Parameter determination of anisotropic yield function using neural network-based indentation plastometry

Understanding the impact of plastic anisotropy on the formability of sheet metals is crucial for their industrial application and high-precision forming simulation. Existing multiple uniaxial tensile tests for measuring the plastic flow of anisotropic materials, however, are costly, time-consuming, and destructive. Therefore, it is more efficient to focus on indentation plastometry, a simple, nondestructive test that can quickly extract tensile properties. The objective of this work is to directly derive the parameters of the advanced Poly6 yield criterion and hardening, which describes strong plastic anisotropy, using indentation plastometry basd on a neural network (NN) system. The identification process for these parameters through conventional tensile tests is inherently complex, thereby determining the parameters directly from indentation data presents an unprecedented challenge. We trained NNs using a database generated from verified finite element (FE) simulations of spherical indentations. To systematically iterate these FE simulations, we designed a strategy generating a set of input anisotropic parameters that ensure the convexity of the yield function. We considered the radial and vertical displacement fields around the indentation mark along with the load-depth curve as indentation responses. Through a comprehensive analysis of the correlation between displacement profiles, we have proposed an optimal feature extraction method for NN training. The developed FE-NN model was evaluated by comparing the predicted parameters from the indentation responses of the target materials with those measured from tensile tests. These parameters were expressed as the yield locus and directional properties. The results demonstrated that the FE-NN modeling approach is robust and can accurately capture the anisotropic plastic flow from indentation responses.