Tension triaxial

For an externally applied pressure, a compression-compression stress field is obtained with a thick-walled sphere. If the sphere wall is thin, a biaxial field is produced. If the pressure is applied internally, a triaxial tension-tension-compression state is generated. A nearly uniform stress field is produced over the entire specimen. The supporting tube is surrounded with a low modulus material to avoid stress concentration and... 

If the particle is bonded firmly to the matrix (we will discuss this point later), the initial uniaxial tension stress is changed into a triaxial tension stress field, due to the low rubber incompressibility. The stress field around rubbery particles is not the same as that around a void. 

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. 

When a thin bonded block is subjected to tensile loading, a state of approximately equal triaxial tension is set up in the central region of the block. The magnitude of the stress in each direction is given by the tensile stress, or negative pressure, <72 at r = 0 that is, Eea /h, from Eq. (1.32). Under this outwardly directed tension a small cavity in the central region of the block will expand indefinitely at a critical value of the tension, of about 5 /6. Thus, if cavities are present in the interior of a bonded block, they are predicted to expand indefinitely (i.e., rupture) at a critical tensile strain Cc, given approximately by... 

FIGURE 10.7 Expansion of a cavity under a triaxial tension. 

Cavitation near small rigid inclusions is more difficult to induce (Gent and Park, 1984), probably because the volume of rubber subjected to a critical triaxial tension is too small to contain relatively large precursor voids. And larger stresses are necessary to expand small voids less than about 0.5 p,m in diameter. 

If elastomers could be prepared without any microcavities greater than, say, 10 nm in radius, they would be much more resistant to cavitation. This seems an unlikely development, however, so Fq. (10.30) remains an important general fracture criterion for elastomers. It predicts a surprisingly low critical triaxial tension, of the order of only a few atmospheres, for soft, low-modulus elastomers. Conditions of triaxial tension should probably be avoided altogether in these cases. 

The critical stress predicted by Eq. (14) depends only on the elastic modulus and not at all on the strength of the elastomer. In agreement with this, cavitation stresses in bonded rubber blocks under tension (Figs. 8 and 9) [35], and near rigid inclusions, at points where a triaxial tension is set up (Figs. 

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