Cellular automaton development for the study of the neighborhood effect within polycrystals stress-fields

Abstract

The objective of this Ph.D. project was to develop an analytical model able to predict the heterogeneous micromechanical fields within polycrystals for a very low computational cost in order to evaluate a material fatigue life probability. Many analytical models already exist for that matter, but they have disadvantages: either they are not efficient enough to rapidly generate a large database and perform a static analysis, or the impacts of certain heterogeneities on the stress fields, such as the neighborhood effect, are neglected. The mechanisms underlying the neighborhood effect, which is the grain stress variations due to a given close environment, are unheralded or misunderstood. A finite element analysis has been carried out on this question in the case of polycrystals oriented randomly with a single phase submitted to an elastic loading. The study revealed that a grain stress level is as much dependent on the crystallographic orientation of the grain as the neighborhood effect. Approximations were drawn from this analysis leading to the development of an analytical model, the cellular automaton. The model applies to regular polycrystalline structures with spherical grains and its development was conducted in two steps: first in elasticity then in elasto-plasticity. In elasticity, the model showed excellent predictions of micromechanical in comparison to the finite element predictions. The model was then used to evaluate the worst grain-neighborhood configurations and their probability to occur. It has been shown in the case of the iron crystal that certain neighborhood configurations can increase by 2 times a grain stress level. In elasto-plasticity, the model underestimates the grains plasticity in comparison to the finite element predictions. Nonetheless, the model proved its capacity to identify the worst grain-neighborhood configurations leading important localized plasticity. It has been shown that grains elastic behaviors determine the location and the level of plasticity within polycrystals in the context of high cycle fatigue regime. The grains undergoing the highest resolved shear stress in elasticity are the grains plastifying the most in high cycle fatigue regime. A statistical study of the neighborhood effect was conducted to evaluate the probability of the true yield stress (stress level applied to the material for which the first sign of plasticity would occur in a grain). The study revealed, in the case of the 316L steel, a significant difference between the true elastic limit at 99% and 1% probability, which could be one of the causes of the fatigue life scatter often observed experimentally in high cycle fatigue regime. Further studies on the effect of a free surface and the morphology of the grains were carried out. The study showed that a free surface have the effect to spread even more the grains stress levels distributions. The neighborhood effect approximations used in the developed model were unaffected by a free area. The grains morphology also has shown to have a significant impact on the stress fields. It has been shown that in the case of a high morphology ratio, the stress variations induced by the morphology of the grains are as important as those induced by the neighborhood effect.

Date	22 Jan 2020
Original language	American English
Awarding Institution	École de technologie supérieure
Supervisor	Philippe Bocher (Supervisor) & Martin Lévesque (Co-supervisor)