PSI - Issue 68

Robert Szlosarek et al. / Procedia Structural Integrity 68 (2025) 1173–1180 Robert Szlosarek et al./ Structural Integrity Procedia 00 (2025) 000–000

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Instead of using the actual stress and strain loading situation it is possible to express the equation by using the strain life curve of Basquin (1910), Manson (1965), Coffin (1954) and Morrow (1965). This results if the following equation, which can be solved to calculate the lifetime & as unknown parameter. ,( " + ! ) ∙ $," ∙ = 1 + ! , # , 22 & 4 -. + & , ∙ & , 22 & 4 ./0 (2) The parameters , , & , and & , are the Basquin, respectively Manson-Coffin and Morrow parameters. They are constant. The total strain amplitude $," is also constant in the considered framework of constant total strain controlled tests. The corresponding stress to the total strain can be calculated by solving the Ramberg-Osgood (1943) equation $," = + $ , +6 + $ 12 7 3542 . (3) The common approach to determine the parameters ′ and ′ is to analyze the hysteresis loop in the stress-strain diagram at half of the lifetime of all tests. Hence, for each test with a certain total strain amplitude a corresponding stress amplitude can be observed. Fig. 1 shows the measured stress amplitude " versus the cycles. The markers show the stress amplitudes at half of the lifetime for each test. For instance, the amplitude at half of the lifetime is not representative for the whole lifetime, especially for large total strain amplitudes. The common procedure would be to create a cyclic stress-strain curve out of the marked values. Subsequent, it is possible to make a regression to determine ′ and ′ . The graphs point out that it is not useful to create a single, representative cyclic stress-strain curve out of the values obtained at half of the lifetime. Since the material undergoes a pronounced cyclic hardening, the curves would look different in dependency of the analyzed point of the relative lifetime as it is presented by Droste et al. (2022).

Fig. 1. courses of the stress amplitude over the lifetime for tests with different total strain amplitude of swaged X2CrNiCuN17-6-4 steel. To overcome this issue the cyclic stress-strain curve shouldn’t be assumed as constant over the lifetime. This can be reached by making the material parameters, in detail ′ and ′ , nonconstant, respectively transient. Therefore, a uniform scale is needed like the relative lifetime (N/N f ) . If we assume linear damage this is equal to the damage value of the material. In this research eleven equally distributed points over the lifetime are used. The first determination was done at 1 % following at 5 % of the lifetime and the last one at 95 % of the lifetime with an increment 10 %. All in all, eleven datasets for ′ and ′ are available with this approach. These datasets were fitted by a polynomial function of 3 rd order. By using this framework, the stress amplitude is different in each cycle. Hence, Eq. (2) will lead to different lifetimes. Therefore, the computational process was modified as it is shown in