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The mechanical response of polycrystalline metals is significantly affected by the behaviour of grain boundaries, in particular when these interfaces constitute a relatively large fraction of the material volume. One of the current challenges in the modelling of grain boundaries at a continuum (polycrystalline) scale is the incorporation of the many different interaction mechanisms between dislocations and grain boundaries, as identified from fine-scale experiments and simulations. In this paper, the objective is to develop a model that accounts for the redistribution of the defects along the grain boundary in the context of gradient crystal plasticity. The proposed model incorporates the nonlocal relaxation of the grain boundary net defect density. A numerical study on a bicrystal specimen in simple shear is carried out, showing that the spreading of the defect content has a clear influence on the macroscopic response, as well as on the microscopic fields. This work provides a basis that enables a more thorough analysis of the plasticity of polycrystalline metals at the continuum level, where the plasticity at grain boundaries matters.

Grain boundaries play an important role in the mechanical and physical properties of polycrystalline metals. While continuum macroscale simulations are appropriate for modeling grain boundaries in coarse-grained materials, only atomistic simulations provide access to the details of the grain boundary (GB) structure and energy. Hence, a multiscale description is required to capture these GB details. The objective of this paper is to consolidate various approaches for characterizing grain boundaries in an effort to develop a multiscale model of the initial GB structure and energy. The technical approach is detailed using various 〈 1 0 0 〉 , 〈 1 1 0 〉 and 〈 1 1 1 〉 symmetric tilt grain boundaries in copper and aluminum. Characteristic features are: (i) GB energies obtained from atomistic simulations and boundary period vectors from crystallography, (ii) structural unit and dislocation descriptions of the GB structure and (iii) the Frank–Bilby equation to determine the dislocation content. The proposed approach defines an intrinsic net defect density scalar that is used to accurately compute the GB energy for these GB systems. The significance of the present work is that the developed atomistic-to-continuum approach is suitable for realistically inserting the initial GB structure and energy into continuum level frameworks.

Interactions between dislocations and grain boundaries play an important role in the plastic deformation of polycrystalline metals. Capturing accurately the behaviour of these internal interfaces is particularly important for applications where the relative grain boundary fraction is significant, such as ultra fine-grained metals, thin films and micro-devices. Incorporating these micro-scale interactions (which are sensitive to a number of dislocation, interface and crystallographic parameters) within a macro-scale crystal plasticity model poses a challenge. The innovative features in the present paper include (i) the formulation of a thermodynamically consistent grain boundary interface model within a microstructurally motivated strain gradient crystal plasticity framework, (ii) the presence of intra-grain slip system coupling through a microstructurally derived internal stress, (iii) the incorporation of inter-grain slip system coupling via an interface energy accounting for both the magnitude and direction of contributions to the residual defect from all slip systems in the two neighbouring grains, and (iv) the numerical implementation of the grain boundary model to directly investigate the influence of the interface constitutive parameters on plastic deformation. The model problem of a bicrystal deforming in plane strain is analysed. The influence of dissipative and energetic interface hardening, grain misorientation, asymmetry in the grain orientations and the grain size are systematically investigated. In each case, the crystal response is compared with reference calculations with grain boundaries that are either ‘microhard’ (impenetrable to dislocations) or ‘microfree’ (an infinite dislocation sink).

Modelling the behaviour of grain boundaries in polycrystalline metals using macroscopic continuum frameworks demands a multi-scale description of the underlying details of the structure and energy of grain boundaries. The objective in this work is the incorporation of a multi-scale atomistic-to-continuum approach of the initial grain boundary structure and energy into a grain boundary extended crystal plasticity framework in order to investigate the role of the grain boundary energetics on the macroscopic response. To this end, the methodology includes: (i) the generalisation of the atomistic-to-continuum results of the initial grain boundary structure and energy, (ii) an analytical analysis of the resulting grain boundary energetics in the continuum framework, (iii) the numerical implementation of the developed framework in the case of a periodic bicrystal subjected to simple shear deformation considering a symmetric tilt boundary system in the full misorientation range. This work provides a step forward towards the physically based continuum modelling of grain boundary interfacial plasticity.