Dynamic interfacial fracture

Dynamic interfacial fracture is the branch of fracture mechanics that considers the fracture behaviour of structures with an interface under dynamic loads, such as laminated composites and adhesively bonded or welded structures. In this work, a new and completely analytical framework is developed to determine the dynamic energy release rate (ERR) of pure mode-I and -II fractures in double cantilever beam (DCB) and end-loaded split (ELS) specimens, respectively. For the first time, structural vibration and flexural-wave propagation are accounted for. It is shown that the effect of vibration on interfacial fracture behaviour is significant and cannot be neglected as it conventionally has been. The developed analytical framework is successfully used to study stationary and propagating cracks, cracks at non-rigid elastic interfaces, and to investigate the mode mixity by combining it with a quasi-static mode-partition theory.

The developed analytical framework is established based on the mode-I stationary crack of a DCB and the classical dynamic beam theory with time-dependent boundary conditions. The transverse motion is decomposed into a quasi-static one and a local vibration resulting in three ERR components due to the strain and kinetic energies of quasi-static motion, and the kinetic energy due to motion coupling. It is found that the conventional global approach accounting for the global energy balance method to determine the ERR cannot be used, as it results in non-physical divergence of the vibrating ERR amplitude with addition of more vibration modes. It is discovered that accounting for wave propagation and dispersion of flexural waves and considering the energy flux through a small crack-tip contour solves this divergence, leading to dispersion-corrected global approach. For a mode-I propagating crack, the ERR is derived by incorporating an energy-conservation condition and a correction for the Doppler effect. The crack-propagation behaviour and the limiting crack-propagation speed are thereby determined.

Building on this developed analytical framework, an elastic foundation is introduced to represent a crack at a non-rigid elastic interface. This boundary condition not only significantly improves the vibration-phase agreement between the analytical theory and results of the finite-element-method (FEM) simulations but also allows a study of the relationship between dynamic effects and foundation stiffness. For the dynamic mode-II interfacial fracture in an ELS specimen, the dynamic ERR is derived using the vibrating crack-tip loads. It is found that the ith modal contribution is dependent on the

iv

ratio of the crack length to the total length of the ELS specimen and that for a given ratio, there is a vibration mode with a zero contribution to the ERR.

The developed theory is verified against the results of the FEM simulations and experiments and is in excellent agreement for all the cases considered. The resulting analytical expressions are relatively short, mathematically elegant, physically understandable and convenient-to-use by engineers and researchers. The developed analytical framework provides a detailed physical understanding of dynamic interfacial fracture behaviour. Among other potential uses, it can be employed to predict the extent of interfacial fracture in a dynamically-loaded structure, to post-process the test data on high-loading-rate fracture to determine the loading-rate-dependent interfacial fracture toughness for crack initiation and propagation, and potentially provides solutions for the verification of numerical software.