Fractal Damage Modelling Of Crazing Polymers

The crazing phenomenon is unique to amorphous glassy polymers. The crazing damage evolves in three different levels: the orientating, untwisting and breaking of macromolecular chains in microscopic state; the initiation, growth and breakdown of crazes in mesoscopic layer; the formation, expansion and rupture of mesocracks in macroscopic view. A craze can sustain a definite amount of tensile stress and the mechanical properties of crazing polymers are the competitive result between crazing damage and toughening, which means the damage model of crazing polymers should be distinguished from other materials due to their particular damage mechanism.Based on the standard linear solid model, a one-dimensional nonlinear viscoelastic model of polymers for small deformation is set up to describe strain- rate-dependency elasticity and nonlinear viscosity. The corresponding three- dimensional model is developed by generalizing the one-dimensional nonlinear viscoelastic model according to the correspondence principle.The former construction serves as a starting point for the development of a three-dimensional, finite deformation, viscoelastic constitutive model. So the Updated Lagrange coordinate system and the second Piola-Kirchhoff stress tensor/the Green strain tensor are selected to extend small-strain model on the base of the Noll principles, the work conjugation theory and the true stress principle. A one-dimensional, finite strain, viscoelastic constitutive model is proposed according to the nonequilibrium thermodynamics and its internal variable theory.The fractal theory is introduced to study crazes for the first time. Firstly, it is proved that the interval of fractal dimension of crazes is [0 , 2). The fractal dimension represents the fiberizing degree and the cavitating level of polymers. Secondly, a new concept—crazing variable is defined base on the damage variable and the toughening equation set up by the fractal dimension of crazes, which allows the two important properties of crazing: damage and toughening. The finite-strain crazing variable is proposed by use of the new computing method of fractal dimension modified by area transformation under the condition...