State of stress

The contact fatigue creates independent part of the fatigue tests. As consequence of triaxial state of stress and flexible plastic state in contact area occurrence comes to very considerable scattering of experimental data. From this reason it is necessary to test statistic meaningful number of samples. 

The eddy current method allows to evalute the state of stress in ferromagnetic material. The given method is used for determining own stress as well as that formed in effect of outside load. With regard to physical principles of own stress analysis, the dependence between the magnetic permeability and the distance between atomic surfaces is utilized. 

The state of stress in a cylinder subjected to an internal pressure has been shown to be equivalent to a simple shear stress, T, which varies across the wall thickness in accordance with equation 5 together with a superimposed uniform (triaxial) tensile stress (6). 

Imagine a block of material to which we apply a force F, as in Fig. 3.1(a). The force is transmitted through the block and is balanced by the equal, opposite force which the base exerts on the block (if this were not so, the block would move). We can replace the base by the equal and opposite force, f, which acts on all sections through the block parallel to the original surface the whole of the block is said to be in a state of stress. The intensity of the stress, ct, is measured by the force F divided by the area. A, of the block face, giving... 

There are four commonly occurring states of stress, shown in Fig. 3.2. The simplest is that of simple tension or compression (as in a tension member loaded by pin joints at its ends or in a pillar supporting a structure in compression). The stress is, of course, the force divided by the section area of the member or pillar. The second common state of stress is that of biaxial tension. If a spherical shell (like a balloon) contains an internal pressure, then the skin of the shell is loaded in two directions, not one, as shown in Fig. 3.2. This state of stress is called biaxial tension (unequal biaxial tension is obviously the state in which the two tensile stresses are unequal). The third common state of stress is that of hydrostatic pressure. This occurs deep in the earth s crust, or deep in the ocean, when a solid is subjected to equal compression on all sides. There is a convention that stresses are positive when they pull, as we have drawn them in earlier figures. Pressure,... 

In order to describe completely the state of triaxial (as opposed to biaxial) stress in an anisotropic material, the compliance matrix will have 36 terms. The reader is referred to the more advanced composites texts listed in the Bibliography if these more complex states of stress are of interest. It is conventional to be consistent and use the terminology of the more general analysis even when one is considering the simpler plane stress situation. Hence, the compliance matrix [5] has the terms... 

Note that this question involved a biaxial state of stress in the material and hence, strictly speaking, the creep curves used are not appropriate. However, creep curves for biaxial states of stress are rarely available, and one possible approach is to calculate an equivalent stress, a , using a van Mises type criterion... 

The laminate stress-analysis elements are affected by the state of the material and, in turn, determine the state of stress. For example, the laminate stiffnesses are usually a function of temperature and can be a function of moisture, too. The laminae hygrothermomechanical properties, thicknesses, and orientations are important in determining the directional characteristics of laminate strength. The stacking sequence... 

Finally, both the state of the material and the state of stress affect the laminate strength evaluation. That is, the actual temperature and moisture conditions influence the laminae strengths. Taken together with the laminae stresses, the laminae strengths and the laminate loads lead to an evaluation of the laminate capabilities. 

The objective of this chapter is to address introductory sketches of some fundamental behavior issues that affect the performance of composite materials and structures. The basic questions are, given the mechanics of the problem (primarily the state of stress) and the materials basis of the problem (essentially the state of the material) (1) what are the stiffnesses, (2) what are the strengths, and (3) what is the life of the composite material or structure as influenced by the behavioral or environmental issues in Figure 6-1 ... 

If a multidimensional state of stress exists, the Poisson s ratio effect causes the tensile and compressive strains to be dependent upon each of the components of stress. 

For most practical purposes, the onset of plastic deformation constitutes failure. In an axially loaded part, the yield point is known from testing (see Tables 2-15 through 2-18), and failure prediction is no problem. However, it is often necessary to use uniaxial tensile data to predict yielding due to a multidimensional state of stress. Many failure theories have been developed for this purpose. For elastoplastic materials (steel, aluminum, brass, etc.), the maximum distortion energy theory or von Mises theory is in general application. With this theory the components of stress are combined into a single effective stress, denoted as uniaxial yielding. Tlie ratio of the measure yield stress to the effective stress is known as the factor of safety. 

Calculations for the minimum performance properties of drill pipe are based on formulas given in Appendix A of API RP 7G. It must be remembered that numbers in Tables 4-80-4-83 have been obtained for the uniaxial state of stress, e.g., torsion only or tension only, etc. The tensile stress resistance is decreased when the drill string is subjected to both axial tension and torque a collapse... 

The reduction in the tensile load capacity of the drill pipe is 311,400 -260,500 = 50,900 lb. That is about 17% of the tensile drill pipe resistance calculated at the minimum yield strength in uniaxial state of stress. For practical purposes, depending upon drilling conditions, a reasonable value of safety factor should be applied. 

From Table 4-84, the collapse pressure resistance in uniaxial state of stress, P - 6,010 psi. Reduced wall thickness for class 2 drill pipe = (0.65)(0.337) = 0.219 in. Reduced D for class 2 drill pipe = 3.826 + (2)(0.219) = 4.264 in. Reduced cross-sectional area of class 2 drill pipe equals ... 

