Fracture crazing and

Empirical criteria for the formation of crazes in multiaxial stress states, analogous to the von Mises criterion for yield [Eq. (59)], are based on the observation that crazing is absent in both compression and simple shear, which is reasonable given that one would expect cavitation to be favored by large values of p. A critical strain to craze, = A + B/p, is generally found to provide a reasonable description of craze nucleation, so that in terms of the principal stresses the criterion is given by Eq. (70), where A, B, C, and D are constants. 

The macroscopic properly of immediate practical concern is often not so much craze formation as fracture resistance. In a cracked specimen, stress is concentrated at the crack tip, and the local stress state depends on the crack length. For small global deformations, it may be expressed in terms of a stress intensity factor, K, given by Eq. (71), where a is the crack length and F is a dimensionless function of the specimen geometry [31, 32]. 

In many fracture mechanics-based approaches, crack advance is taken to occur when K reaches some critical value Kc (equivalent energy-based criteria are also widely used). Kc may then be measured using a pre-cracked specimen, in which a and hence K are well defined. In some cases (PMMA, for example) crack advance is observed to proceed via breakdown of a single craze at the crack tip. By modeling a craze as an orthotropic linear elastic body it has been shown that Kc is given by Eq. (72), where v is Poisson s ratio, a is related to the craze anisotropy, C7c is the draw stress normal to the craze-bulk interface, Vf is the fibril volume fraction in the craze, and oy is the stress to break a craze fibril [33]. 

The aim of this contribution has been to link the basic macroscopic phenomena associated with polymers with the unique features of their structure, the most obvious being the presence of long, flexible molecular chains. The important role of the conformational entropy of flexible chains, not only for rubber elasticity but for polymer dynamics in general, has been demonstrated. Moreover, the concept of an entanglement network, which underpins much of the theory of polymer dynamics in the melt, has also been shown to have important repercussions for the high strain behavior of solid polymers, namely plastic deformation, crazing, and fracture. 

WLF constant WLF constant [K] characteristic ratio tensile compliance [Pa ] craze fibril spacing [m] 

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Materials exposed to the out-of-doors are particularly vulnerable since they are exposed to a higher concentration of chemicals (such as SOj, HC1, and Oj) ultraviolet radiation, which promotes many chemical reactions and moisture, which can ead to increased crazing and fracture of surface as the seasons change. Further, surface temperatures can reach almost 100 C on a hot day, increasing the susceptibility to attack as well as the rate of reactions already proceeding. 

At the fundamental level, current understanding of crazing and fracture in semicrystalline polymers remains less advanced than in glassy polymers. Even in these latter, phenomena such as disentanglement are generally subject to unverified assumptions concerning their kinetics, or even their exis-... 

Opfermann, J. Investigations of Crazing and Fracture of Amorphous Polymers, Aachen, Institut fur Kunststoffverarbcitung (IKV) der TH Aachen, 1978... 

Friedrich, K., Karsch, U. A. The Influence of Molecular Weight on Crazing and Fracture in Polypropylene, in Proc. 27th Int. Symp. on Macromolecules, Vol. 2, p. 1035, Strasbourg, France, July 1981... 

Opfermann J (1978) Investigations of crazing and fracture of amorphous polymers. Institut... 

The influence of solvents has been touched on in Sect. 2.3.2. In fact, the influence of environment on crazing and fracture properties of polymers is of major importance in the practical uses of these materials. There are many ways for the environment to induce fracture by means of stress cracking, stress crazing, chain scission, chain crosslinking, etc. Therefore, environmental fracture has been widely studied, specially from the experimental point of view. Reference is a review of environmental cracking of polymers. Most work on environmental crazing has been done in liquid environments - (solvents and non solvents of the material), or high pressure gas environment, near condensation pressure (liquid nitro-... 

Other difTcrent aspects of crazing and fracture are found in POM. Figure 16 shows the temperature dependence of bending moment-displacement relations of a notched POM sample. Fracture occurs in a nearly brittle manner for the samples loaded at 296 K (room temperature) and 313 K. At 333 K final fracture is also brittle after exhibiting considerable nonlinear deformation under nearly constant load. The... 

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