Crystal orientation strain behavior

However, when compared with pure copolymer, the highly stretched nanocomposite exhibited a higher amount of unoriented crystals, a lower degree of crystal orientation, and a higher amount of 7-crystals. This behavior indicated that polymer crystals in the filled nanocomposite experienced a reduced load, suggesting an effective load transfer from the matrix to MCNF. At elevated temperatures, the presence of MCNF resulted in a thermally stable physically cross-linked network, which facilitated strain-induced crystallization and led to a remarkable improvement in the mechanical properties. For example, the toughness of the 10 wt% nanocomposite was found to increase by a factor of 150 times at 55°C. Although nanofillers... 

Figure 6.21 Stress-strain behavior for a single crystal that is favorably oriented for plastic flow.

The stress-strain behavior of ceramic polycrystals is substantially different from single crystals. The same dislocation processes proceed within the individual grains but these must be constrained by the deformation of the adjacent grains. This constraint increases the difficulty of plastic deformation in polycrystals compared to the respective single crystals. As seen in Chapter 2, a general strain must involve six components, but only five will be independent at constant volume (e,=constant). This implies that a material must have at least five independent slip systems before it can undergo an arbitrary strain. A slip system is independent if the same strain cannot be obtained from a combination of slip on other systems. The lack of a sufficient number of independent slip systems is the reason why ceramics that are ductile when stressed in certain orientations as single crystals are often brittle as polycrystals. This scarcity of slip systems also leads to the formation of stress concentrations and subsequent crack formation. Various mechanisms have been postulated for crack nucleation by the pile-up of dislocations, as shown in Fig. 6.24. In these examples, the dislocation pile-up at a boundary or slip-band intersection leads to a stress concentration that is sufficient to nucleate a crack. 

Figure 17.7a shows the stress-strain behavior for a single crystal that is favorably oriented for plastic flow. This type of behavior is seen in MgO and other ceramics with a rocksalt structure. There are three distinct stages ... 

Figure 2. Effect of piezoelectric anisotropy on the single-crystal orientational behavior. Left inset embodies the polar response of the normalized piezoelectric behavior for different anisotropy factors. Note that the optimal orientation changes as the degree of anisotropy increases. Left inset shows the optimal orientation of each single-crystal, as a function of crystallographic anisotropy. Note that contrary to what it is intuitively expected, in the limit of high anisotropy, A 2/3, the crystallographic orientation at which highest piezoelectric strains will occur will asymptotically align with the direction of the applied field. Furthermore, the optimal orientation for materials with weak anisotropy will asymptotically converge to 0=54.16°.

The manner in which a metal deforms after its yield strength has been exceeded by the applied stress depends on many factors. Parameters controlling the deformation process include the alloy s composition, its class (i.e., whether a, a -i- p, or P), its condition (i.e., whether quenched— e.g., P r, a + P-annealed, low-temperat ire aged, etc.), and the rate and temperature at which the deformation is carried out. Some observables or results of the deformation process include the anomalous stress-strain behavior alluded to above and discussed in Chapter 12,phase transformation under stress (i.e., transformation-assisted deformation), and texturization (i.e., the development of preferential crystal orientation or the formation of deformation cells or subbands in response to heavy cold work). 

Neither does the microbrownian motion of the amorphous mesh inhibit the liquid crystal phase, nor does the positional order of the molecules interfere with the elasticity. Hence, as a hybrid material that combines LC and rubber characteristics, LCEs have unique properties in which the molecular orientation of the liquid crystal is strongly correlated with the macroscopic shape (deformation) which is unparalleled to other materials. The most prominent example in the physical properties derived from this property is the huge thermal deformation. Figure 10.1 shows an example of the thermal deformation behavior of side-chain nematic elastomers (NE) [3]. When the molecules transform from the random orientation in the isotropic phase to the macroscopic planar orientation in the nematic phase, the rubber extends in the direction of the liquid crystal orientation and increases with decreasing temperature as a result of an increase in the degree of liquid crystal orientation. This thermal deformation behavior is reversible, and LCEs can be even considered as a shape-memory material. Figure 10.1 is from a report of the early research on thermal deformation of LCEs, and a strain of about 40 % was observed [3]. It is said that LCEs show the largest thermal effect of all materials, and it has been reported that the thermal deformation reaches about 400 % in a main-chain type NE [4]. 

Uniaxial tensile tests of poly (ethylene terephthalate) (PET)/montmorillonite(MMT) nanocomposites were preformed over a temperature range of 85°C-105°C and stretch rate of 7.5mm/s-12.5mm/s. The stress-strain curves consisted of three regions the hnear visoelasticity, the rubbery plateau and the strain hardening. The effects of temperature and stretch rate on stress-strain behavior were discussed. The results of differential scanning calorimetry (DSC) measurements indicated that the stretch lead the increase of the crystallinity degree of specimens. The wide angle X-ray diffraction (WAXD) measurements revealed that the more perfect crystal structures were obtained with the increase of temperature and oriented along the stretch direction. 

The effects of stretch rate on stress-strain behavior can be seen from Fig. 3. In the range between 85 °C to 95 °C, the stress level increases with the increase of stretch rate. At 105°C the stress-strain curves in three stretch rates are almost overlapped. It indicates that the effect of stretch rate on stress-strain behavior is small. This case can be explained as follows. There are two molecular chain motion mechanisms one is the molecular orientation the other is the chain relaxation. The different stress-strain behavior is the result of these two mechanisms completeness. At fast stretch rate and low temperature the molecular relaxation is inhibited. In other words the rate of molecular chain relaxation can not keep up with that of orientation, and therefore the stress level is high. Owing to the fast rate of quiescent crystallization, at 105°C, quite a few quiescent crystallization existed before stretching results the high stress level and lessen the effect of stretch rates. 

Figure 2.28 shows the orientation conventions for single crystals relative to orthogonal stress and strain axes for description of the elastic constants. Table 2.3 shows the form of the elastic constants for these crystal types. Comparing this table with Eq. (2.55), one can determine which elastic constants are equivalent and which are zero. For example, in the triclinic system, one can see that C2i=Ci2, etc., indicating the tensor is symmetric. Thus 21 elastic constants are needed to describe the linear elastic behavior of a triclinic crystal. In the hexagonal system one finds, in addition to symmetry of the tensor, that C, =C22, 13 23 44 55 I many other elastic constants are zero. 

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... 

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