Generalized Creep Behavior

Thermal stress— dependence on coefficient of thermal expansion, modulus of elasticity, and temperature change 

Thermal fatigue is normally induced at elevated temperatures by fluctuating thermal stresses mechanical stresses from an external somce need not be present. The origin of these thermal stresses is the restraint to the dimensional expansion and/or contraction that would normally occm in a structural member with variations in tempera-tme. The magnitude of a thermal stress developed by a temperatme change AT depends on the coefficient of thermal expansion and the modulus of elasticity E according to 

Several approaches to corrosion fatigue prevention exist. On one hand, we can take measures to reduce the rate of corrosion by some of the techniques discussed in Chapter 17—for example, apply protective surface coatings, select a more corrosion-resistant material, and reduce the corrosiveness of the environment. On the other hand, it might be advisable to take actions to minimize the probability of normal fatigue failure, as outlined previously—for example, reduce the applied tensile stress level and impose residual compressive stresses on the surface of the member. 

A typical creep tesF consists of subjecting a specimen to a constant load or stress while maintaining the temperature constant deformation or strain is measured and plotted as a function of elapsed time. Most tests are the constant-load type, which yield informa- 

Concept Check 8.5 Superimpose on the same strain-versus-time plot schematic creep curves for both constant tensile stress and constant tensile load, and explain the differences in behavior. 

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In general, creep behavior of ceramics is similar to that of metals. However, in ceramics it usually occurs at higher temperatures, typically >0.5 Tni. In comparison, creep is a consideration in aluminum alloys at 100°C and in polymers at room temperature. Creep is particularly important in ice, which creeps extensively at low temperatures. The creep of ice is responsible for the movement of glaciers and the spreading of the Antarctic ice cap. 

Creep. The phenomenon of creep refers to time-dependent deformation. In practice, at least for most metals and ceramics, the creep behavior becomes important at high temperatures and thus sets a limit on the maximum appHcation temperature. In general, this limit increases with the melting point of a material. An approximate limit can be estimated to He at about half of the Kelvin melting temperature. The basic governing equation of steady-state creep can be written as foUows ... 

Boltzmann s constant, and T is tempeiatuie in kelvin. In general, the creep resistance of metal is improved by the incorporation of ceramic reinforcements. The steady-state creep rate as a function of appHed stress for silver matrix and tungsten fiber—silver matrix composites at 600°C is an example (Fig. 18) (52). The modeling of creep behavior of MMCs is compHcated because in the temperature regime where the metal matrix may be creeping, the ceramic reinforcement is likely to be deforming elastically. 

General Metallurgical Behaviors in Gas Turbines Creep and Rupture... 

Although the creep behavior of a material could be measured in any mode, such experiments are most often run in tension or flexure. In the first, a test specimen is subjected to a constant tensile load and its elongation is measured as a function of time. After a sufficiently long period of time, the specimen will fracture that is a phenomenon called tensile creep failure. In general, the higher the applied tensile stress, the shorter the time and the greater the total strain to specimen failure. Furthermore, as the stress level decreases, the fracture mode changes from ductile to brittle. With flexural, a test specimen... 

Very simple models can illustrate the general creep and stress-relaxation behavior of polymers except that the time scales are greatly collapsed in the models compared to actual materials. In the models most of the in-... 

The observed results shown in Figures 7 and 8 are in general agreement with the predictions of Buknall and Drinkwater (8). They suggested, based on the influence of stress on the creep behavior of ABS polymers that crazing (cavitation) should be the dominant factor under impact conditions. Their predictions were based on low strain (< 5% ) observations and are clearly substantiated by the data shown in Figures 7 and 8. 

For a crossllnked rubber sample, one simple parameter which can be used to roughly characterize the material is the crosslink density (v) or the average molecular weight between crosslinks (Mg a 1/v). It should be clear that this single parameter cannot completely represent a network in general. Nevertheless, it is well known that the viscoelastic behavior of a polymer network will vary with crosslink density as schematically depicted in Figure 1 for the creep behavior of a polymer at two crosslink densities < Vq. Here the kinetic theory of rubber elasticity... 

PPO -PS levels with other additives provides a myriad of resins that cover a very wide range of physical and thermomechanical properties. Their general characteristics include high heat resistance, excellent electrical properties over a wide range of temperatures and frequencies, low density, high hydrolytic stability, chemical resistance to most acids, dimensional stability, low mold shrinkage, and very low creep behavior at elevated temperatures. 

In the general case, the nonlinear creep behavior could be described by a multiple integral representation using several kernels. The practical application of such equations is limited by the absence of a clearly defined strategy of creep kernel determination as well as relations between the kernel and resolvent. Various simplified versions of this approach have also been proposed. Usually it is assumed that the creep kernel and relaxation time are independent of the stress value. At the same time, it is known that a good approximation to nonlinear creep may be obtained by using the following equation ... 

Trantina (3) analyzed the creep behavior of talc-filled polypropylene composites under constant uniaxial stress loads. He proposed a general expression for the strain ec attributed to creep alone as a superposition of time (f), stress (a), and temperature (T) dependence. The model equation is written as a product of three separate functions for each parameter ... 

For the designer there is generally a less-pronounced curvature when creep and relaxation data are plotted log-log. Predictions can be made on creep behavior based on creep and relaxation data. This usual approach makes it easier to extrapolate, particularly with creep modulus and creep-rupture data. 

Finally, it is worth mentioning another approach used to describe nonlinear viscoelastic solids nonlinear differential viscoelasticity [49, 178, 179]. This theory has been successfully applied to model finite amplitude waves propagation [180-182]. It is the generalization to the three-dimensional nonlinear case of the rheological element composed by a dashpot in series with a spring. Thus in the simplest case, the stress depends upon the current values of strain and strain rate rally. In this sense, it can account for the nonlinear short-term response and the creep behavior, but it fails to reproduce the long-term material response (e.g., relaxation tests). The so-called Mooney-Rivlin viscoelastic material [183] and the incompressible version of the model proposed by Landau and Lifshitz [184] belraig to this class. 

The creep and creep recovery behavior of a four-parameter fluid is shown in Fig. 5.4 and is recognized as the response of a thermoplastic type polymer as given earlier in Fig. 3.13. The three stages of instantaneous elasticity, delayed elasticity and flow represents the most general type behavior possible for a linear viscoelastic material. Note Some texts do not include the flow term as a viscoelastic component, preferring instead... 

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