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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2. Description of Models

2D plane strain finite element models were constructed using the software package FRANC2D (see website cited), providing incremental crack propagation while remeshing for each propagation step. The basic geometry for the different models is a rectangle of width 400 mm and height 500 mm having a varying discontinuity in the middle big enough to cause stress disturbance with respect to the overall geometry. The width of this model was selected carefully to be wide enough to maintain the “ infinite plane ” solution, as illustrated by Iskander and Shrive (2018). The thickness of this rectangle is 100 mm. The material is isotropic and linear elastic having a Y oung’s modulus of elasticity E = 25 GPa and Poisson’s ratio of 0.2. Symmetry was invoked so that only half of the geometry was modelled. Meshing was performed carefully to maintain mesh refinement around the discontinuity providing a maximum mesh size of 0.01 mm around the region encountering crack propagation, as shown in Fig. 2 (b). Load was applied as a static displacement of 1.3 mm; this displacement value is based on previous laboratory measurements on similar models which failed at a mean displacement value of 1.3 mm. Crack propagation calculations are based on the J-integral assessment around the crack tip which is calculated automatically by the software in each propagation step. The study described here includes five models constructed to find the effect of the size and shape of the void on the propagation of the crack. The mode I (opening) stress intensity factor (K I ) for the five models is compared.

(a)

(b)

Fig. 2. (a) Whole model; (b) Expanded view of mesh refinement around the void (discontinuity) and crack propagation

Three of the models contain circular voids of varying diameter, namely: 5, 10 and 20 mm (Fig 3 (a)). The other two models have elliptical voids of width 10 mm and heights of either 20 mm or 5 mm (Fig 3 (b)). Therefore, we can compare the first three models together to understand the effect of changing the size in terms of diameter (Fig 3 (a)) and investigate – by studying the other two models – the effect of changing the shape configuration of the void in terms of the different heights while keeping the width constant as shown in Fig. 3 (b) – the discontinuities have been enlarged in these figures for clarification (i.e. the figures are not to scale). Finally, the effect of changing the width while keeping the height constant was assessed by studying the 5 mm and 10 mm widths while keeping the height constant at 5 mm (Fig 3 (c)). The three models with circular voids are denoted as C5, C10 and C20 indicating the 5, 10 and 20 mm diameters, respectively. The elliptical voids are denoted E10x5 and E10x20 to indicate the width of 10 mm and heights of 5 and 20 mm, respectively. For all models, the crack was simulated as an initial 0.05 mm hairline crack at the top (highest vertical) point of the discontinuity, in the vertical direction (parallel to the macroscopic compressive stress) (Fig 2 (b)). Propagation of this crack was performed in 0.05 mm increments to construct plots for K I versus crack length. In addition, the total load and strain energy for two models (C10 and C20) were investigated via a commercially available FE software (ABAQUS) for a crack length up to 6 mm in 0.05 mm increments.