The Basic Stresses

As the UTS is approached, significant fiber failures occur, which further reduce the tangent modulus. The basic stress-strain relationship is,64... 

As already mentioned, the basic stress-strain concept explains the correspondence between an external demand to a subject (causing stress) and the individual psychophysiological reactions while fulfilling the demands (resulting in strain). A nonlinear relationship between stress and strain is caused by ... 

ISO/TR 8584-2 1993 Thermoplastics pipes for industrial applications under pressure -Determination of the chemical resistance factor and of the basic stress - Part 2 Pipes made of halogenated polymers. 

The computer can also be used to provide a singular solution to the required cross section. The time-stress-strain data to generate a set of creep curves for a specific material would be provided. The computer is then programmed with the problem of the stress-time profile for the part. Using the inverse curve as the strain relaxation curve, the computer can do an iterative solution to determine the minimum cross section. That would restrict the creep to the set amount in the desired design time. The WLF transformation can be done on the basic stress-strain time data to provide the solution for different operating temperatures. 

Whitney and Drzal [87] presented an analytical model to predict the stresses in a system consisting of a broken fiber surrounded by an unbounded matrix. The model (Fig. 8) is based on the superposition of the solutions to two axisymmetric problems, an exact far-field solution and an approximate transient solution. The approximate solution is based on the knowledge of the basic stress distribution near the end of the broken fiber, represented by a decaying exponential function multiplied by a polynomial. Equilibrium equations and the boundary conditions of classical theory of elasticity are exactly satisfied throughout the fiber and matrix, while compatibility of displacements is only partially satisfied. The far-field solution away from the broken fiber end satisfies all the equations of elasticity. The model also includes the effects of expansional, hygrothermal strains and considers orthotropic fibers of the transversely isotropic class. 

The basic stress intensity limits for various categories relating to an analysis according to the ASME Code, VHI-2, and Section in, Division 1, Subsection NB, and optional Part NC-3200 of Subsection NC are ... 

In Chapter I the basic concepts of testing are discussed along with the purpose of specifications and standards. Also discussed is the basic specification format and classification system. The subsequent chapters deal with the testing of five basic properties mechanical, thermal, electrical, weathering, and optical properties of plastics. The chapter on mechanical properties discusses in detail the basic stress-strain behavior of the plastic materials so that a clear understanding of testing procedures is obtained. Chapter 7 on... 

The properties of elastomeric materials are controlled by their molecular structure which has been discussed earlier (Section 4.5). They are basically all amorphous polymers above their glass transition and normally crosslinked. Their unique deformation behaviour has fascinated scientists for many years and there are even reports of investigations into the deformation of natural rubber from the beginning of the nineteeth century. Elastomer deformation is particularly amenable to analysis using thermodynamics, as an elastomer behaves essentially as an entropy spring . It is even possible to derive the form of the basic stress-strain relationship from first principles by considering the statistical thermodynamic behaviour of the molecular network. 

While viscosity measurements are typically carried out on uncured adhesives that are still in their liquid state or on partially cured materials that can still exhibit flow, measuring the basic stress-strain behavior is one of the most fundamental tests conducted on polymeric adhesives in their cured or solid state. In their simplest form, these tests are intended for characterizing materials with very large Deborah numbers, where the time scale of the test is short compared to any relaxation times within the material, or for crosslinked materials tested at time scales much longer than their characteristic times. Just as with viscosity tests and because of the very broad characteristic time scale of typical polymers, however, stress-strain tests are often conducted in a manner that captures some of the inherent time dependence of the materials being evaluated. 

In this chapter we shall first outline the basic concepts of the various mechanisms for energy redistribution, followed by a very brief overview of collisional intennoleciilar energy transfer in chemical reaction systems. The main part of this chapter deals with true intramolecular energy transfer in polyatomic molecules, which is a topic of particular current importance. Stress is placed on basic ideas and concepts. It is not the aim of this chapter to review in detail the vast literature on this topic we refer to some of the key reviews and books [U, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, and 32] and the literature cited therein. These cover a variety of aspects of tire topic and fiirther, more detailed references will be given tliroiighoiit this review. We should mention here the energy transfer processes, which are of fiindamental importance but are beyond the scope of this review, such as electronic energy transfer by mechanisms of the Forster type [33, 34] and related processes. 

