A model of fibril deformation in crazes

Abstract

A theoretical model is proposed to describe quantitatively the steady‐state deformations of fibrils in crazes. In the model, the total force is represented as the sum of high elastic, plastic (actually, nonlinear viscous), and surface tension forces; the first two being modeled by using elongational rheology and the third represented in exact form. The model description is reduced to a boundary value problem for a second‐order ordinary differential equation describing the profile of fibrils. This problem results in an energy balance which, in turn, leads readily to a thermodynamic description of the equilibrium conditions for the deformations of homogeneous fibrils far from the interface (z → ∞). Two possible regimes of fibril deformation were found, depending on the periodicity of the fibrils in the craze. The first is Paredes and Fischer's regime of static deformations of fibrils under action of elastic forces and surface tension where the periodicity is determined by the condition for the static regime to exist. The second is Kramer's drawing regime where the fibril periodicity is found from the Fields and Achby maximization of craze tip advance speed. The choice between these two regimes is made to minimize the complete Gibbs' free energy including surface tension for the equilibrium state of fibrils at z → ∞. The model predicts that the static regime usually appears under moderate stresses and changes for the drawing regime when stresses increase. Hence, this model solves the contradictions between the static and drawing approaches proposed in literature. Examples of both the static and drawing regimes of fibril deformations are demonstrated and some comparisons with data are represented. Copyright © 1991 John Wiley & Sons, Inc.