Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Cherkaoui, Mohammed; Committee Member: Neu, Richard; Committee Member: van der Sluis, Olaf. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Defect assessment against fracture initiated failure is carried out using fracture characterising parameters determined under quasi-static rates of loading. In practice, however, there are many instances where much higher loading rates prevail such as collision, blast and earthquake damage; and in transport. For these situations the rate sensitivity of the material to fracture should be considered. Fracture toughness tests (COD) have been conducted on C-Mn steel weld metal over a range of temperature and loading rates. The effect of increased loading rates is to reduce the crack-opening displacement whilst changing the fracture behaviour, such change being accompanied by an increase in the ductile-brittle transition temperature. Thermally activated flow is found to be the predominant mechanism governing plastic flow at intermediate strain-rates. It is then possible to evaluate the effect of strain-rate and temperature on the yield strength as a function of rate parameter kT 1n (A/ε), based on the Arrhenius equation. An attempt is presented to model the influence of temperature and loading rate on the fracture initiation toughness, COD. It may be fairly said that numerical results quite well describe the behaviour of the experimentally determined variation of COD with temperature and loading rate over the range 0.1 < K < 10⁶MPam^{1/2 s}^-1 and O < T < 500^oK. Thus, it has been demonstrated that the constitutive surface δI (T, K_I) can be produced numerically using the constitutive relation σy (ε,ε, T). Consideration of the defect sizes for engineering critical assessment showed that a significant reduction in maximum allowable defect size, bar a_max can result as a consequence of increased loading rate.

This dissertation presents three inter-related studies. Chapter 2 presents a study of scaling of crack propagation in rubber sheets. Two different scaling laws for supersonic and subsonic cracks were discovered. Experiments and numerical simulations have been conducted to investigate subsonic and supersonic cracks. The experiments are performed at 85 °C to suppress strain-induced crystallites that complicate experiments at lower temperature. Calibration experiments were performed to obtain the parameters needed to compare with a theory including viscous dissipation. Both experiments and numerical simulations support supersonic cracks, and a transition from subsonic to supersonic is discovered in the plot of experimental crack speed curves versus extension ratio for different sized samples. Both experiments and simulations show two different scaling regimes: the speed of subsonic cracks scales with the elastic energy density while the speed of supersonic cracks scales with the extension ratio. Crack openings have qualitatively different shapes in the two scaling regimes. Chapter 3 describes a theory of oscillating cracks. Oscillating cracks are not seen very widely, but observed in rubber and gels. A theory has been proposed for the onset of oscillation in gels, but the oscillation of cracks in rubber has not been explained. This study provides a theory able to describe both rubber and gels and recover the experimental phase diagram for oscillating cracks in rubber. The main new idea is that the oscillations of cracks follow from basic features of fracture mechanics and are independent of details of the crack equation of motion. From the fact that oscillations exist, one can deduce some conditions on forms that equations of motion can take. A discrete model of hydraulic fracture is mentioned in Chapter 4. Hydraulic fracturing is a stimulation treatment wherein fluids are injected into reservoirs under high pressure to generate fractures in reservoirs. In this study, a lattice-based pseduo-3D model is developed to simulate hydraulic fracturing. This mode has been validated via a comparison with the KGD model. A series of pilot simulations was systematically tested for complex geometries under more realistic operation conditions, including flexible boundary conditions, randomness in elastic properties of shales and perforations. The simulation results confirm that perforation is likely to increase the complexity of fracture networks; the results also suggest that the interference between neighboring fractures is key to fracture network formation. / text

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In this dissertation, first the experimental and theoretical observations on the deformational characteristics of brittle geomaterials are reviewed and discussed. A basic conclusion is that special features such as strain softening can not be considered as true material (continuum) properties. These conclusions created a renewed emphasis on the constitutive modelling of such materials. A model that accounts for structural changes is developed. Such changes are incorporated in the theory through a tensor form of a damage variable. It is shown subsequently that formation of damage is responsible for the degradation in strength (softening) observed in experiments, for the degradation of the elastic shear modulus and for mechanical, damage induced anisotropy. A generalized plasticity model is incorporated for the so-called topical or continuum part of the behavior, whereas the damage part is represented by the so-called stress-relieved behavior. The question of uniqueness in the strain-softening regime is examined. It is shown that the constitutive equations lead to a unique solution for the case of rate dependent as well as rate independent formulation. Its implementation in finite element analysis shows mesh size insensitivity in the hardening and softening regimes. The general order of bifurcation of differential equations is employed in order to study the effect of damage accumulation on formation of narrow, so-called shear bands. It is shown that as the damage accumulates, the material approaches localization of deformation. The theory of mixtures is employed for further theoretical establishment of the proposed model. Energy considerations show the equivalence of the two-component damage body to an elastoplastic body containing cracks; the equivalence is considered in the Griffith sense. The mechanisms of failure are considered and discussed with respect to multiaxial stress pads. An explanation of failure, at the micro level, is given. The material constants involved in the theory are identified and determined from available experimental data. The model is then verified by back-predicting the observed behavior.

The general problem of an anticrack, present in a simple domain and subject to general remote loading is solved using distributed line forces, acting as strain nuclei, along the line of the anticrack. Subsequently, both dislocations and point forces are used as strain nuclei to achieve mixed boundary value conditions. The influence function for a pair of forces applied to the faces of a semi-infinite notch is found and finally this is used to find the true closure length and interfacial contact pressure. When a sharp-edged indenter is pressed into a half plane material in the half-plane is displaced and 'laps around' the edges of the punch, possibly making contact with the side faces. This phenomenon is quantified within (coupled) half-plane theory, and applied first to an idealised indenter having the cross section of a trapezium, and then to a semi-infinite indenter. The latter allows an asymptotic form to be found which, through a generalised stress intensity factor may be collocated into the edge of any notionally sharp-edged indentation problem. The effect of surface strains on the local slip angle, when an infinite cylinder is slid skew-wise across an elastically similar half-plane is found. It is shown that local frictional orthogonality is not completely consistent with global orthogonality. The problems of a square-ended and an almost square-ended rigid punch sliding with both plane and anti-plane velocity components are studied. It is shown that, for a truly complete contact, if the contacting body is incompressible, convection effects are absent. Introducing either: (a) local rounding or (b) finite compressibility of the contacting body into the problem introduces convection, giving rise to an inconsistency between the global and local requirement of the orthogonal friction law. The state of stress in a three-quarter-plane undergoing antiplane shear deformation is studied, due to the presence of a screw dislocation along one of the projection lines extending from the free surfaces. A simple, accurate formula for the state of stress along the line is found, providing a useful kernel for the solution of crack and contact edge slip problems. The state of stress induced in an axi-symmetric solid formed from a half-space and a bonded semi-infinite rod, by a family of ring dislocations of arbitrary Burgers vector is found. Particular care is given to the interaction between the Cauchy singularity near the dislocation core and the geometric singularity at the rod/half-space junction. Torsional contact between a semi-infinite elastic rod with square ends and an elastically similar half-space was then solved using the ring dislocations as influence functions. This provides an excellent illustration of the imposition of orthogonality condition for a complete contact.

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

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