Physics-based constitutive modelling for crystal plasticity finite element computation of cyclic plasticity in fatigue

Metal fatigue during cyclic loading puts an endurance limit on most of today's technology. It impacts the reliability of metallic components used for transportation, electronic devices and energy production because fatigue failure can occur without any apparent forewarning. This phenomenon limits the lifetime of many industrially manufactured items, whose periodic replacement affects the cost of everyday products. The problem of predicting fatigue failure in metals has been addressed using the finite element method, which can provide the stress and strain state of the material in complex geometries. Engineering models describing the material behaviour have been used to predict the damage accumulation, but microstructure and material design require constitutive models at the micrometre length scale, incorporating the physical processes in the material. This involves the study of dislocation dynamics and the formation of dislocation structures, which have been recognized as the key phenomena affecting the macroscopic fatigue behaviour of metals. This problem is computationally challenging, first because of the large number of state variables required to describe the dislocation behaviour, and second because the formation of dislocation structures takes place only after many deformation cycles. In this project a continuum dislocation-based model, specific for cyclic fatigue at the micrometre length scale, is developed. The main novelty is the prediction of 3D dislocation structures starting from a random initial dislocation distribution. In single slip deformation, the characteristic length scale and shape of dislocation structures are predicted using only physical parameters, such as the stacking fault energy, and without any fitting procedure. The model is implemented in a crystal plasticity finite element solver, describing all the slip systems. Therefore, it is possible to model polycrystalline structures and to study the orientation of multiple slip dislocation structures with respect to the loading direction. Compared with existing models, the implementation of the dislocation junction formation mechanism in a continuum framework is a step forward. A collaboration with another PhD student, carrying out electron channeling contrast imaging experiments on fatigued 316 stainless steel, has provided a validation of the model by direct comparison of experimental and simulated dislocation structures close to the specimen surface. The crystal lattice rotation is another variable that can be extracted from finite element simulations. The developed model correlates the forming dislocation structures with the lattice rotation around the coordinate axes. This allows the comparison with Laue microdiffraction experiments carried out on copper single crystal specimens by another PhD student at the SLS, the synchrotron at Paul Scherrer Institut. The dislocation-based model can calculate experimental observables, such as the rotation components and rotation gradients, as a function of the simulated dislocation density in the specimen, which is not directly observable. This provides a validation of the constitutive equations at the micrometre length scale.