Calibration of a viscoplastic cohesive zone for crazing in PMMA

In a numerical analysis of mode I fracture in amorphous polymers, Estevez et al. [Estevez R, Tijssens MGA, Van der Giessen E. Modelling of the competition between shear yielding and crazing in glassy polymers. J Mech Phys Solids 2000;48:2585–617] have shown that the material toughness is governed by the competition between the time scales related to shear yielding and crazing. The present study aims at calibrating the parameters involved in this description, for a commercial PMMA. An elastic–viscoplastic constitutive law featuring softening upon yielding and hardening at continued deformation is used for the bulk while crazing is described with a viscoplastic cohesive zone. The three steps of crazing with initiation for a critical stress state, thickening of the craze surfaces and breakdown of the craze fibrils for a critical opening are characterized separately. In particular, it is demonstrated that the use of a viscoplastic cohesive zone is necessary to capture the variation of the toughness with loading rate. For PMMA, the related energy release rate is shown to depend primarily on the craze critical opening and the craze thickening kinetics while craze initiation is of minor importance for the quasi-static loading conditions under consideration here.