Fatigue Crack Growth of a Mixed Mode Three-Dimensional Crack : 1st Report, Analysis of Stress Intensity Factors of Mixed Mode Three-Dimensional Cracks Based on the J-Integral Concept

Abstract

A method for the determination of stress intensity factors for an arbitrarily mixed mode three-dimensional crack has been developed based on the J-integral concept. J-integral for a mixed mode three-dimensional crack is expressed in the form of J=J_I(Γ)+J_II(Γ)+J_III(Γ)+J₀(Γ), where J_I(Γ), J_II(Γ), J_III(Γ) are the path-dependent line integrals equivalent to the components of mode I, mode II and mode III deformation, respectively, and J₀(Γ) is the surface integral due to the three-dimensional effect. In linear elastic material, the stress intensity factors, K_I, K_II and K_III are determined by J_I, J_II(Γ), and J_III(Γ), which are obtained by extrapolating J_I(Γ), J_II(Γ), J_III(Γ) to the crack front. This method has been applied to obtain the stress intensity factors of mode I and mixed mode three-dimensional cracks in several cases. The numerical calculation was made using the finite element method.