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Thermodynamics and continuum fracture mechanics for nonlocal-elastic plastic materials. (English) Zbl 1032.74007

In this paper, the use of nonlocal elasticity leads to regular strain and stress response fields in cracked body, i.e. no stress singularities arise near crack tips. Fracture is simulated as a particle decohesion process which takes place at a surface (or decohesion interface) between two moving lines, the decohesion and crack fronts, while the advancing crack front generates the crack surface. Two types of therodynamic variables are considered, i.e. those attached to the bulk volume of the body, and those attached to the fracture surface (i.e. the crack surface plus process surface), that is, the volume and surface densities of internal energy, free energy, etc., assuming that no mass density corresponds to the fracture surface.
First, the essentials of nonlocal elasticity are presented, and the crack problem is considered, including the constitutive equations for elasto-plastic material and for the decohesion interface. In the framework of fracture thermodynamics, detailed expressions are given for the nonlocal energy residual, and for energy dissipation densities in the bulk volume and on the decohesion interface; thermodynamics restrictions on evolution equations are also pointed out. Then, the evolution of decohesion interface is discussed in relation to normal and shear modes of local decohesion mechanisms, and a maximum normal stress criterion is proposed for the incipient decohesion mechanism on the decohesion front. The energy dissipated for the formation of a unit crack area is determined and found to be the sum of two contributions, one is a mechanical work done by the bulk volume, and another is free energy released by the decohesion interface’s microstructure; the total dissipation energy at any stage of the deformation process is also determined.
Further, the second law of thermodynamics is used to establish a crack local stability criterion expressed in terms of crack front characteristics, i.e. fracture force vector, fracture resistance vector and fracture stiffness matrix. These characteristics, given in terms of energy potentials, are described in terms of response fields and response sensitivities to the crack front advancement. The proposed stability criterion is shown to be equivalent to a stress-based one identified with decohesion criterion. Finally, the limit case of brittle fracture is considered, for which two situations are examined: (i) nonlocal elasticity, which is found to be always accompanied by a finite process surface (quasi-brittle fracture), and (ii) local elasticity, in which perfectly brittle fracture is allowed and Griffith’s stability criterion is recovered, but in a point-wise form on the crack front.

MSC:

74A45 Theories of fracture and damage
74A15 Thermodynamics in solid mechanics
74R20 Anelastic fracture and damage
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