Deformation Behavior of Plastics

As described above, the deformation of plastics compared to metal is viscoelastic and viscous. The temperature-time dependence of the properties of plastics (and 

Viscoelastic deformation results from the parallel overlapping of spring and damper deformation Elongation is delayed, but completely reversible upon relaxation. This is called entropy or rubber elasticity. 

Spontaneous elastic deformations result from the successive overlapping of spring and damper deformation in response to load application and relaxation, there is residual deformation due to the damper. 

Voigt-Kelvin series arrangement with Maxwell model, see Fig. 19. 

The Burger model provides a correct graphic description of the elongation-time behavior of most plastics in a first approximation. The spring 1 results in spontaneous elastic load application and relaxation elongation, 1 + 2 in parallel cause creep during load application and creep recovery (delayed viscoelastic reverse deformation) after relaxation, damper 2 results in residual elongatimi. 

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Also, the AUC (area under curve) of the different materials represents their resilience. Cast iron and ceramics are very brittle steel, copper, and aluminum, as well as the thermoplastics PA and PP, are highly deformable and can therefore absorb large amounts of energy, for example from (impact) load application. It must be remembered here that the deformation behavior of plastics is highly dependent on time and temperature factors (see Fig. 15). Simplified explanations of deformation terminology follow. 

The deformation behavior of plastic melts, and therefore of plastics and materials in general can be described in simplified, clear terms by using spring and dampening elements. 

Long-term deformation behavior of plastics materials, Institut for Leichtbau and okonomische Verwendung von Werkstoffen, Dresden, Schriftenreihe Materialokonomie , Heft 32 14 No data available, tests required l l See literature list in the guideline... 

As an example, for room-temperature applications most metals can be considered to be truly elastic. When stresses beyond the yield point are permitted in the design, permanent deformation is considered to be a function only of applied load and can be determined directly from the stress-strain diagram. The behavior of most plastics is much more dependent on the time of application of the load, the past history of loading, the current and past temperature cycles, and the environmental conditions. Ignorance of these conditions has resulted in the appearance on the market of plastic products that were improperly designed. Fortunately, product performance has been greatly improved as the amount of technical information on the mechanical properties of plastics has increased in the past half century. More importantly, designers have become more familiar with the behavior of plastics rather than... 

For those not familiar with this type information recognize that the viscoelastic behavior of plastics shows that their deformations are dependent on such factors as the time under load and temperature conditions. Therefore, when structural (load bearing) plastic products are to be designed, it must be remembered that the standard equations that have been historically available for designing steel springs, beams, plates, cylinders, etc. have all been derived under the assumptions that (1) the strains are small, (2) the modulus is constant, (3) the strains are independent of the loading rate or history and are immediately reversible, (4) the material is isotropic, and (5) the material behaves in the same way in tension and compression. 

When the magnitude of deformation is not too great, viscoelastic behavior of plastics is often observed to be linear, i.e., the elastic part of the response is Hookean and the viscous part is Newtonian. Hookean response relates to the modulus of elasticity where the ratio of normal stress to corresponding strain occurs below the proportional limit of the material where it follows Hooke s law. Newtonian response is where the stress-strain curve is a straight line. 

Bicakci, E., Zhou, X. and Cakmak, M., Phase and uniaxial deformation behavior of ternary blends of poly(ethylene naphthalate), poly(ether imide) and poly(ether ether ketone), in Proceedings of the 55th SPE ANTEC 97 Conference, May 5-8, 1997, Toronto, ON, Canada, Society of Plastics Engineers, Brookfield, CT, 1997, Vol. 2, pp. 1593-1599. 

It is always very useful to be able to predict at what level of external stress and in which directions the macroscopic yielding will occur under different loading geometry. Mathematically, the aim is to find functions of all stress components which reach their critical values equal to some material properties for all different test geometries. This is mathematically equivalent to derivation of some plastic instability conditions commonly termed as the yield criterion. Historically, the yield criteria derived for metals were appHed to polymers and, later, these criteria have been modified as the knowledge of the differences in deformation behavior of polymers compared to metals has been acquired [20,25,114,115]. 

