A novel theory of damage materials with microstuctures

Abstract

This paper presents the foundations of a novel thermodynamic theory of damage in elastic solids. The theory is rooted in the so-called "Conservative or Conventional Thermodynamics of Irreversible Processes," where the concept of a local thermodynamic state plays a prominent role. An elastic body prone to damage is regarded as a thermodynamic system characterized by a set of extensive variables that can be defined in both equilibrium and nonequilibrium states and assigned approximately the same values in both the physical space and the abstract state space (i.e., the Gibbsian phase space of constrained equilibria.) The extensive variables introduced include internal parameters which describe the damaged state of the body and whose conjugate intensive variables, or affinities, constitute a generalization of Eshelby's concept of "force on an elastic singularity." The local state approximation is applied by assigning to the entropy and temperature in physical space local values which can be calculated in the Gibbsian phase space by the well-established methods of equilibrium thermodynamics. This leads to an explicit expression for the entropy production. The rate equations for the damage are then postulated in such a way as to conform to the second part of the second law of thermodynamics. The resulting theory captures many features of real material behavior such as loading/unloading paths, quasi-ductility, dependence on the straining or loading rates, transition from brittleness to ductility with temperature rise and dependence on some global geometric parameters (size and shape) of the structure. As a further illustration of the theory, we consider the case of microcracks propagating in an elastic body (one-dimensional bar) and we include the effect of microstructure and the associated toughening mechanisms by considering a power law for the toughness curve. The stress-strain curves obtained are compared with data from experiments performed by other authors on alumina.