Analytical determination of energy release rate and mode mix for interfacial cracks in layered elastic structures

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering


Barry Davidson


fracture, Mechanical engineering, Materials science

Subject Categories

Other Mechanical Engineering


In this dissertation, analytical solutions for energy release rates, stress intensity factors and mode mix for interfacial cracks in layered elastic structures are developed. These solutions are applicable to structures where classical plate theory may be used to predict deflections and strain energies. For these cases, a "crack tip element" is developed. The crack tip element provides analytical expressions for total energy release rate and mode mix in terms of plate theory force and moment resultants near the crack tip. For planar problems, a two-dimensional crack tip element is developed which gives analytical solutions for the stress intensity factor in terms of the external loading and one "mode mix parameter." For three-dimensional problems, a three-dimensional crack tip element is developed. It is found that three mode mix parameters are needed to accomplish the mode decomposition for these cases. For both the two- and three-dimensional crack tip elements, methodologies for determining the mode mix parameters are developed, and specific values of the mode mix parameters are presented for a number of cases. For those interfaces where a linear elastic solution predicts an oscillatory singularity, a "$\beta=0$ approach" is developed to predict the fracture. It is shown that this approach provides the same predictions of fracture as when the full oscillatory field is employed. Finally, a "resin interlayer approach" is also examined as a means to eliminate the oscillatory singularity. The effects of the adhesive interlayer modulus on the energy release rate and fracture mode ratio for two typical graphite/epoxy laminates are presented. Both the "$\beta=0$ approach" and the "resin interlayer approach" are intended primarily for laminated composites.


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