Deep neural network approach to estimate biaxial stress-strain curves of sheet metals

Multiaxial material testing is used to evaluate plastic deformation behavior of sheet metals in multiaxial stress states. A constitutive law calibrated by the results of multiaxial material tests can improve the accuracy of sheet metal forming simulations. However, this testing requires specialized equipment. This proof-of-concept study proposed and validated a deep neural network (DNN) approach to efficiently estimate biaxial stress-strain curves of aluminum alloy sheets from an image of the sample's crystallographic texture. The DNNs were trained using synthetic crystallographic texture datasets, and the corresponding biaxial stress-strain curves were generated by experimentally validated crystal plasticity finite element simulations, referred to as the numerical biaxial tensile tests. The synthetic crystallographic textures included preferred texture components typically found in aluminum alloys. The DNN based on two-dimensional convolutional neural networks (DNN-2D) accurately estimated the biaxial stress-strain curves from an {111} pole figure image. Further, the DNN comprising three dimensional convolutional neural networks (DNN-3D) provided a superior estimation of the biaxial stress-strain curves than DNN-2D using a three-dimensional image of the crystallographic texture. These findings demonstrated that the developed DNNs and their training procedures offer a new approach to efficiently provide virtual data for material modeling to enhance the accuracy of sheet metal forming simulations.