PSI - Issue 18

4

Rainer Wagener et al. / Procedia Structural Integrity 18 (2019) 490–500 Rainer Wagener, Andreas Maciolek, Heinz Kaufmann/ Structural Integrity Procedia 00 (2019) 000–000

493

Figure 2: Development of the cyclic stress-strain behaviour depending on the load history

3. Strain-life relation Coffin (1954) and Manson (1965) describe the dependency of the plastic strain portion of the fatigue life as a line in a double logarithmic coordination system. This knowledge has been gathered by cyclic plastic strain-controlled tests with iron and copper alloys. Due to the plastic strain-controlled fatigue tests and their focus of interest on the Low Cycle Fatigue regime, the number of cycles to crack initiation is limited by N i = 1 ∙ 10 4 cycles in most cases. Morrow (1965) used the sum of the elastic strain – life correlation described by Basquin (1910) and the plastic strain – life correlation of Coffin and Manson to describe the total strain life curve in the case of a fatigue approach, eq. 2. ��� � ��� � ��� � � �� � ∙ �2 ∙ � � � � � � ∙ �2 ∙ � � � (2) Since the strain-life curve has been published, its validity for aluminium alloys as well as its enhancement to the High Cycle Fatigue regime and Very High Cyclic Fatigue regime has been discussed by Endo and Morrow (1969), Sander et al. (1977), Wong (1984), Wigant and Stephens (1987), Stephens et al. (1988), Wong (198), Stephens and Koh (1998) and Fatemi et al. (2005). Independent of the evaluated test results, all authors assert that there should be at least one knee point in the elastic strain line, which is located around 1 ∙ 10 4 cycles to crack initiation, but the definition differs from author to author. 2007 Wagener suggested a distinguishing of the elastic strain-life curve in 3 regimes depending on the stress-strain behaviour. The bases are total strain-controlled fatigue tests with aluminium alloys of the 5xxx and 6xxx series. The first regime is related to the Low Cycle Fatigue regime. Therefore, the stress strain behaviour of initial loading, as well as of the so-called cyclically stabilised material state at 50% of the number of cycles to crack initiation, is elastic-plastic, Figure 3. This means that, within the whole fatigue life, elastic-plastic stress-strain behaviour occurs. Due to the work hardening, the elastic-plastic stress-strain behaviour of the initial loading becomes macroscopically elastic in the second regime, which is related to the High Cycle Fatigue regime. Logically, there should be a third regime up to the Very High Cycle Fatigue regime within macroscopic elastic stress-stain behaviour throughout the fatigue life. This second knee point is well-known from stress-controlled Wöhler-curves, keeping in mind that the stress-strain behaviour is macroscopically elastic. Due to this reason, no differences between stress- and strain controlled fatigue tests should occur. For the mathematical description, equation 2 has been extended by introducing an index I to the properties of the elastic part, eq. 3, representing the three regimes. In order to derive the cyclic stress strain curve, the properties of the first regime should be used.