Macroscopic Deformation

For materials which undergo large scale elastic-plastic deformation, macroscopic crack propagation is preceded by an amount of crack tip blunting. The macroscopic crack initiation point is thus not clearly defined. Many standards address this question ... 

The power of this technique can be illustrated in the measurement of segmental orientation when polymers are deformed macroscopically. Despite the tremendous improvement of signal-to-noise ratio available with the Fourier transform instrument, it has not been possible to measure extremely small changes in segment orientation as a function of strain. The usual polarization measurements involve two separate measurements, one parallel and one perpendicular, followed by calculation of their difference to obtain the dichroic ratio, and then the calculation of the orientation function (eq. 13). For nearly isotropic materials this type of measurement is of marginal value. However, with the polarization modulation technique it is possible to obtain extremely accurate polarization changes when samples are mechanically deformed. Extremely accurate polarization measurements can be obtained in this way, even for amorphous segments in poly(butylene terephthalate-co-tetramethylene oxide) (236). 

When materials are affected by external forces without inertial movement, their geometrical shapes and dimensions will change, and this change is called strain or deformation. When materials deform macroscopically their internal molecules and atoms relatively displace, which brings an additional force against external forces between molecules and atoms. When a balance is reached, the additional internal force is equal to external forces with opposite directions. The internal force per unit area is defined as strain, and its value is equal to that of the external forces. Materials deform in different ways when stressed differently. For the same material, there are three basic types of deformation simple tension, simple shear, and uniform compression. A material is in simple tension when it is affected by two forces that are perpendicular to the section, equal and opposite in direction, and in the same straight line a material has a sheer reaction when it is affected by two forces that are parallel to the section, in equal and opposite direction, and at different straight lines. Uniform compression occurs when the material is surrounded by stress p and the volume decreases. 

In fact, if a weak electrolyte gel such as a poly(acrylic acid) is deformed, macroscopic dielectric polarization is observed. This results from the stretching of polymer chains by the deformation and resultant automatic acceleration of ionization. Utilizing this phenomenon, it is possible to develop a piezoelement that converts deformational stress into electrical energy. A pressure sensor whose diode emits light when the gel is pressed and an artificial contact sensing device also have been proposed [20]. 

To properly restrict the strain energy we allov our system to deform macroscopically from spherical bodies into ellipsoids. Utilizing the invariant quantities associated with the strain tensor mn the simplest form of the equation of constraint can be put into the following form (See Appendix I). 

A constitutive equation is a relation between the extra stress (t) and the rate of deformation that a fluid experiences as it flows. Therefore, theoretically, the constitutive equation of a fluid characterises its macroscopic deformation behaviour under different flow conditions. It is reasonable to assume that the macroscopic behaviour of a fluid mainly depends on its microscopic structure. However, it is extremely difficult, if not impossible, to establish exact quantitative... 

Foams that ate relatively stable on experimentally accessible time scales can be considered a form of matter but defy classification as either soHd, Hquid, or vapor. They are sol id-1 ike in being able to support shear elastically they are Hquid-like in being able to flow and deform into arbitrary shapes and they are vapor-like in being highly compressible. The theology of foams is thus both complex and unique, and makes possible a variety of important appHcations. Many features of foam theology can be understood in terms of its microscopic stmcture and its response to macroscopically imposed forces. 

Fig. 2. The shape-memory process, where Tis temperature, (a) The cycle where the parent phase undergoes a self-accommodating martensite transformation on cooling to the 24 variants of martensite. No macroscopic shape change occurs. The variants coalesce under stress to a single martensite variant, resulting in deformation. Then, upon heating, they revert back to the original austenite crystallographic orientation, and reverse transformation, undergoing complete recovery to complete the cycle, (b) Shape deformation. Strain recovery is typically ca 7%.

