Abstract
A central aim of current materials studies is to develop a predictive modeling that incorporates dislocation-based plastic activity and microstructural evolution. Phase-field method has emerged as a powerful tool for addressing this issue, providing us with a versatile variational framework able to describe the movement of dislocations in interaction with underlying microstructures. In this article, a three-dimensional phase-field model of dislocations (PFMD) is developed with a discretization scheme that explicitly captures the face-centered cubic (FCC) geometry. Within this framework, continuous fields are discretized in a way that allows to consider strongly heterogeneous materials and sharp interfaces (free surfaces, stiffer precipitates, pores...) without generating numerical artifacts. The PFMD exposed in this work reproduces dislocation activity in FCC geometry, their reactions, and a particular attention is devoted to the dislocation core behaviors in order to remove effects present in prior generic PFMDs that can appear to be spurious for micron-scale applications. This allows us to rigorously reproduce the dislocation’s velocity with respect to experimental friction coefficients. The model is discussed and illustrated by applications standing at different space-scales that show how dislocations operate with microstructural heterogeneities such as free-surfaces (cylindrical nanopillar) and voids (pore under isostatic pressure).
Highlights
The macroscopic mechanical behavior of heterogeneous metallic alloys results from the evolution of its microstructure generally coupled to microscopic phenomena
Because face-centered cubic (FCC) crystallographic symmetry is very common, it is crucial to develop a numerical scheme that incorporates the specificity of this symmetry whatever the scale used for the numerical implementation
In a material that contains only a few dislocations, the computational time required for this test is compensated by the time which is saved by avoiding the calculation of the dynamics in every octahedral sites
Summary
The macroscopic mechanical behavior of heterogeneous metallic alloys results from the evolution of its microstructure (solid precipitates, pore network...) generally coupled to microscopic phenomena (dislocations, microcracks...). When the issue is to study the core structure of dislocations, a subatomic refined mesh is required in order to properly reproduce the continuous atomic-scale variations of the core profile [16,17,18,19] In one such situation, the underlying symmetry of the mesh can arbitrarily be chosen since, if the grid spacing is small enough, it does not interfere with the physical symmetry of the PFMD. Because face-centered cubic (FCC) crystallographic symmetry is very common, it is crucial to develop a numerical scheme that incorporates the specificity of this symmetry (glide planes, dislocation line directions and characters...) whatever the scale used for the numerical implementation Our solution to this constraint is to adopt a numerical grid which is always homothetic to crystalline symmetry such that FCC materials can be described irrespective of the mesh refinement. We validate the model and illustrate its potentiality when dislocations operate in the presence of heterogeneities made of voids and free surfaces
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