Phase Deformation

To understand how the dispersed phase is deformed and how morphology is developed in a two-phase system, it is necessary to refer to studies performed specifically on the behavior of a dispersed phase in a liquid medium (the size of the dispersed phase, deformation rate, the viscosities of the matrix and dispersed phase, and their ratio). Many studies have been performed on both Newtonian and non-Newtonian droplet/medium systems [17-20]. These studies have shown that deformation and breakup of the droplet are functions of the viscosity ratio between the dispersity phase and the liquid medium, and the capillary number, which is defined as the ratio of the viscous stress in the fluid, tending to deform the droplet, to the interfacial stress between the phases, tending to prevent deformation ... 

Due to tridimentionality of the elementary cell, the reagent concentration in the solution decreases quickly (as C l/r) near the crystal surface during crystal dissolution. Therefore, the obstacles, namely crystals of a new phase, deform insignificantly the distribution of the concentration around of the crystal discussed. Figure 2 shows this peculiarity, which has been calculated in [13]. 

Our analysis is, however, not complete in any respect. For instance, as the large difference in Fermi momenta renders the BCS-type condensation in the classical 2SC phase difficult, it seems to be worthwhile to consider other possibilities. Among others we thereby think of a crystalline phase, deformed Fermi surfaces [32, 35], spin-1 pairing [20] or the gapless 2SC [33, 34] or CFL phase [60], We conclude that whether quark matter exists in hybrid or... 

Palancher et al. (2005) Sr-X zeolite Phase deformation + + — Dehydration of zeolite... 

The density distribution function, gla (y), that accounts for the break-down of secondary aggregates attributed to non-linear rubber phase deformation. 

The high deformation ratios imposed on polyethylene also lead to a high degree of non-crystalline orientation in solid phase deformed material, as indicated by the orientation of the non-crystalline component in the broad line NMR and the... 

This constraint does not allow an individual rhombus flips, instead a flip of one rhombus should be always followed by a flip of another in the same row. If, however, the phase stiffness is low, the flip of one rhombus can be also compensated by the continous phase deformations in the other rhombi constituting this row, we derive the conditions at which we can exclude these processes below. The simplest allowed process is the simultaneous flip of two rhombi in one row... 

In the above considerations, a sinusoidal shear strain is applied to the sample. It should be clear that a sinusoidal shear stress could also be applied resulting in corresponding compliance functions J and J". The former results from the deformation in phase with the stress, while the latter corresponds to the out-of-phase deformation. The value of tan 5 remains the same, as can be seen from the curves in Figure 2-13, where we can easily imagine the stress as the applied variable and strain as the measured variable. Tensile stress is equally applicable and definitions of E (co), E" (o), D"(co), D co), etc. are completely analogous to the derived shear parameters. At a given frequency, the value of tan 8 is always the same for any of these quantities, i.e., tan 8 = E"/E = D"/D . 

Solid Phase Deformation Processes 3.1 Tensile Drawing... 

Gurtin, M.E. Two-phase deformations of elastic solids. Arch. Ration. Mech. Anal. 84(1), 1-29 (1983)... 

The formation of the fibril is a eonsequence of dispersed phase deformation and orientation correlating with the viscous force and interfacial tension between the dispersed phase and the matrix [236,237]. For good fibrillation to be achieved, the viscosity of dispersed phase should be lower than that of the matrix (i.e., / = rjd/ mtemperature dependence of p of PS to PP is shown in Figure 3.68. Experimental results showed that p is less than 1 above 210°C and reduces to about 0.5. This indicates that polystyrene is able to form the fibrils in polypropylene matrix when the processing temperature is over 210°C, but finds it difficult below 210°C [239]. 

The diameter of as-spun fiber decreased from around 20-30 p,m to about 15 pm after drawing, while the size of the polystyrene morphology reduced about 10%. This indicates the drawing process did not effectively deform the solid dispersed phase, because it is difficult for the draw stress to transfer from the matrix to the dispersed phase through the solid interface, and the free space for the polystyrene phase deformation is limited. 

Figure 10.15. Schematic illustrations of theories of stress softening, (a) Mullins and Tobin (1956) considered the filled rubber as a heterogeneous system comprised of hard and soft phases. Deformation breaks down the hard phase, but the degree of breakdown depends on the maximum extension of the sample, (b) F. Bueche (1965) attributed stress-softening to the breakage of network chains attached to adjacent filler particles (A molecule breaks first), (c) Dannenberg (1966) and Boonstra (1965) suggested that reinforcement can be understood through chain slippage mechanisms. The slippage is shown by the chain marks. (Smith and Rinde, 1969.)...

The aspect of self-reinforcement is of great importance for the performance of the single polymer composites. Apart from the stretching of the molecules, which occurs during the fiber and/or tape production, crystalline structures are also induced [11]. So-called shish kebab structures can be specifically developed by means of melt or solid phase deformation [12] and give the stretched thermoplastic tapes or fibers significantly higher mechanical properties than are possible for a comparable compact material that is not self-reinforced. 

Initially the pseudo-elastic material is in its austenitic phase at room temperature. Initially the material in the austenitic phase deforms like a conventional material linear elastic under load. With increasing loads a stress-induced transformation of the austenitic to the martensitic phase is initiated at the pseudo-yield stress Rpe- This transformation is accompanied with large reversible strains at nearly constant stresses, resulting in a stress plateau shown in Fig. 6.53. At the end of the stress plateau the sample is completely transformed into martensite. Additional loading passing the upper stress plateau causes a conventional elastic and subsequently plastic deformation of the martensitic material. If the load is decreased within the plateau and the stress reaches the lower stress level a reverse transformation from martensite to austenite occurs. Since the strains are fully reversible the material and the sample respectively is completely recovered to its underformed shape. These strains are often called pseudo-elastic because the reversible deformation is caused by a reversible phase transformation and is not only due to a translation of atoms out of their former equilibrium position [74]. 

In the out-of-phase deformation mode, the matrix is loaded in tension and compression, in the in-phase mode, it is sheared. Because of this, the modes are sometimes called extension mode and shear mode. Except at small volume fractions of the fibre, the strength of the composite is smaller in in-phase deformation which is thus the mode of interest. If a purely elastic deformation of the matrix is assumed, the calculated strength values for the composite are very large, but the observed values are usually much smaller. In metal and polymer matrix composites, the matrix deforms plastically in the in-phase mode. If we make the simplifying assumption that the matrix is perfectly plastic with a yield strength of the compressive strength is [122]... 

During the last ten years there have been several notable advances in the development of ultra high modulus polyethylene and polypropylene. This has been achieved most simply by tensile drawing , but also by hydrostatic extrusion , ram extrusion and die drawing all of which are solid phase deformation processes. In polyethylene, an alternative approach has been the production of fine ultra high modulus fibres from dilute solution, either by crystallisation in an elongational flow field or by stretching fine fibres spun to form a gel from dilute or reasonably dilute solution, 13 ... 

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