Crazing in glassy polymers

Equations (12.3) imply that there is an infinite stress at the crack tip. In practice this clearly cannot be so, and there are two possibilities. First, there can be a zone where shear yielding of the polymer occurs. In principle this can occur in both thin sheets where conditions of plane stress pertain and in thick sheets where there is a plane strain. Secondly, for thick specimens under conditions of plane strain, the stress singularity at the crack tip can be released by the formation of a craze, which is a line zone, in contrast to the approximately oval (plane stress) or kidneyshaped (plane strain) shear yield zones. As indicated, its shape approximates very well to the idealized Dugdale plastic zone where the stress singularity at the crack tip is cancelled by the superposition of a second stress field in which the stresses are compressive along the length of the crack (Fig. 12.8). A constant compressive stress is assumed and is identified with the craze stress. It is not the yield stress, 

Rice [21] has shown that the length of the craze for a loaded crack on the point of propagation is 

The eraek opening displaeement (COD) dt is the value of the separation distanee d at the eraek tip, where x = 0, and is therefore 

An alternative approach [24] assumes an additivity rule based on a plane strain K c, which pertains to fracture in the central part of the specimen and is designated ic, and a plane stress K c, which is effective for the two surface skins of depth w/2 and is designated K ic- For the overall specimen it is then proposed that 

Although Equation (12.18a) is more empirically based than Equation (12.18) and is not formally equivalent, it has been shown to model fracture results very well. Moreover, in this formulation w relates to the size of the so-called Irwin plastic zone Ty, which can be defined simply on the basis of Equation (12.3) by assuming that a point Vy the stress reaches the yield stress Oy. Hence 

The influence of temperature on the stress-strain behavior of polymers is generally opposite to that of straining rates. This is not surprising in view of the correspondence of time and temperature in the linear viscoelastic region (Section I l.5.2.iii). The curves in Fig. 11-23 are representative of the behavior of a partially crystalline plastic. 

Glassy polymers with highercohesiveness, like polycarbonate and cross-linked epoxies, preferentially exhibit shear yielding [7], and some materials, such as rubber-modified polypropylene, can either craze or shear yield, depending on the deformation conditions [8]. Application of a stress imparts energy to a body which 

Craze formation is a dominant mechanism in the toughening of glassy polymers by elastomers in polyblends. Examples are high-impact polystyrene (HIPS), impact poly(vinyl chloride), and ABS (acrylonitrile-butadiene-styrene) polymers. Polystyrene and styrene-acrylonitrile (SAN) copolymers fracture at strains of 10 , whereas rubber-modified grades of these polymers (e.g., HIPS and ABS) form many crazes before breaking at strains around 0.5. Rubbery particles in 

This approach offers a deeper understanding of the brittle-ductile transition in glassy polymers in terms of competition between crazing and yielding. Both are activated processes, in general with different temperature and strain rate sensitivities, and one will be favoured over the other for some conditions and vice versa for other conditions. An additional complexity can arise from the nature of the stress field that may favour one process rather than the other, but the latter consideration does not enter into our discussion of the 

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Kramer EJ, Bubeck RA (1978) Growth kinetics of solvent crazes in glassy polymers. J Polym Sci Polym Phys 16(7) 1195-1217... 

Typical values for crazes in glassy polymers [29,30,38] are a few microns in thickness and tenths of millimeters in length. The measures of Acr and Ac are used by Brown and Ward [38] to estimate the toughness and the craze... 

M. Narkis, Crazing in glassy polymers. Polymer-glass bead composites, Polym. Eng. Sci. 15 (1975) 316-320. 

A generic FENE model has also been used to study crazing in glassy polymers (383), with the resulting pictures looking very much hke what one sees in micrographs. Earlier work with a 2-D lattice model of a cross-linked system exhibited much the same phenomena (384). 

This approach incorporates the stress-concentrating effect of cross-tie fibrils, widely observed in crazes in glassy polymers (compare Figure 14.14). In the absence of any stress-concentrating effect, that is, for a —> 0, a time-independent fibril failure criterion oy implies crack advance can never occur, because the stress in a given fibril can never exceed Oc- This result has been confirmed by more detailed micromechanical modeling, and is important in that it provides a direct link between the... 

Kambour, R.P. and Holik, A.S. (1969) Electron microscopy of crazes in glassy polymers - use of reinforcing impregnants during microtomy. J. Polym. Sci. A2,1,1393. 

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