Plastic zone Plasticizers

For extensometers BH156, a difference can be observed in the response of Anchor 4 at very early times the ubiquitous joint model predicts, as is observed in the experiment, a very limited negative displacement, smaller than the elastic model, which indicates that some plastic deformation occurs. This is confirmed by looking at calculated contours of plastic zones plastic shear develops at the drift boundary as early as 3 months. For this extensometer, the right order of magnitude is predicted for Anchor 3 and 4, with an excellent agreement for Anchor 4 using the ubiquitous joint model. 

In the previous sections, it was frequently stressed that linear-elastic fracture mechanics can only be used if the plastic zone near the crack tip is sufficiently small. If this is not the case, we enter the domain of elastic-plastic fracture mechanics (epfm) which can deal with a large plastic zone. The method, however, cannot be used for arbitrarily large plastic zones - plastic behaviour must stiU be restricted to the region around the crack tip and must be mainly determined by the surrounding elastic stress field. 

Fig. 4. (a) The crack tip plastic zone and (b) the Dugdale plastic zone model. Terms are defined in text. 

The distance from the crack tip, along the X-axis, at which the von Mises equivalent stress falls below the yield stress, defines the size of the plastic zone, r. For the plane stress case of unconstrained yielding, which corresponds to the free surface of the specimen in Figure 4, this gives... 

The process zone is a measure of the yield stress or plasticity of the material in comparison to its brittleness. Yielding within the process zone may take place either plastically or by dimise microcracking, depending on the brittleness of the material. For plastic yielding, / is also referred to as the plastic zone size. 

A ubiquitous feature accompanying large deformations in inelastic materials is the appearance of various instabilities. For example, plastic deformation may lead to shear banding, and the development of damage frequently leads to the formation of fault zones. As remarked in Section 5.2.7, normality conditions derived from the work assumption may imply stability which is too strong for such cases. Physical instabilities are likely to be associated with loss of normality and violation of the work assumption. 

The crack propagates when K is equal to the width of the plastic zone, r,, is then given by eqn. (14.2) with K replaced by K. Note that the zone of plasticity shrinks... 

Cracks grow in the way shown in Fig. 15.9. In a pure metal or polymer (left-hand diagram), the tensile stress produces a plastic zone (Chapter 14) which makes the crack... 

We mentioned in Chapter 14 that real engineering alloys always have little inclusions in them. Then (right-hand diagram of Fig. 15.9), within the plastic zone, holes form and link with each other, and with the crack tip. The crack now advances a little faster than before, aided by the holes. 

In metals, inelastic deformation occurs at the crack tip, yielding a plastic zone. Smith [34] has argued that the elastic stress intensity factor is adequate to describe the crack tip field condition if the inelastic zone is limited in size compared with the near crack tip field, which is then assumed to dominate the crack tip inelastic response. He suggested that the inelastic zone be 1/5 of the size of the near crack tip elastic field (a/10). This restriction is in accordance with the generally accepted limitation on the maximum size of the plastic zone allowed in a valid fracture toughness test [35,36]. For the case of crack propagation, the minimum crack size for which continuum considerations hold should be at least 50 x (r ,J. 

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... 

In the case of metals, R is mainly plastic energy associated with the formation of a crack tip plastic zone. It is obvious from Eq. 9 that, for plane stress,... 

The second physical quantity of interest is, r t = 90 pm, the critical crack tip stress field dimension. Irwin s analysis of the crack tip process zone dimension for an elastic-perfectly plastic material began with the perfectly elastic crack tip stress field solution of Eq. 1 and allowed for stress redistribution to account for the fact that the near crack tip field would be limited to Oj . The net result of this analysis is that the crack tip inelastic zone was nearly twice that predicted by Eq. 3, such that... 

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