Bending strength degradation of a cantilever plate with surface energy due to partial debonding at the clamped boundary  

作　　者：Zhenliang HU Xueyang ZHANG Xianfang LI 

机构地区：[1]School of Civil Engineering,University of South China,Hengyang 421001,Hunan Province,China [2]School of Civil Engineering,Central South University,Changsha 410075,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2024年第9期1573-1594,共22页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.12372086,12072374,and 12102485)。

摘　　要：This paper investigates the bending fracture problem of a micro/nanoscale cantilever thin plate with surface energy,where the clamped boundary is partially debonded along the thickness direction.Some fundamental mechanical equations for the bending problem of micro/nanoscale plates are given by the Kirchhoff theory of thin plates,incorporating the Gurtin-Murdoch surface elasticity theory.For two typical cases of constant bending moment and uniform shear force in the debonded segment,the associated problems are reduced to two mixed boundary value problems.By solving the resulting mixed boundary value problems using the Fourier integral transform,a new type of singular integral equation with two Cauchy kernels is obtained for each case,and the exact solutions in terms of the fundamental functions are determined using the PoincareBertrand formula.Asymptotic elastic fields near the debonded tips including the bending moment,effective shear force,and bulk stress components exhibit the oscillatory singularity.The dependence relations among the singular fields,the material constants,and the plate's thickness are analyzed for partially debonded cantilever micro-plates.If surface energy is neglected,these results reduce the bending fracture of a macroscale partially debonded cantilever plate,which has not been previously reported.

关 键 词：micro/nanoscale cantilever plate partially debonded bending fracture singular integral equation oscillatory singularity 

分 类 号：O346.1[理学—固体力学]