Crystals plastic deformation

However, at lower constant loads the rate of crystal plastic deformation decreases and (at 80 °C) disentanglement becomes competitive leading to the development of isolated planar craze-like defects extending perpendicular to the tensile axis (Fig. 15). The ensuing concentration of stress will further localize most of the sample deformation in such creep crazes and lead to a macroscopic ductile-brittle transition—in this material observed at 20 MPa (Fig. 14 [67]). 

The main difference between a solid and a liquid is that the molecules in a solid are not mobile. Therefore, as Gibbs already noted, the work required to create new surface area depends on the way the new solid surface is formed [ 121. Plastic deformations are possible for solids too. An example is the cleavage of a crystal. Plastic deformations are described by the surface tension y also called superficial work, The surface tension may be defined as the reversible work at constant elastic strain, temperature, electric field, and chemical potential required to form a unit area of new surface. It is a scalar quantity. The surface tension is usually measured in adhesion and adsorption experiments. 

As a result of these arguments, within the confines of continuum models of single crystal plastic deformation, the total plastic strain rate can be written as... 

The method of molecular dynamics (MD) provides a remarkable opportunity for the observation of various mechanisms of processes taking place on a micro-(nano-) level, and for the evaluation of the probability of such processes by repeating experiments dozens of times. Figure IX-37 shows the MD simulation of the deformation and fracture of a two-dimensional crystal. Plastic deformation and formation of a dislocation (AB) at elevated temperature (upper part) and the formation of a brittle crack at low temperature (lower part) are shown in Fig. IX-37, a, while simultaneous processes of crack nucleation influenced by the presence of foreign atoms, and their propagation to the tip of the crack, taking place at elevated temperature, are illustrated in both lower and upper portions of Fig. IX-37, b [40,41]. 

In many crystals, plastic deformation occurs by movement of partial dislocations. What defect arises from this phenomenon ... 

Gleason, G.G. DeSisto, S. (2008). A natural example of crystal-plastic deformation enhancing the incorporation of water into quartz. Tectonophysics, Vol. 446, pp. 16-30 Goldman, D.S. Rossman, G.R. (1977). Channel constituents in cordierite. American Mineralogist, Vol. 62, pp. 1144-1157... 

It is reasonable to assume that a solid will deform in an affine manner this is the elastic assumption. Note that in metal crystals plastic deformation by dislocation glide on slip planes is not affine. The crystal between the slip planes is not plastically distorted all the deformation occurs at the slip plane. 

It was shown that for most crystalline polymers, including polypropylene and other polyolefins, the tensile drawing proceeds at a much lower stress than kinematically similar channel die compression [10,17]. Lower stress in tension was always associated with cavitation of the material. Usually a cavitating polymer is characterized by larger and more perfect lamellar crystals and cavities are formed in the amorphous phase before plastic yielding of crystals. If the lamellar crystals are thin and defected then the critical shear stress for crystal plastic deformation is resolved at a stress lower than the stress needed for cavitation. Then voiding is not activated. An example of such behavior is low density polyethylene [10]. 

At the microscale, dislocation dynamics simulations implement the equations of continuum elasticity theory to track the motion and interaction of individual dislocations under an applied stress, leading to the development of a dislocation microstructure and single-crystal plastic deformation. In our multiscale modeling... 

In response to an apphed tensile or compressive stress, slip in a single crystal commences on the most favorably oriented shp system when the resolved shear stress reaches some critical value, termed the critical resolved shear stress it represents the minimmn shear stress required to initiate slip and is a property of the material that determines when yielding occurs. The single crystal plastically deforms or yields when T (max) = t ss, and the magnitude of the apphed stress required to initiate yielding (i.e., the yield strength o-y) is... 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Explain briefly what is meant by a dislocation. Show with diagrams how the motion of (a) an edge dislocation and (b) a screw dislocation can lead to the plastic deformation of a crystal under an applied shear stress. Show how dislocations can account for the following observations ... 

Crystal growth. As we saw in the preceding section, before World War II the dislocation pioneers came to the concept through the enormous disparity between calculated and measured elastic limiting stresses that led to plastic deformation. The same kind of disparity again led to another remarkable leap of imagination in postwar materials science. 

Probably the first to take up this technique for purposes of scientific research was Michael Polanyi (1891-1976) who in 1922-1923, with the metallurgist Erich Schmid (1896-1983) and the polymer scientist-to-be Hermann Mark (1895-1992), studied the plastic deformation of metal crystals, at the Institute of Fibre Chemistry in Berlin-Dahlem in those days, good scientists often earned striking freedom to follow their instincts where they led, irrespective of their nominal specialisms or the stated objective of their place of work. In a splendid autobiographical account of those... 

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