On the singular stress field at the interface of bimaterial systems

grantor: University of TorontoInverse square root, 1/r, singularity characterizes the stress field at the crack tip of homogeneous isotropic elastic media. This 1/r singularity does not, however, hold for the stress field at the interface of a bimaterial system. A number of attempts have been made to treat this class of problems. These attempts reveal the presence of rapid oscillations in the stress and displacement fields and the dependence of the stress singularities upon the geometry and the elastic mismatch of the bimaterial system. These features complicate the determination of the singular stress field significantly. As a result, existing solutions are limited to a few specific configurations and simple loading conditions. It is, therefore, the objective of this thesis to develop a unified approach for treating general bimaterial systems. For this purpose, the bimaterial system is modeled as a bimaterial wedge, thus facilitating the simulation of a wide range of inhomogeneous solids--such as, layered composite materials, coated components and welded structures. Both theoretical and experimental techniques are employed to examine the current problem and the resulting singular stress field. The current boundary value problem is formulated in terms of the complex function method. By examining the resultant eigenequation of the system, the dependence of the stress singularities upon wedge geometry and elastic properties of the constituents is revealed and explicit expressions for the stress and displacement fields around the wedge vertex are obtained. These expressions are then used to develop a new singular finite element. This element enables the determination of the singular stress field and the associated stress intensity factors reliably and efficiently. Both quasi-static and dynamic stress intensity factors are obtained explicitly. To establish the validity of the newly developed method, a number of test cases are examined and compared with existing simplified solutions. The newly proposed method is then used to evaluate the effect of the wedge geometry, elastic mismatch, density ratio and loading conditions upon the resulting stress intensity factors. In the experimental work, a digital photoelastic technique is employed to examine the singular stress field around the vertex of a photoelastic bimaterial wedge. A special casting procedure is introduced to produce bimaterial photoelastic specimens with varied geometries. To determine the stress intensity factors reliably from the resulting isochromatic fringe patterns, a high order representation of the stress field around the vertex is used and a multi-parameter analysis method is developed. The experimental results are compared with the theoretical findings and the results reveal a good agreement between them.Ph.D