A concurrent multiscale model for the thermomechanical response of polycrystalline materials

Abstract

The presented work establishes and implements a novel concurrent multiscale framework to predict the size-dependent thermomechanical response of engineering materials. As such, it focuses on determining the interactions among length scales. More precisely, it aims at capturing the local variations on thermal conductivity at the subgrain level, the repercussion on the mesoscopic temperature field, and the consequent impact on thermal stresses. Therefore, the ultimate goal is to better understand the role of the grain size and the grain shape on heat transfer of polycrystalline materials and the influence on the underlying thermal stresses concentration, driving to the localized failure of the material. A review of current modeling approaches reveals a lack of numerical tools in the determination of the size effect on geometries presenting complex features. Indeed, current numerical methods are only capable of modeling thermomechanical processes at the macroscale. In contrast, analytical models have been developed to quantify the size effect in subgrain structures, but the applications are limited to relatively simple geometries such as thin films, nanowires or single cubic grains. To bridge that gap, a novel concurrent multiscale framework is developed herein to account for any arbitrary microstructural configuration. The proposed technique is achieved by capturing the microscale size effect on the thermal conductivity and incorporating it into the macroscale analysis. In particular, the multiscale scheme accounts for: (a) a submicron scale model for the thermal conductivity based on the Boltzmann transport equation under the relaxation time approximation, (b) a classic Fourier heat transport model at the mesoscale, and (c) a continuum model of thermomechanical deformation that explicitly resolves the microscopic geometric features of the material. The capabilities of the model are demonstrated through a series of examples, which highlight the potential of the procedure for designing materials with enhanced thermomechanical responses. Among other applications, this research uses the developed concurrent multiscale framework to analyze the influence of the microscopic features on the thermal and thermomechanical properties. In particular, the analysis of functionally graded polycrystals is performed, highlighting the influence of the grain size distribution on the temperature field and on the thermal stress distribution. From those results, further novel optimization approaches are conducted using length-dependent modeling of polycrystalline materials. More specifically, the size-dependent thermal properties obtained from the model are coupled with an adaptive topology optimization algorithm to improve the spatial grain size distribution on single-material polycrystalline systems. This technique creates a unique tool for the manufacturing of single-material systems with enhanced thermal properties. Finally, this framework provides a physically based and accurate computational tool for defining a `MFP calibrated' Kapitza resistance at the grain boundary, where both the Kapitza resistance and the intragranular thermal conductivity are size-dependent. This particular study highlights the benefits of the innovative concurrent multiscale framework for the study of thermomechanical phenomena. It notably allows to recover the accurate effective thermal conductivity of polycrystals. Additionally, it reduces spurious temperature jumps and related thermal stresses at the grain boundary, that appears to be artifacts of the current numerical approaches.