Crazing under biaxial stress

Stemstein and Ongchin [47] extended this investigation by examining the formation of crazes under biaxial stress conditions, and found that the stress conditions for crazing involved both the principal stresses o and o-i. The most physically acceptable explanation of these results was proposed by Bowden and Oxborough [48], who suggested that crazing occurs when the extensional strain in any direction reaches a critical value e, which depends on the hydrostatic component of stress. 

Kawagoe M, Kitagawa M (1981) Craze initiation in poly(methyl methacrylate) under biaxial stress. J Polym Sci Polym Phys 19(9) 1423—1433... 

Failure envelope (heavy continuous line) for PMMA under biaxial stress (room temperature, shovring intersection of crazing and shear yielding envelopes (after S. Stemstein and L Ongchin). 

Crazing in PMMA follows a criterion which for fixed time under biaxial stress (ctj = 0) can be written... 

One major diflerence between the two mechanisms of deformation is illustrated in Fig. 5.7, which shows a failure envelope for PMMA under biaxial loading. The pure-shear line, defined by er,j = —<722> marks the boundary between hydrostatic compression and hydrostatic tension. Below this line, crazing and other hole-forming processes do not take place because the pressure component of the stress matrix tends to reduce rather than to increase volume above the line, crazing is the principal mechanism of failure. 

For which polymers and under which conditions do crazes occur Crazes form primarily in amorphous polymers, for molecular weights above the entanglement limit. There is no craze formation under compression or under pure shear. The typical situation leading to craze initiation is the imposition of an uniaxial or biaxial tensile stress. If such stresses are applied and fulfill certain threshold conditions, crazes form statistically, preferentially at first at the sample surface. The initiation rate depends on the applied stress, as is shown in Fig. 8.22. The higher the stress imposed, the shorter is the time for the observation of the first crazes. After the initial increase with time, the craze density saturates. Removing the stress, the crazes close their openings somewhat, but survive. They disappear only if the sample is annealed at temperatures above the glass transition. 

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