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This work is concerned with synthetic microstructure models of polycrystalline materials. Once a representation of the microstructure is generated, the individual grains need to be furnished with suitable crystal orientations, matching a specific crystal orientation distribution. We introduce a novel method for this task, which permits to prescribe the orientations based on tensorial Fourier coefficients. This compact representation gives rise to the texture coefficient optimization for prescribing orientations method, enabling the determination of representative orientations for digital polycrystalline microstructures. We compare the proposed method to established and dedicated algorithms in terms of the linear elastic as well as the non-linear plastic behavior of a polycrystalline material.

In this work, we advocate using Bayesian techniques for inversely identifying material parameters for multiscale crystal plasticity models. Multiscale approaches for modeling polycrystalline materials may significantly reduce the effort necessary for characterizing such material models experimentally, in particular when a large number of cycles is considered, as typical for fatigue applications. Even when appropriate microstructures and microscopic material models are identified, calibrating the individual parameters of the model to some experimental data is necessary for industrial use, and the task is formidable as even a single simulation run is time consuming (although less expensive than a corresponding experiment). For solving this problem, we investigate Gaussian process based Bayesian optimization, which iteratively builds up and improves a surrogate model of the objective function, at the same time accounting for uncertainties encountered during the optimization process. We describe the approach in detail, calibrating the material parameters of a high-strength steel as an application. We demonstrate that the proposed method improves upon comparable approaches based on an evolutionary algorithm and performing derivative-free methods.

International journal of fatigue 160, 106824 (2022). doi:10.1016/j.ijfatigue.2022.106824, Published by Elsevier, Oxford

Generalization of microstructural short crack (MSC) growth simulation across different loading conditions and materials is often not considered in literature. These points are addressed by transferring a previously proposed model for crack initiation and transgranular MSC growth from ferritic steel to the martensitic steel SAE 4150. An accurate depiction of the microstructure is achieved by a novel approach to parameterize martensitic tessellations. Calculated fatigue lifetimes are in similarly good agreement with experimental data for martensite as for previously considered ferrite. The model’s transferability is shown among distinct load ratios and between strain- and stress-controlled loading, subject only to small deviations.

Microstructural short crack (MSC) growth profoundly influences the fatigue lifetime of steels. For finite element simulations with crystal plasticity, a MSC model for industrial application is described for the ferritic steel EN 1.4003. As transgranular cracking is dominant in the early fatigue stages for this material, intergranular crack growth is excluded. Crack data from micro fatigue specimen is used to validate simulated crack paths. With a manual prescription of the crack initiation site, a substantial agreement between the predicted and experimental crack paths is revealed. Using an appropriate calibration strategy for the parametrization of the MSC model, the feasibility for lifetime prediction is also shown.

Ideas from the mathematical theory of optimal transport have recently been transferred to the micromechanics of polycrystalline materials, leading to fast methods for generating polycrystalline microstructures with grains of prescribed volume fraction in terms of centroidal Laguerre tessellations. In this work, we improve the state of the art solvers. For a given set of seeds and corresponding volume fractions summing to unity, there is a set of Laguerre weights such that the corresponding Laguerre tessellation realizes the prescribed volume fractions exactly. Furthermore, the Laguerre weights are unique up to a constant and can be determined by solving a convex optimization problem. However, whenever the optimization algorithm encounters a weight vector leading to an empty cell, the optimization problem is no longer locally strictly convex. To account for the latter, backtracking strategies are typically employed. We show that modern gradient-based optimization algorithms devoid of backtracking, like the Malitsky–Mishchenko method and the Barzilai–Borwein scheme easily overcome the described difficulty, leading to a significant speed-up compared to more traditional solvers. Furthermore, for computing centroidal Laguerre tessellations of prescribed volume fraction, we propose an Anderson-accelerated version of Lloyd’s algorithm, and show, by numerical experiments, that it consistently reduces the run-time. We demonstrate the capabilities of our proposed methods for generating microstructures of polycrystalline materials with prescribed grain size distribution.

This study investigates the small-scale deformation behavior of [1 1 1], [2 1 0] and [0 0 1] NiTi shape memory alloys. In stark contrast to bulk deformation behavior, the pseudoelastic behavior of sub-micron diameter compression pillars is highly dependent on diameter and relatively independent of orientation. Transmission electron microscopy is used to investigate pillars post-compression, giving insight into the deformation mechanisms involved.