Plastic zone size

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. 

Use Ae data in Table 2.2 to compare crack tip plastic zone sizes in acrylic, ABS and polypropylene. 

Where rj is the plastic zone size along the plane of the crack and perpendicular to the applied stress. The above two equations are only a first approximation as the plastic zone contributes to the crack size. The true plastic zone is twice the initial approximation. 

AGS may be expressed as proportional to compressive yield stress), yt (fracture strain), the plastic zone size, and the square of the concentration factor, K. The influence of hydrostatic pressure was taken into account with a modified von Mises criterion (Chapter 12). 

On the other hand, in glassy polymers the zone of crack tip yielding is often found to be a thin wedge rather than a circle. It is now well documented that a good description of the shape and size of this yielded zone at the crack tip can be provided by the plastic zone size model proposed by Dugdale and by the cohesive force model of Barenblatt " . Similar solutions and further developments have been contributed by other authors... 

Fig. 19a. Variation of plastic zone size in a 5 mm thick SEN-spechnen of HDPE al 0.5 mm below the surface, a2 l mm below the surface, a3 2 mm below the surface b Dog bone model of plastic zone radius, r, vs. SEN-specimen thickness (F = load)...

A third method which recently provided considerable insight into the role of crazes in deformation and fracture of amorphous polymers is the optical interference measurement of crazes (preceding a crack). Since the pioneer work of Kambour, this method has been widely used to determine characteristic craze dimensions and critical displacements. W. Doll gives an overview on recent results and on their interpretation in terms of fracture mechanics parameters (stress intensity factor, plastic zone sizes, fracture surface morphology, fracture energy). 

Fringe number of loaded craze Fringe number of unloaded craze Retarded fatigue crack growth Coordinate Plastic zone size... 

EWF determination. After the P-d traces were checked for self-similarity (satisfied by all the systems with post-yielding behaviour and even for PC), wp-L valid points were selected according to the mean value of Omax (Om) criteria 0.9o,n > Omax > 1 lOm [22], and plotted as shown in Fig. 5. In order to increase the accuracy of parameter determination, verification of the upper limit of valid ligamet length (Lmax) was made by the plastic zone size estimation (2rp), using the following relationship ... 

For small values of applied stress (a < 0.3 Oy), the plastic zone size is small compared with the crack length, and Eq. (12) reduces to ... 

The increase in Gjc drown in Eq. (16) is due to a decrease in yield stress, which results in an increase in plastic zone size that is clearly visible as stress-whitening. The factors affecting yield stress in rubber-modified plastics are discussed in Section III. Temperature, strain rate, and rubber phase volume all control Gjc and /, through their influence upon yielding. 

As a result of stress redistribution due to yielding, plastic deformation is expected to extend further ahead of the crack tip than that indicated by the plastic zone correction factors. For simphcity, and to an acceptable degree of accuracy for engineering analyses, the plastic zone size is taken to be equal to twice the plastic zone correction factor, i.e.. 

In Chapters 2 and 3, the restrictions in the use of linear elastic fracture mechanics (LEFM) were discussed in terms of the dimensions of the crack and the body (specimen, component, or structure) relative to the size of the crack-tip plastic zone. Simple estimates of the plastic zone sizes were given in Section 3.6. A more detailed examination of the role of constraint (plane strain versus plane stress) and the variations in plastic zone size from the surface to the interior of a body would help in understanding fracture behavior and the design of practical specimens for measurements of fracture toughness. Note that the plastic zone size in actual materials... 

Figure 4.1. Estimated plastic zone sizes based on von Mises criterion for yielding (u = 0.3 for the plane strain case).

The key points to be gleaned from this exercise are that the plastic zone size depends on the state of stress (or constraint) and is proportional to (Ki/oys). Its size is expected to vary through the thickness of a plate, and it would increase with increasing stress intensity factor Kj and decreasing yield strength ays. The consequence of plastic deformation on fracture behavior and fracture toughness measurements is considered briefly in the next section. 

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