In particular, makeup torque induces a tensile state of stress within the pin and compression stress in the box. Thus, when the tool Joint is exposed to the additional axial load due to the weight of the drill string suspended below the Joint, the load capacity of the tool Joint is determined by the tensile strength of the pin. 

The concept of biomarkers is illustrated in Figure 4.4. As the dose of a chemical increases, the organism moves from a state of homeostasis to a state of stress. With further increases in dose, the organism enters first the state of reversible disease, and eventually the state of irreversible disease, which will lead to death. In concept, all of these stages can be monitored by biomarker assays (lower part of conceptual diagram). 

The state of stress at a point in a structural member under a complex system of loading is described by the magnitude and direction of the principal stresses. The principal stresses are the maximum values of the normal stresses at the point which act on planes on which the shear stress is zero. In a two-dimensional stress system, Figure 13.2, the principal stresses at any point are related to the normal stresses in the x and y directions ax and ay and the shear stress rxy at the point by the following equation ... 

The local heating, and consequent expansion, that occurs during welding can leave the joint in a state of stress. These stresses are relieved by post-welding heat treatment. Not all vessels will be stress relieved. Guidance on the need for post-welding heat treatment is given in the codes and standards, and will depend on the service and conditions, materials of construction, and plate thickness. 

It is also evident that this phenomenological approach to transport processes leads to the conclusion that fluids should behave in the fashion that we have called Newtonian, which does not account for the occurrence of non-Newtonian behavior, which is quite common. This is because the phenomenological laws inherently assume that the molecular transport coefficients depend only upon the thermodyamic state of the material (i.e., temperature, pressure, and density) but not upon its dynamic state, i.e., the state of stress or deformation. This assumption is not valid for fluids of complex structure, e.g., non-Newtonian fluids, as we shall illustrate in subsequent chapters. 

In Section 1.9 it is explained that the state of stress can be described by nine terms. In the above example, the wall shear stress is a particular value of one stress component, that denoted by rrx. In this notation, the second subscript denotes the direction in which the stress component acts, here,... 

The surface layers of solids usually differ from the deeper zones of the same specimen in their chemical composition, their degree of lattice perfection (e.g., the frequency of dislocations), their state of stress, and so on. This renders unpalatable the notion of a surface tension in solids, but suggests the existence of a kind of surface energy, unknown in liquids, which it was proposed to designate as cuticular energy. 

The critical state of stress-induced crystallization at high spinning speeds is governed by the viscoelasticity of the polymer in combination with its crystallization behavior. Any kind of coarse particle obviously disturbs the structure and affects the resistance against deformation. The development of stress is controlled by the rheological properties of the polymer. Shimizu et al. [4] found that increasing the molecular weight drastically promotes the crystallinity under stress conditions. 

Epoxy Curing Agent Technique State of Stress Measurement Frequency Range, Hz Ea, kcal/mole Tg sub-Tg Ref. 

In a recent attempt to bring an engineering approach to multiaxial failure in solid propellants, Siron and Duerr (92) tested two composite double-base formulations under nine distinct states of stress. The tests included triaxial poker chip, biaxial strip, uniaxial extension, shear, diametral compression, uniaxial compression, and pressurized uniaxial extension at several temperatures and strain rates. The data were reduced in terms of an empirically defined constraint parameter which ranged from —1.0 (hydrostatic compression) to +1.0 (hydrostatic tension). The parameter () is defined in terms of principal stresses and indicates the tensile or compressive nature of the stress field at any point in a structure —i.e.,... 

X-ray investigation of inorganic pigments yields information on the structure, fine structure, state of stress, and lattice defects of the smallest coherent regions that are capable of existence (i.e., crystallites) and on their size. This information cannot be obtained in any other way. Crystallite size need not be identical with particle size as measured by the electron microscope, and can, for example, be closely related to the magnetic properties of the pigment. 

The State of Stress in Laminar Shear Flow and its Relation to Flow... 

The state of stress in a flowing liquid is assumed to be describable in the same way as in a solid, viz. by means of a stress-ellipsoid. As is well-known, the axes of this ellipsoid coincide with directions perpendicular to special material planes on which no shear stresses act. From this characterization it follows that e.g. the direction perpendicular to the shearing planes cannot coincide with one of the axes of the stress-ellipsoid. A laboratory coordinate system is chosen, as shown in Fig. 1.1. The x- (or 1-) direction is chosen parallel with the stream lines, the y- (or 2-) direction perpendicular to the shearing planes. The third direction (z- or 3-direction) completes a right-handed Cartesian coordinate system. Only this third (or neutral) direction coincides with one of the principal axes of stress, as in a plane perpendicular to this axis no shear stress is applied. Although the other two principal axes do not coincide with the x- and y-directions, they must lie in the same plane which is sometimes called the plane of flow, or the 1—2 plane. As a consequence, the transformation of tensor components from the principal axes to the axes of the laboratory system becomes a simple two-dimensional one. When the first principal axis is... 

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