PSI - Issue 17

Siegfried Frankl et al. / Procedia Structural Integrity 17 (2019) 51–57 Siegfried Frankl / Structural Integrity Procedia 00 (2019) 000 – 000

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3

Table 1: Yeoh parameters for the rubber part 10 [MPa] 20 [MPa] 30 [MPa] 1 [1/MPa] 2 [1/MPa] 3 [1/MPa] 0.2365 5.778E-02 7.316E-02 0.906 0 0

Table 2. Model parameters Description Outer radius silicone part S Length silicone part Friction coeff. rubber / punch 1 Friction coeff. crack faces 2 Mesh size Initial crack length a 0 Fibre radius F S r Pi Pe Length to retrain Punch inner radius Punch edge radius

Symbol

Value

Unit mm mm mm mm mm mm

0.25

4

10

5

0.4 0.1

0.5

1

0.1

mm mm J/m 2

c

0.25 500

Fracture energy

2.2. Evaluation of energy release rate

At interfaces and for delamination cracks, the classical K -concept with a stress intensity factor is not valid. However, the more general energy release rate concept can be used. The energy release rate G is defined as the change of the energy which is released through crack growth (change of crack face area A crack ) of an existing crack. This energy release rate G consists of the external work W e , the strain energy U (negative) and the frictional dissipation W f (negative) as used by Sun and Davidson (2006): = crack [ e − ( + f )] (1) The derivative can be replaced by a finite difference, where  U = U ( a +  a ) - U ( a ) and similar for W e and W f . If the same displacement is applied for both crack lengths, the change in the external work W e becomes zero and G can be written with  A crack = 2  R f  a as: = − 4 1 [ + ] (2) The values needed for U ( a ), U ( a +  a ), W f ( a ) and W f ( a +  a ) are determined from FE models with according crack lengths. This assumes that running the model with a crack length of a +  a yields the same energies as a model that has initially a crack length of a and then the crack is extended by  a . This path-independency is not necessarily valid if friction is not negligible in the model. This simplification will be discussed in section 3.1, where typical values of U and W f are shown. When the computed energy release rate G reaches its critical value, the fracture energy G c , the crack propagates and keeps propagating until G of the growing crack drops below G c or full separation is reached.

2.3. Incremental crack propagation model

To predict the growth of the delamination crack, an incremental crack propagation model is introduced. It uses the FE model described in section 2.1 and the evaluation of the G values described in section 2.2. The model starts with an existing initial crack with the length a = a 0 . Then, the displacement u is applied stepwise in  u increments