A numerical study on the correlation between the work of separation and the dissipation rate in ductile fracture

Abstract

The present study reports on calculations of ductile tearing and failure. Crack growth is simulated by a cohesive zone model which, by adapting it to the mechanical behavior of voided cells, is a phenomenological representation of the micromechanical process of void growth and coalescence. Crack growth resistance is given in the form of the dissipation rate versus crack extension. The present simulation shows that by a combination of these two concepts a step further in the understanding of the fundamentals of ductile fracture can be obtained. The application of the cohesive zone model allows for a split of the dissipation rate into its two contributions, plastic dissipation rate and separation energy. It is demonstrated that neither the dissipation rate nor one of its components is a material constant. Instead all two quantities are found to depend on specimen geometry and size as well as on the amount of crack extension. Thus, while the use of the dissipation rate avoids some of the basic problems that arise in the use of the J-integral for the characterization of crack growth resistance, it is confirmed that this quantity does not provide a general and simple solution for the transferability problem of fracture toughness data. Due to the micromechanisms of void growth and coalescence, the cohesive zone parameters for ductile tearing, cohesive strength and energy, are predicted to be generally dependent on the amount of crack growth, specimen geometry and size. It is shown that in the present case of tearing under fully plastic conditions, the separation energy is only between 0.5% and 12% of the total dissipation rate depending on specimen geometry, size and crack extension. Assuming the material parameters of a cohesive zone law as a material constant may, from an engineering point of view, provide an admissible approximation, especially in situations of high constraint.