6533b872fe1ef96bd12d3743

RESEARCH PRODUCT

Thermodynamics and continuum fracture mechanics for nonlocal-elastic plastic materials

subject

description

Nonlocal elasticity is used as an improved elasticity model which engenders no crack-tip stress singularities and thus makes applicable the classical stress-based failure criteria. Considering nonlocal-elastic plastic materials exposed to softening by particle decohesion in a process surface and to subsequent surface separation by fracture, fracture mechanics is addressed within the framework of irreversible internal-variable thermodynamics in the hypothesis of small strains and arbitrary (but sufficiently regular) fracture surface (crack surface plus process surface). The state equations and the energy dissipation densities are derived for the bulk material and for the process surface, for both of which thermodynamically consistent evolutive equations are also proposed. The energy consumption for the formation of the unit crack area is evaluated as the sum of two contributions, one as free energy released by the process surface microstructure, the other as mechanical work done by the surrounding bulk material. Basing on the second thermodynamics law, a crack local stability criterion is provided in terms of crack front characteristics, i.e. fracture force vector, fracture resistance vector and fracture (symmetric) stiffness matrix, all defined at the points of the crack front through the response fields and the response sensitivities to virtual crack front advancements. Stability is guaranteed if, at every point of the crack front and for any virtual advancement of the latter, the fracture resistance is greater than the fracture force, or in case of equality, the fracture stiffness matrix is positive definite. The limit case of perfectly brittle fracture is considered, also in the case of local elasticity.