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Nonequilibrium statistical theory of damage and fracture for glassy polymers, 1. The statistical distribution and evolution of microcracks in glassy polymers
Author(s) -
Li Qiang,
He Ziru,
Song Mingshi,
Tang Aoqing
Publication year - 1996
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.1996.040050202
Subject(s) - moment (physics) , fracture (geology) , materials science , fracture mechanics , distribution function , polymer , statistical physics , statistical mechanics , function (biology) , mechanics , non equilibrium thermodynamics , damage mechanics , thermodynamics , physics , composite material , classical mechanics , finite element method , evolutionary biology , biology
The purpose of this paper is to construct a unified theoretical framework to link micro to macro‐mechanical properties of glassy polymers. Starting from a model of microcrack propagation in craze on a mesoscale, the kinetic process of microcrack propagation resulting from fibril breakdown in the crack tip zone is mathematically formulated by a combination of fracture mechanics and fracture kinetics. A microcrack evolution equation involving both the geometric structure parameters of craze and the meso‐mechanical quantities is obtained. After solving this evolution equation, a statistical distribution function of microcrack size which evolves with time and the moment generating function of microcrack size are derived. Any‐order averaged damage functions can be therefore deduced. Specifically, the analytical expressions of the first‐order averaged damage function and its damage rate are presented, which correspond to a similar definition of damage mechanics.