A thermodynamical fibre bundle model for the fracture of disordered materials

We investigate a disordered version of a thermodynamic fibre bundle model proposed by Selinger et al a few years ago. For simple forms of disorder, the model is analytically tractable and displays some new features. At either constant stress or constant strain, there is a non-monotonic increase of the fraction of broken fibres as a function of temperature. Moreover, the same values of some macroscopic quantities such as stress and strain may correspond to different microscopic configurations, which can be essential for determining the thermal activation time of the fracture. We argue that different microscopic states may be characterized by an experimentally accessible analogue of the Edwards-Anderson parameter. At zero temperature, we recover the behaviour of the irreversible fibre bundle model.