Deep learning coupled Bayesian inference method for measuring the elastoplastic properties of SS400 steel welds by nanoindentation experiment

Nanoindentation experiment has shown broad application prospects due to its ability to measure the mechanical properties of various materials at multiple scales. In this paper, a deep learning coupled Bayesian inverse approach is proposed for measuring the elastoplastic parameters of SS400 steel welds by nanoindentation experiment. The nanoindentation experiments were performed on the SS400 steel welds, including base metal (BM), weld zone (WZ), and heat affected zone (HAZ), and the experiment load–displacement (P-h) curves were obtained. The hyper-parameters tunable artificial neural network (ANN) was established to correlate elastoplastic parameters with indentation P-h curves. Based on Bayesian inference theory, the posterior density function for estimating the unknown material parameters was established. Transitional Markov chain Monte Carlo was used for sampling from the posterior density function, and the elastoplastic properties in different regions of SS400 steel welds were identified. The advantage of the established measuring method is that the hyper-parameters optimized ANN model can provide the very accurate forward relationship between material properties and indentation P-h curves. Besides, the inverse Bayesian framework can quantify the potential uncertainty of the identified elastoplastic parameters. The measured elastoplastic properties of the base metal of SS400 steel show good agreement with tensile experiment data, of which the maximum measuring error is less than 12%. The measured elastoplastic properties in WZ and HAZ are also proved to be effective. The uncertainty of the identified elastoplastic parameters of SS400 steel welds can be quantified by posterior marginal distribution, using Mean and Variance values. The results proved that the proposed inverse measuring method is reliable and effective.