Plastic equivalent

In metals, for example, the states before and after the plastic deformation can usually be distinguished macroscopicaUy, for the stress needed for further plastic deformation (called the yield strength, see section 3.2) usually increases. To describe the deformation history, a plastic equivalent strain is defined, which always increases during plastic deformation. This equivalent strain is non-zero after the deformation. It wiU be discussed in section 3.3.5. 

Keratin can be seen as a biological answer to the need for a tough plastic equivalent to nylon. As hair and fur, it is a fiber. As epidermis, it is a film, and as hoof or hom, it is tough solid. The stmcture contains fibrils, which are built from three-stranded ropes of alpha-helical chains in a coiled-coil arrangement. The fibrils are embedded in a cross-linked matrix of amorphous protein that is heavily... 

Here ij denotes a velocity of a plastic part of the curvature. This model is quasi-static, and it reduces to the equivalent inequality... 

Adipic acid is a very large volume organic chemical. Worldwide production in 1986 reached 1.6 x 10 t (3.5 x 10 lb) (158) and in 1989 was estimated at more than 1.9 x 10 t (Table 7). It is one of the top fifty (159) chemicals produced in the United States in terms of volume, with 1989 production estimated at 745,000 t (160). Growth rate in demand in the United States for the period 1988—1993 is estimated at 2.5% per year based on 1987—1989 (160). Table 7 provides individual capacities for U.S. manufacturers. Western European capacity is essentially equivalent to that in the United States at 800,000 t/yr. Demand is highly cycHc (161), reflecting the automotive and housing markets especially. Prices usually foUow the variabiUty in cmde oil prices. Adipic acid for nylon takes about 60% of U.S. cyclohexane production the remainder goes to caprolactam for nylon-6, export, and miscellaneous uses (162). In 1989 about 88% of U.S. adipic acid production was used in nylon-6,6 (77% fiber and 11% resin), 3% in polyurethanes, 2.5% in plasticizers, 2.7% miscellaneous, and 4.5% exported (160). 

The distance from the crack tip, along the X-axis, at which the von Mises equivalent stress falls below the yield stress, defines the size of the plastic zone, r. For the plane stress case of unconstrained yielding, which corresponds to the free surface of the specimen in Figure 4, this gives... 

In tougher materials the minimum thickness required by equation 15 can become excessive. In such cases the /-integral test is an attractive alternative. Because this test considers the stress distribution around the crack inside the plastic 2one, it can be used to obtain a vahd toughness measurement in a thinner specimen, because more extensive plastic yielding does not invaUdate the analysis. The equivalent of equation 15 for the /-integral test is... 

In addition to time-related effects, the soUd-state physical properties are also affected by adsorbed water, which functions as a plasticizer. Water pickup is affected by the nature of the cation, with sodium ionomers absorbing about 10 times the level of the zinc equivalent (6) under the same conditions. Drying must be carried out at temperatures below 100°C and is therefore a slow process. In commercial practice, ionomers are suppUed dry, and techniques have been developed to minimize moisture absorption during processing. 

The and C q iso-phthalates (DINP and DIDP) generally compete with DEHP as commodity general-purpose plasticizers. Other iso-phthalates are available at opposite ends of the carbon number range (eg, diisoheptyl phthalate (DIHP), C, and diisotridecyl phthalate (DTDP), but these serve more speciaUty markets. The Cg iso-phthalate, diisooctyl phthalate (DIOP), has also had traditional sales ia the commodity plasticizer markets where it is seen as an equivalent to DEHP. 

Fig. 1. Relative efficiency of plasticizers where H represents Cg phthalate +, C q phthalate A, phthalate and , phthalate phr = parts per hundred mbber. Values for the trimeUitates fall in the shaded area. BSS 35 is equivalent to a Shore A hardness of 80, test method BS2782.

Polyester plasticizers give the best performance in this area, with performance increasing with molecular weight. Additionally, branched esters have somewhat higher volatUities than their linear equivalents. 

Plasticizers for acryhcs include all common phthalates and adipates. There has been interest in the development of acryUc plastisols similar to those encountered with PVC. Clearly the same aspects of both plastisol viscosity and viscosity stabiUty are important. Patents appear in the Hterature (32) indicating that the number of available plasticizers that show both good compatibiHty with acryHc resins and satisfactory long-term plastisol stabiHty may be fewer than those showing equivalent properties with emulsion PVC resins. 

Patents have appeared (33,34) which show formulations containing PMMA emulsion polymer and PMMA suspension polymer combined with benzyl butyl phthalate and octyl benzyl phthalate. It is likely that polymers of this type will require highly polar plasticizers in order to have both adequate compatibiHty and adequate gelation. When replacing PVC appHcations the use of large quantities of phosphate plasticizers is sometimes required to give equivalent fire performance. 

The aluminum containing compound having the largest worldwide market, estimated to be over 30 x 10 t in 1990, is metal grade alumina. Second, is aluminum hydroxide. In 1990 the market for Al(OH)2 should approach or exceed 3.5 million metric tons which is equivalent to 2.3 million tons on an alumina basis. The spHt between additive and feedstock appHcations for Al(OH)2 (16) is roughly 50 50. Additive appHcations include those as flame retardants (qv) in products such as carpets, and to enhance the properties of paper (qv), plastic, polymer, and mbber products. Significant quantities are also used in pharmaceuticals (qv), cosmetics (qv), adhesives (qv), poHshes (qv), dentifrices (qv), and glass (qv). 

A 2.54-cm Styrofoam plastic foam with thermal conductivity of ca 0.03 W/ (m-K) (0.21 (Btu-in.)/(ft-b°F)) is equivalent to 61 cm of gravel. Any synthetic foam having compressive strength sufficiently high and thermal conductivity sufficiently low is effective. However, the resistance of PS-type foams to water, frost damage, and microorganisms in the sod makes them especially desirable. An interesting and important appHcation of this concept was the use of Styrofoam in the constmction of the Alaska pipeline. In this case, the foam was used to protect the permafrost. 

Data are reported as cellulose acetate flake equivalents plasticizers not included. 

Cellulose acetate ester plastics are produced largely in the United States, Western Europe, and Japan. World consumption is assumed to be approximately equivalent to production of cellulose ester plastics in these three regions. Courtesy of CEH Estimates. 

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