This expression relates the action-at-a-distance forces between atoms to the macroscopic deformations and dominated adhesion theoiy for the next several decades. The advent of quantum mechanics allowed the interatomic interactions giving rise to particle adhesion to be understood in greater depth. 

As is true for macroscopic adhesion and mechanical testing experiments, nanoscale measurements do not a priori sense the intrinsic properties of surfaces or adhesive junctions. Instead, the measurements reflect a combination of interfacial chemistry (surface energy, covalent bonding), mechanics (elastic modulus, Poisson s ratio), and contact geometry (probe shape, radius). Furthermore, the probe/sample interaction may not only consist of elastic deformations, but may also include energy dissipation at the surface and/or in the bulk of the sample (or even within the measurement apparatus). Study of rate-dependent adhesion and mechanical properties is possible with both nanoindentation and... 

Perhaps the most significant complication in the interpretation of nanoscale adhesion and mechanical properties measurements is the fact that the contact sizes are below the optical limit ( 1 t,im). Macroscopic adhesion studies and mechanical property measurements often rely on optical observations of the contact, and many of the contact mechanics models are formulated around direct measurement of the contact area or radius as a function of experimentally controlled parameters, such as load or displacement. In studies of colloids, scanning electron microscopy (SEM) has been used to view particle/surface contact sizes from the side to measure contact radius [3]. However, such a configuration is not easily employed in AFM and nanoindentation studies, and undesirable surface interactions from charging or contamination may arise. For adhesion studies (e.g. Johnson-Kendall-Roberts (JKR) [4] and probe-tack tests [5,6]), the probe/sample contact area is monitored as a function of load or displacement. This allows evaluation of load/area or even stress/strain response [7] as well as comparison to and development of contact mechanics theories. Area measurements are also important in traditional indentation experiments, where hardness is determined by measuring the residual contact area of the deformation optically [8J. For micro- and nanoscale studies, the dimensions of both the contact and residual deformation (if any) are below the optical limit. 

Although the diffusion mechanism can be seen as mechanical but occurring at molecular dimensions, van der Waals intermolecular interactions and conformational entropic energy provide an additional mechanism that increases adhesion [62]. It is interesting to note the analogy that exists between this mechanism at the molecular level with the adherence, adhesion and viscoelastic deformations concept applied for a macroscopic adhesive. 

The defect question delineates solid behavior from liquid behavior. In liquid deformation, there is no fundamental need for an unusual deformation mechanism to explain the observed shock deformation. There may be superficial, macroscopic similarities between the shock deformation of solids and fluids, but the fundamental deformation questions differ in the two cases. Fluids may, in fact, be subjected to intense transient viscous shear stresses that can cause mechanically induced defects, but first-order behaviors do not require defects to provide a fundamental basis for interpretation of mechanical response data. 

The CEs, however, refer to the properties and reactions of macroscopic materials, made up of chemically deformed atoms ([7], p 142). 

Another example of the coupling between microscopic and macroscopic properties is the flexo-electric effect in liquid crystals [33] which was first predicted theoretically by Meyer [34] and later observed in MBBA [35], Here orientational deformations of the director give rise to spontaneous polarisation. In nematic materials, the induced polarisation is given by... 

The large deformability as shown in Figure 21.2, one of the main features of rubber, can be discussed in the category of continuum mechanics, which itself is complete theoretical framework. However, in the textbooks on rubber, we have to explain this feature with molecular theory. This would be the statistical mechanics of network structure where we encounter another serious pitfall and this is what we are concerned with in this chapter the assumption of affine deformation. The assumption is the core idea that appeared both in Gaussian network that treats infinitesimal deformation and in Mooney-Rivlin equation that treats large deformation. The microscopic deformation of a single polymer chain must be proportional to the macroscopic rubber deformation. However, the assumption is merely hypothesis and there is no experimental support. In summary, the theory of rubbery materials is built like a two-storied house of cards, without any experimental evidence on a single polymer chain entropic elasticity and affine deformation. 

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