A bonded particle model was used to study the fracture process zone (FPZ) in three point bending test of notched beams. Five different beam sizes of 20 (height) × 60 (span), 40 × 120, 80 × 240, 160 × 480, and 320 × 960 mm2were tested to investigate the effect of specimen size and material ductility on the length and width of the FPZ at the peak load. The material ductility was controlled by using different slopes for the post-peak behavior of contacts between the circular particles in tension. A statistical approach is proposed to more objectively calculate the width and length of the FPZ. It is shown that the size of FPZ depends on specimen size and material ductility. In particular, the shape of FPZ is affected by the specimen size. Different regression methods are proposed to be able to calculate the length and width of FPZ and the best linear regression method is identified and discussed.


Fracture process zone (FPZ) which is made of micro-cracks and damaged contacts between material grains is a common phenomenon in fracture testing of quasi-brittle materials such as rock and concrete. Physical testing using acoustic emission (AE) and X-ray technics have confirmed the presence of the FPZ in rock, concrete, and asphalt [1,2,3]. While there is agreement on the presence of fracture process zone in the vicinity of a crack tip in quasi-brittle materials, disagreements exist in the literature regarding the size of fracture process zone; it is not clear if size of FPZ can be assumed as an intrinsic material property. Zietlow and Labuz [1] conducted several bending tests on different rocks and studied the evolution of the FPZ by using AE technics. They concluded that size of FPZ varies significantly between different rock types, but the change is small for different beam sizes of the same material. On the other hand, Otsuka and Date [2] physical tests on concrete showed significant change in the size of fracture process zone of concrete as the specimen size was modified.

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