Deformation behaviour

A constitutive equation is a relation between the extra stress (t) and the rate of deformation that a fluid experiences as it flows. Therefore, theoretically, the constitutive equation of a fluid characterises its macroscopic deformation behaviour under different flow conditions. It is reasonable to assume that the macroscopic behaviour of a fluid mainly depends on its microscopic structure. However, it is extremely difficult, if not impossible, to establish exact quantitative... 

It is somewhat difficult conceptually to explain the recoverable high elasticity of these materials in terms of flexible polymer chains cross-linked into an open network structure as commonly envisaged for conventionally vulcanised rubbers. It is probably better to consider the deformation behaviour on a macro, rather than molecular, scale. One such model would envisage a three-dimensional mesh of polypropylene with elastomeric domains embedded within. On application of a stress both the open network of the hard phase and the elastomeric domains will be capable of deformation. On release of the stress, the cross-linked rubbery domains will try to recover their original shape and hence result in recovery from deformation of the blended object. 

Yamaguchi, M. and Umakoshi, Y. (1990) The deformation behaviour of intermetallic superlattice compounds. Prog. Mater. Sci. 34, 1. 

For most traditional materials, the objective of the design method is to determine stress values which will not cause fracture. However, for plastics it is more likely that excessive deformation will be the limiting factor in the selection of working stresses. Therefore this chapter looks specifically at the deformation behaviour of plastics and fracture will be treated separately in the next chapter. 

Since the tensile test has disadvantages when used for plastics, creep tests have evolved as the best method of measuring the deformation behaviour of... 

These latter curves are particularly important when they are obtained experimentally because they are less time consuming and require less specimen preparation than creep curves. Isochronous graphs at several time intervals can also be used to build up creep curves and indicate areas where the main experimental creep programme could be most profitably concentrated. They are also popular as evaluations of deformational behaviour because the data presentation is similar to the conventional tensile test data referred to in Section 2.3. It is interesting to note that the isochronous test method only differs from that of a conventional incremental loading tensile test in that (a) the presence of creep is recognised, and (b) the memory which the material has for its stress history is accounted for by the recovery periods. 

Up to this stage we have considered the deformation behaviour of fibre composites. An equally important topic for the designer is avoidance of failure. If the definition of failure is the attainment of a specified deformation then the earlier analysis may be used. However, if the occurrence of yield or fracture is to be predicted as an extra safeguard then it is necessary to use another approach. 

At room temperature, NiAl deforms almost exclusively by (100) dislocations [4, 9, 10] and the availability of only 3 independent slip systems is thought to be responsible for the limited ductility of polycrystalline NiAl. Only when single crystals are compressed along the (100) direction ( hard orientation), secondary (111) dislocations can be activated [3, 5]. Their mobility appears to be limited by the screw orientation [5] and yield stresses as high as 2 GPa are reported below 50K [5]. However, (110) dislocations are responsible for the increased plasticity in hard oriented crystals above 600K [3, 7]. The competition between (111) and (110) dislocations as secondary slip systems therefore appears to be one of the key issues to explain the observed deformation behaviour of NiAl. 

D.R. Pank, M.V. Nathal, D.A. Koss. Deformation behaviour of NiAl-based alloys containing iron, cobalt and hafnium, in High Temperature Ordered Intermetallic Alloys V, 1. Baker, R.Darolia, J.D.Whittenberger, Man H. Yoo, ed., MRS, (1993), Vol. 288... 

Fig.l. Prediction of the deformation behaviour of the material where three different processes may be rate and stress- controlled dashed line) ... 

Pakula T., Saijo K., Kawai H., and Hashimoto T. Deformation behaviour of styrene butadiene styrene triblock copolymer with cyhndrical morphology, Macromo/ecu/er, 18, 1294, 1985. 

Apostolov A.A. and Fakirov S., Effect of the length on the deformation behaviour of polyetheresters as revealed by smah angle x-ray scattering, J. Macromol. Set, Phys. B, 31, 329, 1992. 

Fakirov S, Fakirov C, Fischer EW, and Stamm M. Deformation behaviour of poly(ether ester) thermoplastic elastomers as revealed by SAXS. Polymer, 1991, 32, 1173-1180. 

In order to appreciate the effect of forces acting on a fluid it is helpful first to consider the behaviour of a solid subjected to forces. Although the deformation behaviour of a fluid is different from that of a solid, the method of describing forces is the same for both. 

