Neural network model predicting forming limits for Bi-linear strain paths

Abstract

The Forming Limit Curve (FLC) describes the maximum in-plane strains that can be applied to sheet metal before necking initiates. It is well known that the FLC depends on the yield locus, the hardening behavior, strain rate, temperature, superposed out-of-plane stresses and the shape of the loading path. There is an infinite number of possible paths for reaching a particular state of strain which makes the formulation of simple analytical models predicting the effect of non-linear loading paths on the FLC particularly challenging. Here, it is demonstrated that a neural network model is able to provide a computationally-efficient approach to describe the effect of non-proportional loading. A finite-element-based Marciniak-Kuczynski model is developed to characterize the forming limits of a DP780 steel through virtual experiments. Subsequently, a large data base is generated to serve as a basis for machine learning. Using a standard backpropagation algorithm with Bayesian regularization, a compact neural network model is trained and tested based on the results from virtual experiments. Even though the experimental data base includes only a finite number of random loading paths, the results show that the neural network model is able to predict the FLCs for a given proportional pre-straining history.