Application of the generalized method of cells principle to particulate-reinforced metal matrix composites
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I. INTRODUCTION
THE use of micromechanical modeling methods offers scope for focusing onto the more likely material and inclusion combinations in metal matrix composites (MMCs) and thus limiting the amount of experimentation necessary to produce suitable materials for the design purpose. Simultaneously, this method will allow more accurate predictions of the elastic behavior of any components and structures that might go into production. Numerous models have been reported in the literature for describing the elastic behavior of composites containing particulate reinforcements. The majority of the analytical estimates are based on Eshelby’s equivalent inclusion approach[1,2] and Hashin–Shtrikman formulations,[3,4] whereas most of the numeric work has used finite-element unit cell descriptions.[5,6] In addition, rigorous bounds for the overall elastic behavior of such materials are also available.[7] One microscale analysis approach that has proven to be quite accurate (in certain situations) for MMCs is that of finite-element analysis (FEA). Commercial FEA software packages, which allow the incorporation of arbitrary inelastic constitutive models for the metal matrix, have been used extensively with unit cell approaches to model MMCs. However, incorporation of inclusion effects such as the residual stresses, fiber-matrix debonding, and fiber breakage is difficult. Further, FEA-based approaches often require complex boundary conditions to be applied to the unit cell. This can make applying different types of loading combinations cumbersome. Finally, FEA unit cell approaches require a large number of elements, so if analysis of a number of fibers in a certain arrangement is desired, or if the composite being analyzed is a part of a larger structural problem, the FEA problem can quickly become intractable. The micromechanical model based on the generalized method of cells (GMC) provides mechanical properties of the composite using the properties of the constituent materials. [1–10]
PREM E.J. BABU, Senior Research Fellow, U.T.S. PILLAI, Scientist, and B.C. PAI, Director Grade Scientist, Metal Processing Division, and S. SAVITHRI, Scientist, Computational Modeling and Simulation Section, are with the Regional Research Laboratory (CSIR), Trivandrum–695 019, Kerala, India. Manuscript submitted August 19, 2003. METALLURGICAL AND MATERIALS TRANSACTIONS B
Subcell continuity and equilibrium are satisfied in an average sense. This modeling method is extremely computationally efficient[8] and yet allows the microstructure to be modeled explicitly. This model is analytical in nature (as opposed to numerical FEA) and its formulation involves application of several governing conditions in an average sense. This averaging renders the model less accurate than FEA at the macroscale due to decoupling between normal and shear field components, but makes it many times more computationally efficient. Unlike some analytical models, GMC does provide the local fields in composite materials, allowing incorporation of arbitrary inelastic co
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