摘要
以物理统计和唯象研究相结合的方法，建立了微孔洞型的损伤函数模型和损伤演化方程．以变形热力学、Drucker公设和内变量理论为基础建立了含损伤热塑性材料的增量型本构关系．用所建立的本构关系及损伤演化方程对内部爆轰作用下的圆管破坏过程完成了系列数值模拟．数值结果与实验结果相比较，在圆管变形过程、破坏时间、破坏速度、破坏应变、破坏应变率等信息方面都是基本一致的．
In this paper, the problem of the deformation, damage and fracture rules of circular steel tubes under inside-explosive loading is studied theoretically and numerically. The damage is defined as the ratio of the void volume to the total volume of the materials, and the surface energy's increase for the void growth is considered to be provided by the strain energy of the materials in a limited neighbourhood, which expands with the volumetric wave speed of the material.Mom the above point of view, the damage function models and the damage evolution equations for the micro voids in materials are established by means of combining the physical statistics method and the phenomenological research method. In our damage evolution equations, the effect of the plastic volumetric strain on the damage evolution is considered. Then on the basis of deformation thermodynamics, the Drucker's postulate and the theory of internal variables, the incremental constitutive relations for damaged thermo-plastic materials are presented. Our constitutive relations are given with the incremental stress expressed by the incremental strain, and can cover plastic hardening behaviors, thermo-softening behaviors, damage softening behaviors and their coupling effects between each other. So they are very convenient for the use in dynamic problems. The thermo-softening effects of the material parameters are also considered in the constitutive relations. After giving the computational routine, applying our constitutive relations and the damage evolution equations to the problem of inside-explosively loaded steel tubes, we have completed the systematic numerical simulations for the deformation and fracture process of the 45~# steel tubes.Compared to each other, the computational results and the experimental ones are in reasonable and good agreement in the informations of the tubes' deformation procedure, fracture moment,fracture velocity, fracture strain and fracture strain rate and so on. This demonstrates that our constitutive relations, the damage function models and the computational method are correct and of academic and predical values. By changing the thickness of the tubes we have obtained the steel tubes' fracture curve ε_f-ε_f (fracture strain versus frature strain rate), which has a so called 'plastic peak' by Ivanov[3]. The computational results show that the steel tubes' fracture curve ε_f-ε_freaches its 'plastic peak' at about the strain rate ε_f = 7.6 × 10~4/s. The computational results also show that because of the combining effeCts of plastic flow, thermo-softening and damage-softening very high temperature about 550℃ ～990℃ can be reached, and the thermo-plastic instability may appear in the tubes, which indeed has been found in our experiments.
出处
《力学学报》
EI
CSCD
北大核心
1999年第4期442-449,共8页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金!19572064
关键词
变形
损伤
破坏规律
圆管
内爆炸载荷
deformation, damage, fracture, circulax tubes, inside-explosive loading
