Theory of Plasticization

This discussion refers to external plasticization only. Several theories, varyiag ia detail and complexity, have been proposed ia order to explain plasticizer action. Some theories iavolve detailed analysis of polarity, solubiHty, and iateraction parameters and the thermodynamics of polymer behavior, whereas others treat plasticization as a simple lubrication of chains of polymer from each other, analogous to the lubrication of metal parts by oil. Although each theory is not exhaustive, an understanding of the plasticization process can be gained by combining ideas from each theory, and an overall theory of plasticization must include all these aspects. 

PS Foams. The eady history of foamed PS is available (244), as are discussions of the theory of plastic foams (245). Foamable PS beads were developed in the 1950s by BASF under the trademark of STYROPOR (246—248). These beads, made by suspension polymerization in the presence of blowing agents such as pentane or hexane, or by post-pressurization with the same blowing agents, have had an almost explosive growth, with 200,000 metric tons used in 1980. Some typical physical properties of PS foams are Hsted in Table 10 (see Foamed plastics). 

In this section, the general inelastic theory of Section 5.2 will be specialized to a simple phenomenological theory of plasticity. The inelastic strain rate tensor e may be identified with the plastic strain rate tensor e . In order to include isotropic and kinematic hardening, the set of internal state variables, denoted collectively by k in the previous theory, is reduced to the set (k, a) where k is a scalar representing isotropic hardening and a is a symmetric second-order tensor representing kinematic hardening. The elastic limit condition in stress space (5.25), now called a yield condition, becomes... 

In the classical theory of plasticity, constitutive equations for the evolution of the isotropic and kinematic hardening parameters are usually expressed as... 

The plasticity equations presented so far are still more general than the equations usually considered in the classical theory of plasticity. Linearity and symmetry assumptions, inherent in most classical treatments, are yet to be made. Particularly simple assumptions are made here to serve as an example. 

R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, 1950. 

Khan, A.S. and Huang, S. (1995) Continuum Theory of Plasticity (Wiley, New York). 

The simplified failure envelopes differ little from the concept of yield surfaces in the theory of plasticity. Both the failure envelopes (or surfaces) and the yield surfaces (or envelopes) represent the end of linear elastic behavior under a multiaxial stress state. The limits of linear elastic... 

The question whether hardness is a property related to modulus (E) or yield stress (Y) is a problem which has been commented before by Bowman and Bevis 13). These authors found an experimental relationship between microhardness and modu-lus/yield-stress for injection-moulded semicrystalline plastics. According to the clasical theory of plasticity the expected indentation hardness value for a Vickers indenter is approximaterly equal to three times the yield stress (Tabor s relation). This assump-... 

PLASTIC DEFORMATION. When a metal or other solid is plastically deformed it suffers a permanent change of shape. The theory of plastic deformation in crystalline solids such as metals is complicated but well advanced. Metals are unique among solids in their ability to undergo severe plastic deformation. The observed yield stresses of single crystals are often 10 4 times smaller than the theoretical strengths of perfect crystals. The fact that actual metal crystals are so easily deformed has been attributed to the presence of lattice defects inside the crystals. The most important type of defect is the dislocation. See also Creep (Metals) Crystal and Hot Working. 

Herrman V (1976) Determining equations of compacting porous materials. In Shapiro GS (ed) Problems of the Theory of Plasticity. Mir, Moscow, p 178... 

De Runtz165) has made an interesting and promising attempt of estimating the strength parameters of syntactic foams. He applied the concepts and mathematical apparatus of the mechanics of discontinuous media and the theory of plasticity. 

Hill R, "The Mathematical Theory of Plasticity", Clarendon Press, Oxford, 1950. 

Hill, R. (1950) Mathematical Theory of Plasticity, Oxford University Press Holloway, D. G. (1973) The Physical Properties of Glass, Wykeham, London Howe, J. M. (1993) Int. Mater. Rev., 38, 233 and 257... 

The demonstration of the validity of the continuum-based modelling approach to tablet compaction requires familiarity with fundamental concepts of applied mechanics. Under the theory of such a mechanism, powder compaction can be viewed as a forming event during which large irrecoverable deformation takes place as the state of the material changes from loose packing to near full density. Moreover, it is important to define the three components of the elastoplastic constitutive models which arose from the growing theory of plasticity, that is the deformation of materials such as powder within a die ... 

Hoffman, O., and Sachs, G. Introduction to the Theory of Plasticity" (McGraw-Hill, New York and London 1953)... 

Hill R (1950) The mathematical theory of plasticity, Oxford University Press, London... 

Today, the theory of plastic foams is concerned with the solution of a problem which the author termed as a direct or physical problem. For any material including foamed materials, the direct problem is formulated as follows in which way are the properties... 

Departing from the maximum shear stress theory of plastic flow R. H. Lance and D. N. Robinson [6] developed yield conditions for fiber reinforced eomposite materials. The authors of [6] assumed that the material could flow plastically if (i) the shear stress on planes parallel to fibers, and in a direction perpendicular to them, reaches a critical value or... 

Gotoh, M., (1977), A theory of plastic anisotropy based on a yield function of fourth order. Int. J. Mech. Sci., 19,505. 

Lance, R.H. and Robinson, D.N., (1972), A maximum shear stress theory of plastic failure of fiber-reinforced materials. J. Mech. Phys. Solids, 19,49. 

The Mathematical Theory of Plasticity by R. Hill, Clarendon Press, Oxford England, 1967. The definitive work on the mathematical theory of plasticity. This book goes well beyond our treatment regarding continuum descriptions of plasticity without entering into the question of how plasticity emerges as the result of defect motion. 

Continuum Theory of Plasticity by A. S. Khan and S. Huang, John Wiley and Sons, New York New York, 1995. The subject of plasticity is lacking in texts that are directed at interpreting plastic deformation on the basis of the underlying mechanisms. This book provides an overview of much of the machinery that is invoked in current considerations of plasticity. 

While elastic buckling of structural walls is fully recoverable, plastic collapse of the plastic hinge sections is not. The theory of plastic collapse corresponds well for materials with a relative density of 0.3 or less materials with greater relative densities do not follow theoretical predictions because their cell partitions are too thick to buckle or hinge readily. The data represented in Figure 6.18, showing SEM from 6.17a, estimates a relative density of 0.345. 

The recent AFM experimental data concerning plastic flow place severe restrictions on possible theoretical accounts of plastic deformation in crystalline solids due to shock or impact. The high spatial resolution of the AFM, = 2 x lO " m, reveals substantial plastic deformation in shocked or impacted crystal lattices and molecules. Understanding how this occurs and its effect on plastic flow requires a quantum mechanical description. The semi-permanent lattice deformation has necessitated the development of a deformed lattice potential which, when combined with a quantum mechanical theory of plastic deformation, makes it possible to describe many of the features found in the AFM records. Both theory and the AFM observations indicate that shock and impact are similar shear driven processes that occur at different shear stress levels and time durations. The role of pressure is to provide an applied shear stress sufficient to cause initiation. 

Hart and coworkers developed a phenomenological theory of plastic deformation by using the concept of equation of state [6, 7]. The proposed deformation model consists essentially of two parallel branches (Fig. 6.10). Branch 1 represents... 

Historical Perspective General Theory of Plasticization Plasticizer Compatibility Compatibility Stability Fusion Properties of Plasticizers Plasticizer Concentration Effects Heat Stability Odor Development... 

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