Fracture in generalized stress states
There are three basic parameters that control the fracture behaviour of a structure: loading of the structure, its resistance to crack initiation and growth, and its resistance to collapse. The last two items are sensitive to the shape and size of defects in the material. Accordingly, this also will affect the load-bearing capacity and service performance of structural elements. Therefore, in order to have plausible criteria for failure assessment one needs information about the applied load, the relevant material properties and defect shapes and sizes. In this dissertation two complementary avenues of approach are employed to give some insight about the effect of loading and defects on the phenomenon of fracture in brittle materials. In the first the stress concentrations resulting from the presence of voids in the medium are studied. In the second, the energy accompanying the extension of these flaws is examined. At the end, these two types of investigation have been correlated to provide a simple theory for fracture of brittle materials under different states of stress, including compression. A particularly versatile analytical technique that accounts for geometric and triaxial effects has been developed to determine the stress and energy variations introduced by the presence of a triaxial ellipsoidal cavity subjected to stresses parallel to its axes. The triaxial void is allowed to increas in size to incorporate the energy-balance concept into the fracture mechanics formulation. The details of the solution are presented. A verification procedure is established to assess the validity of the solution. The results obtained from this procedure substantiate the generality, flexibility, and physical soundness of the present approach. In addition, drawbacks and limitations of other analyses in the literature for special cases are discussed using the developed solution. Several examples are also offered to show how the present analysis can be applied to examine the growth of a predominant defect and to characterize material behaviour. A computer program has been developed to perform all the necessary computations. The influence of various parameters such as the state of applied stress, the cavity shapes and sizes and the 3-D analysis versus 2-D analysis were investigated. The apparent paradox of material fracture behaviour depending on the applied states of stress is interpreted using the proposed theory. An examination of crack extension behaviour under different states of applied stresses is presented. Interaction diagrams in biaxial and triaxial states of stress predicted using the present theory compare favorably with strength diagrams developed by other investigators from experimental data. It is suggested that the method of analysis presented here and the developed computer program will have a wide range of application in the area of fracture. It is hoped that by studying the behaviour of triaxial voids of different shapes and sizes under different states of stress, a rational picture of failure criteria can be built up.
Bibliography: p. 259-272.
El-Rahman, M. M. (1989). Fracture in generalized stress states (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/15265