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In this dissertation, first, the theoretical and experimental viewpoints of instability and bifurcation in mechanics are reviewed and discussed. The onset of instability of bifurcation depends on the constitutive assumptions, and is marked by the loss of ellipticity, singularity of the stiffness matrix, and negative or complex eigenvalues. Non-traditional regularization is necessary to obtain useful post-instability solutions. Based on dissipated energy and elastic potential, energy based instability criterion is considered and developed. The global instability criterion is concerned with global non-uniform deformation while the surface degradation instability criterion deals with near surface non-uniformities. In addition, the connection between surface degradation and size, shape effects for brittle materials is examined. The energy based stability theory is applied for some typical problems through analytical and numerical implementations. It is shown that the onset of both surface instability and global degradation instability occurs in the strain hardening stage, that is, before and close to the peak strength. The theoretical results are compared with experimental observations. Both strain gage tests and ultrasonic scanning tests are processed to study the degradation mechanisms of a brittle material. The surface effects are highlighted by the experiments. Ultrasonically dissipated energy shows a random distribution and it follows, in general, the initial non-homogeneity pattern. The relationship between the ultrasonically dissipated energy and mechanically dissipated energy is dependent on deformation and can be approximated by a power function of the factor of load level. The theory for surface degradation consideration involves a few material constants, and these constants are identified against experimental observations. The degradation mechanism and damage growth patterning of simulated rock under uniaxial load are modeled numerically by implementing the theory for damage and surface degradation with initial state consideration. The theoretical results are compared with experimental observations obtained through ultrasonic scanning tests. To extend the study to post-instability modelling by using various constitutive models, three alternative considerations are proposed to achieve so-called regularization of the problem.

In the research undertaken a finite element formulation has been developed for an elastodynamic problem using a least squares approach. The special requirements of the problem demanded a study of suitability of various elements. The emergence of the final element is a result of both theoretical and numerical study of three different elements. The approximation function is assumed on the basis of the order of the governing differential equations. Then the square of the error resulting from the approximate solution is minimized over the entire domain as well as the boundaries in the same functional. The element equation emerging from the formulation does not yield a singular stiffness matrix, since the boundary conditions are already taken into account in the element equation. The formulation presented in this thesis is only for the normal propagation of phi-wave. A finite element code has been developed based on the new formulation.

The influence of three elastic contact models on the dynamics of the drilling module is studied by representing the percussive drilling process as a drifting oscillator. The Kelvin-Voigt, Hertz stiffness and nonlinear stiffness and damping models were considered. The local dynamics of the system were found to be almost identical for the three models. Hence the Kelvin-Voigt system adequately describes the local dynamics of the system. However, for larger frequency and higher damping the behaviour of the three models differed. Experimental indentation studies were carried out on sandstones samples using static and dynamic loading. A force penetration relation was obtained for the loading and unloading phases of the indentation using a conical and spherical indenter under quasi-static conditions. Conical indentation tests were carried out in dynamic conditions. Both experiments showed that the force penetration relationship that could describe the contact model were closer to that obtained for the elastic-plastic indentation of ductile materials. The dynamic model for the drilling module was developed using an elastic plastic model for conical and spherical indenter. In addition, the model’s parameters were modified to those obtained from the experiments and used for the comparison with the results obtained for the elastic plastic model. The result obtained suggested a topological similarity between the experimental and theoretical parameters. It was also noted that the results suggested that the conical indenter appeared to be more efficient of the two indenter types considered. Finally, the rock fracture as a result of its contact with the drill-bit insert was investigated. For simplicity, the inserts are considered as flat punch and the contact problem is treated as a plane strain problem. Experimental studies were also carried out to determine the crack initiation angle in sandstone.

