PSI - Issue 2_A

σ 3

3

σ 4

4

Sami Holopainen et al. / Procedia Structural Integrity 2 (2016) 2718–2725 S. Holopainen et al. / Structural Integrity Procedia 00 (2016) 000–000

2722

Pri

5

1.4 1.35 1.3 1.25 1.2 1.15 1.1 1.05 1 0.95

5 · 10 5

with inclusion base material

4 · 10 5

S 0 /σ 0

3 · 10 5

k = 1 k = 0

2 · 10 5

10 3

10 4

10 5

10 6

10 7

0.0001

0.001

0.01

N

ω ∆ t/ 2 π

Fig. 3. Convergence of the endurance life as a function of time step ∆ t and the SN-curve of the pure base material and with the alumina inclusion. Printed using Abaqus/CAE on: Mon Apr 18 23:01:44 FLE Daylight Time 2016 Printed using Abaqus/CAE on: Mon Apr 18 23:01:44 FLE Daylight Tim Printed using Abaqus/CAE on: Fri Apr 22 13:36:49 FLE Daylight Time 2016

Printed using Abaqus/CAE on: Fri Apr 22 13:36:49 FLE Daylight Time 20

Fig. 4. Damage field in the base material after cycle 1 for the isotropic AISI-SAE 4340 (lhs) and the forged 34CrMo6 steel (rhs). Notice the di ff erence in scale, the upper color bar refers to the AISI-SAE 4340 and the lower one to the 34CrMo6 steel.

1 growth per cycle in a constant amplitude cyclic loading. At the point of shortest life (A) the von Mises stress has the highest peak value while the hydrostatic stress amplitude is the smallest. In Figs. 9 and 10 damage evolutions for the forged 34CrMo6 steel are shown when the preferred longitudinal direction is either horisontal or vertical, respectively. The load amplitude is S 0 = σ − L . The fatigue lives for the transversely isotropic steel at the considered points di ff ers less than for the isotropic AISI-SAE 4340 steel when the preferred direction, direction of the grain flow, is in horizontal. Also, in this case the fatigue life is one decade shorter as expected.

5. Concluding remarks

A computer implementation of a continuum based transversely isotropic fatigue model is presented. Movement of the postulated endurance surface and the evolution of damage are governed with rate type equations. As an illustrative example a plane strain problem with a circular alumina inclusion in a steel base material is analysed. Two di ff er

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