PSI - Issue 37

Patrick Yadegari et al. / Procedia Structural Integrity 37 (2022) 500–507 P. Yadegari et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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2.2. Damage parameter life curve The “Guideline non - linear” provides two damage parameters to describe the relationship between the number of cycles a material can sustain and the applied load. Firstly, the parameter P RAM , which is based on a further development of the parameter SWT by Smith, Watson and Topper (1970) using the extended mean-stress sensitivity by Bergmann (1983), allows the consideration of the material-dependent mean-stress sensitivity. For each damage-effective load cycle, a value for the damage parameter is calculated with the relevant stress amplitude, mean stress and strain amplitude, Equation 2. For fatigue tests with a predefined mean stress, the factor k takes into account the mean-stress sensitivity, which can be determined experimentally or estimated, Equation 3, using the material group-dependent calculation values, Table 2. RAM = { √( a + ∙ m ) ∙ a ∙ for ( a + ∙ m ) ≥ 0 0 for ( a + ∙ m ) < 0 (2) = { σ ∙ ( σ + 2) for m ≥ 0 σ 3 ∙ ( σ 3 + 2) for m < 0 with σ = M ∙ 10 −3 ∙ m MPa + M (3) Table 2. Calculation values for estimation of the mean-stress sensitivity Material group M M Steel 0.35 -0.1 Ultra-high strength steel 0.39 -0.36 The corresponding damage parameter life curve is defined in double-logarithmic form by a trilinear trend, with a support point P RAM,Z,WS at 10 3 load cycles and the specified slopes d 1 and d 2 for the range of low-cycle fatigue as well as a constant path for the endurance limit P RAM,D,WS , according to Equation 4. = { 10 3 ∙ ( RAM RAM,Z,WS ) 1 1 ⁄ for RAM ≥ RAM,Z,WS 10 3 ∙ ( RAM RAM,Z,WS ) 1 2 ⁄ for RAM,Z,WS > RAM > RAM,D,WS ∞ for RAM,D,WS ≥ RAM (4) For the estimation of the entire curve, the support point and the endurance limit are calculated based on the tensile strength and material group-dependent calculation values, Equation 5. With the factor f 2.5% , the failure probability can be reduced to 2.5 %, since the calculation variables were determined empirically for a probability of 50 %. However, this is not applied in the case of comparisons with test results and f 2.5% = 1.0 is set. RAM,Z,WS = 2.5% ∙ P,Z ∙ ( m MPa ) P,Z , RAM,D,WS = 2.5% ∙ P,D ∙ ( m MPa ) P,D (5) The calculation values required for the estimation of the damage parameter life curve are given in Table 3 for steel, as already defined in the guideline (Fiedler et al. (2019)), and for the new group of ultra-high-strength steels.

P,Z in MPa P,Z P,D in MPa P,D 1 2 2.5% 20.0 0.587 0.82 0.92 -0.302 -0.197 0.71

Table 3. Calculation values for estimation of the damage parameter life curve Material group

Steel

Ultra-high strength steel

18.0

0.587

0.73

0.93

-0.155

-0.145

0.65