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JOURNAL OF MATERIALS SCIENCE LETTERS 10 (1991) 671-674 Growth of tied cracks: a model for polymer crazing K. KENDALL, W. J. CLEGG ICI, PO Box 11, Runcorn WA7 4QE, UK R. D. GREGORY Department of Mathematics, University of Manchester, Oxford Road, Manchester M139PL, UK There is a significant problem in understanding the critical condition for crazes to propagate through polymers, particularly in the presence of craze-indu- cing agents such as petrol, alcohols or water [1-3], which may degrade products such as crash helmets and aircraft windscreens, causing them to fracture prematurely. Since the early 1960s, various criteria for crazing have been proposed based on critical stress [4], critical strain [5], or on the stress intensity factor at a crack tip [6]. The currently accepted view is that the Dugdale [7] model applies [8, 9]; in this model the craze exists only at the tip of a crack, there is no stress concentration at the craze tip and no propagation criterion is derived for the craze. However, experiment shows that crazes can exist in isolation from cracks, that there is a stress concen- tration at the tip of these crazes, especially in swelling solvents [10], and that such crazes propag- ate in a manner rather similar but not quite identical to cracks. Therefore, we suggest that the Dugdale model is not applicable to the description of isolated crazes. We propose a new model of craze propaga- tion, show that this gives a stress concentration at the craze tip, and verify that this model describes the crazing phenomena observed in poly(methyl metha- crylate) (PMMA) swollen in alcohol. A craze is a peculiar form of crack, containing polymer strands strung between the crack faces, tying them together so that the tied crack cannot open as freely as an ordinary crack. The plastic zone at a crack tip in a metal can also be viewed as a tied crack in which plastically deformed metal is ima- gined to fill the crack opening, as postulated by Dugdale [7]. In addition, tying of cracks is known to occur in fibrous composites where fibres bridge the crack, although in this case the stress concentration is still presumed to act at the tied crack tip [11, 12]. Even particulate materials such as cement [13] and alumina ceramic [14] have been shown to give crack-bridging behaviour. Tied cracks are important because they are more difficult to propagate than ordinary cracks, and so give enhanced toughness to an otherwise brittle material. A polymer glass that crazes displays a fracture energy of about 500 Jm -2, but an inorganic glass that cracks gives 5 Jm -2. Moreover, the longer the tied crack is, the greater is the stretching of the ties and the greater the apparent toughness as the tied crack extends. Such "R-curve" behaviour is well-known in metals and composites [15]. Tying of 0261-8028/91 $03.00 + .12 ©1991 Chapman and Hall Ltd. cracks is used practically to repair aircraft panels by fastening a plate over the cracked region to inhibit further opening of the crack [16]. In such structures
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This note was uploaded on 09/28/2011 for the course MSE 4020 at Cornell University (Engineering School).

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