Publication Date


Document Type


Committee Members

Robert Brockman (Committee Member), Jeremy Daily (Committee Member), Nathan Klingbeil (Advisor), Ravi Penmetsa (Committee Member), Joseph Slater (Committee Member)

Degree Name

Doctor of Philosophy (PhD)


An energy-based theory for predicting mode I fatigue crack growth rates in ductile metals based on the total plastic dissipation ahead of a crack tip was proposed in 2003. Since then, this theory has been extended to layered material systems that typically include mixed-mode loading and elastic/plastic mismatch. Previous research by the author first extended this theory to include a graded layer (i.e., no step change in material properties across the crack plane) with which to more accurately model a crack interface between two materials with a mismatch in plastic properties only. In the current research, the graded layer model has been extended to include a mismatch in elastic properties as well. In so doing, the author has derived a beam-theory solution for the strain energy release rate for use in exploring nondimensional effects of graded layer height, elastic mismatch, and mode of loading. In addition, the graded layer model has led to a purely elastic method for determining an unambiguous definition of the mode-mix in the presence of an elastic mismatch and has been validated by elastic-plastic plane strain finite element results illustrating the resulting plastic zones. This has led to an independent validation of a physically based mode-mix definition for bimaterial crack tips based on the total plastic dissipation developed by Daily. In addition, this dissertation provides comprehensive numerical results for the effects of an elastic/plastic mismatch, mode-mix, and graded layer height on the total plastic dissipation for steady-state fatigue cracks on ductile bimaterial interfaces. Finally, experimental results for a brazed specimen under four-point bending that include sustained fatigue cracking along an interface have been provided for use in validating the theory for mixed-mode loading.

Page Count


Department or Program

Ph.D. in Engineering

Year Degree Awarded


Included in

Engineering Commons