Dynamical evolution of fracture process region in ductile materials

Abstract

The aim of this paper is to investigate the dynamics of evolving finite fracture process regions in ductile material taking into account the dislocation motion. Part I is a continuation of our paper [Makowski, J., Stumpf, H., Hackl, K., 2006. The fundamental role of nonlocal and local balance laws of material forces in finite elastoplasticity and damage mechanics. Int. J. Solids Struct. 43, 3940–3959] with special emphasis to weakly-nonlocal and gradient, respectively, theory of finite elastoplasticity. In that paper we postulated balance of microforces, balance of macroforces and balance of macrocouples without taking into account microcouples. In this Part I we derive the balance law of microcouples which determines the skew-symmetric parts of the microstress tensors. From the postulated balance laws of macro- and microforces and couples the associated principle of virtual power is obtained and the application of invariance requirements is investigated. While in our former paper the constitutive model was based on the pointwise form of the Clausius–Duhem inequality, here we derive the thermodynamic constitutive equations from its integral form avoiding by this to consider the weakly-nonlocal energy residual. The non-standard boundary conditions for the plastic active zone and its interior restriction are analyzed. Finally, we derive the principle of virtual power for dissipative processes including the integral dissipation rate. For simplicity the power of microcouples is here neglected. In Part II, we investigate the configurational forces acting on dynamically evolving finite fracture process regions, precursors of macrocracks. The system of configurational forces consists of configurational surface tractions and configurational internal and external body forces. From the principle of virtual power for dissipative processes we derive the configurational surface stress tensor yielding a generalization of the classical dynamical Eshelby tensor as well as the configurational internal and external body forces. It is shown that they satisfy the balance law of configurational forces. Introducing into the configurational stresses and forces the thermodynamically admissible constitutive equations derived in Part I leads to the result that for ductile materials the generalized dynamical Eshelby tensor and the configurational internal body forces acting on the fracture process zone consist of two parts, a non-dissipative part, derivable from the free energy potential, and a dissipative part, which under specified assumptions can be derived from a dissipation pseudo-potential.