สุมิตรา ไชยญาติ. Behaviors of micro-circular cracks and macro-yielding surfaces of cohesive medium in infinite elastic space. Doctoral Degree(Civil Engineering). King Mongkut's University of Technology Thonburi. KMUTT Library. : King Mongkut's University of Technology Thonburi, 2009.
Behaviors of micro-circular cracks and macro-yielding surfaces of cohesive medium in infinite elastic space
Abstract:
This dissertation deals with two crack problems whose geometry is circular in shape
subjected to the far - fielded loading. The proposed cracks are of the Barenblatt -
Dugdale type and consist of the penny - shaped and the external cracks. Tresca yield
criterion is introduced to control crack tip plasticity in the analytical analysis. In order to
derive the corresponding closed - form solutions, Hankel transform is employed.
Accordingly, both cracks individually considered and formulated within the limit of
linear elastic fracture mechanics by assuming that cracks occur in microscopic scale.
The stress components and displacements have been thoroughly evaluated and the
parametric studies of crack problems have been schematically presented. The numerical
approach using the concept of discretization has been developed for the purpose of
verifying the analytical results obtained. Using Dugdale model analytic expressions of
such cracks, the Dugdale model based numerical technique and procedure has been
established performing with good accuracy and convergence. Then, the predictions of
crack behaviors under various yield criteria have also been explicitly carried out and
presented within.
Further, this dissertation arrives at the application of microcrack problem to the macro
level behaviors of cohesive medium subjected to hydrostatic tension state of stress. The
analytical results of a penny - shaped crack have been employed as the basis for the
micromechanics based damage model of cohesive material. By homogenizing penny -
shaped defects prevailing all over the three - dimension representative volume element
(RVE) where the damage process takes place, the macroscopic equivalent stress of
damaged cohesive material has been proceeded together with its corresponding
additional strain. The effective yielding potential function has been obtained for
predicting cohesive material behavior on a macro scale and the influence of material
physical properties on material failure. The results are also compared to other damage
models. It should be emphasized that the proposed damage model can predict the
complete failure of the cohesive medium even for the infinitesimal damage. It also has
the ability to estimate the influence of Poisson ratio on material's damage, because its
effective yield surfaces apparently depends on material's Poisson ratio.