Mixed-mode partition theories for one-dimensional delamination in laminated composite beams

Completely analytical theories are presented for the mixed-mode partitioning of one-dimensional delamination in laminated composite beams. The work builds on previous research by the authors on one-dimensional fractures in layered isotropic beams. The partition theories are developed within the contexts of both Euler and Timoshenko beam theories. Two sets of orthogonal pairs of pure modes are found and used to partition mixed modes. Approximate 'averaged partition rules' are also established for 2D elasticity. The beam partition theories and averaged rules are extensively validated against numerical simulations using the finite element method (FEM). The contact behavior of double cantilever beams (DCBs) is also investigated. Two types of contact exist: crack tip running contact, which results in a region of pure mode II; and point contact at the DCB tip, which can result in either in mixed modes or pure mode II.