Data-oriented description of texture-dependent anisotropic material behavior

In metallurgical processes, as for example cold rolling or deep drawing of sheet metal, it is frequently observed that the crystallographic texture, and with it the anisotropic mechanical properties of a material, evolve dynamically. Hence, to describe such processes, it is necessary to model the functional dependence of anisotropic material parameters on the texture, which itself can vary locally with the different plastic strain histories. In this work, we present a new data-oriented approach to parametrize the anisotropic yield function Barlat Yld2004-18p from micromechanical simulations for different textures. This is accomplished by applying supervised machine learning (ML) methods to express the relationship between different crystallographic textures and the material parameters of the yield function. The crystallographic textures are chosen to vary continuously between a random texture on the one hand side, and a unimodal Goss or Copper texture the other. These crystallographic textures are rather common in sheet metal forming. In this way, furthermore, the transition from isotropic plasticity to a rather severe case of anisotropy can be modeled, which is thought to mimic the dynamical evolution of the texture in a metallurgical process. It is found that a regularization strategy is necessary to circumvent the known non-uniqueness between Yld2004-18p parameters and the resulting plastic yield behavior. After this regularization, a unique relationship between the material parameters and the yield onset is established, making it possible to train different ML models with excellent accuracy and generalization properties to anisotropic plastic material behavior. The trained ML models are able to reliably predict the coefficients of unknown textures even with a small amount of training data and, thus, to correctly represent the yield behavior resulting from the various textures. The proposed method represents an efficient extension of the description of anisotropic plastic yielding as it establishes a data-oriented way to explicitly consider microstructural parameters in the material description, which opens new pathways to formulate material models that include the process history.