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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than the changes in the U values between different crack lengths and therefore do not alter the predictions about crack growth and in the following, the W f value is disregarded in the computation of G . A mesh size of 0.1 mm is chosen for the following models, because U and F reached already the same values as for smaller m . The m value of 0.1 mm is indicated in Fig. 3 with a red, dashed line.

Fig. 3: Contour plot of the von-Mises stresses  mis in the model with a crack length of 4 mm, an applied displacement of 0.4 mm and a mesh size of 0.1 mm. The stress limits are chosen to see the maximum  mis of 8.5 MPa in the rubber. Grey regions have  mis values above 8.5 MPa.

Fig. 4: Results of the normalized values of (a) the external work W e , (b) the strain energy U , (c) the frictional dissipation W f and (d) the tensile force F plotted over the mesh size m . The suitable mesh size is chosen as 0.1 mm and denoted in the figers with a dashed red line.

Table 3: Energies and forces for the calculation with the mesh size of 0.1 mm and a displacement load of 0.4 mm Crack length a [mm] External work W e [J] Strain energy U [J] Frictional dissipation W f [J] Tensile force F [N] 0.25 9.866E-04 9.826E-04 2.262E-06 5.986 1 7.319E-04 7.243E-04 6.221E-06 3.824 4 4.254E-04 4.231E-04 2.087E-06 2.167

3.2. Incremental crack propagation model

3.2.1. Effect of crack growth increment  a Every time a crack is propagated by  a , there is a kink in the energy-displacement and also force-displacement curve. Choosing smaller  a values obviously increases the number of those kinks and makes the curve smoother. To investigate the influence of crack length increment  a , two values of  a = 0.5 mm and  a = 1 mm and the model parameters from Table 2 are used to propagate a delamination crack with an initial crack length a 0 of 0.25 mm. The main interest of these models is to see if lower  a values also shift the crack propagation curves. Fig. 5 shows results of (a) the strain energy U , (b) the crack length a, and (c) the tensile Force F over displacement u for the two different  a values up to a crack length of 9 mm. A smaller  a brings better resolved