脆性材料损伤的概率统计模型研究

A Statistical Damage Model of Brittle Materials

假设脆性材料的强度服从 Weibull统计分布 ,用圆盘扁平裂纹模型模拟材料中的微缺陷 ,运用断裂力学知识和统计理论 ,推导出了在任意应力状态下材料的损伤概率统计模型 ,并讨论了不同应力状态下材料损伤量的大小关系 ,以及损伤量与材料的体积和材料性能参数之间的关系 :在拉应力状态下 ,损伤量的大小满足 D(σ,σ,σ) >D(0 ,σ,σ) >D (σ,0 ,0 ) ;在压应力状态下 ,损伤量的大小关系则为 D(-σ,0 ,0 ) >D(0 ,-σ,-σ) >D (-σ,-σ,-σ) ;结构的受力体积V增大 。

Assuming that the brittle materials′ strength satisfies Weibull′s distribution, a statistical damage model of brittle materials developed by means of selecting penny shaped crack models to simulate the defects in the materials and using statistical fracture theory. The relations of the damages under different stress states and that of the damages with the material′s parameters are discussed. Under tensile stress states, the damage satisfies the following relation:D(σ,σ,σ)>D(0,σ,σ)>D(σ,0,0); Under compression stress states, the relation is: D(-σ,0,0)>D(0,-σ,-σ)> D(-σ,-σ,-σ); The greater the volume of the materials stressed, the greater the damage.