含随机分布裂纹材料的拉压模量  

Tensile and compressive modulus of materials with randomly distributed cracks

作　　者：崔崧[1,2] 吕嫣[1,2] 陈岚峰[1,2] CUI Song;LUY Yan;CHEN Lanfeng(College of Physics Science and Technology,Shenyang Normal University,Shenyang 110034,China;Ray Instrumentation Engineering Technology Research Center of Liaoning Province,Shenyang Normal University,Shenyang 110034,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

出　　处：《沈阳师范大学学报(自然科学版)》2024年第6期510-513,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)。

摘　　要：拉压性能是材料机械性能中的一项重要指标。对于脆性材料来说,其拉伸性能与压缩性能存在着显著的差异,其中包括:当脆性材料内部分布有微细观裂纹时,其宏观压缩弹性模量会显著地大于拉伸弹性模量。这是因为,材料在受到拉伸时,其内部的微裂纹总是张开的,裂纹面上没有承载能力;而材料在受到压缩时,其内部的微裂纹大部分都是闭合的,这些闭合裂纹面上能够同时承载不同程度的压应力和剪应力。为了验证这一点,设计了一套计算方法,考虑一个远端受拉伸或压缩载荷的无限大薄板,其内部含有大量的具有某种随机分布的微裂纹。在薄板中取一体积元,体积元由很多个局部代表性单元组成,每一个代表性单元都包含一条微裂纹。利用弹性力学中的复变函数法,求出每一个局部代表性单元的正应力和正应变,再应用统计和平均化方法,求出体积元的正应力和正应变,进而求出体积元的拉压模量。计算结果表明,脆性材料的拉压模量的表现符合预期。Tensile and compressive performance is an important indicator of material mechanical properties.For brittle materials,there are significant differences between their tensile and compressive properties,including:when there are micro-cracks distributed inside the brittle material,its macroscopic compressive elastic modulus will be significantly greater than the tensile elastic modulus.This is because when the material is subjected to tension,the internal micro-cracks always open,and there is no load-bearing capacity on the crack surface;When the material is compressed,most of the internal micro-cracks are closed,and these closed crack surfaces can simultaneously bear different degrees of compressive and shear stress.To verify this,a calculation method can be designed to consider an infinitely large thin plate subjected to tensile or compressive loads at the far end,which contains a large number of micro-cracks with some random distribution inside.Then,a volume element is taken from the thin plate,which is composed of many locally representative elements,and each representative element contains a micro-crack.By using the complex function method in elasticity,the normal stress and strain of each locally representative element can be calculated.Then,statistical and averaging methods can be applied to calculate the normal stress and strain of the volume element,and finally the tensile and compressive modulus of the volume element.The calculation results indicate that the performance of the tensile and compressive modulus of brittle materials is in line with expectations.

关 键 词：脆性材料 拉压模量 随机分布 弹性力学 

分 类 号：O343.1[理学—固体力学] O341[理学—力学]