PSI - Issue 76

D. Kaschube et al. / Procedia Structural Integrity 76 (2026) 19–26

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Sandner EXA10-0.25 extensometer, whose maximum error was ± 0 . 1%. Data acquisition was performed at 1200 Hz for tests in the HCF regime and at 5 Hz for those in the LCF regime. A runout criterion of 4 · 10 6 load cycles was de fined, and failure was identified by the onset of cracking, determined through assessment of the force envelope curve in accordance with the referenced standard, VDEh (2006). Three di ff erent test series were conducted to investigate the influence of mean strain on the fatigue behaviour. Test series 1 was performed with 0% mean strain, fully reversed, i.e. an R ε of -1. The second test series investigated the influence of compressive mean stresses and was performed at R ε = −∞ , which corresponds to compression release. The third test series investigated the influence of tensile mean stresses and was therefore performed at R ε = 0, which corresponds to tension release. In order to use the Co ffi n-Manson expression described in the introduction, the strain amplitude needs to be sep arated into an elastic ε a , el and a plastic component ε a , pl . The partitioning of elastic and plastic strains was carried out by determining the elastic portion from Young’s modulus E . Since the Co ffi n–Manson relationship assumes a consistent modulus, the same Young’s modulus was used for each separation. To fit the experimental data, linear re gression was employed following established standards, VDEh (2006); ASTM (2015). At very low strain amplitudes, the accuracy of strain measurement becomes insu ffi cient, with errors often exceeding the true plastic strain. For this reason, plastic strain values below 0.01% were omitted from the analysis of the plastic strain–life curve. Following the recommendations of Williams, Williams (2003), plastic strain data outside the LCF regime—defined here as up to 10 4 cycles—were also excluded, regardless of their magnitude, to avoid distortion of the curve by values outside the relevant range. This selective approach resulted in a more extensive dataset for the regression of the elastic strain curve compared to the plastic strain curve. The results of the fatigue experiments for all three mean strains are given in table 1, including the strain ratio R ε , the total strain amplitude ε a , the stress amplitude σ a , the mean stress σ m , the stress ratio R σ and the resulting number of cycles to failure N f . The individual results of the test series with 0% mean strain ( R ε = − 1) were used to generate a strain-life curve according to Co ffi n-Manson. It is shown together with the individual results in Figure 2a. The specimens tested under compression strain exhibited cyclic hardening behaviour, which is why, as with specimens up to N f = 5 · 10 3 , the fracture of the specimen was evaluated as the termination criterion. For all other samples, the termination criterion was selected according to standard, VDEh (2006). This is permissible because crack initiation accounts for the majority of the life in this case and the values therefore remain comparable, Shamsaei et al. (2010). Table 2 shows the static and cyclic material parameters used for further evaluation. Figure 2b shows the results of all three test series together. The results with 0% mean strain are compared with those for compression release ( R ε = −∞ ) and tension release ( R ε = 0). The two curves for 0% mean strain and positive mean strain are shifted approximately parallel, with the samples with mean strain having a shorter fatigue life than those without mean strain, as expected. The influence of a compressive mean strain or a strain completely in the compressive range yields a di ff erent result. In the range below a strain amplitude of approx. 6 . 5 · 10 − 3 , the specimens exhibit longer lifetimes than those without mean strain. However, this changes in the low cycle fatigue range with increasing strain amplitude. This can be explained by the cyclic hardening behaviour of the specimens tested under compressive mean strain, which leads to high local strains and increased dislocations, Dowling (2013). The fatigue data in Table 1 resulting from the three test series is used to test the applicability of the mean strain theories introduced in section 1. Figure 3 shows the results of applying the various mean strain models together with an evaluation that does not take into account the influence of mean strain according to Co ffi n-Manson. All figures show the number of load cycles in the test versus the number of predicted load cycles. Figure 3a shows a comparison of the load cycles when applying the Co ffi n-Manson equation 1. It shows that the fully reversed tests are all within a scatter band of 3, which is why this scatter band was chosen to illustrate the applicability of the mean strain models in the other figures. The figure shows that it is necessary to use a mean strain model, as otherwise the service life is drastically overestimated at tensile mean stress, which in real applications can lead to premature component failure in the worst case. In the case of compressive mean stresses, there is also 3. Experimental results 4. Mean strain models