Critical deformation

Fig. 14.11. Typical data for recrystallised grain size as a function of prior plastic deformation. Note that, below a critical deformation, there is not enough strain energy to nucleate the new strain-free grains. This is just like the critical undercooling needed to nucleate a solid from its liquid (see Fig. 7.4).

At fixed filling ratio, using a hybrid filler may decrease extruded material swelling, raise the critical deformation parameters at which elastic turbulence of the melt may begin [366]. 

Breakup of droplets at the instant that a critical deformation stage has been attained... 

The greater force is ( ) Critical deformation the strong nuclear occurs,... 

The mechanical ways of foam breakdown are realised by various rotating devices (mixers, disks, centrifuges, propellers, etc.) or by employing stream of air, vapour or liquid or by running the foam through cyclones and narrow gaps [1,2]. In all these cases the liquid outflow from the foam is accelerated which creates critical deformations and stresses in films and other foam elements. A convenient classification of the mechanical means of foam breakdown and the methods designing such mechanical devices are considered in [3]. The... 

Fission by thermal neutrons is induced by the binding energy of the neutron (%6MeV) which leads to excitation of the nucleus, oscillation and finally splitting into two parts, if a critical deformation is exceeded. The stages and the time scale of fission by thermal neutrons arc illustrated in Fig. 8.12. Critical deformation is... 

Single-drop studies have shown that a drop in a rotational shear field will both elongate and undergo internal rotation with increasing shear, until the critical deformation D j, is reached. Beyond this point, breakage occurs. Taylor [56] established the relationship between drop deformation, D, and the magnitude of the rotational shear field. This is shown by Equation (9.46), where P =... 

Chauveteau and co-workers 24, 48) examined the flow of PEO and HPAA through the extensional flow produced in severe constrictions. They concluded that a coil-stretch transition was responsible for the dilatant behavior observed, and that the critical shear rate required was of the order of 10 times the reciprocal of the Rouse relaxation time. Perhaps the most extensive studies have been those of Haas and co-workers (25, 26, 49). They have explored the critical dilatant behavior on flow through porous media and pursued the hypothesis that the phenomenon is primarily due to a coil-stretch transition beyond a critical deformation rate. They attempted a semiquantitative description based upon the dependence of the lowest order relaxation time of the random coil upon polymer type, molecular weight, solvent quality, and ionic environment. 

In variable mechanical fields (the type of loading that occurs during friction) the slowest stage that defines the velocity of tribochemical transformations may turn out to be redistribution of elastic stresses in the polymer. In this case, the velocity constant Ki of the mechanical process will be proportional to the redistribution velocity j4(s ) and the probability of accumulating some critical deformation energy U on a given link sufficient for the reaction initiation [82] will be... 

Drop rupture occurred when D > D and this critical deformation was a singled valued function of R. Karam has shown experimentally Figure 14.8) the form of this function. 

Turning to the ultimate drop size, it is generally assumed that the wavelength, A , corresponding to the maximum instability growth rate dominates break-up. The critical deformation, D ix, can be expressed as ... 

However, some substances have a poor compatibility with polymers, but there is evidence of their plasticizing action (a significant increase in critical deformations at temperatures below Tg and a decrease in viscosity). This effect was found in such systems as polypropylene-polysiloxane, PVC-etlyl stearate,"" cellulose triacetate-trimonochloroet-hyl phosphate, nitrocellulose-castor oil," cellulose triacetate-dihexyl sebacate," PVC-ethyl stearate," etc. 

Droplets are disrupted if they are deformed over a period of time tjef that is longer than a critical deformation time fdef, cr and if the deformation (described by the Weber number We or capillary number Ca) exceeds a critical value [3] ... 

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