PSI - Issue 56

Radim Halamaa et al. / Procedia Structural Integrity 56 (2024) 111–119 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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(a)

(b)

Fig. 6. Results of tension-compression fatigue test: (a) the axial force time-history; (b) the hysteresis loop corresponding to the 11 th load cycle.

Fig. 6(b) shows the shape of the hysteresis loop corresponding to the 11 th load cycle, for which the axial strain was determined using the extensometer. From the stable hysteresis loop, the amplitude of the axial stress and the amplitude of the axial strain can be determined and thus a single point on the cyclic strain curve can be obtained, see Fig. 7.

Fig. 7. Cyclic stress-strain curve of tension-compression case corrected for the effect of multi-axial strain.

It is worth noting that the curve for the upper and lower part of the specimen was obtained from a single fatigue test. Each point in the 'conventional method' corresponds to a fatigue test performed under a specific level of strain amplitude. 4.3. Nonproportional loading case The waveforms of the loading quantities for the tension-compression/torsion loading are harmonic and are offset by 90° from each other. The test was set so that the amplitude of the equivalent strain was 1.25 % and the shape of the load path was circular. When the axial force reaches its maximum/zero value, the torque has a zero/minimum magnitude (phase shift 90°). This fact can be exploited, and the test can be independently evaluated at these specific time points, regardless of the existence of biaxial tension. Fig. 8(a) shows a comparison of the results obtained from the DIC (axial stress) with the results of the fatigue tests obtained conventionally. Again, the results for the upper and lower curved parts of the specimen are shown. The approximation in this case is made by using a non-linear function of Chaboche type. The approximation function has the following form ( )= 0 + 1 + 2 (1− − 3 ) , (3) where b i (i = 0, 1, 2, 3) are the unknown parameters optimised by a non-linear least squares method, is the stress amplitude and is the axial plastic strain amplitude. The results obtained for the shear stress component are shown in Fig. 8(b). The approximation by a nonlinear function is denoted here as "DIC, upper/bottom part approx.". The "DIC, averaged" mark then shows the resulting cyclic stress-strain curve obtained by the proposed technique. The parameters obtained from the approximation function (3) considering the axial / shear stress and strain components are summarised in Table 2.

Table 2. Resulting parameters of the approximation of the cyclic stress-strain curve for the 90° out of phase test.