Abstract
The various scales of hierarchical structures of metallic materials range from nm to mm. The notion of crystalline plasticity modeling is generalized to a set of model constructs that address phenomena associated with evolution of dislocations in crystals across a range of corresponding length scales, with time scales ranging from fs to years. These model constructs include coarse-grained atomistic modeling (atomistics), microscopic phase field models, dislocation field models, discrete dislocation dynamics, statistical continuum dislocation models, and mesoscale generalized continuum models of gradient, micropolar or micromorphic type, as well as local continuum crystal plasticity that can be applied to polycrystals. We identify key phenomena of lattice dislocations and discuss how these are mapped onto the capabilities of various scale-specific model constructs. Concurrent and hierarchical multiscale model transitions in space and time are discussed, distinguishing between coarse-graining and spatial domain decomposition approaches for lower scale models. We focus on model order reduction methods for mesoscale to macroscale constructs. In terms of bridging scales, the practical importance of two-scale transitions between models of differing fidelity and/or resolution is emphasized, whether of concurrent or hierarchical nature. Various scale-specific models for crystalline plasticity are considered, along with examples. The chapter closes by summarizing some of the long-standing gaps in modeling dislocation plasticity in crystals and polycrystals.
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Acknowledgment
Thet author is grateful for the support of the Carter N. Paden, Jr. Distinguished Chair in Metals Processing at Georgia Tech, as well as prior support in pursuit of various aspects of metal plasticity from AFOSR, ONR (N00014-05-C-024, N00014-17-1-2036), ARO, Eglin AFB, DARPA, NAVAIR, GE, Pratt & Whitney, Boeing, QuesTek, Simulia, the NSF-funded PSU-GT Center for Computational Materials Design (IIP-0541678, IIP-1034968), and NSF Grants CMMI-1232878, CMMI-0758265, CMMI-1030103, and CMMI-1333083.
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McDowell, D.L. (2019). Multiscale Modeling of Interfaces, Dislocations, and Dislocation Field Plasticity. In: Mesarovic, S., Forest, S., Zbib, H. (eds) Mesoscale Models. CISM International Centre for Mechanical Sciences, vol 587. Springer, Cham. https://doi.org/10.1007/978-3-319-94186-8_5
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