Micromechanical modeling of damage in periodic composites using strain gradient plasticity Reza Azizi ⇑ Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark article info Article history: Received 13 September 2011 Received in revised form 10 April 2012 Accepted 24 April 2012 Keywords: Damage Cohesive zone model Metal matrix composite Strain gradient plasticity abstract Damage evolution at the fiber matrix interface in Metal Matrix Composites (MMCs) is stud- ied using strain gradient theory of plasticity. The study includes the rate independent for- mulation of energetic strain gradient plasticity for the matrix, purely elastic model for the fiber and cohesive zone model for the fiber–matrix interface. For the micro structure, free energy holds both elastic strains and plastic strain gradients. Due to the gradient theory, higher order boundary conditions must be considered. A unit cell with a circular elastic fiber is studied by the numerical finite element cell model under simple shear and trans- verse uniaxial tension using plane strain and periodic boundary conditions. The result of the overall response curve, effective plastic strain, effective stress and higher order stress distributions are shown. The effect of the material length scale, maximum stress carried by the interface and the work of separation per unit interface area on the composites over- all behavior are investigated. The results are compared with those for strong interface. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction The increasing application of reinforced Metal Matrix Composites (MMCs) is due to the improved properties like high stiffness, high tensile strength, creep resistance, wear resistance, low density and damping capabilities. These useful prop- erties are accessible with the cost of poor ductility and fracture properties. Therefore, a comprehensive knowledge of all types of the properties is necessary, which requires an understanding of both constitutive and failure behaviors. Several works have studied the perfectly bonded reinforced metal matrix composites (e.g. [19,2]). However, experimental evidences show the availability of damage upon deformation in composites by debonding at the fiber–matrix interface, particle frac- ture and void growth in the matrix (e.g. [26,21]). The most notoriously critical area for the growth of the crack is fiber–matrix interface. One of the widely used method in the literature for simulation of the interfacial debonding in composites is the cohesive zone model. The idea for the cohesive model is based on the consideration that the damage analysis knows the exis- tence of the crack in advance. In MMCs, fiber–matrix interface appears to be a critical region for the damage and a reasonable presuppose for the cohesive elements as was shown by Niordson and Tvergaard [20] and Legarth and Niordson [14]. Several cohesive zone models have been developed to face different type of crack propagation (e.g. [24,27]). Xu and Needleman [27] used polynomial and exponential types of traction separation equations to study the void nucleation at the interface of par- ticle and matrix metal. Tvergaard [24] extended the Needleman [17] model of pure normal separation to both normal and tangential separation. Tvergaard and Hutchinson [25] used a trapezoidal shape of the traction separation model to calculate the crack growth resistance in elastic–plastic materials. 0013-7944/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engfracmech.2012.04.033 ⇑ Corresponding author. E-mail address: reaz@mek.dtu.dk Engineering Fracture Mechanics 92 (2012) 101–113 Contents lists available at SciVerse ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech