Size effect, material ductility and shape of fracture process zone in quasi-brittle materials

Numerical three-point bending tests were conducted on a softening material model to study the effect of specimen size and material ductility on the shape of the fracture process zone. A bonded particle model (BPM) was used for simulation of the rock. The particles at the contact points were allowed to follow a softening behavior to be able to capture the initiation and development of the process zone. Five different beam sizes of 20 (height) × 60 (span), 40 × 120, 80 × 240, 160 × 480, and 320 × 960 mm2 were used. All beams had a notch at their mid-span to study the mode I fracturing of rock. For each specimen size, six different realizations were introduced to study the effect of particle arrangement on the induced damage zone. The material ductility was controlled and modified by introducing different slopes for the post peak behavior of the contact points between the particles. The shape of the process zone was obtained by calculating both the width and the length of the process zone at the peak load. The results suggest that as the specimen size increases, the process zone expands in its size. In addition, the results indicate that for quasi-brittle materials, the length to width ratio of the process zone is greater compared to that of ductile materials. Furthermore, it is shown that the sizes of the representative elemental volumes corresponding to the width and the length of the process zone may not be identical in the quasi-brittle materials.