Int J Fract (2009) 158:99–105 DOI 10.1007/s10704-009-9351-6 ORIGINAL PAPER Simulation of damage evolution in discontinously reinforced metal matrix composites: a phase-field model S. B. Biner · S. Y. Hu Received: 4 September 2008 / Accepted: 20 April 2009 / Published online: 12 May 2009 © Springer Science+Business Media B.V. 2009 Abstract In this study, a phase-field model is intro- duced to model the damage evolution, due to particle cracking in reinforced composites in which matrix deformation is described by an elastic-plastic constitutive law exhibiting linear hardening behavior. In order to establish the viability of the algorithm, the simulations are carried out for crack extension from a square hole in isotropic elastic solid under the complex loading path, and composites having the same volume fraction of reinforcements with two different particle sizes. The observed cracking patterns and development of the stress-strain curves agree with the experimen- tal observations and previous numerical studies. The algorithm offers significant advantages to describe the microstructure and topological changes associated with the damage evolution in comparison to conventional simulation algorithms, due to the absence of formal meshing. Keywords Metal matrix composites · Phase-field model · Damage · Simulation S. B. Biner (B ) Ames Laboratory, Iowa State University, Ames, IA 50011, USA e-mail: sbbiner@iastate.edu S. Y. Hu Pacific Northwest National Laboratory, Richland, WA 99352, USA 1 Introduction The metal matrix composites may offer significant advantages over conventional alloys in terms of their specific stiffness, better fatigue properties, and in some cases, better toughness and resistance to wear. It is now well established that in composite systems in which matrix deforming with a nonlinear behavior (e.g. elas- toplastic, viscoplastic), the dominant damage mecha- nisms leading to failure are: Brittle failure of the reinforcements, interfacial debonding between the rein- forcements and the matrix, and ductile failure of the matrix by nucleation, growth and coalescence of voids (Gungor and Liaw 1991; Suresh et al. 1993; Chawla and Chawla 2006). These damage mechanisms have been extensively studied by well-known constitutive models of void growth (Gurson 1975; Needleman and Tvergaard 1987; Tvergaard and Needleman 1995) and cohesive zone models (Needleman 1990) within the framework of FEM, for example as given in references (Llorca et al. 1991; Biner 1994; Llorca and Gonzalez 1998; Bohm and Han 2001; Drabek and Bohm 2006; Segurado and Llorca 2006). In this study, an alternative approach, based on the phase-field model, is introduced to elucidate the mech- anisms of damage evolution due to particle cracking in metal matrix composite systems. The algorithm offers significant advantages to describe the microstructure and topological changes associated with the damage evolution in comparison to conventional simulation 123