Effective stress determination for flat bars with sharp notches by combining the theory of critical distances with artificial neural networks

Abstract

This work systematically quantifies the deviations of gradient methods from the Theory of Critical Distances (TCD) and introduces neural-network-based metamodels for the rapid prediction of effective stresses in notched flat bars. Stress-based fatigue and fracture assessment methods often rely on the local stress field around a notch and are commonly referred to as effective stress or stress-gradient methods. In this study, notched flat bars are examined as a representative structural detail. The influence of geometrical variation, critical distance, loading, and plane state on the resulting effective stresses is investigated using the point, line, and area methods of TCD. Deviations of up to 40% are identified across certain geometry–loading combinations, highlighting the sensitivity of TCD based assessment to parameter variations. To eliminate the need for a dedicated numerical simulation for every new notch geometry, a series of feedforward artificial neural network (ANN) metamodels is developed and trained on thousands of finite element simulations. Particular attention is given to the effect of optimization algorithms on training performance and predictive robustness. The resulting metamodels provide fast and accurate estimates of effective stresses across a wide range of geometries and loading conditions, offering a computationally efficient alternative to repeated finite element analysis for the assessment of notched components.