Some results of optical interference measurements of critical displacements at the crack tip

Abstract

In recent years there has been an increasing interest in investigating the openings of cracks in materials under load.In particular this interest has concentrated on the value of the critical displacement at the crack tips at fracture (variously designated as 6c, COS, COD, 2Vc) since these displacements, being essentially determined by the plastic deformations in the crack tip region, should provide a fracture criterion to characterize plastic fracture behaviour.In metals a direct measurement of the critical crack opening is seldom practicable and is, therefore, usually determined by an extrapolation of crack openings measured remote from the crack tip.In optically transparent materials such as glassy thermoplastics, on the other hand, it is possible to measure not only the crack opening very close to the crack tip but also the plastic zone (or craze zone) ahead of the crack tip using optical interference microscopy [1][2][3][4]. Essential requirements for the application of this method are that the crack opening and craze zone thickness should both be comparable in order of magnitude to the wavelength of l~ght and that, additionally, for the craze zone, the refractive index of the crazed material should differ significantly from that of the bulk material and the boundary between the two regions should be sharp.In this work we would like to report results of measurements of the critical displacements of the elastic-plastic boundary directly at the crack tip (here designated as 2v c and marked by an arrow in Fig. 4) and their variation with temperature in some glassy thermoplastics.These measurements were performed on miniature compact tension specimens in an experimental arrangement which permitted the simultaneous recording of the interference fringe pattern and the load acting on the specimen [4]. The materials were PMMA of two different molecular weights (M w ~ 2,200,000 and M w = 120,000) and PVC. Examples of the interference fringe patterns just before the onset of slow crack propagation at room temperature are shown in Fig. i. From the different numbers of fringes in the craze zones it is directly apparent that there are differences in the critical crack tip opening displacements.Based on a quantitative analysis of such fringe patterns (details of which have been given in earlier work [3,411 Fig. 2 shows the critical displacements at the crack tip 2v c in the three materials for temperatures between 0 deg C and 80 deg C. Three quite different patterns of behaviour are apparent: the 2v c values for PVC fall sharply with increasing temperature, those for the lower molecular weight PMMA remain practically constant whilst those for the h~gher molecular weight PMMA show a significant increase.*now at the Open University, Milton Keynes MK7 6ka, UK. Int Journ of Fracture 14 (1978) RI90In contrast to this, the corresponding results for the fracture toughness at the onset of slow crack propagation, Kio , decrease, albeit at different rates, with temperature for all three materials as is shown in Fig. 3. Since, in ge...

Influence of Entanglements on Ultrahigh Strain Rate Deformation of Polystyrene Microprojectiles

“…For craze widths greater than ∼300 nm, fibril fracture occurs (see arrows in Figures c and S6), with craze breakdown occurring at the craze–polymer border, consistent with previous quasi-static observations on PS . In general, the crazes in the most highly deformed regions are still quite narrow (∼300 nm) compared to the typical width (∼1.5 μm) of PS quasi-static crazes. , Atomic force microscopy (AFM) was also employed to measure radial crazes located near the periphery (see Figure S5). The widths of crazes are about 200 nm, fitting with the sizes observed from SEM, with the fibril diameter around 40–70 nm.…”

Modeling and Computational Analysis of Fracture of Glassy Polymers

“…The molecular weight has to be sufficiently large (about M w = 3 × 10 5 g/mol for PMMA and M w = 12 × 10 3 g/mol for PC) for the development of a stable craze. The critical craze thickness and craze length (∆ cr and Λ c ) are also temperature dependent [29,30,43,44] and this effect is amplified with increasing molecular weight [29,30].…”

Stress analysis around a three‐dimensional craze in glassy polymers

“…2, the stress field inside the craze becomes nonuniform. But experiments (8) show that the craze surface stress is still approximately the same as the case without the crack when the crack is small. Thus the stress near the craze surface but inside the craze can be assumed unchanged, as given by Eq 9.…”