The evaluation of S-N curves is a fundamental aspect of fatigue analysis in mechanical engineering. However, the reverse evaluation, defined as the minimization of the error term between the data and the S-N curve model in the direction of the unobserved variable “stress”, represents an area that is still insufficiently addressed in the literature. Consequently, the forward evaluation is defined as the minimization of the error term in the direction of the observed variable “lifetime”. This study systematically investigates both forward and reverse evaluations of S-N curves using Maximum Likelihood across different S-N curve models, including the linear and bi-linear Basquin models, as well as their corresponding statistical representations. A comprehensive analysis is performed to clarify the advantages, disadvantages and limitations of each approach in terms of convergence behavior and effective utilization of experimental data. Given the inherent challenges associated with fatigue testing, which often involves limited datasets and significant costs, it is crucial to optimize the use of available data. The results of this research are expected to improve the understanding of S-N curve evaluations, thereby increasing the accuracy and applicability of fatigue analysis methods.

Welded joints made of ductile materials show a significant reduction in fatigue life when subjected to non-proportional loading compared to proportional loading. While existing research on non-proportional loading strongly focuses on a 90° phase shift between normal and shear stress, which is widely considered to be most damaging, complex loading other than out-of-phase is rarely and insufficiently studied. This paper presents fatigue tests under various forms of non-proportional loading to distinguish the effects on fatigue life. These forms include different phase shifts, different frequencies, different R-ratios of normal and shear stress as well as an alternating application of both stress components. Finally, hypothesis testing is applied to differentiate whether different forms of non-proportional loading have different effects on fatigue life.