An investigation of the low temperature tensile properties of vanadium single crystals was carried out, using zone-refined metal. Single crystals of predetermined axial [110] orientation were grown by a melt solidification technique, using an electron beam, floating-zone refiner. Tensile specimens were prepared from these single crystals. A plot of yield stress versus test temperature was found to be discontinuous and consisted of two curves which intersected at -125° C. The plot of log yield stress versus reciprocal temperature yielded two straight lines which also intersected at -125° C. The slip system was identified as <111>{112}, which is different from that found for iron single crystals. X-ray, metallographic and electrical resistance data indicate that the phenomenon is primarily a yield point effect. The results of tensile tests performed on single crystals at a very low strain rate, and on polycrystalline specimens indicated that the temperature dependence of yield stress is itself orientation dependent. Three possible explanations of the unusual temperature dependence of yield stress are given: (1) A change in deformation mechanism occurs, for example, from slip to twinning. (2) A minor ordering reaction occurs. (3) A change in the mechanism by which dislocations are unlocked from their atmospheres occurs; for example, two impurity atmospheres surrounding different dislocations, each impurity showing a separate temperature dependence of yield stress. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate

This study is concerned with a thermo-elasto-plastic continuum in which the thermodynamic coupling between material deformations, heat generation and flow are included. The elasto-plastic behavior is represented by a linear "rate-type" theory and restricted to infinitesimal deformations. The heat flow equations are posed in incremental form for the linear theory of heat conduction. The theory is such that the conservation laws of thermodynamics are satisfied. A displacement formulation is used and the field equations are shown to be linear operator equations. The operators are tested for symmetry and positive-definiteness in order to test their suitability for solution by a variational method. It is shown that the special case of thermo-elasticity may be solved by minimisation of a functional and that convergence of approximate solutions may be predicted. In the general case of thermo-elasto-plasticity, the operator is shown to be unsymmetric. Therefore an iterative functional is introduced in order to obtain a solution by a variational method. Approximate solutions to some illustrative problems are found using a finite-element-formulation, and it is shown that the results are consistent with expected physical behavior. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

The deformation behavior of the two phase composite Al-CuAl₂ has been studied at ordinary and elevated temperatures using sheath rolling and extrusion. Plasticity was exhibited by the CuAl₂ only at elevated temperatures and contributed little to overall deformation of the composite. Results have been interpreted in terms of simple models for combined stresses involving a hydrostatic component. Examination of microstructures of extruded composites indicated that it may be possible to study the flow of metals in deformation processes by the use of suitable composites. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate

We present an elastic orthotropic plate theory in plane strain and axisym-metric deformations by first developing their uniform asymptotic expansions of the exact solutions for the basic governing boundary value problems. Then, the establishment of the necessary conditions for decaying states, both explicitly and asymptotically, enables us to determine the outer solution without reference to the inner solution and clarify the precise meaning of the well known St.Venant's principle under the circumstances considered here. The possible existence of corner stress singularities was examined by establishing and solving three transcendental governing equations. By developing a generalized Cauchy type singular integral equation for the plane strain deformation and an integral equation of the second kind for the axi-symmetric deformation and taking the corner stress singularities into consideration, we obtained accurate numerical solutions for all canonical boundary value problems which are needed in the asymptotic necessary conditions for decaying states. Finally, the accuracy of the numerical solutions of canonical boundary value problems and the efficiency of the plate theory were confirmed through the applications of solving two physical problems and comparing with the existing results. / Science, Faculty of / Mathematics, Department of / Graduate

No / Polypropylene sheets have been stretched at 160 °C to a state of large biaxial strain of extension ratio 3, and the stresses then allowed to relax at constant strain. The state of strain is reached via a path consisting of two sequential planar extensions, the second perpendicular to the first, under plane stress conditions with zero stress acting normal to the sheet. This strain path is highly relevant to solid phase deformation processes such as stretch blow moulding and thermoforming, and also reveals fundamental aspects of the flow rule required in the constitutive behaviour of the material. The rate of decay of stress is rapid, and such as to be highly significant in the modelling of processes that include stages of constant strain. A constitutive equation is developed that includes Eyring processes to model both the stress relaxation and strain rate dependence of the stress. The axial and transverse stresses observed during loading show that the use of a conventional Levy-Mises flow rule is ineffective, and instead a flow rule is used that takes account of the anisotropic state of the material via a power law function of the principal extension ratios. Finally the constitutive model is demonstrated to give quantitatively useful representation of the stresses both in loading and in stress relaxation.

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