PSI - Issue 19

9

Marc J.W. Kanters et al. / Procedia Structural Integrity 19 (2019) 698–710 Marc Kanters et al./ Structural Integrity Procedia 00 (2019) 000–000

706

Figure 9: (a) Comparison of the model and experiments for samples with 0 o (open markers) and 45 o (solid markers) orientations for different R values. (b) Comparison of the model and experiments and all the coupon data, where different marker types represent different load ratios and colours the various orientations. 4.1.5. Stress concentrations From various studies on metals it is well-known that for accurate lifetime predictions it is necessary to compensate for local stress concentrations, and the same methods are copied and used to model plastics [Sonsino2008, Mortazavian2016, Primetzhofer2019]. This often involves rather empirical methods, where the dependence on stress concentrations by notches is captured using details on the stress field surrounding the local maximum stress, for example via the stress gradient. Although many methods have been explored during the development of the current framework: for example, the point method, the line method, and area method [Askes2013], here we will demonstrate the use of the theory of critical distances [Susmel2008]. Note that although this is not the optimal method and major improvements might be achieved by shifting to other methods, it does highlight the approach in general. To account for a local stress concentration, the magnitude of the local stress, ����� , is scaled down using the fatigue notch factor, � , to obtain an effective stress to use for lifetime calculation, ��� , via: ��� = � ����� � � (2) Traditionally, a value for � is obtained from the ratio between the endurance limits of the SN-curves of a notched specimen and an unnotched specimen. However, since there is no such thing as an endurance limit for polymers, here a different approach is taken: for different geometries, the lifetime is computed using the local stress and the resulting lifetime is compared with the experimental value. Via the stress dependency of the Basquin curve, it is possible to estimate the value for � that would allow to match the experimental results. Preferably, multiple stress levels are used and � is determined by shifting the entire curve to obtain an average over multiple experiments. To allow computation of � for any arbitrary geometry, the theory of critical distances is used. Here, the normalized stress gradient, , is related to � by the characteristic length, ∗ , via: � � ��� � � � � � = 1 + � ∗ (3) For practical reasons, mainly to illustrate the approach, the path perpendicular to the maximum principal stress is used to compute the 1-D stress gradient. Figure 10a shows the dependence of � on for multiple notch radii and different sample orientations, measured at . This displays a severe increase in both stress gradient and