Anthony G. Atkins

Intermittent bonding for high toughness/ high strength composites

High strength and high toughness are usually mutually exclusive in brittle filament/brittle matrix composites. The high tensile strength characteristic of strong interfacial filament/matrix bonding can, however, be combined with the high fracture toughness of weak interfacial bonding, when the filaments are arranged to have alternate sections of high and low shear stress (and low and high toughness). Such weak and strong areas can be achieved by appropriate intermittent coating of the fibres. The strong regions ensure that the filament strength is picked up; weak areas randomly in the path of running cracks serve to blunt them by the Cook/Gordon mechanism which, in turn, produces long pull-out lengths with an associated large contribution to toughness. Boron-epoxy composites of volume fraction 0.20 to 0.25 have been made in this way which have fracture toughnesses of over 200 kJ m−2, whilst retaining rule of mixtures tensile strengths (∼ 650 MN m−2). At the volume fractions used, this apparently representsKIC values greater than 100 MN m−3/2.An analysis is presented for toughness and strength which demonstrates, in broad terms, the effects of varying the coating parameters of concern. Results show that the “toughness” of interfaces is an important parameter, differences in which may not be shown up in terms of interfacial “strength”. The choice of coating material is crucial in getting the desired effect.Some observations are made upon methods of measuring the components of toughness in composites.

Interfacial fracture energy and the toughness of composites

The premises upon which prevailing composite toughness theories are based are discussed in the light of observed strength variations in boron-epoxy composites with differing shear strengths of the interfacial bond. None of the extant toughness theories (pull-out, debonding, stress redistribution) successfully predicts the work of fracture of the boronepoxy system. However, incorporation of the work to create new surfaces into the total toughness analysis gives better agreement with experiment, and work of fracture predictions for other sytems, such as carbon-polyester, can also be modified. The approach is more generalized than the Outwater/Murphy debonding explanation for toughness, which in the way usually presented only applies when the filament fracture strain is greater than the matrix fracture strain. The present analysis suggests how to tailor the interfacial shear strength in order to obtain a reasonable toughness yet still maintain strengths of the order of the rule of mixtures.

Pressure dependent yield criteria for polymers

Summary Y M Different criteria have been proposed to include the influence of pressure (or mean normal stress) on the yield behavior of polymers. It is difficult to distinguish among them using the type of experiments that produce data used in two-dimensional plots of yield loci. This is due to the fact that the maximum range of values of mean normal stress is relatively small in such experiments. Marked differences between these criteria do occur however as the hydrostatic pressure or mean stress is altered substantially. Experiments that show the effect of applied pressure on tensile and/or compressive yield strength provide one means for describing such differences. This paper considers two forms of a pressure modified yon Mises criterion and shows a comparison with available experimental information.

A yield criterion for anisotropic and pressure dependent solids such as oriented polymers

The anisotropic yield criterion first posed by Hill has been modified to account for differences in tensile and compressive yield strengths in a given direction; additionally, the influence of hydrostatic pressure on yielding is also considered. Predictions using this new criterion are compared with published experimental results involving oriented polymers and excellent agreement is found. It is suggested that this criterion is more correct on fundamental grounds than those put forth in earlier publications.

Time-temperature dependent fracture toughness of PMMA: Part 1

A toughness-biased Ree-Eyring relationship gives a good description of fracture toughness data of PMMA over a range of temperatures (283 to 353 K) and crack velocities (10−5 to 1 m sec−1). Fracture toughness was measured by Gurneys sector method. The activation energy associated with the equation supports earlier work which suggests that, in the same temperature and velocity range, cracking in PMMA is controlled by craze growth, which is governed by secondary (β) molecular processes. Unstable cracking at moderate velocities (10−2 to 1 m sec−1) seems to be produced by an isothermal/adiabatic transformation; an analysis for the onset of instability is given. At temperatures below 283 K, changes in toughness behaviour are seen, and below 243 K no stable cracking at all was obtained. A discussion is given of various methods of characterizing resistance to cracking, and methods of transforming R(à, T) and K(à, T) data are compared.

