Deformation schematic illustration

The resistance to plastic flow can be schematically illustrated by dashpots with characteristic viscosities. The resistance to deformations within the elastic regions can be characterized by elastic springs and spring force constants. In real fibers, in contrast to ideal fibers, the mechanical behavior is best characterized by simultaneous elastic and plastic deformations. Materials that undergo simultaneous elastic and plastic effects are said to be viscoelastic. Several models describing viscoelasticity in terms of springs and dashpots in various series and parallel combinations have been proposed. The concepts of elasticity, plasticity, and viscoelasticity have been the subjects of several excellent reviews (21,22). 

The physical processes that occur during indentation are schematically illustrated in Fig. 31. As the indenter is driven into the material, both elastic and plastic deformation occurs, which results in the formation of a hardness impression conforming to the shape of the indenter to some contact depth, h. During indenter withdrawal, only the elastic portion of the displacement is recovered, which facilitates the use of elastic solutions in modeling the contact process. 

Fig. 6a. Schematic illustration of deformation measurement of PVA-PAA gel film in electric fields, b Deflection curves of PVA-PAA gel film under sinusoidally varied electric fields...

This test has an inherent problem associated with the stress concentration and the non-linear plastic deformation induced by the loading nose of small diameter. This is schematically illustrated in Fig 3.17, where the effects of stress concentration in a thin specimen are compared with those in a thick specimen. Both specimens have the same span-to-depth ratio (SDR). The stress state is much more complex than the pure shear stress state predicted by the simple beam theory (Berg et al., 1972 ... 

Fig. 2. Schematic Illustration of the photolmmoblllzatlon of blomolecules (Immunoglobulin) on the surface of an azopolymer. The surface of the azopolymer Is deformed to the shape of the Immunoglobulin after photoirradlatlon.

Figure 5.9 Schematic illustration of plastic deformation in single crystals by (a) slip and (b) twinning. From Z. Jastrzebski, The Nature and Properties of Engineering Materials, 2nd ed. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

Some crystals exhibit a texture called a center-cross pattern, the origin of which was, at one time, a subject of controversy, as to whether the origin was by growth or by plastic deformation. The center-cross pattern is schematically illustrated in Fig. 9.12 it corresponds to a texture shown by the growth sectors of two coexisting crystal faces, lll and 100. This pattern indicates that the arms of the cross correspond to the growth sectors of 100, which disappear at the later stage of... 

Schematic illustration of the difference between shape memory and superelastic effects. For shape memory, the deformation occurs at a temperature for which the material is martensitic. A superelastic effect occurs when the deformation occurs just above the Af temperature. From J. A. Shaw, Int. J. Plasticity 16 (2000) 542. 

Besides deformation, fracture is the other response of materials to a stress. Fracture is the stress-induced breakup of a material. Two types of fracture are commonly defined. A brittle fracture is breakup which occurs abruptly without localized reduction in area. A ductile fracture is the failure of the material which is preceded by appreciable plastic deformation and localized reduction in area (necked region). The brittle fracture and ductile fracture are schematically illustrated in Fig. 1.10. 

Fig. 10.31. Schematic illustration of deformation gradients in different wells for the cubic to tetragonal transformation that satisfy the rank-one connection condition (adapted from Ball and James (1992)).

FIGURE 10.32 Interfacial rheology. Schematic illustration of various types of deformation of a square surface element and the approximate result for the force (F) needed for deformation as a function of the concentration of surfactant (c). In (a) the surface element is seen in perspective, in (b) and (c) from above. A — area of surface element, f = surface excess. 

The friction of polymers or CMP processes can be attributed to two major sources in mixed modes deformation involving the dissipation of energy in quite a large volume around the local area of contact, and adhesion originating from the interface between the wafer and the pads (brush). The details of the deformation and adhesion will be discussed in Chapter 5, along with a clear schematic illustration. 

The DNF model incorporates the experimentally observed characteristics by using a micromechanism-inspired approach in which the material behavior is decomposed into a viscoplastic response, corresponding to irreversible molecular chain sliding due to the lack of chemical crosslinks in the material, and atime-dependent viscoelastic response. The viscoelastic response is further decomposed into the response of two molecular networks acting in parallel the first network (A) captures the equilibrium response and the second network (B) the time-dependent deviation from the viscoelastic equilibrium state. A onedimensional rheological representation of the model framework and a schematic illustrating the kinematics of deformation are shown in Fig. 11.6. 

Fig. 14.6 (a) Schematic illustration of selective superplasticity, where only the region undergoing superplastic deformation is fric- tion stir processed (FSPed). (b) Brighter areas in the commercial 7075 Al rolled sheet are selected to be FSPed to... 

FIGURE 39.3 Schematic illustration of three types of film response (a)elastic half-space behavior, dominated by bulk compression of the film, (b) plate behavior, dominated by bending deformation of the film, and (c) membrane behavior, dominated by axial stretching of the film. 

Fig. 10 Schematic illustration of the experimental setup (A), photographs of LCP films exhibiting photoinduced deformation (B), and schematic illustrations of the photoinduced deformation...

Large plastic deformation can be identified by the accumulation of slips at the macroscopic scale as well as at the atomic scale. During tensile deformation, metal blocks slip on slip planes and rotate, as schematically illustrated in Fig. 1. Increasing plastic deformation results in numerous cross slips. Such slips can be observed as Luders bands in annealed low-carbon steel subjected to tensile deformation. 

Figure 10.15. Schematic illustrations of theories of stress softening, (a) Mullins and Tobin (1956) considered the filled rubber as a heterogeneous system comprised of hard and soft phases. Deformation breaks down the hard phase, but the degree of breakdown depends on the maximum extension of the sample, (b) F. Bueche (1965) attributed stress-softening to the breakage of network chains attached to adjacent filler particles (A molecule breaks first), (c) Dannenberg (1966) and Boonstra (1965) suggested that reinforcement can be understood through chain slippage mechanisms. The slippage is shown by the chain marks. (Smith and Rinde, 1969.)...

Figure 12.13. Schematic illustration of plastic zone (extensive deformation) at tip of a crack. Actual shape may vary from shape shown.

FIGURE 7.4. Schematic illustration of plastic deformation and flow under load at points of contact between asperities of a soft material and a relatively hard surface. 

FIGURE 10 Schematic illustration of compound Taylor cone formation (A) Surface charges on the sheath solution, (B) viscous drag exerted on the core by the deformed sheath droplet, (C) Sheath-core compound Taylor cone formed due to continuous viscous drag). 

---