PSI - Issue 42

Florian Garnadt et al. / Procedia Structural Integrity 42 (2022) 1113–1120 F. Garnadt et al. / Structural Integrity Procedia 00 (2019) 000–000

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5

(a)

(b)

F, U

� F

F

a a+ � a

upper branch

U

� F

lower branch

� U

� U

Fig. 3. (a) Section of the round bar specimen with notch used for an axisymmetric FE model, (b) global force displacement curves as a result of the simulation used for the evaluation of the cyclic J -Integral by referencing to the points of load reversal and evaluation of the energy di ff erence between two crack configurations a and a + ∆ a .

3.3. Crack closure

The consideration of crack closure in form of PICC is crucial for a precise computation of ECG in the vicinity of a notch. Therefore, di ff erent criteria for crack opening or closure, like the displacement of the first node behind the crack tip or the di ff erence in applied force and reaction force at the symmetry plane, are investigated. The latter has shown to be the most robust criterion in the described framework and is applied exclusively in the following. Furthermore, the impact of dwell times has a major influence on crack closure as described in detail in Garnadt et al. (2022). An example for this influence is given by Fig. 4. The loading in terms of the global strain range in all three cases is the same. The highest crack tip loading is achieved, if crack closure is neglected (Static). In case of the triangular cycle without dwell times t h / t h = 0 / 0 min / min, the result for the upper and lower hysteresis branch is approximately the same, but in case of the trapezoidal cycle with three minutes dwell time in tension and compression t h / t h = 3 / 3 min / min, there is a di ff erence between loading and unloading. This leads to a higher fatigue crack growth rate and together with the additional creep crack growth to a reduction of ECG cycles.

16

Static t h / t h = 0 / 0 min / min, Loading t h / t h = 0 / 0 min / min, Unloading t h / t h = 3 / 3 min / min, Loading t h / t h = 3 / 3 min / min, Unloading

14

0 Cyclic Effective J -Integral ∆ J eff in N / mm 2 4 6 8 10 12

0.0

0.2

0.4

0.6

0.8

1.0

Crack Depth a in mm

Fig. 4. Impact of dwell times on cyclic e ff ective J -Integral for the round bar specimen with mild notch at a consistent global strain range of 0.29% in all three cases, static, cyclic without and with dwell times.