Mixed mode partition theories for double cantilever beam with rigid and non-rigid interfaces

The double cantilever beam (DCB) fracture problem has been studied by many researchers for several decades. Many analytical theories, numerical and experimental methods have been developed for understanding the fracture initiation and propagation, however considerable confusion has arisen in calculating the mode I and II energy release rates (ERR) of mixed modes. In this work, new analytical mixed mode partition theories are developed for DCBs with rigid and non-rigid interfaces based on Euler beam theory, Timoshenko beam theory and 2D elasticity theory. Most of the confusion is cleared up. Based on Wang-Harvey's mixed mode partition theories for straight DCB, two sets of pure modes are successfully and clearly proven by analytical derivations for curved DCB with rigid interface. From these two sets of pure modes, two new mixed mode partition theories are developed for curved DCB with rigid interface based on both Euler beam theory and Timoshenko beam theory respectively. Two sets of pure modes and the mixed mode partition theories are validated against numerical simulations and excellent agreements are achieved. Then these mixed mode partition theories for rigid interfaces are extended to non-rigid cohesive interfaces for DCBs within the contexts of 2D elasticity theory based on Wang-Harvey's work which is within the contexts of Euler beam theory and Timoshenko beam theory. A new mixed mode partition theory is developed and axial forces are taken into consideration in this mixed mode partition theories for non-rigid interface DCBs. 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. Fully analytical partition theories are developed to calculate the ERR of the bending moment and axial force loading contribution, and empirical formulas are developed to calculate the ERR of the shear force loading contribution with any interface stiffness and geometry. So with any loading conditions, interface stiffness and geometry, total ERR and its partitions can be calculated without any FEM simulations. Numerical simulations are conducted to verify these theories.