Stress intensity factor analysis of interface cracks using X‐FEM

Abstract

SUMMARYThe extended ÿnite element method (X-FEM) proposed by Belytschko et al. (International Journal for Numerical Methods in Engineering 1999; 45:602;1999; 46:131; 50:993) uses interpolation functions based on the concept of partition of unity, and considers the asymptotic solution and the discontinuity of displacement ÿelds near a crack independently of the ÿnite element mesh. This paper describes the application of X-FEM to stress analyses of structures containing interface cracks between dissimilar materials. In X-FEM, an interface crack can be modelled by locally changing an interpolation function in the element near a crack. The energy release rate should be separated into individual stress intensity factors, K 1 and K 2 , because the stress ÿeld around the interface crack has mixed modes coupled with mode-I and mode-II. For this purpose, various evaluation methods used in conjunction with numerical methods such as FEM and BEM are reviewed. These methods are examined in numerical examples of elastostatic analyses of structures containing interface cracks using X-FEM. The numerical results show that X-FEM is an e ective method for performing stress analyses and evaluating stress intensity factors in problems related to bi-material fractures.

The extended/generalized finite element method: An overview of the method and its applications

“…Since the early works, the stress intensity factors have been computed by the domain form of the J-integral, [75,32,52,79]. Liu et al [68] proposed a direct evaluation of the stress intensity factors, based on enrichment functions expressed in terms of stress intensity factors.…”

Investigation on Fracture Mechanisms and Crack Propagation Process of Natural Rock-Concrete Interface

“…To measure the initial load, four stain gauges were attached vertically in front of the precast notch on the both sides of specimen, and the distance of two strain gauges was 10 mm. The experimental setup for TPB test is shown in The displacement extrapolation method [5] was used to calculate the stress intensity factors (SIFs) K 1 and K 2 of bi-materials interface crack through relative crack surface displacements δ x and δ y. It should be noted that stress intensity factors K 1 and K 2 can be denoted as ini 1 K and ini 2 K , which are the initial fracture toughness, when δ x and δ y are caused by initial load.…”

BEMs to evaluate interface cracks

“…In the case of bimaterial interface cracks, the complex SIFs, gained by dint of the displacement correlation technique, are related by (see [18]…”

“…It has been demonstrated that a global strain of 1% already integral methodology is grounded on the superposition of two equilibrium states, formulated by the current problem and a set of auxiliary known solutions. The procedure has been recently announced in a number of papers using FEM to calculate stress intensity factors along three-dimensional interface cracks [8,9]. In the field of fracture mechanics the solution to the applications of very interest is facilitated by using a multi-domain technique grounded on the boundary contour method [15].…”