Extension of fibre bundle models for creep rupture and interface failure

Abstract

We present two extensions of the classical fibre bundle model to study the creep rupture of heterogeneous materials and the shear failure of glued interfaces of solid blocks. To model creep rupture, we assume that the fibres of a parallel bundle present time dependent behaviour under an external load and fail when the deformation exceeds their local breaking threshold. Assuming global load sharing among fibres, analytical and numerical calculations showed that there exists a critical load below which only partial failure occurs while above which the system fails globally after a finite time. Approaching the critical point from both sides the system exhibits scaling behaviour which implies that creep rupture is analogous to continuous phase transitions. To describe interfacial failure, we model the interface as an array of elastic beams which experience stretching and bending under shear load and break if the two deformation modes exceed randomly distributed breaking thresholds. The two breaking modes can be independent or combined in the form of a von Mises type breaking criterion. In the framework of global load sharing, we obtain analytically the macroscopic constitutive behaviour of the system and describe the microscopic process of the progressive failure of the interface.