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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results but has no influence on the trend of the curves. However, there is a clear dependency of the maximum tensile forces F on  a, so for an accurate calculation of maximum F values,  a has to be chosen even smaller than 0.5 mm.

Fig. 5: Results for the incremental crack propagation model with different crack length increments  a showing (a) the strain energy U , (b) the crack length a and (c) the tensile force F plotted over the applied displacement u .

3.2.2. Effect of fracture energy To examine the effects of a change in fracture energy on the crack propagation model results, three fracture energy G c values of 300 J/m 2 , 500 J/m 2 and 700 J/m 2 are used in the simulations with a crack increment of 1 mm. Fig. 6 shows results of (a) the strain energy U , (b) the crack length a and (c) the tensile Force F over the displacement u for the three G c values up to a crack length of 9 mm. Obviously, higher G c values shift the crack growth towards higher energy values and higher displacements u. In addition, higher force values are reached, and force-displacement curves from Fig. 6c could be compared to test curves to estimate G c values for the rubber-fibre bundle interface.

Fig. 6: Results for the incremental crack propagation model with different fracture energies G c showing (a) the strain energy U , (b) the crack length a and (c) the tensile force F plotted over the applied displacement u .

3.2.3. Effect of friction coefficients In section 3.1, it has already been stated that the frictional dissipation W f is much smaller than the strain energy U and was therefore not regarded in the computation of the energy release rate G . To investigate how the friction influences the strain energy in the model and thus the G values, the incremental crack propagation model is calculated with the default parameters from Table 2 with the friction coefficient µ ( µ 1 = µ 2 ) set to 0.3, 0.5 and 0.7. For the fracture energy G c , a value of 700 J/m 2 is chosen. The initial crack length is 0.25 mm. Fig. 7 shows the results of the incremental crack propagation model for the three friction coefficients. A slight shift to earlier crack propagation is seen for higher friction coefficients. This is because the crack is closed in the region close to the punch (see Fig. 3), where different friction coefficients can influence stress fields.