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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

The application of instrumented indentation to assess material properties like Young&rsquo, s modulus and microhardness has become a standard method. In recent developments, indentation experiments and simulations have been combined to inverse methods, from which further material parameters such as yield strength, work hardening rate, and tensile strength can be determined. In this work, an inverse method is introduced by which material parameters for cyclic plasticity, i.e., kinematic hardening parameters, can be determined. To accomplish this, cyclic Vickers indentation experiments are combined with finite element simulations of the indentation with unknown material properties, which are then determined by inverse analysis. To validate the proposed method, these parameters are subsequently applied to predict the uniaxial stress&ndash, strain response of a material with success. The method has been validated successfully for a quenched and tempered martensitic steel and for technically pure copper, where an excellent agreement between measured and predicted cyclic stress&ndash, strain curves has been achieved. Hence, the proposed inverse method based on cyclic nanoindentation, as a quasi-nondestructive method, could complement or even substitute the resource-intensive conventional fatigue testing in the future for some applications.

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.

Micromechanical fatigue lifetime predictions, in particular for the high cycle fatigue regime, require an appropriate modelling of mean stress effects in order to account for lifetime reducing positive mean stresses. Focus of this micromechanical study is the comparison of three selected fatigue indicator parameters (FIPs), with respect to their applicability to different total strain ratios. In this work, investigations are performed on the modelling and prediction of the fatigue crack initiation life of the martensitic high-strength steel SAE 4150 for two different total strain ratios. First, multiple martensitic statistical volume elements (SVEs) are generated by multiscale Voronoi tessellations. Micromechanical fatigue simulations are then performed on these SVEs by means of a crystal plasticity model to obtain microstructure dependent fatigue responses. In order to account for the material specific fatigue damage zone, a non-local homogenisation scheme for the FIPs is introduced for lath martensitic microstructures. The numerical results of the different non-local FIPs are compared with experimental fatigue crack initiation results for two different total strain ratios. It is concluded that the multiaxial fatigue criteria proposed by Fatemi-Socie is superior for predicting fatigue crack initiation life to the energy dissipation criteria and the accumulated plastic slip criteria for the investigated total strain ratios.

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.

Martensitic high-strength steels are prone to exhibit premature fatigue failure due to fatigue crack nucleation at non-metallic inclusions and other microstructural defects. This study investigates the fatigue crack nucleation behavior of the martensitic steel SAE 4150 at different microstructural defects by means of micromechanical simulations. Inclusion statistics based on experimental data serve as a reference for the identification of failure-relevant inclusions and defects for the material of interest. A comprehensive numerical design of experiment was performed to systematically assess the influencing parameters of the microstructural defects with respect to their fatigue crack nucleation potential. In particular, the effects of defect type, inclusion&ndash, matrix interface configuration, defect size, defect shape and defect alignment to loading axis on fatigue damage behavior were studied and discussed in detail. To account for the evolution of residual stresses around inclusions due to previous heat treatments of the material, an elasto-plastic extension of the micromechanical model is proposed. The non-local Fatemi&ndash, Socie parameter was used in this study to quantify the fatigue crack nucleation potential. The numerical results of the study exhibit a loading level-dependent damage potential of the different inclusion&ndash, matrix configurations and a fundamental influence of the alignment of specific defect types to the loading axis. These results illustrate that the micromechanical model can quantitatively evaluate the different defects, which can make a valuable contribution to the comparison of different material grades in the future.