Inelastic plasticity, mechanisms

Indeed the radius in front of the crack tip is not zero and inelastic deformation mechanisms, such as local plasticity or crazes, can be initiated at the crack tip. This is particularly true in heterogeneous polymers such as those investigated here, in which very small size inclusions initiate local plasticity in interparticle domains, even when the external stress applied is well below the yield stress of the neat matrix. 

As it has been noted in chapter five, the local plasticity zone type defines the fracture type if a craze forms at critical defect tip, then polymer failed quasibrittle and if deformation zone (ZD) or local shear yielding zone ( shear lips ) - then quasiductile [13]. The inelastic deformation mechanism change is considered as brittle-ductile transition [14]. The treatment of the indicated tiarrsition will be considered below within the frameworks of both cluster model and solid body synergetics. 

A formal theory of inelastic compression is presented in one of the chapters, which rigorously lays out the theoretical foundations and provides a rational mechanics framework for describing the plastic compression prop-... 

The utility of K or any elastic plastic fracture mechanics (EPFM) parameter to describe the mechanical driving force for crack growth is based on the ability of that parameter to characterize the stress-strain conditions at the crack tip in a maimer which accounts for a variety of crack lengths, component geometries and loading conditions. Equal values of K should correspond to equal crack tip stress-strain conditions and, consequently, to equivalent crack growth behavior. In such a case we have mechanical similitude. Mechanical similitude implies equivalent crack tip inelastic zones and equivalent elastic stress fields. Fracture mechanics is... 

When the experimentalist set an ambitious objective to evaluate micromechanical properties quantitatively, he will predictably encounter a few fundamental problems. At first, the continuum description which is usually used in contact mechanics might be not applicable for contact areas as small as 1 -10 nm [116,117]. Secondly, since most of the polymers demonstrate a combination of elastic and viscous behaviour, an appropriate model is required to derive the contact area and the stress field upon indentation a viscoelastic and adhesive sample [116,120]. In this case, the duration of the contact and the scanning rate are not unimportant parameters. Moreover, bending of the cantilever results in a complicated motion of the tip including compression, shear and friction effects [131,132]. Third, plastic or inelastic deformation has to be taken into account in data interpretation. Concerning experimental conditions, the most important is to perform a set of calibrations procedures which includes the (x,y,z) calibration of the piezoelectric transducers, the determination of the spring constants of the cantilever, and the evaluation of the tip shape. The experimentalist has to eliminate surface contamination s and be certain about the chemical composition of the tip and the sample. 

We note from the outset that crazing, which is a form of cavitational localization of deformation, can be viewed as a form of transformation plasticity made possible by the long chain molecular nature of the material and the natural molecular entanglements that give rise to well-defined cavitational transformation strains. Therefore, we have called craze plasticity also dilatational plasticity. Thus, if well managed to avoid fracture in the fibrilated craze matter, crazing can be an attractive mechanism of inelastic deformation and a source of toughness. 

M. Becker, W. Hauger (1982). Granular material - Experimental realization of a plastic Cosserat continuum In Mechanics of Inelastic Media and Structures (eds. O. Mahrenholtz, A. Sawczuk), pp. 23-39. 

It is well known that the main mechanisms of inelastic deformation are shear yielding and multiple crazing in the rigid matrix phase, as well as cavitation in the soft dispersed phase in rubber-toughened plastics and multiphase polymers [42]. Eor many years, these mechanisms have been studied using microscopy techniques. 

Inelastic deformation can occur in crystalline materials by plastic flow . This behavior can lead to large permanent strains, in some cases, at rapid strain rates. In spite of the large strains, the materials retain crystallinity during the deformation process. Surface observations on single crystals often show the presence of lines and steps, such that it appears one portion of the crystal has slipped over another, as shown schematically in Fig. 6.1(a). The slip occurs on specific crystallographic planes in well-defined directions. Clearly, it is important to understand the mechanisms involved in such deformations and identify structural means to control this process. Permanent deformation can also be accomplished by twinning (Fig. 6.1(b)) but the emphasis in this book will be on plastic deformation by glide (slip). 

Demkowicz, M. J. and Argon, A. S. (2005b) Autocatalytic avalanches of unit inelastic shearing events are the mechanism of plastic deformation in amorphous silicon, Phys. Rev.,B, 72, 245206 (1-17). 

The crystalline phase follows a few independent slip systems in which classical crystal plasticity theories cannot be utilized to model them [93-95]. Similar to the metallic crystalline phases, inelastic deformation in crystalline polymeric systems follows three different mechanisms (a) crystallographic slip, (b) twining, and (c) Martensite transformations [96]. All these mechanisms leave the crystallographic axis inextensible and provide less than five independent... 

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