2种损伤变量之间关系的分析  

Analysis of the relationship between two damage variables

作　　者：崔崧[1,2] 吕嫣[1,2] 李惠玲 CUI Song;LÜYan;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）》2020年第6期495-498,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11703018);辽宁省教育厅科学研究经费项目(L2014442)。

摘　　要：损伤变量是损伤力学中的重要概念,反映了结构中微细观缺陷对材料宏观力学性能的影响。在受到拉伸和剪切2种不同载荷作用下,微细观缺陷对材料的拉伸和剪切的宏观影响程度是不同的,工程实际中通常引入拉伸和剪切损伤变量,分别描述其对材料拉伸模量和剪切模量的影响。这2种损伤变量均与微细观缺陷的微观基准有某种联系,因此它们之间必然有一定的关系而非相互独立。采用分析一个含1条裂纹的单元体的方法,令其分别承受拉伸和剪切2种载荷,用弹性力学理论中的复变函数法,通过分析单元体边界和裂纹面上的位移,得到拉伸和剪切2种损伤变量的表达式。再通过调整单元体和裂纹的尺寸以及数值分析等方法,得到2种损伤变量之间的函数关系。这种方法适用于分析脆性材料二维微裂纹损伤。Damage variable is an important concept in damage mechanics,which reflects the influence of micro defects on the macro mechanical properties of materials.Under the action of tensile and shear loads,the macro influence of micro defects on the tensile and shear properties of materials is different.In engineering practice,tensile and shear damage variables are usually introduced to describe the effects on the tensile modulus and shear modulus of materials respectively.The two kinds of damage variables are related to the micro datum of micro defects,so they must be related rather than independent.An element with one crack is analyzed,which is subjected to tensile and shear loads respectively.The expressions of tensile and shear damage variables are obtained by analyzing the displacements on the boundary of the element and the crack surface by using the complex function method in elastic theory.By adjusting the size of the element and crack,and using numerical analysis,the functional relationship between the two damage variables can be obtained.This method is suitable for the analysis of two-dimensional micro-crack damage in brittle materials.

关 键 词：损伤变量 拉伸 剪切 弹性力学 脆性材料 

分 类 号：O343.1[理学—固体力学] O341[理学—力学]