On the development of a multi-scale modelling framework to study plasticity and damage through the coupling of finite element crystal plasticity and discrete dislocation plasticity

Abstract

The microstructure of polycrystalline materials crucially determines their mechanical performance in engineering applications. A multi-scale modelling approach is capable of representing the microstructure and thus capturing the material performance for various resolution requirement at different scales. Besides, the application of multi-scale modelling effectively reduces expense and improves efficiency of computations without loss of accuracy at sensitive zones. A method of concurrent coupling of planar discrete dislocation plasticity (DDP) and a crystal plasticity finite element (CPFE) method was devised for simulating plastic deformation in large polycrystals with discrete dislocation resolution in a single grain or cluster of grains for computational efficiency; computation time using the coupling method can be reduced by an order of magnitude compared to DDP. The method is based on an iterative scheme initiated by a sub-model calculation, which ensures displacement and traction compatibility at all nodes at the interface between the DDP and CPFE domains. The proposed coupling approach is demonstrated using two plane strain problems: (i) uniaxial tension of a bi-crystal film and (ii) indentation of a thin film on a substrate. The latter demonstrated that the rigid substrate assumption used in earlier discrete dislocation plasticity studies is inadequate for indentation depths that are large compared to the film thickness, i.e. the effect of the polycrystalline plastic substrate modelled using CPFE becomes important. The coupling method can be used to study a wider range of indentation depths than previously possible using DDP alone, without sacrificing the indentation size effect regime captured by DDP. A comprehensive indentation pressure formula has been developed by applying the proposed multi-scale modelling approach on a polycrystalline coating system. Planar nano-sliding and fretting calculations have been performed on thin films modelling by CPFE and DDP at different scales. Results of CPFE simulations provide an understanding of the role of microstructure on the plasticity and crack initiation during a contact problem. Beside, a new DDP computational framework has been proposed for a nano-fretting problem which is able to capture the contact size effect, simulate the dislocation evolution and predict the surface profile variation of thin films. Calculations of DDP simulations potentially provide CPFE simulations with fatigue parameters that is of more physical significance. The method is general and can be applied to any problem where finer resolution of dislocation mediated plasticity is required to study the mechanical response of polycrystalline materials, e.g. to capture size effects locally within a larger elastic/plastic boundary value problem. Also, the model described here will provide further opportunities for directly coupled, three-tiered multi-scale models compromising an overall macroscopic continua having embedded crystal plasticity and discrete dislocation plasticity models, respectively, as the length scale decreases in the area of interest. Finally, the methodology of the proposed coupling method will shed light on archiving a general compatibility of sub-regions and thus benefit other researchers who are working on coupling methods among other scales.