含裂纹脆性材料的拉压模量  

Tensile and compressive modulus of brittle materials containing crack

作　　者：崔崧[1,2] 吕嫣[1,2] 陈岚峰[1,2] CUI Song;LYU Yan;CHEN Lanfeng(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)

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）》2023年第4期289-292,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：脆性材料在承受拉伸和压缩时,其机械性能会显示出较大的差异性。这种差异性体现在2个方面:1)脆性材料的抗压强度(强度极限)远远高于抗拉强度;2)含缺陷的脆性材料在受压时,由于裂纹面的闭合效应和摩擦效应,其有效压缩模量会显著地高于有效拉伸模量。为了考察含缺陷脆性材料的拉压模量的差异,可以考虑一个远端受拉伸或压缩应力的无限大薄板,分析在其上截取的一个含一条任意方向裂纹的单元。采用弹性力学理论中的复变函数法,得到代表性单元边界处各点的位移和应力,再通过平均化法,得到作用在单元边界上的正应变和正应力,从而求出单元的有效拉压模量。分析表明,薄板远端受拉伸时,单元内的裂纹始终处于张开状态;远端受压时,裂纹大多情况下处于闭合状态,闭合时裂纹面上的正应力与裂纹方向有关,从而影响了有效压缩模量。计算结果很好地符合了预期。Brittle materials exhibit significant differences in mechanical properties when subjected to tension and compression.This difference is reflected in two aspects:one is that the compressive strength(strength limit)of brittle materials is much higher than the tensile strength;another issue is that brittle materials containing defects,when subjected to compression,have significantly higher effective compressive modulus than effective tensile modulus due to the closure effect and friction effect of the crack surface.In order to investigate the differences in tensile and compressive modulus of brittle materials with defects,an infinite thin plate subjected to tensile or compressive stress at the far end can be considered.An element containing a crack in any direction cut from it can be analyzed,and the displacement and stress at each point at the boundary of the representative element can be obtained using the complex function method in elasticity;then,the normal strain and stress acting on the element boundary can be obtained through the averaging method;thus,the effective tensile and compressive modulus of the element can be determined.The analysis shows that when the thin plate is stretched at the far end,the cracks within the element are always in an open state.When subjected to remote compression,cracks are mostly in a closed state,and the normal stress on the crack surface in a closed state is related to the direction of the crack,thereby affecting the effective compression modulus.The calculated results are in good agreement with expectations.

关 键 词：拉压模量 弹性力学 复变函数法 闭合效应 摩擦效应 

分 类 号：O343.1[理学—固体力学] O341[理学—力学]