Time-temperature dependent fracture toughness of PMMA

Some observations are made on the fractography of surfaces obtained by cracking “compact tension” profile testpieces of PMMA over a range of temperatures and crack speeds, both stably and unstably. To a first approximation, it was possible to group and “shift” (as in visco-elastic transformations) characteristic surface markings at various fracture toughness/temperature/crack velocity combinations, particularly in the range where a toughness-biased Ree-Eyring relationship described the experimental toughness data.

The laws of similitude and crack propagation

Abstract The mechanics of cracking follow the laws of similitude in an odd sense. As a result, crack load-external displacement-crack extension data are not usually non-dimensionalized. It follows that a new “group” should be used (analogous to the Reynolds, Froude or Cauchy numbers) when scaling ship ice-breaking resistance from tests of models in ice-towing-tanks.

HYDRODYNAMIC LUBRICATION IN COLD ROLLING

Summary Particular attention has been paid to the effects of roll flattening and to the inlet zone of pressure build-up in the determination of lubricant film thickness in cold rolling. It is shown that under present-day practical conditions, the thicknesses of the lubricant films relative to surface roughnesses are insufficient to maintain full fluid film lubrication. Although the mathematical model predicts a “speed effect” for rolling (plots of rolling load against speed looking like a Sommerfeld diagram for a journal bearing), the speeds involved are much faster than present commercial rates. Thus speed effects in the literature must have been caused by a change over from boundary to mixed lubrication and lubricant puddle entrapment in surface microcrevices. The non-dimensional form of the solutions shows that laboratory experiments rarely approach full-scale mill conditions, thus reflecting the notoriously difficult problem of evaluating commercial metal-working lubricants.

Effects of rate, temperature and absorption of organic solvents on the fracture of plain and glass-filled polystyrene

The rate/temperature dependent fracture behaviour of plain and glass-filled polystyrene has been investigated over the crack speed (a) range of 10−6 to 10−2 m sec−1 and in the temperature (T) range of 296 to 363 K. TheKc (a, T) relationships obtained, whereKc is the stress intensity factor at fracture, are shown to follow those given by the Williams/Marshall relaxation crack growth model and the toughness-biased rate theory. Crack propagation in both materials is shown to be controlled by aβ-relaxation molecular process associated with crazing. Crack instabilities observed in plain polystyrene are analysed successfully in terms of isothermal-adiabatic transitions at the crack tip. Fracture initiation experiments are also conducted in which the effects of organic liquids on the fracture resistances of both plain/glass-filled polystyrene have been determined. Good correlations betweenKi2 (Ki being the crack initiation stress intensity factor) and δs, solvent solubility parameter, of various liquid environments have been obtained, which give a minimumKi2 value at δs ≈ δp, where δp is the solubility parameter of the polymer. For a given temperature, liquid environment and crack speed, the glass-filled polystyrene is shown to possess greater resistances to crack propagation than plain polystyrene.

On the velocity-dependent fracture toughness of epoxy resins

In a recent paper [1], Drs Selby and Miller described three methods of determining the fracture toughness (R), or equivalently, the fracture surface energy (23) for an epoxy resin. These methods are respectively (a) Berrys method, (b) Irwin-Kies equation and (c) Gurneys irreversible work area method. While the experimental data obtained from tapered double-cantilever beam (TDCB) specimens supported the equivalence of the first two methods (based on crack initiation), they apparently have difficulties in the interpretation of these data using Gurneys method because of the crack-jumping nature of the epoxy resin. They have found that the segmental areas give fracture surface energies (23) less than that obtained from either Berrys method or Irwin-Kies equation. It would thus appear at first sight that there is a limitation to the usefulness of the Gurney-method for fracture toughness determination for such crack-jumping materials. In the present note, we wish to show that such limitations really do not exist once the criteria governing stability in cracking are investigated. Conditions governing the stability of cracks under constraints of both loadand displacementcontrolled machines are given in [2 -4] . In general, the stability criteria may be written as