Crystal plasticity and scale transition: the case of the single crystal

Crystalline materials are by nature heterogeneous. For example, polycrystals are made up of agglomerates of single-crystal grains in which lines of defects, known as dislocations, propagate shear on crystallographic planes. This spatial heterogeneity has led to the development of different models for each of the scales involved. The advent of ever more powerful computing power (microprocessor speeds are doubling every eighteen months) has stimulated the development of sophisticated numerical tools dedicated to simulating the mechanical behavior of materials. At each scale of study, a major effort has been made to set up reliable models adapted to the various situations encountered during the forming processes and in-service conditions of industrial components (figure 1 ). Little by little, each model is becoming more and more efficient: both the volume that can be simulated and the physical time are becoming ever greater. There is now an overlap between the capacities of the different models to simulate the response of volumes of a given size for a given physical time.

Even if it is still utopian to think of simulating the forming process from atomic simulations or even from the dynamics of dislocations, it is already possible to "move up" the space and time scales in a continuous manner, for example by carrying out specific simulations, the results of which can be used to establish a model on a higher scale. At the scale of continuous media, phenomenological behavior laws are gradually giving way to behavior relations deduced from the physical mechanisms behind plastic deformation, such as dislocation movements. This transition of scale between the dynamics of a dislocation line and the behavior of a continuous medium, for which the internal variables are generally the dislocation densities on the various sliding systems, implies an average and therefore a statistic for all potential events, as well as homogenization over an arbitrary volume. This ultimately leads to behavioral relationships that are always more or less phenomenological. The same applies to homogenization techniques modeling the transition from single crystal to polycrystal.

This article is devoted to the numerical modeling of the behavior of crystalline materials, mainly metals, at different scales using specifically adapted numerical tools, focusing on the potential applications of these tools, their ability to reproduce the plastic deformation of crystals, but also their intrinsic limitations. After a description of atomic-scale simulation...