Showing papers on "Stress field published in 1969"

Stress-history of folding

Abstract: The velocity field and hence stress field for two-dimensional large-amplitude folding of a viscous layer in a less viscous matrix has been determined theoretically by a series of linear incremental problems. The velocity field for each problem was found numerically using a modification of the finite element method. The model considered most representative of natural folds had the following properties: eta /eta 1 , (viscosity contrast)=42, L/h (wavelength/thickness)=12, A o (initial amplitude)=0.1h. Microstructures induced by intragranular flow of calcite and quartz have been used by many to determine principal stress orientations around natural folds of many styles and sizes, generally with similar results. Fabric data record cumulative intragranular flow during folding.

The use of eigenfunction expansions in the general solution of three-dimensional crack problems

Abstract: Eigenfunction expansion technique to analyze three dimensional crack and wedge problems, emphasizing stress field near straight edged crack

The End Problem for a Laminated Elastic Strip —: I. The General Solution

Abstract: A plane elasticity solution is derived for the end problem in a two- layer laminated strip. The laminae may have arbitrary elastic constants and an arbitrary thickness ratio. The solution is obtained as a series of non-orthogonal eigenfunctions, each of which varies exponentially along the axis of the strip. Each exponential coefficient is a complex root of an eigenvalue equation that results from the requirement of compatible displacements at the interface.The general solution obtained in this paper may be used to find the stress field in a two-layer laminated strip subjected to specified self- equilibrating end loading. It thus permits the determination of the stress concentration near the end which is usually neglected by invok ing St. Venant's Principle.

Yield criteria for plastic deformation on glassy high polymers in general stress fields

Abstract: Yield criteria for plastic deformation on glassy high polymers induced by stress field, noting crazing and shear yielding dependence on first stress invariant

Mechanics of Second Order Faults and Tension Gashes

Abstract: The origin of en echelon second order shear fractures and tension gashes associated with first order, or primary, faults is examined analytically and experimentally. It is postulated that en echelon second order structures form under the influence of a stress mechanism similar to the one occurring in the direct shear test. The direct shear or modified direct shear state of stress could develop at certain points along a forming primary fault as a result of a local reduction in the normal stress acting on planes perpendicular to the displacement direction. It is argued that in most en echelon arrays the orientation of the individual fractures reflects the existence of a local state of stress, and cannot directly be correlated with the regional (primary) stress field. The zone in which they occur, however, may represent planes of high effective shear stress within the regional framework. The direct shear model (full relief of transverse normal stress) offers a stress mechanism which can explain the origin of not only en echelon tension gashes but also second order faults. For a given set of strength parameters, the type of en echelon fractures that will develop depends on the normal stress acting in the primary fault plane. In general, tension fractures form at low normal stress, shear fractures at intermediate values of normal stress, and at high normal stress a crush or shear zone is produced. If the state of stress is one of modified direct shear (only partial relief of transverse normal stress), the development of second order faults is favored.

The End Problem for a Laminated Elastic Strip — II. Differential Expansion Stresses

Abstract: A plane elasticity solution is presented for the state of stress resulting from differential expansion in a composite made up of two rectangular strips bonded on an interface. The stress field that has long been known to exist in the middle of such a laminated strip (to the St. Venant approximation) includes neither normal nor shear traction on the bonded interface. These stress components are shown to be significant only within a distance from each end equal to the total thickness, and their distribution is determined for a wide range of elastic moduli and strip dimensions.It is found that the distribution of normal stress at the interface is quite sensitive to the modulus and thickness ratios of the laminae. By making use of the form of this dependence, it may be possible to design bonded structures to withstand curing and/or temperature changes which would otherwise cause failure.

Tension field theory, a new approach which shows its duality with inextensional theory

Abstract: Tension field theory describes the highly buckled (wrinkled) state of membranes or very thin plates whose boundaries are subjected to certain planar displacements well in excess of those necessary to initiate buckling. The present interest in tension field theory is because lightweight structures with stretched membrane components have potential applications in space. In addition, membrane structures which are pretensioned by internal pressure have application to lightweight portable bridges, protective coverings and various air cushion devices. The theory was conceived by Wagner (1929) [1] whose primary concern was to explain the behaviour of thin metal webs in beams and spars carrying a shear load well in excess of the initial buckling value. Such webs offer little resistance to the compressive strain component of the shear and the spar flanges must be held apart by struts to prevent collapse. In the simple case of rigid spar flanges and rigid perpendicular struts the stress field in the web in the highly buckled state is primarily that of tension at 45°. As the shear load increases so does the magnitude of this tensile stress field and, just as a taut string resists a kinking action, so too does this tensile stress field resist the out-of-plane displacements engendered by the buckling action of the compressive stresses; these opposing actions result in a decreasing wavelength along the compressive buckles which form at right angles to the tension field. Strictly speaking such problems are non-linear and their exact analysis presents formidable difficulties. However, within the framework of large-deflexion plate theory it may be shown that for large values of the ratio (applied shear strain)/(shear strain at initial buckling) the relation between applied loads and planar displacements and stresses again approaches linearity, and it is this asymptotic regime for which tension field theory is applicable. In this regime the flexural stresses and the planar compressive (post-buckling) stresses are negligible compared with the tensile stresses; the assumption that their magnitude is zero is physically equivalent to the assumption of zero flexural membrane stiffness, and it is this which characterises tension field theory: the membrane is envisaged as being finely wrinkled at right angles to the lines of tension. In general these “tension rays” are not necessarily parallel and the boundary conditions need not be those of pure shear, as in our previous example, but shear must play a dominant role in the boundary deformation because of the requirement that the principal strains at any point are of opposite sign. This requirement will be considered in greater detail later but it is clear that if the principal strains are both positive so too are the principal stresses, and if the principal strains are both negative the membrane is ineffective in carrying load.

