PSI - Issue 5

Maria Paarmann et al. / Procedia Structural Integrity 5 (2017) 869–874 M. Paarmann et al / Structural Integrity Procedia 00 (2017) 000 – 000

872 4

a)

c)

b)

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60

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Sc 1.1 Sc 1.2 Sc 1.3

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 K I /  K I,Sc2

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Fig. 3. Comparison of cyclic SIF over crack growth for different temperature transients on (a) the surface point in the sphere, (b) the deepest point of crack front and (c) the surface point in the connector

In order to investigate the influence of the crack shape, a circumferential crack was inserted as initial crack front for scenario 1.1. Due to numerical problems the simulations of the semi-elliptical cracks stop at a crack depth of 32.8 mm. The cyclic SIF of the circumferential crack is about 25% higher than the SIF of the semi-elliptical crack on its deepest point (A). On the other hand the SIF of the surface point C of the semi-elliptical crack front is nearly constant and larger than the SIF of the circumferential crack starting at a = 15mm. This results from higher thermal loadings at smaller crack depth. The comparison underlines that cracks grow faster in the width than in the depth direction and crack growth gets slower with increasing wall thickness depending on the loading.

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semi-ellipt ical A semi-ellipt ical C circumferent ial

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 K I /  K I,Sc2

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a [mm]

Fig. 4. Comparison of cyclic SIF over crack depth of semi-elliptical and circumferential crack shapes on position E for scenario 1

4. Lifetime prediction of the ball-shaped part based on experimental and numerical results

With the experimental and numerical results from chapters 2 and 3 lifetime predictions are achievable. Therefore, the cyclic SIF Δ K in the cases of scenarios 1 and 2 was defined with a stress ratio of R = 0. For scenario 2, Fig. 5 shows exemplarily the necessary temperature dependent crack depth for crack growth. It becomes obvious that only for position F crack growth starts at the initial crack size. For position E the temperature dependent threshold values Δ K th are exceeded for crack depths between 13 mm and 17 mm. For that reason a ( N )-curve were only determined for position F starting at the initial crack size a 0 = 5 mm. Moreover, investigations for the steady state scenario 2 at different temperatures were made to test the influence of constant temperature on the residual lifetime of an actual use case. Fig. 6 shows a ( N )-curves for the experimentally analyzed temperatures.