Plastic deformation zone

Various models 1-2,42 43) have been proposed to describe the extent and shape of the localised plastic deformation zone at the crack tip. From these models one may define a parameter known as the crack opening displacement, 5, (see Fig. 16) and the value of 5,c for the onset of crack growth is given by... 

Extensive theoretical investigations devoted to calculation of residual stresses have been carried out for metals. The principal theme of this work is assumption that residual stresses and strains are the result of differences between pure elastic and elastic-plastic deformations under fixed loading.127 128 The same mechanism, i.e., the appearance of plastic deformed zones, is responsible for the residual stresses arising during crystallization of metals, which occurs on quenching from the melt or cooling after welding. 

The presence of residual elastic stresses is inevitable in a surface which contains a plastically deformed zone whose thickness is limited compared with that of the bulk s pecimen. Alternatively, the relief of these stresses may cause distortion of the specimens in cases where the thickness of the two is comparable. Very little work has been done on this important subject and, so far as can be ascertained, none that can be related to the complexities of die plastically-deformed layer. Considerable complications are introduced because the residual stresses may be of thermal as well as mechanical origin and because those of mechanical origin may be altered by the thermal effects. 

Figure 9.21. Schematic diagram of a microcrack-ladder showing the longitudinal array of inclusions parallel to the applied stress, the horizontal unloading fractures within the plastically deformed zone, and the surrounding undeformed crystal. (From Fitz Gerald et al. 1990.)...

The semi-ductile behaviour observed with 30 wt% of fibres (Fig. 7) is explained by the superposition of different damage mechanisms (i) the overlapping of the plastic deformation zones of adjacent fibres (ii) generation of deformation bands in the small matrix hiytrs... 

Figure 9a shows a typical load-loadline displacement curve of a nylon compact tensiiin specimen. The slight deviation from linear elastic behaviour prior to fracture relates to the presence of a plastic deformation zone confined near the pre-crack tip (Fig. 9b). This stable crack propagation domain is adjoining a wide hackle zone (rapid crack growth domain) characteristic of a brittle fracture.

The question now is how much nonlinearity is considered to be not excessive. Formally, the nonlinearity should not exceed that which would correspond to an increase in the initial (or physical) crack diameter (2ao) by the plane strain plastic zone correction factor i.e., by Iriy (see Eqn. (3.49)). Physically, it is acceptance of the fact that a plastically deformed zone would develop at the crack tip, and its presence is equivalent to a change in the effective crack length at the onset of fracture from Itto to Itto -I- 2riy i.e.,... 

The initial compression and plastic deformation zone. This zone begins about 90 m in front of the face. As the face advances, the top coal undergoes vertical compression and deformation under the influence of the initial coal mining operation. The deformation is derived mainly from the compression of the inherent horizontal fractures in the coal seam. As the face continues to advance, the front abutment pressure also continues to increase, plastic deformation and lateral deformation begin to occur in the top coal. This process produces micro-cracks in the coal. Field measurements showed that there are no bed separations between the immediate roof and top coal, and within the top coal. 

The front abutment zone of the top coal in panel 21121 could be divided into four zones Initial compression and plastic deformation zone, intensive compression and damage zone, roof rotation action zone, and shield supports action zone. 

To be able to compare grain size and indentation size influences, the size of the plastically deformed zone must be known. This information comes from TEM investigations where an approximately constant ratio 2R /2a 4-5 between the plastic zone size 2/ pi and the length of the Vickers diagonals 2a can be derived for single as well as po/ycrystalline ceramics and for hard materials with fundamentally different bonding like (ionic) alumina [2] and (covalent) SiC [8]. 

As shown in Figure 9.8 and Figure 9.9, directly under the grit, a plastically deformed zone can be noticed. Two principal crack systems are generated in the process. These are median/radial cracks and lateral cracks. The brittle mode removal of material is because of the formation and propagation of these lateral cracks. 

Provided these conditions are met, the spatial extent of the plastically deformed zone at the crack tip is less than 2% of the above dimensions, the specimen fractures in plane-strain and the measured is a true material property. 

Shear yielding in any plastically deformed zone will further protect against immediate and catastrophic crack growth and, finally, microcracking, or crazing, will help dissipate stress concentrations. 

Figure 11.16 Effect of plastic deformation on stress intensity at crack tip (a) in the absence and (h) in the presence of a plastic deformation zone (schematic).

This applies only to the plane state of stress. In a state of plane strain, all three main stress components occur and the stress profiles within the plastic deformation zone may be more complicated. 

In the discussion so far we have considered only linear elastic fracture mechanics (LEFM) the term linear elastic means that the cracked specimen obeys Hooke s law to a good approximation. In the context of fracture mechanics, the requirement is that the extent of yielding in the neighbourhood of the crack tip is negligible, so that the force-deflection curves for test specimens are linear. In addition, the value of B must be sufficiently high that the deformation at the crack tip occurs under plane-strain conditions. It is found experimentally that these conditions are met if B, (IV — a), and a are all greater than 2.5(K,c/ffy). Provided these conditions are met, the spatial extent of the plastically deformed zone at the crack tip is less than 2 % of the above dimensions, the specimen fractures in plane-strain and the measured is a true material property. 

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