An improved numerical method for computation of stress intensity factors along 3D curved non-planar cracks in FGMs

Abstract

a b s t r a c tA simplified strategy based on the interaction energy integral is implemented in the finite element framework to evaluate mixed mode Stress Intensity Factors (SIFs) in 3D non-planar cracks. The proposed approach does not require any a priori information about crack front and crack surface curvatures, therefore different arbitrary non-planar cracks can be easily investigated. In particular, both conical and lensshaped cracks in homogeneous materials are considered as case studies in order to demonstrate the accuracy of the present approach. Finally, the computational strategy is extended to Functionally Graded Materials (FGMs) and the effect of graded material properties (Young's modulus and Poisson's ratio) on the SIFs is studied in detail.

Computing stress intensity factors for curvilinear cracks

“…The analysis of the term β S /r is similar to the one performed in (29), and thus ∂β S /∂r ∈ L 2 (B ρ (x t ); R 2×2 ) follows from the boundedness of g 1 and g 2 and (28a).…”

Determining the mixed mode stress intensity factors of surface cracks in functionally graded hollow cylinders

“…The implementation of domain integrals in the finite element framework is summarized in the appendix given at the end of this paper, while further details are given in our previous works [37,36,40]. It is emphasized that, as reported in [37], the interaction energy integral in domain form is not sensitive to the detail of mesh near the crack front. Therefore, the finite element mesh herein has been made using 20-noded brick elements (C3D20 4 ), and singular elements were not employed.…”

“…The third term in Eq. (4) is the interaction integral and is given as: The relation between interaction integral and stress intensity factors are given by [37]:…”

“…The finite element procedure employed herein to extract the SIFs is based on the extension of the interaction energy integral to graded materials. It was originally proposed by the authors in [36,37] to investigate the SIFs of 3D curved non-planar cracks, e.g. lens shaped and conical cracks.…”

“…To define the auxiliary fields the numerical procedure reported in[37] has been employed. Therefore, for further details interested readers are directed to that work.…”