Thickness strain

Although this analysis should be conducted for both straight-walled and rib-walled pipe, it is particularly important in the case of rib walled. That is, because the rib is often thicker than the structural wall of the pipe, by several times the wall s thickness. Strains along the ribs may be higher than along the straight-walled sections, particularly at the top of the rib. For the sake of this discussion, assume that strain analysis in the hoop direction has confirmed that... 

These materials have shown thickness strains on the order of 5% with fast response times [18]. Representative results are shown in Rg. 1.5. As seen in the figure, the required fields are quite high as in most electronic EAPs. Strains tend to show a peak and decrease for stresses above and below the peak value. Reported values for irradiated P(VDF-TrFE) show peak strains at 20 MPa, dropping to 50% of the maximum value above 40 MPa and below 5 MPa [112]. Elastic moduli in the range of 0.3-1.2 GPa have been reported with energy densities around 1 MJ m [7]. In order to compete as artificial muscles, strain values will have to be improved. 

Polymer (specific type) Prestrain (x, y%) Energy density (MJ Actuation pressure (MPa) Thickness strain (-%) Area strain (%) Young s modulus (MPa) Electic field (MV m ) Dielectric constant Dielectric loss factor Mechanical loss factor Coupling efficiency (%) Efficiency (%) Ref. 

Carpi et al. have reported on the actuation characteristics of another commercially available elastomer (Dr Scholl s, Canada, Gelactiv tubing) [167]. The material was capable of thickness strains of 1.8% at 27 MV m with an actuation stress of 3.7 kPa at 24 MV m . ... 

Fig. 1.18 Thickness strain S3A as a function of the applied-field amplitude for composites of PANI/ yPolyCuPc/PU (from lowest strain to highest strain) 0/0/100, 0/15/85, 4.6/15/85, 9.3/15/85, 14/15/85 [184]. Appl Phys Lett 2004, reprinted with permission...

Material Prestrain ix, y) (%) Actuated relative thickness strain (%) Actuated relative area strain (%) Field strength (MV/m) Effective compressive stress (MPa) Estimated Mle (MJW)... 

The strains in the linear strain test can be quite large, up to 215% for the VHB 4910 acrylic adhesive (Table B.l). The VHB 4910 acrylic elastomer, when undergoing 160% strain in a linear strain test, exhibited budding (the vertical wrinkles in Fig. B.3d) that was not seen in properly stretched silicone films. Buckling indicates that the film is no longer in tension in the horizontal direction during actuation, and that the overall relative thickness strain is greater than indicated by measurements of the electrode boundaries. That is, the relative strain numbers for VHB 4910 in Table B.l may be undervalued. 

To describe this kind of anisotropic material behavior precisely, the yield surface is needed. For quite simple but well-known and established yield surfaces, the so-called r-values are used to describe this behavior. The r-value (normal anisotropy) is defined by the ratio of width to thickness strain (measured as ttue strains). The index indicates the angle between drawing and rolling direction of the material. Usually, the r-values are determined in 0°, 45°, and 90°. 

Tensile and lateral strains are monitored by an extensometer, the weight of which is supported by the main frame of the machine, and the design is such that the maximum loads applied to the specimen by the extensometer are negligibly small compared with the creep load. In Fig. 1 the tensile extensometer (4) and the extensometer measuring thickness strain (5) are shown. A third extensometer measuring width strain can be accommodated simultaneously from a mounting attached to the front face of the frame. 

Fig, L General view of uniaxial tensile creep machine (Darlington, 1971, unpublished), 1, Lever arm 2, upper hooks 3 linear spring guide 4, tensile extenso-meter 5, lateral extensometer (for thickness strain). 

Specimens with gauge lengths as small as 12 mm can be accommodated with simultaneous measurement of length and thickness strains. All three principal strains may be measured within a gauge length of 26 mm. Specimens are carefully machined from oriented sheet by high speed routing to produce the necessary surface finish. 

The correlation between the midgap interfacial state density Du and the thickness strain in thermally grown Si02 films has been studied [110]. The At decreases with the oxidation temperature and with the oxide film thickness. The frequency of the Si—O stretching vibrations increases with increasing oxidation temperature and film thickness. The peak position v is expressed as a function of the average Si—O—Si bond angle as... 

Here, vi = 1079 cm is the bond-stretching frequency of a fully relaxed film and V is the corresponding bond-stretching frequency in the stressed oxide. The calculation of the microscopic strain from the Si—O—Si stretching frequency shows the existence of a linear relationship between and the thickness strain in Si02 [110]. 

Loading can be either load (or stress) controlled, displacement (or strain) controlled, or something in between. Examples include aerodynamic loads on an aircraft (see Aerospace applications), which tend to be load controlled, and the displacement of a sealant between relatively stiff adherends, which is displacement controlled. Because average adhesive strain, in its simplest form, is defined as displacement divided by bond thickness, strains and resulting stresses are higher in thin bondlines subjected to displacement-controlled loading scenarios. Joints loaded in such a manner often perform better with thicker bondlines. Displacement-controlled situations include thermal expansion/shrinkage of adherends, mismatched adherend expansion, and attachments bonded to pressure vessels or other adherends that are stressed. 

To get a better understanding of the pucker mechanism, the correlation coefficient between fabric properties and the thickness strain values are required. By taking one fabric property at a time with thickness strain values, it is possible to find out the contribution of each fabric parameter. These fabric properties are fabric mass, thickness compression, bending rigidity, shear stiffness, extensibility, cover factor, and formability in the warp and filling direction. 

Thickness strains S can be analytically described, by assuming that the dielectric elastomer is a linearly elastic body, with a Youngs modulus Y and a relative dielectric constant Cr, as follows (eo = 8.85 10 F/m is the free-space dielectric permittivity) [280-283] ... 

Table 16.1 The thickness strain response and corresponding electromechanical performance of different materials at room temperature...

Many electrostrictive polymers have been developed in the last decade [1] and these newly developed electrostrictive polymers exhibit a high electric-field-induced strain, as shown in Figiure 16.5a, where the maximum thickness strain response of the polymer at different fields is given. A typical relationship between the strain response and the electric field observed in these polymers is shown in Figure 16.5b. All these electrostrictive polymers are polar polymers that contain polar units in the polymer chain. The electrostrictive strain response reflects the change in these polar units due to an electric field. 

Figure 16.5 (a) The maximum thickness strain at different electric fields for three newly developed electrostrictive polymers, (b) The relationship between the strain response and electric field for a typical electrostrictive polymer... 

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