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The characteristics of a manufacturing product are influenced by a variety of different factors, such as the material properties of the base product. The prediction of properties that give optimal results in metal forming applications is a complex task but of high interest for the manufacturer. To realize such a prediction scheme, the process chain is split up into individual process steps and for each of them an inverse modeling is required. The specific aim of this work is to present an approach for the inverse problem formulation of a process step and to solve it using methods of machine learning. Moreover, the challenges that often arise due to the ill-posed nature of inverse problems will be discussed. The main focus is on the crystallographic texture of metals, which strongly affects the deformation behavior during a process step and highly influences the characteristics of the final product. Description of the inverse problem and a solution approachIn order to formulate the inverse problem, we first describe the direct problem to which our inverse problem is inverse to. The direct problem can be expressed by an operator equationwhere m is a set of model parameters (material properties of the base product) and d is a set of data parameters (desired properties of the final product). g describes the so-called forward operator mapping m on d. Based on Eq.(1) we formulate the inverse problemwhere G is the inverse of the forward operator [1], which is the quantity of our interest. For non invertible problems a solution can be approximated by solving a minimization problem,In our work, we use machine learning to emulate the inverse operator G. The algorithms we use are feed-forward neural networks [2] and mixture density networks [3]. The former is a regression model unable to handle ambiguities, the latter is a generative model combining the structure of neural networks and mixture models forming probability density functions. Neural network algorithms are constructed to learn correlations between data sets. Once the networks are trained, we use the algorithms to predict model parameters from given data parameters. Since neural networks are able to handle almost every kind of data, we are not bounded by specific model or data parameters and can define them individually depending on our specific problem. The major challenge for the machine learning approach is the ill-posed nature of almost every inverse problem [4]. There are three conditions for a problem to be well-posed in the sense of Hadamard [5]: Existence, uniqueness, and stability. If any of the conditions is not met, the problem is called ill-posed. In our approach difficulties arise with the first two conditions, namely existence and uniqueness. The stability condition is fulfilled by the applied machine learning algorithms.The following section deals with the modeling of property-structure linkages in a simplified rolling process. These linkages are the solution to the inverse problem of determining optimal microstructures from given material properti...

Abstract.A crystal plasticity based full-field microstructure simulation approach is used to virtually determine mechanical properties of sheet metals. Microstructural features like the specific grain morphology and the crystallographic texture are taken into account to predict the plastic anisotropy. A special focus is on the determination of the Lankford coefficients and on the yield surface under plane stress conditions. Compared to experimental procedures, virtual material testing allows to generate significantly more data points on the yield surface. This data is used to calibrate anisotropic elasto-plastic material models which are commonly used for sheet metal forming simulations. A numerical study is carried out to analyze the influence of the chosen points on the yield surface on the calibration procedure. IntroductionAn accurate description of the elasto-plastic material behavior is needed for a precise simulation of sheet metal forming processes. Here, the two most important aspects of the material models are the description of the hardening and the yield locus. To account for the anisotropy of sheet metals, an increasing number of anisotropic yield locus models is available, starting from the well-known Hill48 [1] yield locus description up to more modern models like Yld2000-2d [2]. It is known, that the simpler yield locus descriptions are usually not sufficient to model the plastic material behavior accurately, especially for recently developed advanced high strength steels and also for aluminum alloys. In the case of an associated flow rule, the curvature of the yield locus defines also the development of the plastic strain components which is of high importance for sheet metal forming simulations.Besides the choice of an appropriate yield locus model, the identification of the model parameters is an important issue, especially when more complex yield locus models with more parameters are considered. The determination of the parameters of more sophisticated yield locus models requires a large number of experiments which can be difficult and expensive to realize. In a standard parameter identification procedure the number of experimental results (yield stresses, r-values) usually corresponds to the number of free parameters in the yield locus model. The experimental data which were considered for the parameter identification can then be precisely reproduced by the yield locus model. However, accuracy for other stress states is unclear.Here, the concept of virtual material testing is an interesting approach. It allows to significantly extend the limited experimental data base by additional virtual experiments. These virtual data can be used as additional input for a precise parameter identification or for the assessment of yield locus models.