For the generation of representative volume elements a statistical description of the relevant parameters is necessary. These parameters usually describe the geometric structure of a single grain. Commonly, parameters like area, aspect ratio, and slope of the grain axis relative to the rolling direction are applied. However, usually simple distribution functions like log normal or gamma distribution are used. Yet, these do not take the interdependencies between the microstructural parameters into account. To fully describe any metallic microstructure though, these interdependencies between the singular parameters need to be accounted for. To accomplish this representation, a machine learning approach was applied in this study. By implementing a Wasserstein generative adversarial network, the distribution, as well as the interdependencies could accurately be described. A validation scheme was applied to verify the excellent match between microstructure input data and synthetically generated output data.

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The use of a simulative approach with representative volume elements (RVE’s) is particularly well suited to investigate the influence of different microstructural parameters on the damage behavior of a material. In order to statistically analyze the individual components of the microstructure (e.g. geometric structure of grains and inclusions), well-known distribution functions such as logNormal/Gamma are normally used, but these do not take into account the interdependencies between the different parameters. However, newer approaches like machine learning techniques can only describe one phase of a single material at a time. Therefore, in this study, we extended an existing Wasserstein Generative Adversarial Network (WGAN) to a Conditional Wasserstein GAN with Gradient Penalty (CWGAN-GP), with which it is possible to process multiple materials/phases simultaneously. Training this algorithm on different steels and associated inclusions showed that a single trained network can generate synthetic microstructure for all different phases and materials with very high quality. A newly implemented evaluation method using the regularized Wasserstein-distance confirmed the excellent agreement of the real data with the synthetic data for all phases/materials. As a use case for our algorithm, the influence of different inclusions on the stress accumulation and concentration of X65 pipeline steel was investigated to find initiation sites for damage in the material. These investigations showed a pronounced correlation between stress concentration and inclusion parameters, thus confirming the usefulness of the CWGAN-GP as an input-generator for RVE’s.

For the generation of representative volume elements a statistical description of the relevant parameters is necessary. These parameters usually describe the geometric structure of a single grain. Commonly, parameters like area, aspect ratio and slope of the grain relative to the rolling direction are applied. However, usually simple distribution functions like log normal or gamma distribution are used. Yet, these do not take the interdependencies between the microstructural parameters into account. To fully describe any metallic microstructure though, these interdependencies between the singular parameters need to be accounted for. To accomplish this representation, a machine learning approach was applied in this study. By implementing a Wasserstein generative adversarial network, the distribution, as well as the interdependencies could accurately be described. A validation scheme was applied to verify the excellent match between microstructure input data and synthetically generated output data.