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Molecular weight dependence of the fracture toughness of glassy polymers arising from crack propagation through a craze
Author(s) -
Hui C. Y.,
Kramer E. J.
Publication year - 1995
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760350507
Subject(s) - crazing , materials science , composite material , micromechanics , stress (linguistics) , polymer , fracture toughness , fracture mechanics , fracture (geology) , toughness , microstructure , stress field , structural engineering , finite element method , linguistics , philosophy , composite number , engineering
We investigate criteria for craze failure at a crack tip and the dependence of craze failure on the molecular weight of the polymer. Our micromechanics model is based on the presence of cross‐tie fibrils in the craze microstructure. These cross‐tie fibrils give the craze some small lateral load bearing capacity so that they can transfer stress between the main fibrils. This load transfer mechanism allows the normal stress on the fibrils directly ahead of the crack tip in the center of the craze to reach the breaking stress of the polymer chains. We solve for stress field near the crack trip and use it to relate craze failure to the external loading and microstructural quantities such as the craze widening (drawing) stress, the fibril spacing, the molecular weight, and the force to break a single polymer chain. The relationship between energy flow to the crack tip due to external loading and the work of local fracture by fibril breakdown is also obtained. Our analysis shows that the normal stress acting on the fibrils at the crack tip increases linearly as the square root of the craze thickness, assuming that the normal stress distribution is uniform and is equal to the drawing stress acting on the craze‐bulk interface. The critical crack opening displacement, and hence the fracture toghness is shown to be proportional to [1–( M e /q M n )] 2 , where M e is the entanglement molecular weight, M n is the number average molecular weight of polymer before crazing, and q is the fraction of entangled strands that do not undergo chain scission in forming the craze.