A Bayesian defect-based physics-guided neural network model for probabilistic fatigue endurance limit evaluation

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

On the significance of diffuse crack width self-evolution in the phase-field model for residually stressed brittle materials

The Phase-Field method is an attractive numerical technique to simulate fracture propagation in materials relying on Finite Element Method. Its peculiar diffuse representation of cracks makes it suitable for a myriad of problems, especially those involving multiple physics and complex-shaped crack patterns. Recent literature provided linear relationships between the width of the diffuse crack and the material intrinsic fracture toughness, through a material characteristic length. However, lately, it was shown how the existence of a residual stress field can affect the represented crack width even for fully homogeneous materials, in terms of toughness. In this short note, the authors tried to shed some light on the factors influencing the width of the diffuse crack representation. By simulating crack propagation in several residually stressed brittle materials, it was shown how the width of the diffuse crack is affected by the ratio between the driving force - due to the externally applied load - and the driving force required to propagate the crack. In other words, the diffuse crack extent can be linked to the degree of crack propagation stability/instability. Monitoring the evolution of the studied quantity can be of great interest to rapidly assess crack instability circumstances, under displacement control

Probabilistic defect-based modelling of fatigue strength for incomplete datasets assisted by literature data

Probabilistic defect-tolerant fatigue design protocols have become the leading paradigms in structural engineering. To effectively deal with this problem, El Haddad's (EH) curves are generally employed for the evaluation of the fatigue endurance limit. Herein, the synergic exploitation of Logistic Regression (LR) and Maximum a Posteriori (MAP) allows for calibrating EH parameters using the sole data from fatigue characterisation and post-mortem fractography. An extensive literature research provided the ground to introduce, when necessary, prior information for some of the more commonly used metallic alloys. Eventually, EH curves are retrieved upon a Monte Carlo simulation to support probabilistic engineering practice

Contour Method with Uncertainty Quantification: A Robust and Optimised Framework via Gaussian Process Regression

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

Quantification of uncertainty in a defect-based Physics-Informed Neural Network for fatigue evaluation and insights on influencing factors

Substantial advances in fatigue estimation of defective materials can be attained through the employment of a Physics-Informed Neural Network (PINN). The fundamental strength of such a framework is the ability to account for several defect descriptors while maintaining predictions physically sound. The first objective of the present work is the assessment of the PINN estimated fatigue life variability due to uncertainties carried by the inputs. Additionally, a set of sensitivity indices are employed to explore the influence of defect descriptors in fatigue life. The work suggested that some traditionally neglected defect descriptors may play a relevant role under specific circumstances

Contour Method with Uncertainty Quantification: A Robust and Optimised Framework via Gaussian Process Regression

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.Team Luca Laurent

A Bayesian defect-based physics-guided neural network model for probabilistic fatigue endurance limit evaluation

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.Team Luca Laurent

Investigation and modeling of the performance degradation of a H2/O2 PEM Fuel Cell stack under constant current solicitation

International audienc

Evaluation and Origin of Residual Stress in Hybrid Metal and Extrusion Bonding and Comparison with Friction Stir Welding

Hybrid metal and extrusion bonding (HYB) is an emerging solid-state welding technique that was developed about ten years ago. HYB exploits the fundamental idea of the well-established friction stir welding (FSW) technology, but a filler material is employed to enhance control of the microstructure and the mechanical properties of the joint. HYB and FSW allow joining to be performed at lower temperatures than classical fusion welding methods. Still, thermal gradient effects seem impossible to be entirely avoided, thus leading to residual stress within the weld region and neighbouring material. Although the FSW-induced residual stress evaluation has been extensively studied and understood, the evaluation and interpretation of HYB-induced residual stress have not been tackled so far. In the present paper, a quantitative investigation on residual stress and its origin in HYB was carried out for the first time. Specifically, a 4 mm thick AA6082-T6 HYB and a 4 mm thick AA6082-T6 FSW butt welds were considered. For the particular case of HYB, an AA6082-T4 was used as the filler material. In both cases, the full-field longitudinal residual stress was experimentally assessed using the Contour Method. The results showed that the HYB joint yields a higher magnitude of tensile residual stress compared to that of the FSW counterpart. A physical explanation for this difference in magnitude was attributed to the lower yield stress point exhibited by the filler material. Furthermore, the analysis revealed peak values of residual stress as high as 205±25 MPa and 165±15 MPa, for the HYB and FSW joint, respectively. Despite this, a similar distribution of residual stress across the weld was observed in both cases. An additional qualitative analysis on the transverse distortion of the welds outlined a pronounced undesired “V-like” deformation of the HYB joint of approximately 1.4°. By contrast, the FSW joint seemed not to show any perceptible bend