Crazing critical strain

Detection of crazes is very difficult yet craze formation should be avoided in critical applications (such as gas pipes). In order to achieve that, one uses the expression critical strain , which is based on the observation that, as long as a certain level of strain is not exceeded, no crazes are formed. It would be convenient if this critical strain would be independent of the applied stress this is, unfortunately, not the case, as illustrated in the bundle of isochrones in Figure 7.23... 

Crazes usually form under tensile stress when a critical strain is surpassed they do not occur under compressive stress applying hydrostatic pressure during tensile deformation can even inhibit their development. Crazes always nucleate preferentially at points of triaxial stress concentration. It is the dilatational strain which initiates crazes and cracks. 

FIG. 26.13 Critical strain of poly(2,6-dimethyl-l,4-phenylene oxide) vs. solubility parameter 5 of crazing and cracking liquids. Minimum in cr occurs at 8 equal to that of the polymer. Band at top indicates critical strain of polymer in air (Bernier and Kambour, 1968 reproduced by permission of the American Chemical Society). 

Kambour et al. performed extensive studies on the mechanisms of plasticization [18-25]. The correlation observed between the critical strain to craze and the extent of the glass-transition temperature (Tg) depression speaks strongly in favor of a mechanism of easier chain motion and hence easier void formation. In various studies on polycarbonate [19,24], polyphenylene oxide [20], polysulfone [21], polystyrene [22], and polyetherimide [25], Kambour and coauthors showed that the absorption of solvent and accompanying reduction in the polymer s glass-transition temperature could be correlated with a propensity for stress cracking. The experiments, performed over a wide range of polymer-solvent systems, allowed Kambour to observe that the critical strain to craze or crack was least in those systems where the polymer and the solvent had similar solubility values. The Hildebrand solubility parameter S [26] is defined as... 

This critical-strain concept is widely used in conjunction with bend-test methods, with the aim of specifying and comparing the severity of ESC for a range of environments [11,14,55,61]. It has been found experimentally that crazing occurs fairly rapidly when the strain is greater than some characteristic critical value ecrit, while crazing remains effectively absent below this value, even for very long test times. The value of cr t can therefore be used as... 

A shortening in relaxation time in the critically strained region makes some materials tough. The shift of relaxation time is attributed to strain-induced dilatation and can reach as much as five decades. Thermal history, on the other hand, dictates the initial state from which this dilatation starts and may be expressed in terms of excess entropy and enthalpy. The excess enthalpy at Tg is measurable by differential scanning calorimetry. Brittle to ductile transition behavior is determined by the strain-induced reduction in relaxation time, the initial amount of excess entropy, and the maximum elastic strain that the material can undergo without fracturing or crazing. 

Bowden, P. B., Oxborough, R. J., A Critical Strain Criterion for Craze... 

The results of Plummer and Donald also clearly show qualitatively the strain rate dependent behavior to be expectal from the model. Figure 22 shows their results for PES strained at a rate of 1 x 10 s contrasted with their results at a much slower rate of 6x 10 s F The critical strain for shear deformation and the critical strain for van-der-Waals crazing both increase with the increase in strain... 

Critical strain for craze initiation Interfacial length Extension ratio... 

Attempts have been made to rationalise the susceptibility of glassy polymers to ESC. The critical strain for crazing is a minimum when the solubility parameter 8 of the liquid is the same as that of the polymer (Fig. 10.19). The former is calculated from the energy of vaporisation and molar volume V of the solvent... 

Figure lO. I9 Critical strain for crazing polycarbonate vs. solubility parameter of liquids (data from Arnold, J. C. and Taylor, J. E., J, AppL Polym. Sci, 71, 2155, 1999). 

Figure 7. Effect of physical aging at 60 C on the critical strain for crazing.

Unlike the shear yield process, crazing is an inherently non-isovolume event. Cavitation of the material requires a dilatational component of the stress tensor, such as occurs in triaxial stress systems that may be foimd in samples subjected to plane strain conditions. In addition, it is foimd in practice that there is a time dependency on the appearance of crazing. That is, there is generally a time delay between application of the load and the first visible appearance of a craze. A number of models have been proposed which require either a critical cavitation stress, a critical strain, or the presence of inherent microvoids, which can grow under the applied local stress or strain. 

V is the Poisson s ratio and assuming that crazing occurs at the critical strain given by equation 45, they derived a criterion for crazing that is written in terms of the principal stresses ... 

Fig. 19. Correlation between the critical strain for crazing, and the product of the cohesive energy density (CED), the difference between the test temperature and the glass-transition temperature AT, and the elastic modulus E. Reprinted from Ref. 129, with permission from Elsevier.

R. J. Oxborough and P. B. Bowden, A General Critical-Strain Criterion for Crazing in Amorphous Glassy Polymers , Philos. Mag. 28, 547-559 (1973). 

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