PSI - Issue 13

Mina Iskander et al. / Procedia Structural Integrity 13 (2018) 976–981 Iskander and Shrive/ Structural Integrity Procedia 00 (2018) 000 – 000

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Fig. 3. (a) Discontinuity size comparison; (b) Discontinuity height comparison; (c) Discontinuity width comparison

3. Results and Discussion: K I

For all the models, the horizontal stress before cracking at the highest vertical points of the discontinuity (i.e. at the top and bottom of the void) was tension with a value equivalent to the distant stress at the ends subjected to loading (65 MPa). The vertical stress before cracking at the horizontal ends of the discontinuity was compression with values depending on the shape of the void: threefold the distant applied stress for circular discontinuities, fivefold for E10x5 and twofold for E10x20.

Fig. 4. K I vs. crack length

The mode I stress intensity (K I ) shows a consistent pattern for the five models: the value of K I rises with initial crack extension until a peak value is reached and then drops, as shown in Fig. 4. The value of K II was checked and found to be almost zero throughout the plotted crack propagation, as expected from symmetry. The interesting part about the plots is that the value of K I reaches a peak and then drops. In the uniaxial tension case K I would continue to rise as the crack extends, following Eq 1. However, for compression, the fall in K I means that if a certain load is applied to cause a crack to initiate and propagate, and the load is not increased, the crack will stop propagating at a certain extension and will not propagate further until more load is applied. This behaviour is observed experimentally in brittle and quasi-brittle materials and is in complete contrast to crack propagation under uniaxial tension in such materials where the crack propagates unstably as soon as the stress intensity reaches the fracture toughness (K IC ). The peak values of K I and the corresponding crack lengths from Fig. 4 are recorded in Table 1. These values are all due to the applied 1.3 mm displacement, so no load steps are included in this study. If we compare the plots for the circular discontinuities (i.e. C5, C10 and C20) in Fig. 4, it is obvious that a bigger void produces a higher stress intensity at the crack tip and greater crack extension before propagation will cease. This can be justified by observing the values presented in Table 1. Looking at the K I values for a 0.45 mm long crack, C10 and C20 have larger values of K I than C5 and therefore they are more critical. Thus, although the three circular voids produce the same stress at their top and bottom tips, they produce different stress intensities.