Plastic resistive force

Neglecting the elastic forces, lumping the geometric factors into a constant, b, and assuming the plastic shear deformation is x/r, yields the plastic resistive force ... 

This P -I type of response curve can also be easily shown to apply to a simple rigid-plastic mechanical system, in the manner shown in Figure 16 (see Refs. 15 and 22). Here, the spring in the system is replaced with a pure Coulomb friction element, with resisting force f, which is independent of displacement once the mass starts to move. All other symbols are defined above. 

In determining the temperature dependence of the plastic resistances in uniaxial deformation the temperature dependence of the shear modulus fj. = C55 is needed. Karasawa et al. (1991) provide such information derived from theoretical force-field methods. Their calculated results for C55 appear as the upper curve in Fig. 9.20. However, for a variety of reasons discussed by Argon et al. (2005), including the defected nature of the usual HDPE, the C55 modulus needs to be attenuated by a factor of 0.635. This attenuated modulus is also shown in Fig. 9.20, as the lower curve. 

A necessary connection between the traditional impact experiments and more definitive and quantitative methods of fracture mechanics was made by Plati and Williams (1975a, 1975b) for cases of moderate plastic response of small-scale yielding (SSY) and accounted for yielding, whereby the measured impact-fracture work could be related to the size of the fracture area by consideration of the character of the deformation geometry of the bent bar and the crack-tip field. For a standard Izod or Charpy geometry as shown, e.g., for the Izod experiment depicted in Fig. 12.23, Plati and Williams considered the connection for two forms of approach that were based on measurement of the peak resistive force. Pc, or on measurement of the work of fracture W. 

There may be other ways to evaluate plastic resistance of coatings based on the data of micro-scratch experiment. Nevertheless, mar resistance can be evaluated or ranked mechanistically and objectively with the area under the plastic deformation curve and the critical normal force before fracture. 

The separation of two surfaces in contact is resisted by adhesive forces. As the nonnal force is decreased, the contact regions pass from conditions of compressive to tensile stress. As revealed by JKR theory, surface tension alone is sufficient to ensure that there is a finite contact area between the two at zero nonnal force. One contribution to adhesion is the work that must be done to increase surface area during separation. If the surfaces have undergone plastic defonnation, the contact area will be even greater at zero nonnal force than predicted by JKR theory. In reality, continued plastic defonnation can occur during separation and also contributes to adhesive work. 

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). 

The resistance to plastic flow can be schematically illustrated by dashpots with characteristic viscosities. The resistance to deformations within the elastic regions can be characterized by elastic springs and spring force constants. In real fibers, in contrast to ideal fibers, the mechanical behavior is best characterized by simultaneous elastic and plastic deformations. Materials that undergo simultaneous elastic and plastic effects are said to be viscoelastic. Several models describing viscoelasticity in terms of springs and dashpots in various series and parallel combinations have been proposed. The concepts of elasticity, plasticity, and viscoelasticity have been the subjects of several excellent reviews (21,22). 

Physical Factors. Unsatuiated elastomers must be stretched for ozone cracking to occur. Elongations of 3—5% are generally sufficient. Crack growth studies (10—18) have shown that some minimum force, called the critical stress, rather than a minimum elongation is required for cracking to occur. Critical stress values are neady the same for most unsaturated mbbers. However, polychloroprene has a higher critical stress value than other diene mbbers, consistent with its better ozone resistance. It has been found that temperature, plasticization, and ozone concentration have httie effect on critical stress values. 

If you flick a small plastic ball on a table top with your finger, thereby exerting a small force on the ball, you will see it move rapidly from its resting position. But if you do the same with a steel ball of the same size, the same dick of the dnger (the same force) will produce noticeably less motion. The steel ball has gi eater mass and therefore greater resistance to being accelerated. The ratio of the accelerations of two objects experiencing the same force is equal to the ratio of their masses. 

Methods employed to determine the impact resistance of plastics include pendulum methods (Izod, Charpy, tensile impact, falling dart, Gardner, Dynatup, etc.) and instrumented techniques. In the case of the Izod test, what is measured is the energy required to break a test specimen transversely struck (the test can be done either with the specimen notched or unnotched). The tensile impact test has a bar loaded in tension and the striking force tends to elongate the bar (Chapter 5, Impact Strength). 

A different type of low friction or low drag application is encountered with sliding doors or conveyor belts sliding on support surfaces. In applications like this the normal forces are generally quite small and the friction load problems are of the sticking variety. Some plastics exhibit excellent track surfaces for this type of application. TFEs have the lowest coefficient of any solid material and represent one of the most slippery surfaces known. The major problem with TFE is that its abrasion resistance is low so that most of the applications utilize filled compositions with ceramic filler materials to improve the abrasion resistance. 

Production molds are usually made from steel for pressure molding that requires heating or cooling channels, strength to resist the forming forces, and/or wear resistance to withstand the wear due to plastic melts, particularly that which has glass and other abrasive fillers. However most blow molds are cast or machined from aluminum, beryllium copper, zinc, or Kirksite due to their fast heat transfer characteristics. But where they require extra performances steel is used. 

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