Elastic and plastic deformation

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). 

A hardness indentation causes both elastic and plastic deformations which activate certain strengthening mechanisms in metals. Dislocations created by the deformation result in strain hardening of metals. Thus the indentation hardness test, which is a measure of resistance to deformation, is affected by the rate of strain hardening. 

Collectively, the shock/release sequence amounts to a single cycle stress/ strain path change excursion with elastic and plastic deformation operative during both loading and unloading. 

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. 

The mechanical properties of materials, though not often studied in detail, can have a profound effect on solids processing. Clearly, tableting properties are influenced by the elastic and plastic deformation properties as well as the viscoelastic properties of a material. As we have pointed out, the powder flow properties are also affected, as well as the tendency of materials to set up on storage. Because of the importance of mechanical properties, it is important to be able to... 

Figure 5.8 Illustration of (a) ideal elastic deformation followed by ideal plastic deformation and (b) typical elastic and plastic deformation in rigid bodies. 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.

This chapter is concerned with the influence of mechanical stress upon the chemical processes in solids. The most important properties to consider are elasticity and plasticity. We wish, for example, to understand how reaction kinetics and transport in crystalline systems respond to homogeneous or inhomogeneous elastic and plastic deformations [A.P. Chupakhin, et al. (1987)]. An example of such a process influenced by stress is the photoisomerization of a [Co(NH3)5N02]C12 crystal set under a (uniaxial) chemical load [E.V. Boldyreva, A. A. Sidelnikov (1987)]. The kinetics of the isomerization of the N02 group is noticeably different when the crystal is not stressed. An example of the influence of an inhomogeneous stress field on transport is the redistribution of solute atoms or point defects around dislocations created by plastic deformation. 

Three important properties can be inferred from the tensile test i.e. elastic limit (i.e. the point of maximum elastic elongation), tensile strength and E-modulus. In many cases the transition point between the elastic and plastic deformation is not visible in the graph. For that reason it has been determined that this point is situated at an value of 0.002 and the accompanying tensile stress is determined as represented in figure 10.9. 

Fig. 10.9 Transition between elastic and plastic deformation (0.2% elastic limit).

First, for both elastic and plastic deformation, we have... 

Brittle erosion is the loss of material from a solid surface due to fatigue cracking and brittle cracking caused by the normal collisional force Fn. Materials with very limited capacity for elastic and plastic deformation, such as ceramics and glass, respond to particle impacts by fracturing. The yield stress for brittle failure Fb for normal impacts is about... 

PROCESSES The two surfaces may contact each other. Elastic and plastic deformation. Frictional heat. Wear. EXOEMISSION Triboemission (radicals, electrons, photons, positive ions, X-ray emission). After-emission electrons. STRUCTURE Upper layer long chain polyphosphates. Lower layer short chain polyphosphates. 

Nascent surface Explain the difference in the concept of liquid lubrication mechanism in (a) hydrodynamic, (b) elastohydrodynamic and (c) boundary lubrication. Which of the following characterize (a), (b), and (c) lubrication regime continuous fluid film, negligible deformation, complete separation of the surfaces, elastic and plastic deformation, no wear takes place, no contact between the sliding surfaces, involving surface topography, physical and chemical adsorption, catalysis and reaction kinetics, and tribochemical film formation ... 

Errors are a result of the elastic and plastic nature of the ceramic particles themselves. Several other authors [81,82] have calculated the pressure distribution in cylindrical dies and other forms using finite element numerical methods. Bortzmeyer [81] has incorporated cohesion, elastic, and plastic deformation of the particles into finite element calculations for more complicated geometries, as shown in... 

Fixed arm peel and T-peel test procedures are used to measure peel strength for flexible laminates. Analysis of the contributions from elastic and plastic deformations of the peel arms during these tests enables the energy contribution from plastic effects to be subtracted from the energy required to peel the laminate. In this way, the adhesive fracture toughness is determined. 

A deformation, which does not totally recover after the stress is released, is a plastic deformation. Elastic and plastic deformations can occur simultaneously, but one effect usually predominates. 

For elastic perfectly plastic models there is no elastic deformation in the post-yielding phase however, with the power law strain hardening there is continued elastic and plastic deformation combined. The extent of elastic and plastic deformation post-yielding can be determined by looking at. some arbitrary stress a as shown on Figure 17B. For this stress the elastic and plastic deformations are... 

Elastic and plastic deformations flatten the contact regions into micrometer-scale patches, which are many times larger than molecular scales. The static friction corresponds to an average yield stress within these contacts of ts - Fs/Areai, and a similar relation gives the local shear stress Tt corresponding to the kinetic friction. Experimental studies of a wide range of materials indicate that T rises linearly with the local pressure P [35 40] ... 

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