一种基于空穴聚集的层裂模型

A spallation model based on void coalescence

基于如下假设,给出了层裂过程中的应力松弛方程,并建立了一种基于空穴聚集的延性层裂模型:在层裂早期,微空穴的主要效应是减小应力作用面积;在层裂后期,应力按空穴聚集时的应力-空隙度依赖关系减小。把P.F.Thomason、D.L.Tonks等及S.Cochran等给出的依赖于应力(压力)的层裂空隙度方程分别耦合于守恒方程、计及损伤的状态方程及本构方程,建立了求解所有变量包括损伤的封闭方程组。这种基于空穴聚集的层裂模型已被应用于一维层裂试验的数值模拟。模型中的层裂强度及临界损伤度初始可以估计,最终的确定将使数值模拟结果与实测的速度(或应力)剖面以及观测的层裂面上的损伤基本一致。分别基于D.L.Tonk等及S.Cochran等给出的依赖于压力的层裂空隙度方程所作的一维层裂试验数值模拟结果基本一致,而与基于P.F.Thomason给出的依赖于应力的层裂空隙度方程所作的相应数值模拟结果有明显差异。

Assuming that the main effect of the voids is to reduce the area over which the stress acts in the early stage and the stress decreases to porosity-dependent value in the void coalescence stages, the stress relaxation equations in the spall process are given and a void coalescence-based spall model is proposed. The stress（or pressure）-dependent spall porosities given by Thomason, Tonks, et al and Cochran et al are respectively combined with conservation equations, equation of state and constitutive equations for the damaged aggregate to establish a series of close equations for all variables including damage. The void coalescence-based spall model is applied to numerical simulations of one-dimensional spall tests. The spall strength and the critical damage in the proposed spall model can be initially estimated and final determination of them should make the calcualted results of spall test under initial and boundary conditions consistent with the experimental velocity（stress） profile and the observed damage at spall plane. The calculated results based on the pressure-dependent spall porosities given by Tonk et al and Cochran et al are consistent but different from the calculated results based on Thomason＇ s stress-dependent spall porosity.