A higher-order direct boundary integral-displacement discontinuity method for fracture propagation in layered elastic media
This thesis presents the development of a direct boundary integral-displacement discontinuity method for plane-strain elastostatics boundary value problems in layered materials with cracks. Somigliana's identity for displacements inside an elastic region is extended to take account of crack-like geometries. The resulting boundary integral equations involve integrals with unknown as the displacement discontinuities over the cracks. These equations are supplemented with traction boundary integral equations derived by differentiating the displacements. The kernel functions for the dual boundary integral equations are developed from the closed form solution to the problem of a concentrated force within one of two bonded half-planes in which the interface continuity conditions are fulfilled exactly. A four-layer elastic region with cracks is developed using a substructuring approach to construct one of the interfaces for the problem under consideration; the other two interfaces are automatically included by virtue of using the fundamental solution for the bonded half-planes. Quadratic variation boundary elements are used to model all boundary contours, cracks and the numerical interface. Crack tips are modeled with square-root variation boundary elements. Linear elastic mixed-mode fracture propagation criteria are reviewed and an algorithm based on the maximum circumferential tensile stress criterion is developed and incorporated into the numerical model for quasi-static crack propagation in layered materials. For cracks propagating away from a material interface, the criterion uses the linear elastic fracture mechanics solutions for stresses in the vicinity of a crack tip in a homogeneous region. The analytical solution for the stress field near the tip of an interfacial crack is used for the maximum tensile stress criterion to determine whether or not the crack will kink out of the interface.
- Research Organization:
- Minnesota Univ., Crookston, MN (United States)
- OSTI ID:
- 7070948
- Country of Publication:
- United States
- Language:
- English
Similar Records
Elastodynamic stress intensity factors of an interface finite-width crack. [Elastic layer over different material with crack at interface]
Some characteristcs of a propagating brittle tensile crack