Crack velocity dependent toughness in rate dependent materials

Mode I, quasi-static, steady-state crack growth is analyzed for rate dependent materials under plane strain conditions in small scale yielding. The solid is characterized by an elastic–viscoplastic constitutive law and the plane ahead of the crack tip is embedded with a rate dependent fracture process zone. The macroscopic work of fracture of the material is computed as a function of the crack velocity and the parameters characterizing the fracture process zone and the solid. With increasing crack velocity a competition exists between the strain rate hardening of the solid, which causes elevated tractions ahead of the crack tip that tend to drive crack propagation, and the rate strengthening of the fracture process zone which tends to resist fracture. Results for material parameters characteristic of polymers show that the toughness of the material can either increase or decrease with increasing crack velocity. To motivate the model, the cohesive zone parameters are discussed in terms of failure mechanisms such as crazing and void growth ahead of the crack tip. The toughness of rubber modified epoxies is explained by employing the fracture model along with micromechanical void cell calculations.