Investigation of mixed-mode stress intensity factors for nonhomogeneous materials using an interaction integral method

Abstract

a b s t r a c tAn interaction (energy) integral is derived for the computation of mixed-mode stress intensity factors (SIFs) in nonhomogeneous materials with continuous or discontinuous properties. This method is based on a conservation integral that relies on two admissible mechanical states (actual and auxiliary fields). In general, the interaction energy contour integral is converted into an equivalent domain integral in numerical computations. It can be seen from the equivalent domain integral, the integrand does not involve any derivatives of material properties. Moreover, the formulation can be proved valid even when the integral domain contains material interfaces. Therefore, it is not necessary to limit the material properties to be continuous for the present method. Due to these advantages the application range of the interaction integral method can be greatly enlarged. The numerical implementation of the derived expression is combined with the extended finite element method (XFEM). Using this method, the influences of material properties on the mixed-mode SIFs are investigated for four types of material properties selected in this work. Numerical results show that the mechanical properties and their first-order derivatives can affect mode I and II SIFs greatly, while the higher-order derivatives affect the SIFs very slightly.

Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant of EFG Method

“…Such a case study was reported earlier in [74]. The observations in the SIF variation, for both the cases, are consistent with the results of reference [58]. The crack opening displacement ( COD v ) profiles, obtained using the proposed EFG method and FEM are compared in Fig.…”

“…The same interaction integral is also used to extract the T-stress with the help of different auxiliary functions [57]. A modified interaction integral [58] is used to extract mixed-mode SIFs for a crack when it is close to material interfaces.…”

“…3(b). This is given [58] In the case of an interface crack in bi-materials (Fig. 4) subjected to mechanical and thermal load, ΔT , the interaction integral [59] is given by …”

An experimental/numerical investigation into the main driving force for crack propagation in uni-directional fibre-reinforced composite laminae

“…The interested reader is referred to the review paper on stress intensity factor calculations within an XFE framework [43]. An important adaptation to the interaction integral was introduced in [44] for non-homogeneous, isotropic materials with arbitrarily continuous properties. This approach takes account of the difference in material properties between the crack tip and the Gauss points contained within the J-domain.…”

Dynamic stress intensity factors for homogeneous and non-homogeneous materials using the interaction integral method

“…It has been found that the J-integral and its related techniques play an important role in static fracture mechanics, which can be referenced to the article written by Yu et al [1]. In the case of dynamic fracture mechanics, Kishimoto et al [2] developed a modified J-integral, which involves the inertial effects to determine DSIFs in conjunction with the finite element method (FEM).…”