双轴压力下的压缩损伤变量  

Compressive damage variable under biaxial compression

作　　者：崔崧[1,2] 吕嫣[1,2] 李慧玲[1,2,3] CUI Song;LYU Yan;LI Huiling(College of Physical Science and Technology,Shenyang Normal University,Shenyang 110034,China;Ray Instrumentation Engineering Technology Research Center of Liaoning Province,Shenyang Normal University,Shenyang 110034,China;School of Physics,University of Electronics Science and Technology of China,Chengdu 611731,China)

机构地区：[1]沈阳师范大学物理科学与技术学院,沈阳110034 [2]沈阳师范大学辽宁省射线仪器仪表工程技术研究中心,沈阳110034 [3]电子科技大学物理学院,成都611731

出　　处：《沈阳师范大学学报（自然科学版）》2018年第4期301-304,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金青年科学基金资助项目(11703018);辽宁省教育厅科学研究项目(L2014442)

摘　　要：损伤力学主要研究材料内部的微缺陷的形成和演化对各项机械性能的影响。对于脆性材料,其内部的各微裂纹的形状、大小和方向的分布是杂乱无章的,因此在复杂加载条件下会表现出非常复杂的力学行为。其中,各微裂纹面是否闭合,以及闭合裂纹面间的正应力和剪应力数值上的差异,是造成这种复杂性的原因之一。解决这类问题,可以从分析闭合裂纹间的正应力出发,在弹性力学理论的基础上,考虑一个含裂隙的受双轴压力的代表性单元,通过分析裂纹面上的正应力的影响,利用某种平均化方法得到单元体在边界和裂纹面上的平均位移,从而推导出该单元在双轴压力下的应力应变本构关系以及对应的损伤变量。计算结果表明,与侧压有关的裂纹面间的正应力对受压缩时材料的损伤变量数值,以及承载能力均有一定程度的影响。Damage mechanics mainly study the effect of formation and evolution of micro defects on mechanical properties.For brittle materials,the shape,size and orientation of each micro crack inside are scattered.Therefore,complex mechanical behaviors are observed under complex loading conditions.Among them,whether the micro crack surfaces are closed or not,and the difference of normal stress and shear stress in the closed crack surfaces is one of the reasons for the complexity.To solve such problems,we can start with analyzing the normal stress between closed cracks,and based on the theory of elasticity,a representative unit under biaxial compression is considered.By analyzing the influence of the normal stress on the crack surface,the average displacement of the element on the boundary and the crack surface is obtained by some averaging method.Thus the stress-strain constitutive relation of the element under biaxial compression and the corresponding damage variable are derived.The calculate results show that the normal stress between the cracks related to the lateral pressure can has some effect on the damage variable and the load-bearing ability of materials under compression.

关 键 词：损伤力学 裂纹面 弹性力学 双轴压力 损伤变量 

分 类 号：O343.1[理学—固体力学] O341[理学—力学]