Constitutive modeling of damage accumulation and fracture in multiphase materials Original Research Article

The dominant mechanisms of energy dissipation associated with the deformation processes preceding and accompanying failure in multiphase materials, the so-called pre-fracture processes, are described quantitatively as the evolution of microdefects randomly distributed in the volume of specimen. Damage kinetics in a composite material are studied in detail. It is demonstrated that a large number of secondary discontinuities present in multiphase materials, such as matrix cracks, debonding of particulates and/or fibers, fiber breaking, bridging and fiber pull-out, enhance the apparent material resistance to the continuing growth of damage. Constitutive modeling of these effects incorporates the basic concepts of Continuous Damage Mechanics and it leads to an integro-differential equation which governs the evolution of the microdefects, their coalescence and interaction with the dominant crack-like defect and finally, the ensuing time-dependent fracture of the component. The principal evolution equation is solved by finite difference and finite element methods. Results pertaining to various crack growth histories are then used as the data-base sufficient to suggest a closed form solution which defines the material resistance curve, or an ‘R-curve’ routinely used in Nonlinear Fracture Mechanics as a standard for evaluation of fracture response in nonelastic metals. In this way we are able to propose a unified theory explaining enhancement of the fracture toughness during the early stages of failure in all dissipative media.