PSI - Issue 79

Daniel Hofferberth et al. / Procedia Structural Integrity 79 (2026) 313–321

316

The stress concentration factor was determined numerically, equation (1) and analytically according to equation (2). For the numerical analysis of the ISO specimens, Fig 1 and Fig. 2 (a) , the FEA software ABAQUS 2024 HF2 was used. As discretization, brick-elements with a quadratic shape function (Abaqus: C3D20) have been used. To achieve converged stresses, the meshing of the specimens was performed in accordance with the recommendation in [Baumgartner13]. All calculations were performed with the complete specimen geometry, applying a symmetrical loading with the value of 1 N axial load on both sides. The resulting stress distribution, overall and local, and maximum principal stress value were used for the calculation of K t . The nominal stress was calculated with the ideal specimen geometries, taken from the technical drawings. The resulting stress concentration factor is shown in Fig. 3 (a). In addition to the numerical calculations the stress concentration factors were calculated analytically according to the equation (2) [Rainer678, Neuber01] using the geometric parameters (notch radius and width of the specimen) from the drawings for axial loading. The parameters of equation (2) can be filled with geometric values, as well as the axial correction parameters p and q according to Neuber. For these three types of flat specimens under axial loading, the parameters are set to p = 1.32 and q = 2, based on the literature. The results are listed together with the numerical values in Table 1. � , � � � � , ��� � ��� � � � , ��� � � � �� � (1) � � 1 � � � � ����������������� � �� �� �� � � �� � � (2) With the existing FE-model the calculation of the highly stressed volume V 90% was performed in a second calculation step. The V 90% is the volume including the stresses above 90 % of the maximum stress level in the specimen (Kuguel61, Sonsino93). The V 90% approach considers the statistical size effect based on the different stress gradients which influence the highly stressed volume (Kuguel61). It assumes that a flatter stress gradient, leading to a larger highly stressed volume suggests a higher probability for the presence of a defect, which in turn affects the fatigue strength. For calculation of V 90% , a minimum element length-to-height ratio of 2:1 of the brick-elements with quadratic shape functions was applied. For the ISO 2740 specimen, the element size was adapted to the rectangular area to obtain good element distribution. The calculation of the V 90% was performed in the post-processor of the FEA software. This approach was successfully applied for the pre-assessment of components made of sintered materials [Hofferberth10]. The exemplary result of the ISO specimen is depicted in Fig. 3 (b), showing the V 90% of the specimen. Fig. 3 (a) shows the resulting overall and local stress distribution for the ISO 3928 R30 specimen. The maximum resulting first principal stress in the notched area was selected automatically and the stress concentration factor was calculated to K t = 1.057. The results of the V 90% calculation are plotted for the same specimen in Fig. 3(b).

Fig. 3: (a) Calculated stress concentration factor K t,a ; (b) Calculated highly stressed volume V 90%