This work focuses on the prediction of the multiaxial fatigue limit at constant amplitude for metallic materials weakened by stress concentrators. Developing predictive models for multiaxial fatigue limits, which enable the analysis of the effects of defects and notches, is especially relevant in the context of the rapid advancement of Additive Manufacturing (AM) technologies. This is due to two main reasons: (i) current AM processes are inherently prone to defects, and (ii) AM technologies allow manufacturing components with complex geometries, such as lattice structures, characterized by the presence of notches and multiaxial stress states. More specifically, the study addresses the engineering estimation of the multiaxial fatigue limit in the presence of defects, cracks, and sharp U or V notches and proposes a unified design criterion based on the Averaged Strain Energy Density (SED) approach, which extends the Atzori-Lazzarin-Meneghetti (ALM) diagram to multiaxial loadings. The SED framework offers a method to define both an equivalent defect-free material fatigue limit, denoted as Δσ0eq, and an equivalent fatigue threshold, for any local stress field. By combining these two parameters using an El Haddad Smith Topper-type equation, defect sensitivity under local multiaxial stresses can be described. An extensive validation against experimental multiaxial fatigue limits is included, demonstrating the sound correlation between theoretical estimations and experimental results. This validation highlights the robustness and reliability of the proposed method in view of real-world applications, where understanding the impact of stress raisers, such as defects and notches, is critical to ensure the structural integrity of mechanical components.

The field of fatigue stress-life estimation addresses the effects mentioned in the title differently. The load effect differentiates among various loading modes that lead to uneven stress distributions across the critical cross-section. The notch effect accounts for this uneven stress distribution when induced by structural irregularities. Conversely, the size effect – sometimes referred to as the “statistical” size effect – addresses the weak-link mechanism of fatigue damage, where larger components subjected to the maximum stress are more likely to initiate cracks if compared to smaller components with the same maximum stress. This effect may interact with both the load and notch effects.

The FKM Guideline identifies two additional effects to consider: (1) the mechanical deformation effect, which assesses the material’s yielding capability, and (2) fracture mechanics effect, which slows crack propagation in the presence of stress gradients. The latter effect shares similarities with both the load and notch effects.

This paper proposes an attempt to unify the notch and size effects into a critical volume effect, relating to the size of the control volume directly influenced by stress distribution within the component. The evaluation is based on a test case involving six variants of specimens manufactured from a single batch of S355J2 structural steel. These variants include one unnotched hollow configuration and five notched configurations with varying notch acuities. The specimens are subject to load control through three different fatigue loading modes: push-pull, torsion and plane bending.

Based on experimental results, the critical volume solution is developed to address this issue. The paper discusses its current limitations and provides a comparison with typical stress-gradient solutions and with the application of the theory of critical distances.