Micromechanical analysis of thermoelastoplastic behavior of metal matrix composites Tian Tang ⇑ , M.F. Horstemeyer, Paul Wang Center for Advanced Vehicular Systems, Mississippi State University, United States article info Article history: Received 23 August 2011 Accepted 13 October 2011 Available online 8 November 2011 Keywords: Thermo-elasto-plastic behavior Instantaneous elasto-plastic matrix Instantaneous thermal stress tensor Metal matrix composite materials Variational asymptotic method abstract A micromechanics model based on the variational asymptotic method for periodic compos- ites was developed using an incremental formulation to capture the coupled thermo- elasto-plastic behavior of metal matrix composites. Taking advantage of the small size of the microstructure, a variational statement of the unit cell through an asymptotic expan- sion of an functional of energy change was formulated to calculate the effective instanta- neous tangential elasto-plastic matrix and thermal stress matrix of the composite materials. An iterative homogenization and localization technique was proposed to simulate the nonlinear thermo-elasto-plastic behavior of metal matrix composites. This model was implemented using the finite element method. For validation, a numerical example was examined to demonstrate the application and accuracy of this theory and companion code. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Due to their high stiffness, high strength, better fatigue resistance, and better elevated temperature properties over con- ventional materials, metal matrix composites (MMCs) have been widely used in aerospace, automotive, energy applica- tions, etc. In these various uses, MMCs are subjected to not only the mechanical loading, but also thermal changes. Due to a large discrepancy between the coefficient of thermal expansion (CTEs) of the metal matrix itself and the integrated reinforcement material of the composite, thermomechanical loading generates the local thermal stresses, in turn leading to elasto-plastic behavior significantly different from that of stress free state. In addition, the thermal stresses exert dual but contradictory effects on the mechanical behavior of MMCs; namely, they may either strengthen the composites or cause premature failure (Sayman, Akbulut, & Meric, 2000). To improve the design and performance of MMCs, it is partic- ularly important to get better understanding of how the thermal stresses affect the mechanical behavior of MMCs under external loading. Numerous models have been constructed to analyze the effective thermoelastoplastic behavior of MMCs. Kennedy, Moel- ler, and Steven Johnson (1990) derived a constitutive equation for fiber MMCs using a vanishing fiber diameter model. Aboudi (1985a, 1985b, 1985c) employed his method of cell to investigate the thermal-inelastic behavior of MMCs. Pettermann, Plankensteiner, Böhm, and Rammerstorfer (1999) developed a thermo-elasto-plastic constitutive law using an incremental Mori–Tanaka mean field approach. They extended their approach to account for large strains by means of co-rotational Cauchy stresses and logarithmic strains (Pettermann, Huber, Luxner, Nogales, & Böhm, 2010). Finite element method was also used to investigate elasto-plastic thermal stresses in a MMCs (Seo & Kang, 1998; Sen & Sayer, 2006). 0020-7225/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijengsci.2011.10.008 ⇑ Corresponding author. Tel.: +1 662 325 9222. E-mail address: tian.tang@aggiemail.usu.edu (T. Tang). International Journal of Engineering Science 51 (2012) 161–167 Contents lists available at SciVerse ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci