Mechanism deformation

The area has been divided up into elastic deformation and plastic deformation (shear yielding and crazing). They have been considered as essentially time-independent processes. It is clear from Section 5.2 that there will always be an underlying time dependence, but since the discussion is limited to polymers which are generally well away from the viscoelastic region the approximation of time-independent behaviour does not cause too many problems. 

It is useful to consider the deformation of single- and multi-phase polymers separately. Unfilled elastomers, polymer glasses and polymer single crystals 

TABLE 5.1 Typical values of Young s modulus for different types of polymers. 

It is possible to obtain expressions for SI and SO in terms of the applied force /. Consideration of the bond stretching allows SI to be determined. The component of the force acting along the bond direction is/cos a. This can be related to the extension through the force constant for bond stretching ki which can be determined from infra-red or Raman spectroscopy. ki is the constant of proportionality relating the force along the bond to its extension. It follows therefore that 

But since it can be shown by a simple geometrical construction that a = 90° - Of 2 then it follows that 

The characteristic mechanical property of the amorphous polymers is high strength and a brittle up to ductile deformation behavior. The reason for this behavior is the formation of localized deformation zones under load, such as crazes, deformation bands, or shear bands [12]. The typical type of deformation seen in the amorphous brittle, glassy polymers is the craze. Crazes are often visible with the naked eye in reflected light see Fig. 1.4. The word craze recalls a macroscopic crack-like appearance craze comes from an old English word. 

Synonyms include craquele (from the pattern of fine cracks in the glaze of porcelain (china) or pottery), microcracks, and silvercracks (from the Russian name treschina cerebra ) or xpemnna cepebpo [5,13].  

The fibrillated crazes grow through the continuous stretching of new material at the craze boundaries surface drawing or pull-out mechanism). The situation at a craze/bulk interface is illustrated in Fig. 1.7. Stretching of the fibrils occurs up to an elongation that depends on the parameters f and d of the entanglement network. The transition zone (active zone g) forms the craze interphase with a characteristic thickness g. 

A fine entanglement network with small meshes deforms in a dense pattern of small stretched meshes in a homogeneous manner (Fig. 1.10(b)) [13]. There are several criteria for craze initiation and growth, reviewed in [5, 13,17]. 

Alternative deformation zones are shear bands due to stretching and yielding of macromolecules (usually under an angle of 45° to the loading direction) with a pattern of crossed shear bands. Differences in the molecular deformation mechanisms are sketched in Fig. 1.11. Crazing is accompanied by a volume increase, and shear formation shows no change of volume, that is, no creation of internal surfaces. 

The proportionality constant (E) is the elastic or Youngs modulus [20]. It is a measure of the stiffness or resistance against deformation. The material behaves elastically up to the yield point (P at which the stress is called yield stress (o ). Beyond this point the material behaves as a plastic, rather than as an elastic solid. Brittle materials can be distinguished from plastic materials by the absence of the P stress increases proportionally with strain until the material breaks. 

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H. J. Frost and M. F. Ashby, Deformation Mechanism Maps, Pergamon Press, New York, 1982. 

P.S. Follansbee, High-Strain-Rate Deformation Mechanisms in Copper and Implications for Behavior during Shock-Wave Deformation, in Shock Waves in Con-... 

Micromechanical theories of deformation must be based on physical evidence of shock-induced deformation mechanisms. One of the chapters in this book deals with the difficult problem of recovering specimens from shocked materials to perform material properties studies. At present, shock-recovery methods provide the only proven teclfniques for post-shock examination of deformation mechanisms. The recovery techniques are yielding important information about microscopic deformations that occur on the short time scales (typically 10 -10 s) of the compression process. 

This competition between mechanisms is conveniently summarised on Deformation Mechanism Diagrams (Figs. 19.5 and 19.6). They show the range of stress and temperature (Fig. 19.5) or of strain-rate and stress (Fig. 19.6) in which we expect to find each sort of creep (they also show where plastic yielding occurs, and where deformation is simply elastic). Diagrams like these are available for many metals and ceramics, and are a useful summary of creep behaviour, helpful in selecting a material for high-temperature applications. 

Fig. 19.6. Deformation mechanisms at different strain-rates and stresses.

Frost, H.J. and Ashby, M.F. (1982) Deformation-Mechanism Maps The Plasticity and Creep of Metals and Ceramics (Pergamon Press, Oxford). 

The various densification mechanisms at different temperatures can be modelled and displayed in HIP diagrams, in which relative temperature is plotted against temperature normalised with respect to the melting-point (Arzt el al. 1983). This procedure relates closely to the deformation-mechanism maps discussed in Section 5.1.2.2. 

Figure 5.5. Deformation-mechanism maps for MAR-M200 superalloy with (a) 100 pm and (b) 10 mm grain size. The rectangular box shows typical conditions of operation of a turbine blade, (after Frost and Ashby 1982). (c) A barchart showing the range of values of expansion coefficient for generic materials classes. The range for all materials spans a factor of almost. 3000 that for a class spans, typically, a factor of 20 (after Ashby 1998).

Step 3. The set of fracture properties G(t) are related to the interfaee structure H(t) through suitable deformation mechanisms deduced from the micromechanics of fracture. This is the most difficult part of the problem but the analysis of the fracture process in situ can lead to valuable information on the microscopic deformation mechanisms. SEM, optical and XPS analysis of the fractured interface usually determine the mode of fracture (cohesive, adhesive or mixed) and details of the fracture micromechanics. However, considerable modeling may be required with entanglement and chain fracture mechanisms to realize useful solutions since most of the important events occur within the deformation zone before new fracture surfaces are created. We then obtain a solution to the problem. 

The defect question delineates solid behavior from liquid behavior. In liquid deformation, there is no fundamental need for an unusual deformation mechanism to explain the observed shock deformation. There may be superficial, macroscopic similarities between the shock deformation of solids and fluids, but the fundamental deformation questions differ in the two cases. Fluids may, in fact, be subjected to intense transient viscous shear stresses that can cause mechanically induced defects, but first-order behaviors do not require defects to provide a fundamental basis for interpretation of mechanical response data. 

A workable theory behind why unsymmetric cross-ply laminates deform as they do has been developed by Hyer (who has extended these papers). Thus, a reasonable understanding of the deformation mechanics exists and can be used to design laminates with specified curvatures. 

Fig. 12. The scheme of the press for backward forming of cups m one action by means of the superplastic deformation mechanism. The deformation was done at temperature T = 523 K and at stamp velocity of about 1 mm/min.

K. Higashi, "Deformation Mechanisms of Positive Exponent Superplasticity in Advanced Aluminum Alloys with Nano or Near-Nano Scale Grained Structures," in Materials Science Forum Vols. 170-172, pp. 131-140, T.G. Langdon ed., Trans Tech Publications, Switzerland, (1994). 

Likewise, the longer the duration of material stress or strain, the more time for viscous flow to occur. Finally, the greater the material stress or strain, the greater the likelihood of viscous flow and significant permanent deformation. For example, when a TP product is loaded or deformed beyond a certain point, the material comprising it yields and immediate or eventually fails. Conversely, as the temperature or the duration or magnitude of material stress or strain decreases, viscous flow becomes less likely and less significant as a contributor to the overall response of the material and the essentially instantaneous elastic deformation mechanism becomes predominant. 

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