Antiplane shear crack in a functionally graded material strip with surface elasticity

• Published in: Archive of applied mechanics (1991) Vol. 91; no. 7; pp. 3035 - 3052
• Main Authors: Yang, Ying, Ma, Wei-Li, Hu, Zhen-Liang, Li, Xian-Fang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2021; Springer Nature B.V
• Subjects: Chebyshev approximation; Classical Mechanics; Crack tips; Differential equations; Displacement; Elasticity; Engineering; Fourier transforms; Functionally gradient materials; Galerkin method; Linear equations; Mathematical analysis; Mechanical properties; Original; Shear modulus; Stress intensity factors; Strip; Theoretical and Applied Mechanics; Mode III crack; Soft-core structure; Stress intensity factor; Surface elasticity; Functionally graded materials
• ISSN: 0939-1533; 1432-0681
• DOI: 10.1007/s00419-021-01948-8

When the dimension of a structure falls to the micro-/nanoscale, surface effect is significant and plays a key role in affecting the mechanical behavior. This article studies the influence of surface elasticity on the stress intensity factor of an antiplane shear crack embedded in an elastic strip made of functionally graded materials. Surface elasticity is applied on the strip surfaces and crack faces, and classic elasticity is invoked for the strip interior. An antiplane shear crack problem is solved for a symmetric FGM with a crack parallel to the strip surfaces. The associated problem is converted to a hypersingular integro-differential equation for the out-of-plane displacement on the crack faces through the Fourier transform and then to a singular integro-differential equation with Cauchy kernel. The Galerkin method is applied to expand the crack face displacement as a Chebyshev series, and the singular integro-differential equation reduces to a system of algebraic linear equations. Stress intensity factors at the crack tips and the out-of-plane displacement on the crack faces are calculated numerically. It is found that surface elasticity and gradient index strongly alter the bulk stress and its intensity factors near the crack tips. Positive surface shear modulus decreases the mode III stress intensity factors and negative surface shear modulus has an opposite behavior. The influence of the variation of material gradient on the mode III stress intensity factors is expounded in graph.