Plasticity notch root

The criteria (Eqs. 11 and 12) are similar and are derived from studies on materials that are elastic at initiation of crazing, while more ductile materials like polycarbonate show a more pronounced sensitivity to the hydrostatic tension. This has been found experimentally by Ishikawa and coworkers [1, 27] for notched specimens of polycarbonate. Crazing appears ahead of the notch root, at the intersection of well-developed shear bands. From a slip fine field analysis, the tip of the plastic zone corresponds to the location of the maximum hydrostatic stress. This has been confirmed by Lai and Van der Giessen [8] with a more realistic material constitutive law. Therefore, Ishikawa and coworkers [1,27] suggested the use of a criterion for initiation based on a critical hydrostatic stress. Such a stress state condition can be expressed by Eq. 11 with erg = 0 and I r = B°/A°. Thus, the criterion (Eq. 11) can be considered general enough to describe craze initiation in many glassy polymers. For the case of polycarbonate, a similar criterion is proposed in [28] as... 

The mechanism for craze nucleation and growth describai here is essentially possible in semicrystalline polymers since the criterion is only related with a stress field due to plastic constraint. Therefore, the size and geometry of a local plastic zone at the notch root is responsible for the formation of crazes (sometimes named internal crazes by the authors). 

Consequently, the expansion of the plastic zone below the notch root induces the increase of the maximum bending moment even though the sample fractures in a brittle way. 

For a brittle glassy polymer like PMMA, the results for both sharp and blunted cracks are reproducible and show negligible scattering. The sharp cracks give a lower estimation of the toughness but this is not only related to a notch root effect. In the case of a blunt crack with notch radius of 250 micrometers, stress induced birefringence related to plasticity is observed... 

The latter can be determined experimentally if the response is in the form of LEFM or when plasticity is confined to yielding only at the notch root. 

Argon and Cohen 2003). However, if plasticity prevails at the notch root, the local strain rate there will be strongly accentuated and would be... 

These considerations show that the component does not fracture although it yields at the notch root. However, plastic deformation is confined to a small volume. The global deformation is thus small so that limited plastic flow in the notch root is also acceptable from this point of view. 

Still linear while kfis, applied when strains are well into the plastic domain. Walker [42] using aluminum specimens with lateral groves to maintain triaxiaUty also on the external surface, found that when notch root stresses remain elastic an analysis based on the theoretical stress concentration factor Iq with a triaxial cyclic stress-strain curve yields the same results as with the kf notch factor and an uniaxial stress-strain cyclic curve, as schematized in Fig. 6.29. 

When plastic deformation occurs at the notch root, Oy drops from its high elastic value to Oy M- Once the first imaginary tensile element at the notch root starts yielding, it deforms plastically at a constant volume that requires Poisson s value to be v = 0.5 instead of about 0.3 during elastic deformation. Therefore, a higher transverse stress, o = Ee = -E(v y) = -E[v(Oy/E)], will be developed to maintain the material continuity. The stress will also increase with the distance from the notch root more quickly than in the... 

In case of HDPE-1, there is very limited fibrillation observed on the crack surface close to notch root (initiation stage of ES crack). Unlike HDPE-1, larger fibrillation is observed in HDPE-2 even at the initiation stage of ES crack. It can be concluded that more plasticizing of fibrils in the process zone is possible for HDPE-2, perhaps related with a larger amount of diffusion/permeation of IGEPAL solution. 

The stresses near the root of a notch are extremely complex and the stress analysis becomes exceedingly difficult when the strain is large, as is the case when yield or failure is imminent. A sharp notch causes constraints and introduces a state of triaxial tension behind the root of the notch (5). This state of stress is consistent with LeGrand s observation of the growth of a flaw behind a notch in a bar of polycarbonate (4). A blunt notch causes constraints when the thickness of the specimen is large. Such a notch can also introduce a state of triaxial tension. While it is desirable to investigate the behavior of polymers in a well-defined state of triaxial tension, it is difficult to accomplish experimentally. However, as we demonstate below, a state of plane strain is relatively easy to produce. The relationship between plane strain and brittleness of plastics is the subject of our investigation. 

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