On the law of fatigue crack layer propagation in polymers

A generalized theory of fatigue crack propagation in polymers is presented. The theory accounts for crack propagation through root craze extension accompanied by the dissemination of micro defects around the main crack thereby describing a crack layer (CL) system. In addition to the conventional crack length( l ), the CL width( w ) is introduced as another kinematic parameter. Applying the principle of minimum thermodynamic forces, evolution of l and w is formulated in terms of reciprocal thermodynamic forces. Accordingly the law of Fatigue Crack Layer Propagation (FCLP) is derived in the following dimensionless form\documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{{d\lambda }}{{dN}} = \frac{{\beta \prime\lambda ^2 - Q\prime}}{{\omega - \lambda }} $$\end{document} where N is the number of cycles, λ ≈ l ( N )/ l *; l * being the critical CL length, ω = w ( l )/ w *; w * being the value of w corresponding to l *, β′ and Q ′ are energy dissipation and heat evolution functions, respectively. A version of this law provides good description of growth rates from published data.