The purpose of this investigation was to apply the logarithmic hypothesis of the plane elastic dislocation theory to approximate a plane fracture problem. The region of study is essentially elastic except for a very small region in the neighborhood of the crack which is at some undefined plastic state. The model is a large, thin plate, tensile specimen bounded at the interior by a circular hole from which two stable natural cracks are originated. The experimental model was developed by Ju and Shafer, who also obtained the dislocation function along the crack used in the analysis.
The present fracture analysis relieved the rigorous traction-free condition along the cut and thus allowed solutions other than the theoretical elastic fracture solutions of Inglis and Williams. Governing equations describing the stress field in the vicinity of the crack were obtained; they were based upon the logarithmic dislocation theory with the following boundary and dislocation conditions:
1) Uniform tensile stress applied at large distance from the inner hole,
2) Traction-free hole boundary,
3) Prescribed dislocation values (displacement discontinuity) , expressed as polynomials, along the cracks.
The solution showed that the stress intensity at the neighborhood of the crack tip is definitely lower than that obtained by Inglis or Williams. The maximum shear stress reached a limiting value there, while the principal stresses diverged logarithmically. In general the present theory yields a better approximation to an Irwin-Griffith type fracture than the exact elastic theory. This was shown by comparing these results with the experimental data obtained by Ju and Shafer. Along the fracture edge, the approximate elastic analysis resulted in a distribution of residual traction. The residual traction should account for the energy dissipation due to the plastic deformation.
In the process of solution, a computer program in FORTRAN IV was developed. It is included in the report as a user's program.
Level of Degree
First Committee Member (Chair)
Frederick Dsuin Ju
Second Committee Member
H. L. Schreyer
Third Committee Member
Richard Charles Dove
Fourth Committee Member
The Air Force Weapons Laboratory Computer Group at Kirkland Air Force Base
Arcache, Alfred S.. "Stress Fluid in the Vicinity of a Crack." (1968). https://digitalrepository.unm.edu/me_etds/158