A cohesive zone model approach is used in order to study the behaviour of cracks in elasto-plastic materials. The cohesive zone model being studied is time-dependent, unlike standard cohesive zone models in elasto-plasticity. The stress distribution over the cohesive zone is related to the normalised equivalent stress functional, and is expressed in the form of an Abel-type integral equation. During the stationary crack stage as well as the propagating crack stage, the aim is to study the behaviour of the cohesive zone length with respect to time as well as the crack tip opening. To aid accomplishing this aim, the stress intensity factor was set to zero at the cohesive zone tip. As well as other material parameters, the external applied load participates in the model equations. We will consider two cases for the external load, namely the case when this load is constant in time, and the case when this load behaves linearly with time. We will implement numerical schemes to obtain the crack growth as well as the cohesive zone growth with respect to time for both the elastic case and the visco-elastic case while considering different sets of parameters. The numerical convergence rates are obtained for each of the problems solved. This justifies the suitability of the numerical schemes used.

A combined theoretical and experimental study of the criteria governing the failure analysis of pressure vessels with defects has been performed. The fields of fracture mechanics (linear elastic and elastic-plastic behaviour), failure governed by large scale plastic deformation and energy balance methods are critically reviewed. All three approaches are shown to have relevance in the complete failure analysis of a structure with defects. An experimental study of the failure mechanisms of precracked polycarbonate and maraging steel plates and model polycarbonate vessels is presented. Room temperature, static loading tests are performed on 85 mm wide, 5 mm thick compact specimens of polycarbonate (0.013 andle; ^aandfrasl;_W andle; 0.810). For comparison, 51 mm wide maraging steel compact specimens are monotonically loaded at room temperature. The influence of through-thickness constraint on the fracture toughness and slow crack growth characteristics of the steel is investigated using plates of varying thickness (3.1 mm-25.4 mm) and initial crack length (0.386 andle; ^aandfrasl;_W andle; 0.766 for 3.1 mm thick sheet); various ancillary studies (scanning electron microscopy, surface deformation studies) complement the results. The crack growth behaviour of longitudinal through (0.704 ≤ c / andradic;‾DT/2</span> ≤ 1.434) and deep part-through (^dandfrasl;_T = 0.700 and 0.878) cracks in 50.8mm and 102mm diameter (5mm and 6mm wall thickness) polycarbonate cylinders is also studied. Bowling and Townley's two-criteria approach to failure i.e. LEFM on the one hand and limit analysis on the other, is shown to provide a useful method for assessing the relative importance of crack initiation, in the presence of limited crack tip plasticity and general yield as failure criteria for a given sized defect. Thus, for crack tip plasticity fully contained by an outer elastic field i.e. not general yield, the LEFM parameter, K_Ic (with the possibility of a plasticity correction factor for thin sheet) can be used to predict crack initiation. For the low strain-hardening maraging steel, Irwin's plane strain plasticity correction, ¹andfrasl;_6π (K_{Ic/σ_y})² is shown to be applicable to sheet thicknesses comparable to ¹andfrasl;_π (K_{Ic/σ_y})² i.e. twice Irwin's plane stress plastic zone radius.

Thesis (M.Sc.)--University of the Witwatersrand, Faculty of Engineering, 1996 / One of the major impediments in the field of numerical modelling in rock mechanics is limited knowledge of the mechanisms of fracture and failure of brittle rock. One important tool for improving the understanding of rock behaviour is the use of laboratory experiments under controlled conditions. The Displacement Discontinuity Method, capable of fracture growth simulation (DIGS), has been used to model fracturing in samples under punch loading. A Finite Difference Method, capable of plastic deformations due to its explicit time marching scheme (FLAC), has also been used to model the punch tests. By comparing numerical simulations with results from laboratory experiments of punch tests, it has been possible to define the basic failure mechanism for pillar foundation failure. Two different test set-ups were used namely, steel jacketed axisymmetric punch tests and long strip punch tests in the triaxial cell which is built for these specific tests. The layered structure of the test specimens and in the test procedure had significant effects on the fracture pattern as well as the failure load. When the layer is near to the punch area, then both the layer and the layer conditions had a strong effect on the failure load. When the layer was frictionless, the failure stress dropped by about 20 percent. The same result occurred in both the axisymmetry and strip loading tests. When shear fractures intersect a layer with either low or high friction it terminates. This is not the case for the tensile fractures, which can pass through the layer media. However, it is important to note that the tensile fractures which originate from near the cone area can not pass through the layers. They stop at the interface.

Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography: leaves 204-211. / by Thomas Dale Ketcham. / Sc.D.

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