The Effects of Surface Elasticity on an Elastic Solid With Mode-III Crack: Complete Solution

被引:90
作者
Kim, C. I. [1 ]
Schiavone, P. [1 ]
Ru, C-Q [1 ]
机构
[1] Univ Alberta, Dept Mech Engn, Edmonton, AB T6G 2G8, Canada
来源
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME | 2010年 / 77卷 / 02期
基金
加拿大自然科学与工程研究理事会;
关键词
crack-edge stress field analysis; elasticity; fracture mechanics; integro-differential equations; shear deformation; surface cracks; SINGULAR INTEGRODIFFERENTIAL EQUATION; CONFIGURATIONAL EQUILIBRIUM; INTERFACE STRESS; FRACTURE; CONTINUUM; HYPERELASTICITY; ELEMENTS; FIELDS; TIPS;
D O I
10.1115/1.3177000
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
We examined the effects of surface elasticity in a classical mode-III crack problem arising in the antiplane shear deformations of a linearly elastic solid. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. Complex variable methods are used to obtain an exact solution valid everywhere in the domain of interest (including at the crack tip) by reducing the problem to a Cauchy singular integro-differential equation of the first order. Finally, we adapt classical collocation methods to obtain numerical solutions, which demonstrate several interesting phenomena in the case when the solid incorporates a traction-free crack face and is subjected to uniform remote loading. In particular, we note that, in contrast to the classical result from linear elastic fracture mechanics, the stresses at the (sharp) crack tip remain finite.
引用
收藏
页码:1 / 7
页数:7
相关论文
共 25 条
[1]   Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture [J].
Abraham, FF ;
Broughton, JQ ;
Bernstein, N ;
Kaxiras, E .
EUROPHYSICS LETTERS, 1998, 44 (06) :783-787
[2]  
[Anonymous], 1971, Complex variable methods in elasticity
[3]   Dynamical fracture instabilities due to local hyperelasticity at crack tips [J].
Buehler, MJ ;
Gao, HJ .
NATURE, 2006, 439 (7074) :307-310
[4]   Atomistic and continuum studies of stress and strain fields near a rapidly propagating crack in a harmonic lattice [J].
Buehler, MJ ;
Gao, HJ ;
Huang, YG .
THEORETICAL AND APPLIED FRACTURE MECHANICS, 2004, 41 (1-3) :21-42
[5]   Hyperelasticity governs dynamic fracture at a critical length scale [J].
Buehler, MJ ;
Abraham, FF ;
Gao, HJ .
NATURE, 2003, 426 (6963) :141-146
[6]   Surface and interface stress effects on interfacial and nanostructured materials [J].
Cammarata, RC .
MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, 1997, 237 (02) :180-184
[7]  
Chakrabarti A, 1999, Z ANGEW MATH MECH, V79, P233, DOI 10.1002/(SICI)1521-4001(199904)79:4<233::AID-ZAMM233>3.0.CO
[8]  
2-6
[9]   Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress [J].
Duan, HL ;
Wang, J ;
Huang, ZP ;
Karihaloo, BL .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2005, 53 (07) :1574-1596