Simple beam model for the shear failure of interfaces

Abstract

We propose a model for the shear failure of a glued interface between two solid blocks. 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. Assuming global load sharing following the beam breaking, we obtain analytically the macroscopic constitutive behavior of the system and describe the microscopic process of the progressive failure of the interface. We work out an efficient simulation technique which allows for the study of large systems. The limiting case of very localized interaction of surface elements is explored by computer simulations.

Brittle-to-ductile transition in a fiber bundle with strong heterogeneity

“…Recently, the application of statistical physics has revealed interesting novel aspects of the damage and fracture of heterogeneous materials increasing our understanding both on the microscales and macroscales of fracture processes [1]. Most of these theoretical investigations rely on mesoscopic discrete models such as fiber bundles [2][3][4][5][6] and lattices of fuses [7,8], springs, or beams [9][10][11], where disorder is typically captured by the random strength of elements. Analytic calculations and computer simulations have revealed that for a broad class of disorder distributions, the fracture of heterogeneous materials exhibits universal aspects both on the microlevel and macrolevel: the size of bursts has a power law distribution with universal exponents [4][5][6]12,13], furthermore, macroscopic failure occurs in the form of localization after a precursory sequence of microcracking [14][15][16].…”

Extension of fibre bundle models for creep rupture and interface failure

“…The failure functions f (ε) and g(ε) can be determined from the elasticity equations of beams, but in general the only restriction for them is that they have to be monotonous. For our specific case of sheared beams they take the form f (ε) = ε and g(ε) = √ ε, where E = 1 is assumed (Raischel et al, 2005). In the plane of breaking thresholds each beam is represented by a point with coordinates (ε 1 , ε 2 ).…”

“…Our model represents the interface as an ensemble of parallel beams connecting the surface of two rigid blocks (Raischel et al, 2005) (see Figure 4). The beams are assumed to have identical geometrical extensions (length l and width d) and linearly elastic behaviour characterized by the Young modulus E. In order to capture the failure of the interface, the beams are assumed to break when their deformation exceeds a certain threshold value.…”

“…Interfacial failure also occurs in fibre reinforced composites, where debonding of the fibrematrix interface is an important damage mechanism. Since disordered properties of the glue play a crucial role in the failure of interfaces, most of the theoretical studies in this field rely on discrete models (Herrmann and Roux, 1990;Chakrabarti and Benguigui, 1997;Delaplace et al, 1999;Roux, 2000;Hidalgo et al, 2001;Dill-Langer et al, 2003;Raischel and Herrmann, 2005) which are able to capture heterogeneities and can account for the complicated interaction of nucleated cracks.…”

Acoustic Emission in the Friction of Composite Materials

“…The models of AE are based on the destruction of CM elements presented in the FBM concept (fiber bundle model) (Turcotte et al 2003;Shcherbakov 2002;Raischel et al 2005), and the kinetic regularities of the destruction process (Malamedov 1970). The analytical expressions of formed AE signals were received during CM destruction under conditions of tension and operation of shear force.…”