Limitation on crack speed for a strip-craze model applied to PMMA

Abstract

A strip-craze model is proposed to study crack propagation in polymers. A nonlinear differential equation is derived to govern the dynamic process of crack propagation. The viscous feature of the material in the craze zone is taken into account by means of an experimentally determined relationship between the craze stress and crack speed. By fitting experimental data of PMMA into the model, some parameters including the strip-craze length are deduced. A non-singular stress is introduced to control the crack propagation with a strip craze at its tip. Variations of the crack length and the crack speed with time are computed and their dependence on the non-singular stress is investigated. For PMMA, three stages of crack propagation are identified in terms of initial non-singular stress σ ns0. When σ ns0<60 MPa, the crack speed a ̇ <10 −8 mm/s and the crack is basically stationary; when 60 < σ ns0<95 MPa, then 10 −8< a ̇ <10 −2 mm/s the crack is in slow propagation; when σ ns0>95 MPa, then a ̇ >10 −2 mm/s and the crack is in rapid propagation. The proposed model is applicable only in slow crack propagation.