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

This paper was accepted for publication in the journal Composite Structures and the definitive published version is available at http://dx.doi.org/10.1016/j.compstruct.2015.06.080Fracture on bimaterial interfaces is an important consideration in the design and application of composite materials and structures. It has, however, proved an extremely challenging problem for many decades to obtain an analytical solution for the complex stress intensity factors (SIFs) and the crack extension size-dependent energy release rates (ERRs), based on 2D elasticity. This work reports such an analytical solution for brittle interfacial cracking between two dissimilar elastic layers. The solution is achieved by developing two types of pure fracture modes and two powerful mathematical techniques. The two types of pure fracture modes are a SIF type and a load type. The two mathematical techniques are a shifting technique and an orthogonal pure mode technique. Overall, excellent agreement is observed between the analytical solutions and numerical simulations by using the finite element method (FEM). This paper reports the analytical development of the work. The numerical verification using the FEM is reported in Part 2 by Harvey, Wood and Wang (2015)

Partition of mixed-mode fractures in 2D elastic orthotropic laminated beams under general loading

This paper was accepted for publication in the journal Composite Structures and the definitive published version is available at http://dx.doi.org/10.1016/j.compstruct.2016.04.016An analytical method for partitioning mixed-mode fractures on rigid interfaces in orthotropic laminated double cantilever beams (DCBs) under through-thickness shear forces, in addition to bending moments and axial forces, is developed by extending recent work by the authors (Harvey et al., 2014). First, two pure through-thickness-shear-force modes (one pure mode I and one pure mode II) are discovered by extending the authors’ mixed-mode partition theory for Timoshenko beams. Partition of mixed-mode fractures under pure through-thickness shear forces is then achieved by using these two pure modes in conjunction with two thickness ratio-dependent correction factors: (1) a shear correction factor, and (2) a pure-mode-II energy release rate (ERR) correction factor. Both correction factors closely follow an elegant normal distribution around a symmetric DCB geometry. The principle of orthogonality between all pure mode I and all pure mode II fracture modes is then used to complete the mixed-mode fracture partition theory for a general loading condition, including bending moments, axial forces, and through-thickness shear forces. Excellent agreement is observed between the present analytical partition theory and numerical results from finite element method (FEM) simulations