Discrete element modeling of the process zone shape in mode I fracture at peak load and in post-peak regime

• Discrete element method is used to study the fracture process zone.
• A servo-controlled loading system is defined to capture the post-peak rock behavior.
• Two methods to define the process zone domain are introduced.
• Material ductility and specimen size do not affect the shape of the process zone if the macro-crack extension at the peak load is considered.
• Preferential orientation of damaged contacts in the process zone suggests development of an anisotropic region around the macro-crack.

The bonded particle discrete element method is used to study the fracture process zone in three point bending tests of notched beams. Five different specimen sizes and different material ductility are studied. To capture the damaged contacts around the induced macro-crack (fully softened and detached contacts in front of the notch), a contact bond model with softening is implemented. Material ductility is modified by changing the post-peak slope of the load-displacement curve of the contact points between the particles. A servo-controlled loading routine is defined to capture the post-peak behavior and to reveal the impact of macro-crack extension on the size of the process zone. The results show that with the increase in the specimen size, both the width and length of the fracture process zone increase. Examination of the orientation of the contacts around the macro-crack suggests that while close to the macro-crack, contacts with a wide orientation range enter into the softening regime, damaged contacts at some horizontal distance from the induced vertical macro-crack have preferential directions; the damaged contacts are parallel or sub-parallel to the macro-crack at some distance from the macro-crack.