Thickness strain response direction

Piezoelectricity links the fields of electricity and acoustics. Piezoelectric materials are key components in acoustic transducers such as microphones, loudspeakers, transmitters, burglar alarms and submarine detectors. The Curie brothers [7] in 1880 first observed the phenomenon in quartz crystals. Langevin [8] in 1916 first reported the application of piezoelectrics to acoustics. He used piezoelectric quartz crystals in an ultrasonic sending and detection system - a forerunner to present day sonar systems. Subsequently, other materials with piezoelectric properties were discovered. These included the crystal Rochelle salt [9], the ceramics lead barium titanate/zirconate (pzt) and barium titanate [10] and the polymer poly(vinylidene fluoride) [11]. Other polymers such as nylon 11 [12], poly(vinyl chloride) [13] and poly (vinyl fluoride) [14] exhibit piezoelectric behavior, but to a much smaller extent. Strain constants characterize the piezoelectric response. These relate a vector quantity, the electrical field, to a tensor quantity, the mechanical stress (or strain). In this convention, the film orientation direction is denoted by 1, the width by 2 and the thickness by 3. Thus, the piezoelectric strain constant dl3 refers to a polymer film held in the orientation direction with the electrical field applied parallel to the thickness or 3 direction. The requirements for observing piezoelectricity in materials are a non-symmetric unit cell and a net dipole movement in the structure. There are 32-point groups, but only 30 of these have non-symmetric unit cells and are therefore capable of exhibiting piezoelectricity. Further, only 10 out of these twenty point groups exhibit both piezoelectricity and pyroelectricity. The piezoelectric strain constant, d, is related to the piezoelectric stress coefficient, g, by... 

A thermoplastic composite pipe produced by the tape winding process consists of two building blocks the mandrel (wall thickness t , internal radius r ) and the load-bearing composite tape (thickness f ) wound under a winding angle a with respect to the axial direction of the pipe and restraining the mandrel (Figure 2). The extruded mandrel is based on one constituent only, i.e. a viscoelastic polymer of the stress/strain response described by ct = f A, B, C, e). The three parameters are relatable to the initial stiffness and the coordinates of the yield point. The... 

The microlenses of Holmes [17] were bistate types. Chandra et al. utilized a similar mechanism to fabricate a single component, strain-responsive microlens array capable of continuous focus tuning [19]. Figure 6.22 shows the fabrication of the array. A flat PDMS sheet 0.5 mm thick was prepared first. The sheet was clamped at four edges (Figure 6.22a) and then stretched to 20% strain in both planar directions simultaneously (Figure 6.22b). 

The general response observed as the mismatch strain was increased was a range of axially symmetric deformation, with the substrate midplane curvature becoming ever more nonuniform. Then, over a very narrow range of values of nominal mismatch strain, the midplane showed first a shght waviness in the circumferential direction (compared to substrate thickness) followed by large amplitude waviness in the circumferential direction. This behavior is illustrated in Figure 2.29 which shows plots of the normalized... 

During compression of polymeric foams, three characteristic stages of deformation are commonly observed. At low deformations, the polymer foam is in the linear elastic response regime, i.e., the stress increases linearly with deformation and the strain is recoverable. The second phase is characterized by continued deformation at relatively constant stress, known as the stress collapse plateau. And the final phase of deformation is densification where the foam begins to respond as a compacted solid. At this point the cellular structure within the material is collapsed, and further deformation requires compression of the solid foam material (Ouellet et al. 2006). As mentioned above, a specific technique is required to obtain stress-strain curves of ferroelectrets in thickness direction because the thickness in ferroelectrets is normally very thin, corresponding to very small defiections. Dansachmiiller et al. developed an experimental technique that allows obtaining the stress-strain curves in ferroelectret films (Dansachmiiller et al. 2005). This method may also be used to obtain the stress-stain curve for a polymer foam film without oriented macro-dipoles. The schematic of the experimental setup is shown in Fig. 4. 

Here the symbols po, L, y, and e(x) denote the density, the sample thickness, the electrostriction coefficient, and the piezoelectric strain coefficient. From Eqs. 24 and 25, one sees that from the current response J t) of the pressure pulse experiment, the direct image of the space-charge distribution p x) or the gradient of the piezoelectric coefficient can be deduced by using the simple transformation x = ct. 

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