Deformation static

Controlled Deformation Static or Dynamic MIxers/Reactors... 

These equations cannot be used indiscriminately. Each case must be considered on its merits, with account being taken of the plastic behavior in time imder load, mode of deformation, static and/or dynamic loads, service temperature, fabrication method, environment, and others. The traditional engineering equations are derived using the relationship that stress equals modulus time s strain, where the modulus... 

A number of friction studies have been carried out on organic polymers in recent years. Coefficients of friction are for the most part in the normal range, with values about as expected from Eq. XII-5. The detailed results show some serious complications, however. First, n is very dependent on load, as illustrated in Fig. XlI-5, for a copolymer of hexafluoroethylene and hexafluoropropylene [31], and evidently the area of contact is determined more by elastic than by plastic deformation. The difference between static and kinetic coefficients of friction was attributed to transfer of an oriented film of polymer to the steel rider during sliding and to low adhesion between this film and the polymer surface. Tetrafluoroethylene (Telfon) has a low coefficient of friction, around 0.1, and in a detailed study, this lower coefficient and other differences were attributed to the rather smooth molecular profile of the Teflon molecule [32]. 

Here ij denotes a plastic deformation velocity. Adding the relations (1.10), (1.11), we obtain the quasi-static elastoplastic model... 

Knoop developed an accepted method of measuring abrasive hardness using a diamond indenter of pyramidal shape and forcing it into the material to be evaluated with a fixed, often 100-g, load. The depth of penetration is then determined from the length and width of the indentation produced. Unlike WoodeU s method, Knoop values are static and primarily measure resistance to plastic flow and surface deformation. Variables such as load, temperature, and environment, which affect determination of hardness by the Knoop procedure, have been examined in detail (9). 

Creep. The creep characteristic of plastic foams must be considered when they are used in stmctural appHcations. Creep is the change in dimensions of a material when it is maintained under a constant stress. Data on the deformation of polystyrene foam under various static loads have been compiled (158). There are two types of creep in this material short-term and long-term. Short-term creep exists in foams at all stress levels however, a threshold stress level exists below which there is no detectable long-term creep. The minimum load required to cause long-term creep in molded polystyrene foam varies with density ranging from 50 kPa (7.3 psi) for foam density 16 kg/m (1 lb /ft ) to 455 kPa (66 psi) at foam density 160 kg/m (10... 

Another measure of refractoriaess is the hot-compressive strength or hot-load test for refractory bricks or formed specialties. The specimen carries a static load from 69 kPa (10 psi) to 172 kPa (25 psi). It is heated at a specific rate to a specific temperature which is then held for 1.5 h, or it is heated at a specific rate until it fads. The percent deformation or the temperature of fadure is measured. The procedure is described ia ASTM C16. 

Some tests, while undergoing deformation, are usually referred to as static in that they are performed at slow speeds or low cycles. Examples of these tests are stretch modulus, ultimate tensile, and elongation to break, ie, a measure of total energy capabiUties or mpture phenomena. 

Shock loading in most metals and alloys produces greater hardening than quasi-static deformation to the same total strain, particularly if the metal undergoes a polymorphic phase transition, such as is observed in pure iron [1]-[10]. Figure 6.1 compares the stress-strain response of an annealed... 

Figure 6.1. Stress-strain behavior of shock-loaded copper compared to the annealed starting condition illustrating an enhanced flow stress following shock-wave deformation compared to quasi-static deformation (based on an equivalent strain basis).

In this study, the appearance and evolution sequence of planar slip bands, in addition to a dislocation cell structure with increasing e,, is identical to that observed in quasi-static studies of the effects of stress path changes on dislocation substructure development [27]. The substructure evolution in copper deformed quasi-statically is known to be influenced by changes in stress path [27]. Deforming a sample in tension at 90° orthogonal to the... 

P.S. Follansbee and G.T. Gray III, The Response of Single Crystal and Polycrystal Nickel to Quasi-Static and Shock Deformation, in Advances in Plasticity 1989 (edited by A.S. Khan and M. Tokuda), Pergamon Press, Oxford, 1989, pp. 385-388. 

When the pressures to induce shock-induced transformations are compared to those of static high pressure, the values are sufficiently close to indicate that they are the same events. In spite of this first-order agreement, differences between the values observed between static and shock compression are usually significant and reveal effects controlled by the physical and chemical nature of the imposed deformation. Improved time resolution of wave profile measurements has not led to more accurate shock values rather. 

Saint-Venant stated that two different loadings that are statically equivalent produce the same stresses and deformations at a distance sufficiently far removed from the area of application of the loadings. Thus, if two statically equivalent loadings are applied and the observation point is near the end where the loading is applied, then the stresses and deformations will be different for each loading. Hence the name Saint-Venant end effects. 

Irrespective of the analysis approach, the representative volume element must be carefully defined and used. In fact, the representative volume element is crucial to the analysis and is the micromechanics analog of the free-body diagram in statics and dynamics. The representative volume element is of higher order than the free-body diagram because deformations and stresses are addressed in addition to forces. 

As a plastic is subjected to a fixed stress or strain, the deformation versus time curve will show an initial rapid deformation followed by a continuous action. Examples of the standard type tests are included in Fig. 2-1. Details on using these type specimens under static and dynamic loads will be reviewed throughout this chapter. (Review also Fig. 8-9 that relates elasticity to strain under different conditions.)... 

Dynamic loading in the present context is taken to include deformation rates above those achieved on the standard laboratorytesting machine (commonly designated as static or quasi-static). These slower tests may encounter minimal time-dependent effects, such as creep and stress-relaxation, and therefore are in a sense dynamic. Thus the terms static and dynamic can be overlapping. 

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. 

FEA is applicable in several types of analyses. The most common one is static analysis to solve for deflections, strains, and stresses in a structure that is under a constant set of applied loads. In FEA material is generally assumed to be linear elastic, but nonlinear behavior such as plastic deformation, creep, and large deflections also are capable of being analyzed. The designer must be aware that as the degree of anisotropy increases the number of constants or moduli required to describe the material increases. 

The static properties of an isolated chain constitute a good starting point to study polymer dynamics many of the features of the chain in a quiescent fluid could be extrapolated to the kinetics theories of molecular coil deformation. As a matter of fact, it has been pointed out that the equations of chain statistics and chain dynamics are intimately related through the simplest notions of graph theory [16]. 

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