PSI - Issue 75

Jan Papuga et al. / Procedia Structural Integrity 75 (2025) 289–298 Author name / Structural Integrity Procedia (2025)

290

2

where larger components subjected to the maximum stress are more likely to initiate cracks earlier if compared to smaller components with the same maximum stress. This effect may interact with both the load and notch effects. The FKM Guideline from its 6 th version [1] identifies two further effects to consider in addition to the statistical effect: (1) the mechanical deformation effect, which assesses the yielding capability, and (2) fracture mechanics effect, which slows crack propagation in the presence of stress gradients. This paper proposes an attempt to unify the notch and size effects into a critical volume effect, related to the size of the control volume directly influenced by stress distribution within the component. The evaluation is based on a test case involving seven variants of specimens manufactured from a single batch of S355J2 structural steel. This paper extends the analysis made by Nesládek et al. [2] on a limited set of three notched configurations in two load modes (push-pull or torsion) by more notched configurations with significantly more varying notch acuities. The specimens are subject to 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 shows its current limitations and provides a comparison with typical stress-gradient solutions and with the application of the theory of critical distances. 2. Effects related to the critical volume The critical volume in this paper refers to the volume of material loaded by an effective stress value higher than z multiple of the maximum value of the effective stress in the detected hot-spot nearby. Its relation to the fatigue strength of the part can be used to estimate the fatigue strength simply from the evaluation of the critical volume for the specific load combination and load cycle. This approach is sometimes referred to as the Highly-Stressed Volume (HSV) thanks to its originator Kuguel, see [3], or [4]. However, it did not reach such a popularity that it would be implemented into a commercial fatigue solver. Moreover, the validation of the solution provided in [4] refers only to axially loaded unnotched and notched specimens compared to the bending and torsion load modes present in this paper. The leading idea to apply it here was that this approach might cover multiple effects addressed in other solutions separately. These other effects commonly referred to in other computational approaches and analyzed separately are: • Notch effect describes the effect of some macro-notch on reduction of the nominal fatigue strength. Because the concept of nominal stresses is too cumbersome to deal with in the post-processing of finite element (FE) calculations, this phenomenon is more often today translated to the stress gradient effect. • Load effect describes the effect of the load mode on the fatigue life of a part. This older concept (applied, e.g., in Mischke et al. [5]) differentiates between bending and axial load. In reality, it refers to differences in the stress distribution across the evaluated cross-section. Thanks to that, it can be integrated into the stress gradient effect. • Stress gradient effect: The effect describes the dependency between the local fatigue strength at the notch root and the stress gradient, with which the stress diminishes in the direction normal to the surface. • Size effect: It conforms to the expectation of the weakest-link concept – the larger is the part, the higher probability of internal defects causing the crack initiation and its subsequent failure. Notch and load effects are today rather transferred to be addressed via the stress gradient effect. However, the remaining two effects (stress gradient effect and size effect) are rarely integrated into one calculation approach. Within the fatigue solvers available today, there are two major commonly applied approaches to solve the problem of notches in structures: • Relative stress gradient (RSG) approach [1,6] : The value of RSG from the notch root is used to define a new local component S-N curve, which lies above the S-N curve related to material (i.e. to the specimen without notches and of nearly homogeneous stress distribution across the minimum cross-section). Thanks to that, the local stress at the notch root can be used with this local component S-N curve to provide the fatigue life estimate (see Fig. 1). • Theory of critical distances (TCD) [2,7] : The material S-N curve can be directly used, but the reference stress at the component is not obtained at the hot-spot (e.g. notch root), but at some critical distance from it, see Fig. 1.