Accurate fatigue assessment of material plagued by defects is of utmost importance to guarantee safety and service continuity in engineering components. This study shows how state-of-the-art semi-empirical models can be endowed with additional defect descriptors to probabilistically predict the occurrence of fatigue failures by exploiting advanced Bayesian Physics-guided Neural Network (B-PGNN) approaches. A B-PGNN is thereby developed to predict the fatigue failure probability of a sample containing defects, referred to a given fatigue endurance limit. In this framework, a robustly calibrated El Haddad's curve is exploited as the prior physics reinforcement of the probabilistic model, i.e., prior knowledge. Following, a likelihood function is built and the B-PGNN is trained via Bayesian Inference, thus calculating the posterior of the parameters. The arbitrariness of the choice of the related architecture is circumvented through a Bayesian model selection strategy. A case-study is analysed to prove the robustness of the proposed approach. This methodology proposes an advanced practical approach to help support the probabilistic design against fatigue failure.

Background: Over the past 20 years, the Contour Method (CM) has been extensively implemented to evaluate residual stress at the macro scale, especially in products where material processing is involved. Despite this, insufficient attention has been devoted to addressing the problems of input data filtering and residual stress uncertainties quantification. Objective: The present research aims to tackle this fundamental issue by combining Gaussian Process Regression (GPR) with the CM. Thanks to its stochastic nature, GPR associates a Gaussian distribution with every subset of data, thus holding the potential to model the inherent uncertainty of the input data set and to link it to the measurements and the surface roughness. Methods: The conventional and unrobust spline smoothing process is effectively replaced by the GPR which is capable of providing uncertainties over the fitting. Indeed, the GPR stochastically and automatically identifies the fitting parameter, thus making the experimental data post-processing practically unaffected by the user’s experience. Moreover, the final residual stress uncertainty is efficiently evaluated through an optimised Monte Carlo Finite Element simulation, by appropriately perturbing the input dataset according to the GPR predictions. Results: The simulation is globally optimised exploiting numerical techniques, such as LU-factorisation, and developing an on-line convergence criterion. In order to show the capability of the presented approach, a Friction Stir Welded plate is considered as a case study. For this problem, it was shown how residual stress and its uncertainty can be accurately evaluated in approximately 15 minutes using a low-budget personal computer. Conclusions: The method developed herein overcomes the key limitation of the standard spline smoothing approach and this provides a robust and optimised computational framework for routinely evaluating the residual stress and its associated uncertainty. The implications are very significant as the evaluation accuracy of the CM is now taken to a higher level.

Defects in additively manufactured materials are one of the leading sources of uncertainty in mechanical fatigue. Fracture mechanics concepts are useful to evaluate their influence, nevertheless, these approaches cannot account for the real morphology of defects. Preliminary attempts to exploit a more comprehensive description of defects can be found in the literature, by using Machine Learning. These approaches are notoriously data-hungry and neither physics laws nor phenomenological rules are introduced to assess the soundness of the outcome. Hereby, to overcome this limitation, an approach to predicting fatigue finite life of defective materials, based on a Physics-Informed Neural Network framework, is presented for the first time. The training process of a Neural Network is reinforced by introducing novel Fracture Mechanics constraints. Experimental results obtained from the literature, including detailed defect analysis from computer tomography and fractography, were used to check its accuracy. The proposed predictive tool fully exploits the advanced capabilities of machine learning to account for morphological aspects of defects that could not be accounted for otherwise, while at the same time obeying fracture mechanics laws and requiring a smaller experimental dataset. The approach paves the way for new structural design approaches with an unprecedented degree of accuracy.