A mode-I crack embedded in a prestressed material with microstructure

Abstract

This article studies a mode-I crack embedded in a material with microstructure and initial stress. The couple stress theory is adopted to analyze the mechanical behavior of a prestressed cracked medium. The governing equations and associated boundary conditions are derived. By using the Fourier transform, the mixed boundary-value problem associated with a mode-I crack is converted to two integral equations with weakly-singular and hypersingular kernels. The two integral equations are numerically solved by expanding the solution as a Chebyshev series. The convergence of the numerical solution is confirmed. The present results are capable of capturing the size-dependent behaviors through the characteristic length l. Introduction of l decreases the opening displacement and energy release rate. A tensile initial stress retards the crack to advance and vice versa. When the characteristic length and initial stress vanish, all the results reduce to the classical counterparts.