脆性材料统计断裂判据的研究

STUDY ON CRITERION OF STATISTICAL FRACTURE FOR BRITTLE MATERIALS

基于统计断裂理论,用分币裂纹模型模拟脆性材料中的缺陷,通过用裂纹面的法向矢量反映材料中裂纹面的随机取向,用"等效应力"等效实际应力状态的破坏效应,提出了多轴应力状态下脆性材料统计断裂的判据。本判据反映了结构的破坏强度与其所受的应力状态、破坏概率及材料的性能参数之间的联系关系。通过本判据可推导得到如下结论:1)在压应力状态下:围压越大,材料的强度就越大;裂纹面之间的摩擦系数越大,材料的强度越大;2)受载体积越大,材料的强度就越低。这些结论均与当前研究成果相一致。最后用本判据的预测与实验数据进行比较,结果较吻合。

The criterion of statistical fracture for brittle materials under multi-axial stress is developed based on statistical fracture theory. In this criterion, the penny-shaped crack model is selected to simulate the defects in brittle material, the normal vector of the crack＇s plan is used to describe the random direction of the crack＇s plan in the material, and the effective stress is employed to represent the stress state. The criterion describes the relationship between the ultimate strength, stress state, failure probability and material＇s property coefficients. According to the criterion, the following conclusions can be drawn： 1） Under multi-axial compressive stress states, the greater the confining pressure is, the greater the ultimate strength is; the greater the friction factor of the crack＇s plan is, the greater the ultimate strength is; 2） The greater the volume stressed is, the less the ultimate strength is. Theses conclusions are consistent with current study results. The predicted results by this criterion are in good agreement with the test data.