爆轰驱动Cu界面的Richtmyer-Meshkov扰动增长稳定性

Stability analysis of interfacial Richtmyer-Meshkov flow of explosion-driven copper interface

研究了爆轰驱动Cu界面的扰动增长过程,分析了不同初始条件下的扰动增长规律和主要失稳机制.研究结果表明:温度相关的熔化失稳和塑性变形相关的拉伸断裂失稳是界面扰动增长过程的主要失稳机制;高能炸药爆轰驱动Cu材料界面时,冲击波加载引起的温升和扰动增长阶段塑性功转换引起的温升不足以熔化Cu材料,拉伸断裂是导致扰动增长不稳定的主要机制;扰动增长非线性阶段尖钉的最大累积有效塑性应变与尖钉振幅之间存在定标关系,结合熔化条件和断裂应变判据建立的尖钉振幅失稳条件可用于分析界面扰动增长的稳定性.

In this paper, a stability analysis is given to study the unstable mechanism of the Richtmyer-Meshkov flow of explosion-driven copper interface. The Richtmyer-Meshkov flow refers as an interfacial instability growth under shockwave incident loading. Numerical investigations are performed to check the applicability of the two-dimensional hydrocode, which is named AFE 2 D, and the physical models of detonation waves propagating in the high explosives,equations of state and the constitutive behaviors of solids in the analysis of Richtmyer-Meshkov flow problems. Here we theoretically analyze the two key issues of the unstable mechanism in Richtmyer-Meshkov flow in solids. The unstable mechanism includes temperature related melting mechanism and the plastic evolution related tensile fracture mechanism. In the analysis of the temperature related unstable mechanisms, the calculated temperature increase during the shockwave compression from the shock Hugoniot data in the shockwave physics is not enough to melt the material near the perturbed interface. On the other hand, the temperature increase from the translation of plastic work during perturbation growth which relats to the distribution of the cumulative effective plastic strain is also not enough to supply the thermal energy which is needed to melt the crystal lattice of solid, either. Therefore, the temperature related melting mechanism is not the main factor of the unstable growth of copper interface under explosion driven. In the analysis of the plastic tensile fracture related unstable mechanism, a scaling law between the maximum cumulative effective plastic strain and the scaled maximum amplitude of spikes is proposed to describe the relationship between the plastic deformation of material and the perturbation growth of interface. Combined with a critical plastic strain fracture criterion,the unstable condition of the scaled maximum amplitude of spikes is given. If the spikes grow sufficiently to meet the unstable condition, the interfacial growth will be unstable. Numerical simulations with varying initial configurations of perturbation and yield strength of materials show good agreement with the theoretical stability analysis. Finally, a criterion to judging whether the growth is stable is discussed in the form of competition between the temperature related unstable mechanism and the tensile fracture unstable mechanism.