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

Practice in the field of limit design has tended to place certain restrictions on structural loading patterns in order to simplify the calculations involved in the limit design procedure. The loads considered in this simplified approach are assumed to either remain constant and fixed, or if they vary then this is to be in such a manner that their magnitudes stand in a constant relationship one to the other. Actual structural loadings seldom satisfy these restrictive conditions and the question naturally arises as to whether or not this simplified limit design procedure is valid for general use in practical design problems in which external loads may be wholly independent in their individual actions. This question is investigated in the present paper through the examination of several practical forms of structure which portray the more adverse conditions of independent and variable loading to be met in practice. These structures are, respectively, single and double bay gable bents of lightweight construction, and two forms of multispan bridge girders. The study indicates that all of these structures are able to support the ultimate loads predicted by the simplified limit design method; the actual ultimate loads exceeding the predicted values by up to twenty percent. It is concluded that structural failure in practice can always be expected to occur within acceptable limits of the ultimate load capacity as predicted by the simplified method. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

No abstract / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

A bar cell in the form of an isosceles trapezoid suitable for solution of two dimensional problems is introduced involving two new concepts, one that of overlapping bars and the other of a variable angle parameter. Based on the Identity of corner displacements of the cell and a similarly shaped piece of plate in conditions of uniform stress, expressions for the bar areas are derived in terms of Poisson's ratio, the geometry of the cell and a variable angle parameter. The stiffness matrix of the cell is derived further by combining different displacement modes. Two methods of calculating stresses, one by the nodal displacements and the other by the nodal force concentrations, are described. Two examples involving a rectangular plate and a partial sector of a circular plate illustrate the application of the finite element method using trapezoidal bar as well as no-bar cells and their results are compared with the exact elasticity solution. / Applied Science, Faculty of / Civil 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

In the testing of materials, structures and structural components it is often desired to determine the surface displacement and strain fields due to some external loading. Numerous optical techniques have been developed for this purpose and successfully used in particular applications. Unfortunately, when the surface deformation is quite large, as is usually the case in practical testing, most of these methods fail and only a few suitable optical interferometric techniques will work. Two of the recently developed techniques that seem to work are based on laser speckle interferometry. The first technique was described in 1972 by Duffy [l] who showed that a Double Aperture Speckle Camera (DASC) is suitable for measurement of a reasonably large in-plane displacement having its direction parallel to the line connecting the two apertures of the camera. A second technique was described in 1973 by Hung [3] . He showed that a Double Aperture Speckle Shearing Camera (DASSC) may be used to measure both the in and out-of-plane strains of planar surfaces. Duffy has not considered the fringe formation by DASC due to the displacement normal to the surface and the displacement normal to the line connecting the two apertures of DASC. Hung, in turn, has not considered the effect on fringe formation of either the in and out-of-plane displacements, or the in-plane strain, which is the partial derivative w,v (see Fig. 3.11 for the definition of w,y). Because of the great potential of DASC and DASSC stemming from their ability to measure displacements and strains over many orders of magnitude, a considerable effort was made to determine the fringe formation of the two cameras due to all displacements and strains occuring in a general deformation of a specimen surface. The theoretical analysis of models of DASC and DASSC was performed and resulted in two "new" equations describing the fringe formation by these cameras. The equations take into account the effect of all displacements , and strains on the fringe formation; in addition, the equations are "symmetric" and the equation governing DASSC reduces to the one governing DASC for the lateral shear set equal to zero. The accuracy of these equations was then verified by a number of simple experiments. Various ways of using the two cameras were proposed so that the unknown displacements and strains in the specimen surface may be calculated from the least number of fringe patterns. Computer programs based on these proposed methods were written and used in several experiments. In all instances the actual and the calculated displacements and strains agreed quite well. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Recent progress in structural engineering has been marked by the increased use of thin shells as load carrying members. In particular, shells of revolution have been widely utilized in the missile industry whereas shells of arbitrary shape have been incorporated in the architectural design of today's modern buildings. Missile applications have been extensively studied both statically and dynamically. However, architechural applications have generally been limited to the statics problem with little consideration being given to the dynamic behavior of these unique structures.

The welding of steel occupies an important place as a major fabricating process in industry. The welding of steel has been a subject of research for many years, and much information has been obtained about the strength of weldments.

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