A schematic stress-strain curve of an uncrimped, ideal textile fiber is shown in Figure 4. It is from curves such as these that the basic factors that define fiber mechanical properties are obtained. 

The failure rate changes over the lifetime of a population of devices. An example of a failure-rate vs product-life curve is shown in Figure 9 where only three basic causes of failure are present. The quaUty-, stress-, and wearout-related failure rates sum to produce the overall failure rate over product life. The initial decreasing failure rate is termed infant mortaUty and is due to the early failure of substandard products. Latent material defects, poor assembly methods, and poor quaUty control can contribute to an initial high failure rate. A short period of in-plant product testing, termed bum-in, is used by manufacturers to eliminate these early failures from the consumer market. 

In the large-diameter vertical cylindrical tanks, because hoop stress is proportional to diameter, the thickness is set by the hydrostatic hoop stresses. Although the hydrostatic forces increase proportionally with the depth of Hquid in the tank, the thickness must be based on the hydrostatic pressure at the point of greatest depth in the tank. At the bottom, however, the expansion of the shell owing to internal hydrostatic pressure is limited so that the actual point of maximum stress is slightly above the bottom. Assuming this point to be about 1 ft (0.305 m) above the tank bottom provides tank shells of adequate strength. The basic equation modified for this anomaly is... 

The SE values in Table 10-49 are equal to the basic allowable stresses in tension S multiplied by a quality factor E (see subsection Pressure Design of Metallic Components Wall Tliick-ness"). The design stress values for bolting materials are equal to die basic allowable stresses S. The stress values in shear shall be 0.80 times the allowable stresses in tension derived from tabulated values in Table 10-49 adjusted when applicable in accordance widi Note 13. 8tress values in bearing shall be twice those in shear. 

The allowable stress range for displacement stresses and permissible additive stresses shall be as specified in Eqs. (10-93) and (10-94) for systems primarily stressed in bending and/or torsion. For pipe or piping components containing longitudinal welds the basic allowable stress S may be used to determine S. (See Table 10-49, Note 13.)... 

The diagnostics applied to shock experiments can be characterized as either prompt or delayed. Prompt instrumentation measures shock velocity, particle velocity, stress history, or temperature during the initial few shock transits of the specimen, and leads to the basic equation of state information on the specimen material. Delayed instrumentation includes optical photography and flash X-rays of shock-compression events, as well as post-mortem examinations of shock-produced craters and soft-recovered debris material. 

The left-hand side of our equation says that fast fracture will occur when, in a material subjected to a stress a, a crack reaches some critical size a or, alternatively, when material containing cracks of size a is subjected to some critical stress cr. The right-hand side of our result depends on material properties only E is obviously a material constant, and G, the energy required to generate unit area of crack, again must depend only on the basic properties of our material. Thus, the important point about the equation is that the critical combination of stress and crack length at which fast fracture commences is a material constant. 

Electrochemical corrosion is understood to include all corrosion processes that can be influenced electrically. This is the case for all the types of corrosion described in this handbook and means that data on corrosion velocities (e.g., removal rate, penetration rate in pitting corrosion, or rate of pit formation, time to failure of stressed specimens in stress corrosion) are dependent on the potential U [5]. Potential can be altered by chemical action (influence of a redox system) or by electrical factors (electric currents), thereby reducing or enhancing the corrosion. Thus exact knowledge of the dependence of corrosion on potential is the basic hypothesis for the concept of electrochemical corrosion protection processes. 

The disadvantage of the quasi-resonant converter compared to the newer lossless snubber and active clamp techniques in addition to the basic PWM converters, is the voltage or current stresses placed upon the power components. The peak voltage or current values that exist within quasi-resonant converters can be two to three times higher than in PWM converters. This forces the designer to use higher-rated power switches and rectifiers which may not have as good conduction characteristics. 

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