A direct method to extract strain energy release rates using XFEM and Irwin’s integral

An analytical formulation based on Irwin’s integral and combined with the extended finite element method is proposed to extract mixed-mode components of strain energy release rates in linear elastic fracture mechanics. High-order crack tip enrichment functions in XFEM allow for evaluation of integral quantities in closed form, resulting in a simple, accurate, and efficient method. Hence, SIFs can directly be obtained upon solution of the XFEM discrete system. Several benchmark examples on pure and mixed mode problems are studied, investigating the effects of the order of the enrichment, mesh refinement, and the length of crack extension. The numerical results show that high accuracy can be achieved on structured as well as unstructured meshes. Examples of a crack approaching a hole and two cracks approaching each other are also investigated. The latter illustrate the advantage of this method over a J-integral class of methods, as SIFs can still be calculated when cracks are in close proximity and no remeshing is required. Hence potentially this method can address crack coalescence and branching more rigorously

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

Numerical modeling of friction stir welded aluminum joints under high rate loading

Prediction of shear band formation and other strain localization processes presents many computational challenges that must be overcome to enable dynamic failure prediction and material design of ductile material systems. The current work presents a finite element based computational framework accounting for this critical deformation process, as applied to a detailed investigation of friction stir welded (FSW) aluminum joints. A stir welded joint has several zones, each with distinct microstructural characteristics and material properties. For applications in Army land vehicles, which may be subject to under-body blast, an understanding of the energy absorption capability of these joints is needed. Thus material inhomogeneity, dynamic loading, and detailed understanding of small scale failure processes must all be accounted for to accurately model FSW material behavior. In this study, an implicit nonlinear consistent (INC) or monolithic solution technique is used to predict shear band formation and estimate the energy absorption and failure strain of a stir welded aluminum joint. It has been shown that failure initiating at material interface regions can be predicted, and furthermore that abrupt material property gradients predominantly contribute to FSW joint failure. •We apply a nonlinear consistent finite element based method for predicting shear band formation.•Fundamental impact analysis cases are investigated for friction stir welded aluminum joints.•Results provide insight into the failure process and the effect of microstructure on response.•Failure generally initiates at material zone interfaces rather than process-weakened areas.•Results suggest the importance of manufacturing methods which minimize abrupt property changes

Fatigue failure theory for lithium diffusion induced fracture in lithium-ion battery electrode particles

To gain better insights into the structural reliability of lithium-ion battery electrodes and the nucleation as well as propagation of cracks during the charge and discharge cycles, it is crucial to enhance our understanding of the degradation mechanisms of electrode particles. This work presents a rigorous mathematical formulation for a fatigue failure theory for lithium-ion battery electrode particles for lithium diffusion induced fracture. The prediction of fatigue cracking for lithium-ion battery during the charge and discharge steps is an particularly challenging task and plays an crucial role in various electronic-based applications. Here, to simulate fatigue cracking, we rely on the phase-field approach for fracture which is a widely adopted framework for modeling and computing fracture failure phenomena in solids. The primary goal here is to describe a variationally consistent energetic formulation for gradient-extended dissipative solids, which is rooted in incremental energy minimization. The formulation has been derived as a coupled system of partial differential equations (PDEs) that governs the gradient-extended elastic-chemo damage response. Additionally, since the damage mechanisms of the lithium-ion battery electrode particles result from swelling and shrinkage, an additive decomposition of the strain tensor is performed. Several numerical simulations with different case studies are performed to demonstrate the correctness of our algorithmic developments. Furthermore, we investigate the effect of randomly distributed micro cavities (voids) and micro notches on fracture resistance