Stress uniaxial stretching

We carried out thermodynamic studies on the crystallization from melts of flexible-chain polymers uniaxially stretched at various degrees of molecular orientation in the melt and studied the effect of the stretching stress on thermodynamic parameters such as degree of... 

Studies involving fluid shear, hydrostatic compression, biaxial and uniaxial stretch, or a combination of two or more of these factors indicate that fluid shear is a major factor affecting bone cell metabolism and cells subjected to mechanical stress reshape and align themselves with their long axis perpendicular to the axis of force. Cells also exhibited remodeling of the actin cytoskeleton and increases in PKC levels, processes thought to be involved in the early phase of mechanochemical transduction. 

For filler reinforced rubbers, both contributions of the free energy density Eq. (35) have to be considered and the strain amplification factor X, given by Eq. (39) differs from one. The nominal stress contributions of the cluster deformation are determined by oAtfJ=dWA/dzA, where the sum over all stretching directions, that differ for the up- and down cycle, have to be considered. For uniaxial deformations E =e, E2=Ej= +E) m- one obtains a positive contribution to the total nominal stress in stretching direction for the up-cycle if Eqs. (29)-(36) are used ... 

Figure 46a shows that a reasonable adaptation of the stress contribution of the clusters can be obtained, if the distribution function Eq. (55) with mean cluster size =25 and distribution width b= 0.8 is used. Obviously, the form of the distribution function is roughly the same as the one in Fig. 45b. The simulation curve of the first uniaxial stretching cycle now fits much better to the experimental data than in Fig. 45c. Furthermore, a fair simulation is also obtained for the equi-biaxial measurement data, implying that the plausibility criterion , discussed at the end of Sect. 5.2.2, is also fulfilled for the present model of filler reinforced rubbers. Note that for the simulation of the equi-biaxial stress-strain curve, Eq. (47) is used together with Eqs. (45) and (38). The strain amplification factor X(E) is evaluated by referring to Eqs. (53) and (54) with i= 2= and 3=(l+ ) 2-l.

Fig. 14 Stress distribution in a cracked film. The dotted lines correspond to the elastic behavior of the film/substrate system, the solid lines to the presence of plasticity in the substrate at the crack/interface intersection (a) crack opening in a film deposited on a substrate which is uniaxially stretched, (b) longitudinal strain distribution In the film, (c) normal stress distribution in the film, and (d) shear stress distribution In the film at the Interface.

Table 4.4 summarizes the physical properties of common metals used for diaphragms. Young s modulus is a measure of the stiffness of elastic materials and is defined as the ratio of stress (uniaxial) versus the strain (uniaxial), i.e. the ratio of the change in length of an elastic material as a function of a tensile or compressive load. The Poisson s ratio is a measure of a material s tendency to contract under a tensile load, i.e. the contraction in the direction normal to the direction in which the material is stretched. The symbol for the shear modulus of elasticity is G. 

Stress-strain measurements at uniaxial extension are the most frequently performed experiments on stress-strain behaviour, and the typical deviations from the phantom network behaviour, which can be observed in many experiments, provided the most important motivation for the development of theories of real networks. However, it has turned out that the stress-strain relations in uniaxial deformation are unable to distinguish between different models. This can be demonstrated by comparing Eqs. (49) and (54) with precise experimental data of Kawabata et al. on uniaxially stretched natural rubber crosslinked with sulphur. The corresponding stress-strain curves and the experimental points are shown in Fig. 4. The predictions of both... 

For the case of uniaxial stretching at constant volume, the stress (see equations 7.40 to 7.48) modified for swelling is given by... 

Such ideas formed the basis of the Kuhn and Grun model for the stress-optical behaviour of rubbers. The birefringence of a uniaxially stretched rubber is given by... 

Quantitative investigations of photoelasticity (birefringence in films due to the action of uniaxial stretching stresses) showed (Fig. 6) that birefringence in CLPhS films is of a complex type. 

Nominal stress versus den ion ratio, for uniaxial stretching of a sample of crosslinked natural rubber. Full line shows the Gaussian prediction (eqn 3.38). 

The different morphologies generated in the bulk polymer samples prepared using catalyst 10a in combination with either MAO or borate activation (A and B series. Table 9.2) can be implicated in variations in mechanical behavior. To study the influence of the morphology on macroscopic mechanical behavior, melt-pressed samples were subjected to uniaxial stretching until they failed (A series. Figure 9.28 B series. Figure 9.29). For mmmm contents below 40%, stress-strain curves are observed that are characteristic of elastomeric materials. 

The theory of Bernstein, Kearsley and Zapas [20] and developments of it (e.g. Zapas and Craft [21]) - so-called BKZ theories - are aimed in particular at large deformation behaviour. The Gaussian model of rubber elasticity tells us that in uniaxial stretching the true stress o is in the form... 

Perhaps the most important feature of the BKZ model, which distinguishes it from all the models discussed so far, is the choice of strain measure. Hitherto, all the materials have been assumed to be solids, in that they have an initial undeformed, stress-free state that acts as a reference relative to which all strained states are measured. In BKZ theories there is no such special state, and the material therefore may be classed as a flmd. At any present time t, the state of strain is measured relative to the state at previous times t. This is done by adopting as the strain measure the quantity A(f)/A(T). Reflecting on the remarks in the paragraph above now suggests the importance of the quantity [A (r)/A (r)] — [A(T)/A(f)] in a theory in which the stress depends on the strain history. The BKZ form given by Zapas and Craft [21] in uniaxial stretching is... 

In Sect. 3.2 it was shown that uniaxial stretching or compression of Sc elastomers does not produce macroscopically oriented samples. Due to the Sc symmetry, uniaxial deformation only induces a uniform orientation of the director but leaves the smectic layer normals conically distributed around the stress axis. Usually such elastomers remain opaque. For the preparation of Sc LSCEs a more complex orientation strategy is necessary which can be realized by deploying two successive orientation processes. 

M = 182 X 10 g.moLe" ) and 25 % of polyisoprene chains of low molecular weight (M = 50,000), the microstructure of which is similar to that of IR 307. Tfiese matrices (99 %) were mixed in solution with labeled anionic polyisoprene chains containing a dimethylanthracene (DMA) fluorescent group at their centers. The labeled polyisoprene had the same microstructure as IR 307 and its molecular weight was M = 60.10 g.mole. Samples were molded and cross-linked with dicumyl peroxide. Measurements of stress and orientation were done during uniaxial stretching at constant cross-head speed, V = 50 mm/min, and at a temperature of 298 K. 

The first chiral smectic C elastomer was synthesized by Zentel et al. in 1988 [13], [24]. The preparation of the network is similar to the synthesis of the cholesteric networks described above. The network was uniaxially stretched. An unwinding of the helicoidal superstructure is observed and an orientation of the director, as well as of the smectic layer normal roughly parallel to the stress axis occurs. A macroscopically uniform alignment of the sample was not observed as explained below. 

Uniaxial stretch Tensional stress No May also generate shear stress due to motion of cells relative to fluid... 

Take as an example the simple case of uniaxial stretching along the I direction with an applied stress ai = a, an = am = 0. The extension ratio along 1 is A,i = X, with the symmetry so that the extension ratios in the other two principal directions are equal. Then, the incompressibility condition (3.30) becomes... 

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