Partition of mixed modes in layered isotropic double cantilever beams with non-rigid cohesive interfaces

Abstract

The authors' existing mixed-mode partition theories for rigid interfaces are extended to non-rigid cohesive interfaces for layered isotropic double cantilever beams. Within the context of Euler beam theory, it is shown that the two sets of orthogonal pure modes coincide at the first set of pure modes due to the absence of any crack tip stress singularity for a non-rigid interface. The total energy release rate in a mixed mode is then partitioned using this first set of pure modes without considering any 'stealthy interaction'. Within the context of Timoshenko beam theory, it is shown that the mode II component of energy release rate is the same as that in Euler beam theory while the mode I component is different due to the through-thickness shear effect. Within the context of 2D elasticity, a mixed-mode partition theory is developed using the two sets of orthogonal pure modes from Euler beam theory with rigid interfaces and a powerful orthogonal pure mode methodology. Numerical simulations are conducted to verify the theories.

The Effects of Shear on Mode II Delamination

“…In general, they found an influence of shear forces and shear deformation on both fracture modes. Wang et al [46] compared several mixed-mode partition methods based on SBT and TBT with rigid and deformable interfaces. In general, they found that shear forces cause additional contributions to both modes I and II.…”

“…Besides the adoption of a more or less refined structural theory for the sublaminates, the connection between them has to be suitably described. To this aim, models of growing complexity can be chosen, ranging from rigid connections [15][16][17][18][19][20][21][22][23][24] to elastic interfaces [25][26][27][28][29][30][31][32][33][34][35][36][37][38] and cohesive zone models [39][40][41][42][43][44][45][46][47]. This choice is relevant not only for the accurate prediction of the laminate structural response -e.g.…”

A novel method for the partition of mixed-mode fractures in 2D elastic laminated unidirectional composite beams

“…[2][3][4][5][6] also shows that in Timoshenko beam theory with either rigid or non-rigid interfaces, these two sets of modes coincide on the first set of pure modes from Euler beam theory resulting in no stealthy interaction. Furthermore, Ref.…”

“…Conclusions are made in Section 4. Based on the authors' previous work [2][3][4][5], the total ERR G is calculated as follows: The work in Refs. [2][3][4]6] has shown that in Euler beam theory with rigid interfaces, the two sets of orthogonal pure modes do not coincide and that this results in 'stealthy' interactions which change the ERR partitions I G and II G but do not change the total ERR G .…”

Brittle interfacial cracking between two dissimilar elastic layers: Part 1—Analytical development

“…(47) and (48), are determined using the orthogonal methodology [25][26][27][28][29][30][31][32][33][34]. The pure mode II (18) to (24).…”