Sample Deformation

Dynamic mechanical load on elastomer products is often exerted at small deformations and low deformation rates but over extended time periods. Then part of the mechanical energy is dissipated into heat depending on the value of the loss modulus. As a consequence, a temperature profile is established within the sample. Then the modulus 

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By analogy with Eq. (3.1), we seek a description for the relationship between stress and strain. The former is the shearing force per unit area, which we symbolize as as in Chap. 2. For shear strain we use the symbol y it is the rate of change of 7 that is involved in the definition of viscosity in Eq. (2.2). As in the analysis of tensile deformation, we write the strain AL/L, but this time AL is in the direction of the force, while L is at right angles to it. These quantities are shown in Fig. 3.6. It is convenient to describe the sample deformation in terms of the angle 6, also shown in Fig. 3.6. For distortion which is independent of time we continue to consider only the equilibrium behavior-stress and strain are proportional with proportionality constant G ... 

During these types of test it is the energy absorbed at fracture, Uc, which is recorded. In terms of the applied force, Fc, and sample deformation, 5, this will be given by... 

Several Intermetallics, for example Ni3Al, are ordered right up to the melting temperature showing only minor variation of order parameter with temperature. In the present paper LRO-kinetics is studied in CusAu, where a Ti of about 390°C allows a considerable variation of the degree of LRO until its complete dissolution. We report on results of recrystallized material as well as samples deformed in the disordered and the ordered state. Part of this work was already presented at an earlier conference. ... 

Whereas for the sample deformed to 40% a very small decrease of resistivity is obtained at 170°C not being visible in Figure 2 (very small number of excess vacancies) a slight increase results above 170°C for the sample deformed to 80%. This may be a consequence of increasing SRO within the disordered matrix before changes in LRO are enabled. 

Figure 2 Relative change of resistivity during isochronal annealing (AT=10K, At=10min) of deformed samples Deformed in disordered state 40% (A) and 80% reduction ( ) deformed in ordered state 30% reduction ( )...

The samples deformed in the disordered state show a behaviour different for the two degrees of deformation The sample cold-rolled to 40% at 260°C starts to decrease continuously to the completely recrystallized value, whereas the more highly deformed sample (80%) increases slightly (18%) until 390°C where a drastic decrease in hardness starts. 

The sample deformed to 30/o reduction in the ordered state shows an S-shape behaviour within the ordered region with a drop of about 30% at 400°C. The first decrease of microhardness at about 130°C seems to be correlated with the early decrease of resistivity and, therefore, may be attributed to the recovery of a great number of deformation induced excess vacancies. 

From a comparison of the evolution of hardness of all samples during isochronal armealing it can be concluded that for high deformation in the disordered state and deformation in the ordered state, recovery and recrystallization is prevented up to T, in the sample deformed to 40% reduction in the disordered state recovery and recrystallization processes seem to start as soon as atomic mobility is enabled (260°C). 

Fig. 11. Profiles of orienlation density along the most pronounced <110> fibre of the AlZn78 alloy-samples deformed at different temperatures.

Because modes of operation are different, obtained topographic images may not resemble each other if the sample deformation caused by frictional or adhesive interaction become dominant. 

FIGURE 21.10 (a) The schematic drawing of the sample deformation for an elastic sample, (b) The comparison between force-distance curves for stiff and elastic samples. 

Force curve gives the relationship between the z-piezo displacement and the cantilever deflection as shown in Figure 21.10b. When a cantilever approaches to a stiff sample surface, cantilever deflection. A, is equal to the z-piezo displacement, z — Zo- The value of zo is defined as the position where the tip-sample contact is realized. On the other hand, z-piezo displacement becomes larger to achieve the preset trigger value (set point) of the cantilever deflection in the case of an elastic sample due to the deformation of the sample itself. In other words, we can obtain information about a sample deformation, 8, from the force-distance curve of the elastic surface by the following relationship ... 

We consider four possible relationships between sample deformation and chain deformation. 

Fluctuations are larger in networks of low functionality and they are unaffected by sample deformation. The mean squared chain dimensions in the principal directions are less anisotropic than in the macroscopic sample. This is the phantom network model. 

The parameters of neutron scattering theory of polymer networks are A, the macroscopic stretching of the sample, or linear degree of swelling, f, the network functionality, K. which accounts for restricted junction fluctuations and a, a measure of the degree to which chain extension parallels the macroscopic sample deformation. The functionality is known from knowledge of the chemistry of network formation, and A is measured. Both K and a must be extracted from experiments. 

At extremely short distances, for example, zo < 3 A, the repulsive force becomes dominant. It has a very steep distance dependence. The tip-sample distance is virtually determined by the short-ranged repulsive force. By pushing the tip farther toward the sample surface, the tip and sample deform accordingly. 

These formulas are important in the discussion of tip and sample deformation (see, for example, Pethica and Oliver, 1987), as well as some mechanical design problems of STM and AFM. 

Block and clay regions of SEBS nanocomposite Modulus from Hertz model ( Sample) MPa Localized sample deformation (d), nm Modulus from JKR model ( Sample) MP Bulk modulus3 of SEBS/clay nanocomposite, MPa... 

The presence of phase transitions at 19 and 30°C provides an opportunity to test the proposed deformation model. Below 19°C the lattice contracts into a triclinic structure witli strong intermolecular interaction. 5,26 sjamplcs deformed below 19°C should develop off-c-axis orientation while samples deformed above 30°C should not. Figures 1.12 and 1.13 show inverse pole figures for samples deformed at 2 and 70°C. The observed orientation agrees with our proposed model. - With tlris set of experiments, it is possible to activate the oblique slip process or, alternatively, to deactivate it in the high-temperature phase above 30°C. 

Peyron, M.A. and Mioche, L. (1993). Bite force and sample deformation during hardness assessment of visco-elastic products. J. Sensory Studies, (in Press). 

However, at lower constant loads the rate of crystal plastic deformation decreases and (at 80 °C) disentanglement becomes competitive leading to the development of isolated planar craze-like defects extending perpendicular to the tensile axis (Fig. 15). The ensuing concentration of stress will further localize most of the sample deformation in such creep crazes and lead to a macroscopic ductile-brittle transition—in this material observed at 20 MPa (Fig. 14 [67]). 

A numerical model to simulate the lattice expansion behavior of the doped lanthanum chromites under a cell operating condition has been proposed, and the deformation of the lanthanum chromite interconnectors has been calculated [33], In the model, the sample deformation is calculated from the profile of the oxygen vacancy concentration in the interconnector. Under a practical cell operation, the oxygen vacancy concentration in the interconnector distributes unevenly from the air side to the fuel side. The distribution of the oxygen vacancy concentration in the interconnector depends on both the temperature distribution in the interconnector and the profile of the oxygen partial pressure at the interconnector surface. Here, a numerical model calculation for the expansion behavior of the LaCrC>3 interconnector under a practical cell operation is carried out, and the uneven distribution of... 

Fig.1.a Variation of the interaction force between a flat surface and an isolated atom in the near field of the surface. The dot line corresponds to the lateral displacement of the atom by one interatomic distance. The grey line indicates the force profile sensed by the atom as it moves parallel to the surface plane, b Scheme of a SFM probe a sharp tip mounted on a cantilever. The interaction force Fi=Fs+Fd is a sum of many interatomic interactions, where Fs is the surface force and force Fd results from the sample deformation. The interaction force is balanced by force Fc due to the cantilever bending... 

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