Fracture analysis in micropolar elasticity: mode-I crack

Abstract

Micropolar elasticity theory links together the macro mechanical behavior and the micro geometrical scales and makes it possible to study the macro and micro fracture of micro-structural materials by classical methods. The present work aims at comparing the effects of micropolarity on the fracture parameters of a micro-crack and a macro-crack. Through Fourier integral transform, the problem of a mode-I crack in an infinite micropolar plane is reduced as a system of Cauchy singular integral equations, which are further solved numerically by the Lobatto–Chebyshev collocation method. Parametric studies on the numerical solutions of the force stress and couple stress intensity factors indicate that: the fracture behavior of the micropolar material depends on not only micropolar parameters but also the loading; when the force traction is applied, the micropolar material with a micro-crack behaves more softly than classical elastic materials, but the micropolar material with a macro-crack behaves more stiffly than the classical case. It is concluded that the micropolarity is beneficial to reducing the driving force of a micro-crack, but it may also enhance the driving force of a macro-crack meanwhile.