Stress Intensity Factors For Interface Crack Research Articles

XFEM with high-order material-dependent enrichment functions for stress intensity factors calculation of interface cracks using Irwin’s crack closure integral

This paper presents a high-order extended finite element method (XFEM) with a novel set of material-dependent enrichment functions for the linear elastic analysis of bimaterial interface cracks. With the proposed material-dependent high-order enrichment functions, highly accurate near-tip displacement and stress fields can be obtained for arbitrary material combinations. The aim of this contribution is the direct evaluation of the complex stress intensity factors (SIFs) of interface cracks based on Irwin’s crack closure integral. To this end, a closed-form SIF formulation in terms of the enriched degrees of freedom is derived by matching the leading term in the XFEM with an analytical expression of Irwin’s integral. Hence, the SIFs of interface cracks can be directly obtained upon the solution of the XFEM discrete system without cumbersome post-processing requirements.The performance of the proposed method is validated on several benchmark examples involving straight and curved interface cracks. In particular, we examine the effect of enrichment order, mesh refinement, bimaterial mismatch, crack tip position, and integration limit of Irwin’s integral. The method is shown to work well on all examples, giving accurate SIF results. Furthermore, while the popular interaction integral method requires special auxiliary fields for curved interface cracks and also needs cracks to be sufficiently apart from each other in settings with multiple cracks, none of these limitations are required by the proposed approach.

Effect of arbitrary bi‐material combination and bending loading conditions on stress intensity factors of an edge interface crack

PurposeThe purpose of this paper is to compute the stress intensity factors (SIFs) of single edge interface crack for arbitrary material combinations and various relative crack lengths, and compare with those for the bonded plates subjected to tensile loading conditions. It aims to discuss the results of the shallow edge interface crack on the basis of the singular stress near the free‐edge corner without the crack.Design/methodology/approachIn this study, the SIFs of interface crack in dissimilar bonded plates subjected to bending loading conditions are analyzed by the finite element method and a post‐processing technique. The use of post‐processing technique of extrapolation reduces the computational cost and improves the accuracy of the obtained result.FindingsThe empirical expressions are proposed for evaluating the SIFs of arbitrary material combinations.Originality/valueEmpirical functions can be used to obtain the SIFs for arbitrary material combinations for the bending loading conditions easily. It is very convenient for engineering application.

Accurate Determination of Stress Intensity Factor for Interface Crack by Finite Element Method

This paper presents the simple method to determine the complex stress intensity factor of interface crack problem by the finite element method. The proportional method is extended to the interface crack problem. In the present method, the stress values at the crack tip calculated by FEM are used and the stress intensity factors of interface crack are evaluated from the ratio of stress values between a given and a reference problems. A single interface crack in an infinite bi-material plate subjected to tension and shear is selected as the reference problem in this study. The accuracy of the present analysis is discussed through the results obtained by other methods. As the result, it is confirmed that the present method is useful for analyzing the interface crack problem.

Modeling of interface cracks in fiber-reinforced composites with the presence of interphases using the boundary element method

An advanced boundary element method (BEM) with thin-body capabilities was developed recently for the study of interphases in fiber-reinforced composite materials (Y.J. Liu, N. Xu and J.F. Luo, Modeling of interphases in fiber-reinforced composites under transverse loading using the boundary element method, ASME J. Appl. Mech. 67 (2000) 41–49). In this BEM approach, the interphases are modeled as thin elastic layers based on the elasticity theory, as opposed to spring-like models in the previous BEM and some FEM work. In the present paper, this advanced BEM is extended to study the interface cracks at the interphases in the fiber-reinforced composites. These interface cracks are curved cracks between the fiber and matrix, with the presence of the interphases. Stress intensity factors (SIFs) for these interface cracks are evaluated based on the developed models. The BEM approach is validated first using available analytical and other numerical results for curved cracks in a single material and straight interface cracks between two materials. Then, the interface cracks at the interphases of fiber-reinforced composites are studied and the effects of the interphases (such as the thickness and materials) on the SIFs are investigated. As a special case, results of the SIFs for sub-interface cracks are also presented. It is shown that the developed BEM is very accurate and efficient for the interface crack analyses, and that the properties of the interphases have significant influences on the SIFs for interface cracks in fiber-reinforced composites.

Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under impact loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The integral transformation method and singular integral equation approach are used to get the solution. By virtue of the integral transformation method, the viscoelastic mixed boundary problem is reduced to a set of dual integral equations of crack open displacement function in the transformation domain. The dual integral equations can be further transformed into the first kind of Cauchy-type singular integral equation (SIE) by introduction of crack dislocation density function. A piecewise continuous function approach is adopted to get the numerical solution of SIE. Finally, numerical inverse integral transformation is performed and the dynamic SIF in transformation domain is recovered to that in time domain. The dynamic SIF during a small time-interval is evaluated, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.

An improved photo-elastic technique for determining the mixed-mode stress-intensity factors for interfacial cracks in a bi-material

Attempts to employ the photo-elastic technique to determine the complex stress-intensity factors of interfacial cracks in a bi-material reveal the weakness of the technique. This weakness is due to the large errors arising from the measurement of the coordinates of data points and fringe orders near the crack tip. In this paper, an improved photo-elastic approach is proposed to reduce the effects of the measurement errors. The results obtained by this modified method are compared with both a traditional photo-elastic solution and a theoretical solution derived from complex potentials. The comparison shows that the modified solution is in better agreement with the theoretical solution as compared with the traditional solution.