Forming limit curve prediction with neural network for non-proportional loadings

Resumen

Obtaining the forming limit strains for proportional loading paths of sheet metals allows predicting the onset of necking during metal forming processes. These limit strains are arranged in the major and minor principal strain space generating the so-called Forming Limit Curves (FLC). These have been successfully applied for several decades to assess the forming operations in automotive and aerospace industry. The FLC depends on the particular material’s plasticity behaviour, i.e. yield function and work hardening, and on the stress or strain state. These diagrams are typically determined experimentally, numerically by finite element analysis or analytically, employing necking models based on bifurcation theory, such as the Marciniak-Kuczynski model. The dependence of the FLC with the loading path introduces an infinite number of possibilities to reach a particular state strain. Neural Networks (NN) provide an extremely efficient approach to consider and predict this non-proportional loading dependence. The Marciniak-Kuczynski model has been formulated and used in the present work to numerically determine the limit strains corresponding to non-proportional loadings for a particular steel. A database of virtual tests has been generated, considering four degrees of freedom to test and train the NN. Several NN architectures, modifying the number of hidden layers, number of neurons, and activation functions have been tested. The final output is an optimum neural network that predict in real time the FLC diagram for a nonproportional path with four degrees of freedom for a particular steel.