Viscoplasticity of heterogeneous metallic materials

Abstract

Viscoplastic behavior of metallic materials is manifested by collective behavior of lattice defects at multiple length scales. The full gamut of length scales, from atomic to macroscopic, is considered in terms of both concurrent and hierarchical multiscale modeling of plasticity of metals. Particular challenges are identified in the realm between atomistic simulations and the scale of dislocation substructure formation in establishing next generation constitutive models. Bottom–up modeling is useful in applications such as fracture or dislocation mediation by interfaces. This is differentiated from top–down modeling that supports design of a material as a hierarchy of sub-systems. Examples of hierarchical microstructure-sensitive models are presented for both Ni-base superalloys and α–β Ti alloys, with emphasis on cyclic deformation behavior. Future directions to advance both discrete dislocation and crystal plasticity theories are discussed, emphasizing the need for additional focus on dislocation sources and dislocation line curvature in modeling scale dependent behavior. Difficulties with low order approximations of the dislocation density distribution, such as second-order gradient theories, are discussed in terms of predictive capability and transferability among geometric configurations. The multiscale nature of the decomposition of the deformation gradient into elastic and plastic parts is discussed in light of sources of incompatibility at each scale considered, with interpretation offered at different scales of Burgers circuits that highlight dislocation substructures and polycrystals, respectively. Recent atomistic studies of dislocation nucleation at grain boundaries are outlined and some thoughts are offered towards potentially fruitful directions to incorporate this understanding into statistical continuum models that account for the role of grain boundary structure as an element of the evolving incompatibility field.