Boundary element methods for linear and nonlinear solid mechanics problems; and fracture toughness enhancement mechanisms in ceramic materials

Thesis/Dissertation · Mon Jan 01 04:00:00 EST 1990

OSTI ID:5566453

Okada, H

The boundary element method is applied to the analyses of linear elasticity, small strain elastoplasticity, and large strain elastoplasticity. New non-hyper singular integral equations for the displacement (velocity) gradients are derived for small strain linear elasticity, small strain elastoplasticity, large strain semi-linear elasticity, and large strain elastoplasticity. The newly derived integral representations have one order lesser singularity than the conventional integral equations for the gradients, and is numerically tractable to compute the gradients at the boundary. By the use of these newly derived integral equations, the displacement gradients at the boundary of, as well as, at the interior of the body are accurately obtained. For the analysis of the problems, which contain plastic instabilities, a full tangent stiffness formulation of the field-boundary element method is proposed. Initially perfect tensile plate is analyzed. The bifurcation of the solution path is captured, and the post bifurcation diffused necking is successfully analyzed. The micromechanics of toughness enhancement mechanisms in certain ceramic materials is examined. Transformation toughening and microcracking were found to be very useful in enhancing the fracture toughness of ceramic composite materials. A nonlinear constitutive model for the transformation induced plasticity is presented. This nonlinear constitutive model is implemented in a nonlinear finite element method and applied to crack problems. Stationary cracks as well as stably propagating crack problems are analyzed to estimate the fracture toughness enhancement due to the transformation effect. The stress induced phase transformation has a significant effect on the enhancement of fracture toughness. In order to derive the constitutive equation, a self-consistent method is used.

• Research Organization: Georgia Inst. of Tech., Atlanta, GA (United States)
• OSTI ID: 5566453
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360203* -- Ceramics
Cermets
& Refractories-- Mechanical Properties
CERAMICS
CHALCOGENIDES
CRACK PROPAGATION
FINITE ELEMENT METHOD
FRACTURE MECHANICS
MATHEMATICAL MODELS
MECHANICS
NUMERICAL SOLUTION
OXIDES
OXYGEN COMPOUNDS
PHASE TRANSFORMATIONS
TRANSITION ELEMENT COMPOUNDS
ZIRCONIUM COMPOUNDS
ZIRCONIUM OXIDES