Finite Elements in Analysis and Design 43 (2007) 397 – 410 www.elsevier.com/locate/finel Modeling interfacial debonding and matrix cracking in fiber reinforced composites by the extended Voronoi cell FEM S. Li, S. Ghosh ∗ Department of Mechanical Engineering, The Ohio State University, Columbus, OH, USA Received 10 October 2006; accepted 30 November 2006 Available online 24 January 2007 Abstract This paper introduces an extended Voronoi cell finite element model (X-VCFEM) for modeling the initiation and propagation of interfacial debonding and matrix cracking in fiber reinforced composite materials. Bilinear and linear cohesive zone models are added for representing interfacial debonding and matrix crack propagation, respectively. A series of criteria based on cohesive zone models are proposed for assessing the direction of damage development, which includes the crack propagation in matrix and its deflection behavior at an interface. Comparisons of X-VCFEM simulations with reference results validate the effectiveness of this new model. The capability of predicting the development of microcracks in composites is of great importance to the design and evaluation of structure. Effect of stereographic features such as size and shape of heterogeneities on damage evolution is also discussed. 2007 Elsevier B.V. All rights reserved. Keywords: The extended Voronoi cell finite element method (X-VCFEM); Cohesive zone models; Interfacial debonding; Matrix cracking 1. Introduction Interfacial debonding and brittle-matrix cracking are two im- portant damage phenomena in fiber-matrix composites. Numer- ical simulation of the growth and interaction of the two kinds of damages is a challenging topic due to various kinematic and morphological complexities. Conventional finite element approaches suffer from very slow convergence since the ele- ment formulation does not account for high gradients and sin- gularities from heterogeneities and damages. Various methods have been proposed for improving the effectiveness of compu- tational methods in modeling damages in composites [1–11]. However, most of these analyses are limited to only one of the two damages analysis. The Voronoi cell finite element method (VCFEM), developed on the principles of the assumed stress hybrid FEM formulation [6,12], has had considerable success in the micromechanical analysis of multi-phase heterogeneous materials [13–20]. The extended Voronoi cell finite element model (X-VCFEM) has ∗ Corresponding author. Tel.: +1 614 292 2599; fax: +1 614 292 7369. E-mail address: [email protected] (S. Ghosh). 0168-874X/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.finel.2006.11.010 been developed by incorporating the cohesive crack propaga- tion model and special stress functions in VCFEM [13,19,20] to model interfacial debonding in composites and crack prop- agation in homogenous materials. Computational efficiency of X-VCFEM is substantially higher than many conventional FE models. This paper discusses how to combine interfacial decohe- sion and matrix cracking models based on X-VCFEM for fiber-reinforced composite microstructures. The improved X-VCFEM is developed for modeling both the growth of in- terfacial debonding and the propagation of multiple cohesive cracks in the brittle-matrix composites. Researches regarding a crack meeting a bimaterial interface to either grow along the interface or branch into the next layer were made in [21–24], where the criterion of deflection was established based on the energy release rate and fracture energy. However, the present research is aimed at only elastic cases, which requires that the fracture process zone at the crack tip is small compared to the size of the crack and the size of the specimen. In this paper, a criterion based on cohesive zone models is proposed for assessing the crack growth at the bifurcation point, at which position the cracks branch into matrix from interface.
Modeling interfacial debonding and matrix cracking in fiber reinforced composites by the extended Voronoi cell FEM
May 17, 2023
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