Study of residual stresses in linearly varying biaxial-stress fields

Abstract: A theory has been developed for the calculation of relaxation strains effected by drilling a hole in a plate with a linearly varying stress field. With this theory, a technique was developed for the measurement of residual stress at the toe of tee-fillet welds. The above technique was employed for the measurement of residual stresses at the toe of tee-fillet welds in 11/2-in. HY-80 steel with the fillet in the as-welded, ground, shot peened, ground and shot peened, and mechanically peened condition. It was found that experimental data conform to the assumed theory, and that residual stresses in aswelded tee-fillet welds in both the transverse and longitudinal directions approach the yield strength of the steel. It was also found that residual stresses are reduced approximately 25 percent by grinding, 50 percent by shot peening and 50 percent by grinding and shot peening. Mechanical peening drastically affected residual stresses by converting high tension at the toe of the fillet weld to high compression of approximately the same magnitude.

Effects of time and plasticity on fracture

Abstract: The prime objective of this work is to show that the strength of solids as a function of crack dimension varies in a way different from that predicted by the Griffith-Irwin theory of fracture if the range of the initial crack length is chosen to be of the order of a certain characteristic length l*. This length is related to the stress intensity factor (K) and the yield stress magnified by a constraint factor (Y) appropriate to a given stress field. In other words, a characteristic quantity l*=K2/2πY2 determines the limits of applicability of the Griffith-Irwin theory. The second objective is to introduce time as a meaningful variable in fracture mechanics and to study its effect upon the strength. This is done by accepting a certain model which allows for linear time-dependent behaviour of the matrix in which the crack is embedded, and by assuming that the non-linear effects due to large plastic and viscous deformations are confined to the Dugdale-type narrow zones in the crack plane. As the final result we obtain in place of one (static) curve of strength against crack length a continuous time spectrum of such curves, each of which is valid for a different moment t. A simple `cut-ends cigar' model of a crack is proposed to describe the effects of plasticity (small-scale yielding) and time on fracture.

Fatigue crack nucleation in metals.

Abstract: One of the unanswered questions in the study of fatigue is how cracks nucleate at stresses far below the static fracture strength. Previous theories show possible qualitative mechanisms that may operate in a crystal at room and low temperatures but none provides a quantitiative theory of this phenomenon. We show here a quantitative mechanism of fatigue crack initiation. With a small initial stress field, two closely located thin slices slide in opposite directions under cyclic loading. The increase of the local plastic strain with cycles of loading is calculated. The local plastic shear strain, positive in one slice and negative in the other, reaches 100 per cent at the free surface in a few hundred cycles. These large strains clearly cause the start of an extrusion or intrusion and fatigue crack nucleation.

Stress analysis of an infinite plate containing an elastic rectangular inclusion

Abstract: A solution is presented for determining the stresses in an infinite elastic plate containing an elastic rectangular inclusion subjected to a uniform stress field. The bond stresses are obtained by treating the plate and the inclusion separately and satisfying continuity of displacements at discrete points rather than continuously. An example of a square elastic inclusion is treated in detail. Comparison is made between the solution obtained by point-matching techniques and the exact solution for a rigid square inclusion. Excellent agreement is observed. The practical motivation behind this research was the estimation of the bond stresses induced between the fibers and matrix of multifiber composite sheets.

Dislocation Pile‐Up in Half‐Space

Abstract: If an obstacle exists in the vicinity of the free surface of a half‐space and a stress field is applied in such a manner that dislocations are pushed towards the obstacle, an array of dislocations then piles up into an equilibrium distribution against the obstacle. The distributions of dislocations are obtained by the Wiener‐Hopf technique for the edge and screw dislocations. The total strength of dislocations (Burgers vector multiplied by the number of dislocations) distributed in the distance L is calculated as 0.92π(1−v)σAL/G for edge dislocations and 2σAL/G for screw dislocations, where G, v are the shear modulus and Poisson ratio respectively and σA is the applied stress. The result can be applied to crack problems. The above two numbers for the total strength of dislocations give the crack openings at the free surface for the extensional mode and the antiplane shear mode of fracture, respectively.

Development of experimental stress analysis methods to determine stresses and strains in solid propellant grains. stress distribution around a circular bar, with flat and spherical ends, embedded in a matrix in a triaxial stress field,

Abstract: : The report deals with the stress and strain distribution around a circular bar embedded in a matrix and subjected to a mechanically applied triaxial load The three-dimensional 'freezing' technique of photoelasticity was used The results obtained correspond to the case of a rigid circular bar embedded in an homogeneous, elastic matrix Two models were analyzed; in one the axis of the circular bar was parallel to the direction of the loading and in the other the axis of the circular bar was normal to the direction of loading By combining the results obtained independently for these two cases, stress and strain distribution around the circular bar for various ratios of triaxial load can be obtained (Author)

Diffusion phenomena and stress relaxation in the vicinity of a spherical void

Abstract: Based on a linear interrelated set of equations [1], a study was made of diffusion phenomena due to nonuniform stress distribution in the vicinity of a spherical void under the influence of a sufficiently distant uniform stress field. The effect of diffusion on the redistribution of stress in this region was analyzed, it being assumed that in the case of uniaxial tension the void surface is mass-insulated, while in the case of omnidirectional tension a constant chemical potential of the particles of the diffusing substance is maintained on the void surface.