Subject stress behavior

Elastic Behavior. In the following discussion of the equations relevant to the design of thick-walled hoUow cylinders, it should be assumed that the material of which the cylinder is made is isotropic and that the cylinder is long and initially free from stress. It may be shown (1,2) that if a cylinder of inner radius, and outer radius, is subjected to a uniform internal pressure, the principal stresses in the radial and tangential directions, and <7, at any radius r, such that > r > are given by... 

Evidence suggests that there is a threshold tensile stress at which void nucleation occurs and spall fracture initiates. Materials subject to transient internal tensions can support tensile stresses significantly in excess of this threshold level, however. Such behavior is a consequence of kinetics and inertia associated with the nucleation and growth of voids during spall. A fairly large body of experimental and theoretical literature on spall phenomena exists and many aspects of the effect are reasonably well understood. Review articles on spall (Curran et al., 1977 Davision and Graham, 1979 Curran, 1982 Meyer and Aimone, 1983 Novikov, 1981) provide access to most of the literature on the subject. 

The defect question delineates solid behavior from liquid behavior. In liquid deformation, there is no fundamental need for an unusual deformation mechanism to explain the observed shock deformation. There may be superficial, macroscopic similarities between the shock deformation of solids and fluids, but the fundamental deformation questions differ in the two cases. Fluids may, in fact, be subjected to intense transient viscous shear stresses that can cause mechanically induced defects, but first-order behaviors do not require defects to provide a fundamental basis for interpretation of mechanical response data. 

Not all product components are subjected to a load in fact most are not subjected to loads requiring an engineering analysis via engineering equations, etc. Experience in the material behavior on similar products and/or similar performance requirements are all that is needed. In these products designers become involved in their processing features that will prevent or reduce internal stresses, with elements that will lead to consistent and economical production, with appearance and dimensional control, etc. 

When a viscoelastic material is subjected to a constant stress, it undergoes a time-dependent increase in strain. This behavior is called creep. The viscoelastic creep behavior typical of many TPs is illustrated in Figs. 2-22 and 2-23. At time to the material is suddenly subjected to a constant stress that is main-... 

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... 

When a viscoelastic material is subjected to a constant strain, the stress initially induced within it decays in a time-dependent manner. This behavior is called stress relaxation. The viscoelastic stress relaxation behavior is typical of many TPs. The material specimen is a system to which a strain-versus-time profile is applied as input and from which a stress-versus-time profile is obtained as an output. Initially the material is subjected to a constant strain that is maintained for a long period of time. An immediate initial stress gradually approaches zero as time passes. The material responds with an immediate initial stress that decreases with time. When the applied strain is removed, the material responds with an immediate decrease in stress that may result in a change from tensile to compressive stress. The residual stress then gradually approaches zero. 

Creep rupture. Creep-rupture data are obtained in the same way as creep data except that higher stresses are used and the time is measured to failure (Figs. 2-28 and 29). The strains are sometimes recorded, but this is not necessary for creep rupture. The results are generally plotted as the log stress versus log time to failure (110). In creep-rupture tests it is the material s behavior just prior to the rupture that is of primary interest. In these tests a number of samples are subjected to different levels of constant stress, with the time to failure being determined for each stress level. General technical literature and product data sheets seldom provide a complete description of a material s behavior prior to rupture. It should include the development of any crazing and stress whitening, its strain-time... 

Intermittent loading. The creep behavior of plastics that has been considered so far has assumed that the level of the applied stress will be constant. However, in service the material may be subjected to a complex pattern of loading and unloading cycles (Fig. 2-33). This variability can cause design... 

Creep behavior Creep is the deformation that occurs over a long period of time in a material subjected to a continuous load, and stress relaxation is the reduction in stress with time that occurs in a material when it is de-... 

Linear viscoelasticity Linear viscoelastic theory and its application to static stress analysis is now developed. According to this theory, material is linearly viscoelastic if, when it is stressed below some limiting stress (about half the short-time yield stress), small strains are at any time almost linearly proportional to the imposed stresses. Portions of the creep data typify such behavior and furnish the basis for fairly accurate predictions concerning the deformation of plastics when subjected to loads over long periods of time. It should be noted that linear behavior, as defined, does not always persist throughout the time span over which the data are acquired i.e., the theory is not valid in nonlinear regions and other prediction methods must be used in such cases. 

This information is supported by stress-strain behavior data collected in actual materials evaluations. With computers the finite element method (FEA) has greatly enhanced the capability of the structural analyst to calculate displacement, strain, and stress values in complicated plastic structures subjected to arbitrary loading conditions (Chapter 2). FEA techniques have made analyses much more precise, resulting in better and more optimum designs. 

This review concerns the long-term behavior of plastics when exposed to conditions that include continuous stresses, environment, excessive heat, abrasion, and continuous contact with liquids. This subject has been reviewed in Chapter 2 (LONG-TERM LOAD BEHAVIOR) but since it is a very important subject the review is continuing. Tests such as those outlined by ASTM D 2990 that describe in detail the specimen preparations and testing procedure are intended to produce consistency in observations and records by various manufacturers, so that they can be correlated to provide meaningful information to product designers. 

Hydraulic fracturing fluids are solutions of high-molecular-weight polymers whose rheological behavior is non-Newtonian. To describe the flow behavior of these fluids, it is customary to characterize the fluid by the Power Law parameters of Consistency Index (K) and Behavior Index (n). These parameters are obtained experimentally by subjecting the fluid to a series of different shear rates (y) and measuring the resultant shear stresses (t). The slope and Intercept of a log shear rate vs log shear stress plot yield the Behavior Index (n) and Consistency Index (Kv), respectively. Consistency Indices are corrected for the coaxial cylinder viscometers by ... 

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