Machine learning-based sampling of virtual experiments within the full stress state

Abstract

This paper presents a new machine learning-based approach to investigate anisotropic yield surfaces of sheet metals by means of virtual experiments. The new sampling approach is based on the machine learning technique known as active learning, which has been adapted to efficiently sample virtual experiments with respect to the full stress state in order to identify parameters of anisotropic yield functions. The approach was employed to sample virtual experiments based on the crystal plasticity finite element method (CPFEM) for a DX56D deep drawing steel and compared with two state-of-the-art sampling methods taken from the literature. The resulting points on the initial yield surface for all three sampling methods were used to identify parameters of the anisotropic yield functions Hill48, Yld91, Yld2004–18p and Yld2004–27p. These parameters were then applied to a cylindrical cup drawing simulation to analyse the effect of the three sampling methods on a typical sheet forming simulation. The results show that the new machine learning-based sampling approach has a higher sampling efficiency than the two state-of-the-art sampling methods. Consequently, fewer computationally expensive crystal plasticity simulations are required. By comparing different variants of the Hill48, Yld91, Yld2004–18p and Yld2004–27p yield surfaces, it was also found that identifying parameters of anisotropic yield functions based on virtual experiments sampled within the full stress state can lead to a degraded representation of the in-plane anisotropy. With respect to DX56D deep drawing steel, this degradation was observed for the Yld2004–18p yield function. The negative implications following from this degraded in-plane representation were further demonstrated by the results of the cylindrical cup drawing process. As a consequence, the representation of the in-plane anisotropy must be carefully reviewed when taking the full stress state into account. In this context, Yld2004–27p was identified as being sufficiently flexible to simultaneously represent the plastic anisotropy of DX56D with respect to the in-plane and out-of-plane behaviour with high accuracy.