Uniaxial Stresses

In the same way that close-packed directions in a crystal have larger refractive indices, so too can the application of a tensile stress to an isotropic glass increase the index of refraction normal to the direction of the applied stress. Uniaxial compression has the reverse effect. The resulting variation in refractive index with direction is called birefringence, which can be used as a method of measuring stress. 

Table 4.4 summarizes the physical properties of common metals used for diaphragms. Young s modulus is a measure of the stiffness of elastic materials and is defined as the ratio of stress (uniaxial) versus the strain (uniaxial), i.e. the ratio of the change in length of an elastic material as a function of a tensile or compressive load. The Poisson s ratio is a measure of a material s tendency to contract under a tensile load, i.e. the contraction in the direction normal to the direction in which the material is stretched. The symbol for the shear modulus of elasticity is G. 

Fig. 6.24 Notch root strain reduction consequent the passage from a plain stress (uniaxial) to a plain strain condition (multiaxial)...

To a first approximation stress, uniaxial extension ratio X, and shear modulus G are related by... 

Hoop, axial, shear, bending, and torsion stresses should all be considered in the design of a repair system. For those systems whose loads are primarily hoop stress, uniaxial fabric is a good option for the repair. If the axial, bending, and torsional loads are... 

Typical correlation between noise and stress in uniaxial stress state... 

Force per unit area along the axis of the deformation is called the uniaxial tension or stress. We shall use the symbol a as a shorthand replacement for F/A and attach the subscript t to signify tension. The elongation, expressed as a fraction of the original length AL/Lq is called the strain. We shall use 7j as the symbol for the resulting strain (subscript t for tension). Both o... 

This concept is explained by Figure 12 which shows the uniaxial stress— strain curve for a ductile material such as carbon steel. If the stress level is at the yield stress B or above, the problem is no longer a linear one. 

Fig. 12. Uniaxial stress—strain curve for an elastic plastic material. See text.

A sliding plate rheometer (simple shear) can be used to study the response of polymeric Hquids to extension-like deformations involving larger strains and strain rates than can be employed in most uniaxial extensional measurements (56,200—204). The technique requires knowledge of both shear stress and the first normal stress difference, N- (7), but has considerable potential for characteri2ing extensional behavior under conditions closely related to those in industrial processes. 

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

Another commonly used elastic constant is the Poisson s ratio V, which relates the lateral contraction to longitudinal extension in uniaxial tension. Typical Poisson s ratios are also given in Table 1. Other less commonly used elastic moduH include the shear modulus G, which describes the amount of strain induced by a shear stress, and the bulk modulus K, which is a proportionaHty constant between hydrostatic pressure and the negative of the volume... 

Prompt instrumentation is usually intended to measure quantities while uniaxial strain conditions still prevail, i.e., before the arrival of any lateral edge effects. The quantities of interest are nearly always the shock velocity or stress wave velocity, the material (particle) velocity behind the shock or throughout the wave, and the pressure behind the shock or throughout the wave. Knowledge of any two of these quantities allows one to calculate the pressure-volume-energy path followed by the specimen material during the experimental event, i.e., it provides basic information about the material s equation of state (EOS). Time-resolved temperature measurements can further define the equation-of-state characteristics. 

The gauge is usually calibrated in well-controlled uniaxial strain experiments by measuring the fractional change in resistance AR/Rq as a function of the shock stress. The results are empirically correlated to the stress through the relation... 

There are few problems of praetleal interest that ean be adequately approximated by one-dimensional simulations. As an example of sueh, eertain explosive blast problems are eoneerned with shoek attenuation and residual material stresses in nominally homogeneous media, and these ean be modeled as one-dimensional spherieally symmetrie problems. Simulations of planar impaet experiments, designed to produee uniaxial strain loading eonditions on a material sample, are also appropriately modeled with one-dimensional analysis teehniques. In faet, the prineipal use of one-dimensional eodes for the eomputational analyst is in the simulation of planar Impaet experiments for... 

In postulating a statistieal model for a statie stress variable, it is important to distinguish between brittle and duetile materials (Bury, 1975). For simple stress systems, i.e. uniaxial or pure torsion, where only one type of stress aets on the eomponent, the following equations determine the failure eriterion for duetile and brittle types to prediet the reliability (Haugen, 1980) ... 

Stress in crystalline solids produces small shifts, typically a few wavenumbers, in the Raman lines that sometimes are accompanied by a small amount of line broadening. Measurement of a series of Raman spectra in high-pressure equipment under static or uniaxial pressure allows the line shifts to be calibrated in terms of stress level. This information can be used to characterize built-in stress in thin films, along grain boundaries, and in thermally stressed materials. Microfocus spectra can be obtained from crack tips in ceramic material and by a careful spatial mapping along and across the crack estimates can be obtained of the stress fields around the crack. ... 

Type of stress. A uniaxial tensile creep test would not be expected to give the required data if the designer was concerned with torsional or compressive creep. 

For a component subjected to a uniaxial force, the engineering stress, a, in the material is the applied force (tensile or compressive) divided by the original cross-sectional area. The engineering strain, e, in the material is the extension (or reduction in length) divided by the original length. In a perfectly elastic (Hookean) material the stress, a, is directly proportional to be strain, e, and the relationship may be written, for uniaxial stress and strain, as... 

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