the linear model could describe the growth law of the spikes.