Lauke B. and Schultrich B, (1983). Deformation behaviour of short fiber reinforced materials with debonding interfaces. Fiber Sci. Technol. 19, 111-126. 

TENSILE DEFORMATION BEHAVIOUR OF THE POLYMER PHASE OF FLEXIBLE POLYURETHANE FOAMS AND POLYURETHANE ELASTOMERS... 

Rusakov 107 108) recently proposed a simple model of a nematic network in which the chains between crosslinks are approximated by persistent threads. Orientional intermolecular interactions are taken into account using the mean field approximation and the deformation behaviour of the network is described in terms of the Gaussian statistical theory of rubber elasticity. Making use of the methods of statistical physics, the stress-strain equations of the network with its macroscopic orientation are obtained. The theory predicts a number of effects which should accompany deformation of nematic networks such as the temperature-induced orientational phase transitions. The transition is affected by the intermolecular interaction, the rigidity of macromolecules and the degree of crosslinking of the network. The transition into the liquid crystalline state is accompanied by appearence of internal stresses at constant strain or spontaneous elongation at constant force. 

The use of a parallel plate plastimeter to determine both softness and recovery is a simple way of obtaining a measure of both the viscous and elastic components on deformation behaviour, albeit under conditions somewhat removed from those met during processing. An alternative approach is to measure the stress relaxation in a test piece and this was the basis of the Stress Relaxation Processibility Tester developed at RAPRA. 

There is strong interest to analytically describe the fzme-dependence of polymer creep in order to extrapolate the deformation behaviour into otherwise inaccessible time-ranges. Several empirical and thermo-dynamical models have been proposed, such as the Andrade or Findley Potential equation [47,48] or the classical linear and non-linear visco-elastic theories ([36,37,49-51]). In the linear viscoelastic range Findley [48] and Schapery [49] successfully represent the (primary) creep compliance D(t) by a potential equation ... 

The investigation of the ft transition of PMMA ([1], Sect. 8.1.3) has revealed that physical ageing has an influence on the dynamic mechanical response in the ft-a crossover temperature region. As a consequence, it is worth checking whether it leads to some changes in the plastic deformation behaviour [32]. 

These observations lead one to wonder how the motions involved in the ft transition could affect the plastic deformation behaviour of PMMA. 

The molecular mechanism, described in Sect. 3.1.1.6, for the yielding and strain softening of PMMA accounts quite well for the plastic deformation behaviour of CMIMx copolymers. 

The above reported results show that the plastic deformation behaviours of MGIMx copolymers are much closer to those of PMMA than those observed for CMIMx copolymers. 

Fig. 55 Deformation behaviour at intermediate temperatures a craze with diffuse edges in MGIM76 at 21 °C b shear blunting at craze tips inMGIM76 at 50 °C...

Fig. 80 Diagram of thin film deformation behaviour as a function of temperature for unaged and aged BPA-PC (Mw = 31000) strain rate of 4 x 1CT4 s 1 (From [58])...

Nixon, R.D., Chevacharoenkul, S., Davis, R.F., Huckabee, M.L. and Buljan, S.T. Deformation behaviour of SiC whisker reinforced Si3N4 , in Materials Research Society Symposium Proceedings, vol. 78, ed. Becher, P.F., Swain, M.V. and Somia, S. Materials Research Society, Pittsburg, PA (1987) 295-302. 

It can be seen that ceramic multilayer structures have been produced with increments of the hardness of up to 60 GPa, increasing the hardness by up to a factor of almost 3. Initial work in this area has developed a number of ideas, such as the effect of modulus mismatch, which in some cases give good agreement with the models suggested but in many others do not. It is suggested that at least some of this discrepancy can be accounted for by differences in the microstructure and residual stress-state of the film, both of which are often poorly characterized. Furthermore there is very little direct evidence about how these structures deform and in particular about how different layers must be strained in order to accommodate the indenter when it is pressed into the sample. Further advances in this area will require the greater use of numerical techniques to analyse the complex stress and strain behaviour under the indentation, coupled with the use of recently developed techniques that allow the localized deformation behaviour to be observed in detail. 

Usually the deformation behaviour of rubbery crosslinked polymers with long chains between crosslinks obeys the classical theory of rubber elasticity. However, the situation for densely crosslinked polymers is not so simple. 

Fig. 14. Deformational behaviour of networks in the rubbery state. Solid lines correspond to the relation a — GaQ. — 1/X2) with G, measured by torsion pendulum3 ...

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