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Saurabh Puri — 2007-08 Fellow

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The objective of this research is to develop a framework that can follow large strain deformation processes and the development of a physically appropriate non-linear and partially recoverable inelastic strain during unloading. Applications of such a framework are many. For example, it can be used in the design of light weight auto-body panels. Light weighting of automobiles improves fuel efficiency and reduces green house gas emissions. Fabrication of these auto-body panels involves stamping of metal sheets to very large strains. Removal of load after the forming step results in springback due to internal stresses that produces undesirable shapes of various parts. Thus, it is very important to understand springback and stress relaxation in stamped metal sheets to optimize production of auto-body panels.

Another application is enhanced design capabilities of MEMS devices through better understanding of reliability against fatigue and fracture. An approach which is capable of understanding deformation phenomena at micron scale and macroscopic time scale is not yet available in the literature. The conventional theory of plasticity can neither predict experimentally observed size effects at initial yield in micron sized specimens, nor the spatial inhomogeneity in a homogeneous material under boundary conditions corresponding to homogeneous deformation. Strain gradient plasticity models (Fleck et al. 1994) have limited capability of predicting microstructure. There are several atomistic continuum approaches (Yamakov et al., 2001) and discrete dislocation plasticity models (Kubin et al., 1992; van der Giessen & Needleman, 1995) that have proven to be satisfactory at finer scales of resolution but the computational expense at mesoscale is so high that it is impossible to study a practical problem in a reasonable time frame.

The proposed approach overcomes these drawbacks. It is a combination of (a) field dislocation mechanics theory (Acharya 2001, 2003, 2004) – as a model for the plastic flow of polar, mobile dislocation density and long-range internal stress observable at micro-scale, and (b) gradient crystal polycrystal plasticity which is used as a model for plastic flow of statistical dislocation distributions and strength arising from short-range interactions. This approach is not intended to address fine scale phenomena related to individual dislocations. However, it is ideally suited for the applications in this proposal. For example, it has been shown to be successful in predicting benchmark problems in plasticity at small strains, such as size effects in work hardening and at initial yield, Bauschinger effect (an internal stress effect) and spatial inhomogeneity in a homogeneous material under boundary conditions corresponding to homogeneous deformation (Roy & Acharya, 2006). The effect of lattice rotations was neglected in these simulations due to the assumption of small strain. On the contrary, it is well known that in bulk production processes like rolling or extrusion, materials are deformed up to approximately, 100% strain which produce significant lattice rotations and corresponding texture evolution. Thus, the main objective of the present project is to develop a computational tool that is capable of analyzing: 1. the stress field of an evolving dislocation density distribution in finite bodies at finite strains, unrestricted material and geometric nonlinearity, and unrestricted elastic and plastic anisotropy. 2. the stress mediated mobility and recovery of this density, rendering a unique capability at the mesoscale that can provide insight into the development of evolutionary relations for a macroscopic back stress.

The target predictions of this methodology will be (a) phenomenon of dislocation patterning, (b) internal stresses under geometric non-linearity, (c) lattice rotations and (d) the connection between texture and mechanical properties. Such a computational ability will be the first of its kind and will serve as an important contribution in the area of materials science and mechanics.