PSI - Issue 18

Rainer Wagener et al. / Procedia Structural Integrity 18 (2019) 490–500 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The most common way to derive the material properties K’ and n’, as well as the Young’s modulus, is by carrying out cyclic tests with constant amplitudes and evaluating the stress-strain behaviour at 50% of the fatigue life, meaning 50% of the number of cycles to crack initiation. Therefore, the stress amplitude and the plastic strain portion must be determined. Performing a linear regression with the logarithmic stress amplitude dependent and the logarithmic plastic strain portion as the independent variable will determine the properties K’ and n’. Therefore K’ is equal to the theoretical stress that would be reached at a plastic strain amplitude of 100% and n’ is the slope of the best-fit line, Figure 1.

Figure 1: Cyclic flow curve

Due to the character of constant amplitude tests, it is not possible to recognise the influence of higher loads on the cyclic stress-strain behaviour of subsequent lower cycles caused by the glide character. Keeping a fatigue assessment of randomly loaded structures in mind, the main difference in the cyclic stress-strain behaviour under constant amplitude und variable amplitude loading is the field of the highest damage impact of the load-time history. Landgraf et al (1969) introduced different load sequences in order to study the cyclic material behaviour. The established Incremental Step Test is one of these load sequences, which consists of well-defined blocks of increasing and decreasing amplitudes. Due to this load sequence, only one specimen is required to derive the cyclic stress-strain curve, which is represented by the reversal points considering the memory and Masing behaviour, because normally no mean stresses occur or could be neglected. The distinguished evaluation of the tensile and compression reversal points enables a derivation of different stress-strain curves for tensile and compression loading conditions. Furthermore, the research work of Christ (1998) and Wagener (2007) led to the assumption that the cyclic stress-strain behaviour derived by an Incremental Step Test matched the stress-strain behaviour better than the cyclic stress-strain behaviour derived by constant amplitude tests. Hence, Wagener (2010) suggested the use of the stress-strain behaviour of an Incremental Step Test for the fatigue life assessment with the maximum total strain amplitude in the range of the expected maximum service load, because there could be an influence of the maximum load on the stress-strain behaviour. Furthermore, the Incremental Step Test enables the study of the work hardening or softening just by deriving the stress-strain curve for each block, Figure 2. This information could be used to optimise the fatigue approach of cyclic randomly loaded structures shown by Möller (2019). Besides the experimental methods to derive the properties of the cyclic stress-strain curve, a common approach is the usage of the compatibility conditions, which means the calculation of K’ and n’ using the properties of the strain life curve. This is feasible due to the similar structure of the equations. On the other hand, the compatibility conditions imply the enhancement of the two-dimensional strain – life relation to a three-dimensional strain – stress – life relation. Keeping this three-dimensional relation in mind, the compatibility conditions allow for a validation of the derived cyclic material properties. Therefore, the strain-life relation is evaluated and the properties of the cyclic stress-strain relation are derived by the compatibility conditions. If the resulting stress-strain curve matches the test results, the cyclic material properties are valid.