Failure criteria for multiply flawed anisotropic materials

Abstract

This study presents overall failure criteria for an infinite anisotropic solid containing multiple flaws subjected to a set of uniform applied loads. Based on the inclusion method, flaws are treated as elliptical inclusions where their elastic moduli are considered to be zero. The explicit expression of elastic fields is obtained for a cubic crystal multiply flawed solid through the use of the Mori-Tanaka mean field theory. The resulting expression is further utilized to find an interaction energy function between the applied loads and flaws. With this energy function, the energy release rates and critical stresses are acquired separately in a closed form for Mode I, II, and III. The closed forms for energy release rates and critical stresses reveal that they are a function of the aspect ratio and the volume fraction of flaws, the modes of the loading, and the material properties. As an illustrated numerical example, the energy release rates and the critical stresses that vary with both the aspect ratio and the volume fraction of the flaws in a cubic crystal material are discussed.