Necking-induced fracture prediction using an artificial neural network trained on virtual test data

The imperfection-based necking model by Marciniak and Kuczynski (MK) is frequently used for predicting the onset of localized necking under proportional and non-proportional loading, which can be considered a lower limit for the occurrence of fracture in a vehicle body structure subjected to crash loading. A large number of virtual imperfection lines at different orientation angles have to be analysed simultaneously in order to find the critical imperfection causing necking under arbitrary loading. This, and the continuous computation of a "distance to necking" quantity, representing a crucial output quantity for the simulation engineer, makes the model computationally expensive and limits industrial use in full-scale vehicle crash simulations. In this work, an extended MK model is used for creating a virtual test data base under proportional and non-proportional loading for training of a computationally more efficient simple feed-forward neural network (NN). Both models are implemented in a User Material routine of an explicit crash code, where the predictions of the NN are in good agreement with the predictions of the MK reference model, however at a significantly reduced computational cost. Besides a pure numerical validation study, an experimental validation study has been performed, imposing biaxial tension loading followed by plane strain tension loading until necking using a special punch test apparatus. Whereas MK and NN are in good agreement with the experimental observations, the agreement of classical necking models, applied in conjunction with a linear damage accumulation (forming severity) concept was less accurate.