The time-dependency of strength in ceramics and glasses

10.6 The time-dependency of strength in ceramics and glasses

Time and strain-rate have a special relevance to the strength of ceramics. For example, the measured strength of individuals taken from a set of ceramic specimens can show an appreciable decrease over a period of time. With regard to the mechanism of such time-dependent failure, it is first necessary to distin- guish between fast and slow crack growth.

Fast crack growth, as produced in a routine bend Figure 10.21 Idealized plot of relation between crack velocity and stress-intensification test, takes place when the crack reaches a critical .

size. Slow or delayed crack growth takes place in

a stressed ceramic over a relatively long period of again dependent upon K I but is independent of envi- time and involves slow propagation of a crack of

ronment.

sub-critical dimensions. Fast fracture occurs when this Time-to-failure depends primarily upon the profile crack reaches criticality. This phenomenon of progres-

of region I. Its slope (n), sometimes known as the sive weakening and degradation, which is termed static

stress-corrosion constant of the particular material, fatigue or delayed fracture, has long been known in

ranges in value from about 10 to 100. Low values, such glasses. It is now recognized in a wide variety of

as those for glasses (10–40), indicate a susceptibility to ceramics (e.g. alumina, slicon nitride, vitreous car-

slow crack growth. Figure 10.22 shows typical curves bon). Its occurrence in polycrystalline oxide ceramics

for a variety of ceramic materials. Changes in envi- is often related to the presence of a glassy bonding

ronment (temperature, pH, etc.) can displace a curve phase. The stresses capable of causing static fatigue

and/or alter its slope. For instance, at elevated temper- can be continuous or fluctuating: even at quite low

atures, the slopes of curves for carbides and nitrides stress levels, there is a finite probability of failure by

become less steep.

this insidious process. Sometimes chemical agencies Study of the statistical nature and time-dependency have an overriding effect. For example, when mois-

of strength in ceramics led to the development of ture is able to diffuse to crack tips in silica glasses and

strength-probability-time (SPT) diagrams 2 of the type alumina, the velocity of crack growth increases. This

shown in Figure 10.23. These diagrams refer to spe- type of behaviour is understandably regarded as stress-

cific conditions of testing and are plotted on Weibull corrosion. Slow crack growth is a thermally-activated

probability paper. As the n-value (for region I crack process and an increase in the ambient temperature can

growth) decreases, indicating increased sensitivity to have a very significant effect.

environment, the sloping lines close up. Such dia- The nature of delayed crack growth is customarily

grams clearly show the interplay between stress, the expressed by plotting crack velocity (V) against the

probability of survival and the lifetime before stress intensity factor ⊲K I ⊳ , as shown in Figure 10.21.

fracture.

This plot is idealised but is typical of ceramics which Recognition of the fact that there is apparently no are capable of slow crack growth at ambient tempera-

absolutely safe stress for a ceramic which is sub- ture, such as glasses and oxide ceramics. Three regions

ject to long-term service stimulated interest in proof- of crack growth lie between the ‘static fatigue limit’

testing. By eliminating weaker members, such tests ⊲K Io ⊳ , below which crack growth is not of concern, and

provide survivors with a better (narrower) distribution

of strength than that of the original population. Statis- which sudden fracture occurs. In region I, the veloc-

the critical value of the stress-intensity factor ⊲K Ic ⊳ at

tical predictions of service life benefit accordingly. It ity is an exponential function of the stress-intensity

must be borne in mind that the proportion of survivors

factor and can be expressed in the form V D A⊲K I ⊳ n .

reflects the conditions of testing. Obviously, the period

In region II, velocity is independent of K I . Regions

of testing is important; the longer the time, the smaller

I and II are environment-sensitive and correspond to the number of survivors. Ideally, proof-tests should be conditions of stress-corrosion. In region III, velocity is

carried out under conditions that do not cause sub- critical crack growth.

1 The Jaguar XJ220 sports car has compound-curvature front, top and rear screens which blend smoothly with the

2 Devised by R. W. Davidge and co-workers at the Atomic body contours.

Energy Research Establishment, Harwell.

Ceramics and glasses 349

Figure 10.22 Relation between crack velocity and stress intensity factor for various ceramics in neutral water at 25 ° C (after Creyke et al., 1982; by courtesy of Elsevier/Chapman and Hall) .

5 s is regarded as a tentative stress-corrosion limit (after Davidge, 1986, p. 145; by courtesy of Cambridge University Press) .

350 Modern Physical Metallurgy and Materials Engineering

Further reading

Laminated Glass Information Centre (1993). Laminated

Glass . LGIC, London.

Binner, J. (1992). Processing of advanced ceramic pow- McColm, I. J. (1983). Ceramic Science for Materials Tech- ders. Metals and Materials, October, 534–537, Institute

nologists . Leonard Hill, Glasgow. of Materials.

Mantell, C. L. (1968). Carbon and Graphite Handbook. Burkin, A. R. (ed.) (1987). Production of Aluminium and

Wiley-Interscience, New York. Alumina . Wiley, Chichester.

Parke, S. (1989). Glass—a versatile liquid. Metals and Mate- Cahn, R. W. and Harris, B. (1969). Newer forms of carbon

rials , January, 26–32, Institute of Materials. and their uses. Nature, 11 January, 221, 132–141.

Rawson, H. (1980). Properties and Applications of Glass. Creyke, W. E. C., Sainsbury, I. E. J. and Morrell, R. (1982).

Elsevier Science, Oxford.

Design with Non-Ductile Materials , Elsevier/Chapman and Riley, F. L. (ed.) (1977). Nitrogen Ceramics. Noordhoff, Hall, London.

Leiden.

Davidge, R. W. (1986). Mechanical Behaviour of Ceramics. Shinroku Saito (ed.) (1985). Fine Ceramics. Elsevier, New Cambridge University Press, Cambridge.

York.

Jack, K. H. (1987). Silicon nitride, sialons and related ceram- Ubbelohde, A. R. J. P. and Lewis, F. A. (1960). Graphite ics. In Ceramics and Civilisation, 3. American Ceramic

and its Crystal Compounds . Clarendon Press, Oxford. Society Inc., New York.

Wachtman, J. B. (ed.) (c1989). Structural Ceramics, 29, Aca- Kingery, W. D., Bowen, H. K. and Uhlmann, D. R. (1976).

demic Press, New York.

Introduction to Ceramics , 2nd edn. Wiley-Interscience, New York