Issue 47

D. Benasciutti et alii, Frattura ed Integrità Strutturale, 47 (2019) 348-366; DOI: 10.3221/IGF-ESIS.47.26 361 The capability of the PbP criterion to capture the material sensitivity to the local stress state is well summarized by the graph in Fig. 9(b), which plots the values of the damage ratio D Mat2 / D Mat1 vs. ρ ref for each node of the FE model. If the PbP were not sensitive to the material which the structure is made of, the FE analysis would return the same damage value in every node regardless of the material type, and in turn all the dots in Fig. 9(b) would lie on the dashed horizontal line. (a) (b) Figure 9 : (a) Distribution of ρ ref values in FE nodes; (b) damage ratio D Mat2 / D Mat1 vs. ρ ref values (each point refers to one nodal result). Likewise, the trend in Fig. 9(b) remarks how much the fatigue damage (via PbP criterion) is influenced by the hydrostatic stress via ρ ref values. Being dependent on hydrostatic stress, Material 2 is characterized by damage values that depend upon ρ ref more clearly and that differ by up to an order of magnitude from those characterizing Material 1. Though simple, the numerical example discussed so far shows, in fact, the ability of the PbP method to capture the material sensitivity to the local multiaxial stress in a structure. This result is of great relevance in engineering applications, especially at early design phases, when it is desirable to compare the performance of different materials for the same component or, by contrast, it is required to identify a material whose fatigue properties are the most suitable for a given component subjected to a known vibration input. C ONCLUDING REMARKS he writing of this article was primarily motivated by the aim to provide engineers engaged in vibration fatigue with a practical guide to apply the PbP spectral method. After a summary of the main analysis steps of the PbP criterion, the article applied the criterion to some simple numerical case studies, in which three material types are subjected to four different types of biaxial random stress (e.g. tension-tension, tension-torsion, “in-phase” or “out-of- phase”). A simple rectangular PSD for the stress is considered to allow a much easier understanding and interpretation of the obtained results. The results of each analysis step were listed in detail to serve as a benchmark for users interested in implementing the PbP method by their own. Results are also used to highlight the main features characterizing the PbP criterion. For example, the examples allow the role of material sensitivity to hydrostatic and deviatoric stress to be clearly pointed out. The case studies make apparent the capability of the PbP method to take into account the correlation degree between stress components, as well as the different material behavior as a function of the various states of stress. The article concludes by an example in which the PbP method is applied to the FE-based fatigue analysis of a thin structure submitted to a random acceleration. This example shows the advantage of the PbP method in CAE-based design of structural components undergoing multiaxial fatigue loading. It emphasizes, in particular, how the method proves to be an efficient tool in the design of complex structures, e.g. for discriminating among materials with different fatigue properties, or for identifying the material with the most suitable properties. 0 0.5 1 1.5 0 50 100 150 200 250 300  ref No. of counted nodes tension torsion A‐B (ρ ref >1) C‐D (ρ ref =0.5‐0.9) 0 0.5 1 1.5 10 -2 10 -1 10 0 10 1 10 2  ref D Mat2 /D Mat1 T