High speed double torsion tests on tough polymers. I: Linear elastic steady state and dynamic analysis

Abstract

The High Speed Double Torsion test has been used to generate steady rapid crack propagation in tough pipe-grade polyethylenes, at speeds of up to 350 ms^-1. Dynamic plane-strain fracture resistance GD data, computed from the measured displacement and crack length using a linear elastic steady-state analysis, were systematically scattered. The computed fracture loads exceeded measured values by up to 50 percent. Two possible reasons for these discrepancies are the neglect of unsteady deformation, and the use of small-strain dynamic elastic modulus data to represent the material. Since the torsional wave speed calculated from this modulus provided a good estimate for the limiting crack speed, this paper pursues the first possibility. High speed photography was used to study the deformation field, which proved to be less steady than assumed. The observations were used to support development of a fully dynamic, linear elastic torsion-beam-on-elastic-foundation model for computing the transient deformation field from boundary data. The foundation stiffness, computed by matching predicted and observed deformations in the crack tip vicinity, was consistent with that estimated from earlier quasi-static tests. As judged by the continuity of the computed energy release rate G ^dyn (and hence, equivalently, of GD), numerical integration along characteristics is more suitable than a conventional explicit finite difference scheme for solving this one-dimensional problem. The GD solution for intermediate crack lengths is also insensitive to assumed initial conditions, which are therefore chosen to minimise the settling time. The curved double-torsion crack front shape, predicted using an earlier quasi-static criterion, agrees closely with that observed from dynamic arrest lines on the fracture surface, but simply assuming the crack front to be straight and normal to the specimen plane has little effect on computed GD data. The dynamic model, used to compute GD as a function of crack speed for several pipe-grade polyethylenes, reduces but does not eliminate scatter; nevertheless, in provides a more reliable and versatile tool for reconsidering the question of material representation in Part II of the paper.