On fracture criteria for dynamic crack propagation in elastic materials with couple stresses

TL;DR

This paper investigates fracture criteria for dynamic crack propagation in elastic materials with microstructures using couple-stress elasticity theory, analyzing stability and energy release rates near the crack tip.

Contribution

It introduces a fracture analysis framework incorporating microstructural effects via couple-stress elasticity, including inertial effects and asymptotic solutions for dynamic crack propagation.

Findings

Derived the dynamic J-integral for couple-stress materials.

Compared Griffith and shear stress criteria for crack stability.

Analyzed the influence of microstructure on crack propagation.

Abstract

The focus of the article is on fracture criteria for dynamic crack propagation in elastic materials with microstructures. Steady-state propagation of a Mode III semi-infinite crack subject to loading applied on the crack surfaces is considered. The micropolar behavior of the material is described by the theory of couple-stress elasticity developed by Koiter. This constitutive model includes the characteristic lengths in bending and torsion, and thus it is able to account for the underlying microstructures of the material. Both translational and micro-rotational inertial terms are included in the balance equations, and the behavior of the solution near to the crack tip is investigated by means of an asymptotic analysis. The asymptotic fields are used to evaluate the dynamic J-integral for a couple-stress material, and the energy release rate is derived by the corresponding conservation law. The propagation stability is studied according to the energy-based Griffith criterion and the obtained results are compared to those derived by the application of the maximum total shear stress criterion.