Another possibility of analysis is to fit different functions to the force-time data. The research group of Mielck [39, 96-98] described the densification behavior by the pressure-time function (Figure 16). The lower the values of the parameters (5 and y, the more plastically the material deforms the higher the values, the more elastically the material deforms. The parameter y describes the asymmetry of the curve and p the time at maximum densification. A similar function, the Fraser-Suzuki function, which originates from chemical analytics was applied to tableting data [99]. It can also be used to derive parameters that describe the deformation behavior of materials. Information on the reversible and irreversible deformation of the material can be deduced. 

Fig. 24 Differences in the deformation behavior of substances during tableting demonstrated by sorbitol instant as an example for a plastically deforming substance and ascorbic acid as a more brittle one. Tablet compressed at 5 kN (10 mm in diameter) (A) and 30 kN (B). Inner part of a broken tablet showing an ascorbic acid crystal being totally embedded into plastically deformed sorbitol (C) and a crystal being partially removed from the sorbitol matrix through the break down of the tablet (D). A cracked ascorbic acid crystal in a sorbitol matrix (E).

The main utility of Heckel plots arises from their ability to identify the predominant deformation behavior of the material. The relationship is mostly used to distinguish between substances that consolidate by fragmentation and those that consolidate by plastic deformation. 

Considering the several limitations of the Heckel equation (lack of correlation between the mean yield pressure and the plasticity of a material, clear identification of the linear region of a Heckel plot etc.), recently, a new relationship using the Gurnham equation was propo.sed to characterize the deformation behavior of pharmaceutical material by Zhao et al. (94). This relationship was introduced in chemical engineering by Gurnham and Mas.son (95). They proposed that the rate of applied pressure is directly proportional to the apparent density of a given mass of material (94). Thus,... 

David and Augsburger (63) studied the decay of compressional forces for a variety of excipients, compressed with flat-faced punches on a Stokes rotary press. They found that initial compressive force could be subject to a fairly rapid decay and that this rate was dependent on the deformation behavior of the excipient for the materials studied, they found that maximum loss in compression force was for compressible starch and MCC, which was followed by compressible sugar and DCP. This was attributed to differences in the extent of plastic flow. The decay curves were analyzed using the Maxwell model of viscoelastic behavior. Maxwell model implies first order decay of compression force. 

There are three main rheological properties of materials viscous flow, plastic flow, and elastic deformation. The stress deformation behavior of elastic materials is represented by a straight line through the origin. However, in this case, the... 

Fig. 3 Typical deformation behavior of thermal plastic polymers as a function of temperature. (View this art in color at www.dekker.com.)...

The deformation behavior of toughened PA is compared for larger and smaller particles in reference 26. In large particles with an average diameter, D, of about 1 xm and an average minimum interparticle distance, A, of about 0.5 xm, an intense plastic deformation appears in only a few bands. In the case... 

In this section calculations will be under taken to illustrate the ability of the above theory to account for the experimental observations. The first of these to be addressed is the surprising plastic deformation behavior of RDX. 

Rheology is the science that deals with the deformation and flow of matter under various conditions an example is plastic melt flow. The rheology of plastics, particularly TPs, is complex but manageable. These materials combine the properties of an ideal viscous liquid (pure shear deformations) with those of an ideal elastic solid (pure elastic deformation). Plastics are therefore said to be viscoelastic (Figure 17). The mechanical behavior of plastics is dominated by the viscoelastic phenomena such as tensile... 

The long-term behavior of plastics must, in other words, be investigated using static methods. The best-known method is the time-to-mpture or creep test, whereby a workpiece is subjected to stress CTq at time t = 0 and the stress parameter is maintained at a constant level for the entire duration of the test Time-dependent deformation is then measured. Fig. 26. If the elongation is constant, the stress parameter drops off in time with plastics. This is known as relaxation. This knowledge has applications related, for instance, to screw cmmections (plastic... 

Arruda, E. M., Boyce, M. C., and Quintus-Bosz, H. (1993) Effects of initial anisotropy on the finite strain deformation behavior of glassy polymers, Int. J. Plasticity, 9, 783-811. 

Based on the facts presented above, the plastic deformation behavior of semicrystalline polymer materials and the structural changes accompanying the defor-matimi of such materials are craitroUed by the properties of both crystalline and amorphous phases. 

Concerning the MMST the fundamental relation are established v ia analysis of elastic-plastic bulge deformation behavior of a middle thick circular plate loaded at the center for which the circumference is fixed and points at the boundary can move in radial direction. The formulas f or calculating material strengthes and ductility could be derived from the relation. 

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