fracture and fracture mechanics || failure by creep

FAILURE BY CREEP

D. R. H. Jones Department of Engineering, University of Cambridge,

Trumpington Street, Cambridge CB2 1PZ, UK

ABSTRACT

The major mechanisms of creep (power-law creep and diffusion creep) and creep fracture (intergranular, transgranular and rupture) are outlined. We show why creep properties are very sensitive to material composition and microstructure, and explain the criteria for selecting creep-resisting materials. Finally we discuss the application of creep to the analysis of high-temperature failures.

KEYWORDS

Creep; creep failure; creep-resisting materials; deformation-mechanism map; diffusion; diffusion creep; fracture-mechanism map; oxidation and corrosion; power-law creep; reheat cracking; thermal fatigue.

INTRODUCTION

All materials, if they are taken to a high enough temperature and are loaded, will creep. They will deform continuously with time to give a strain ε that is a function of the applied stress σ, the time t and the absolute temperature T. Thus for a creeping solid:

ε = f (σ, t, T). (1)

Continued creep of the material will eventually lead to failure at

ε = ε , t = tf, (2)

where is the strain to failure and t is the time to failure. Components meant to function at high temperature must then be designed so that:

(a) The creep strain during the design life is less, by a suitable safety factor, than ε .

FFM-I 235

236 D.R.H. Jones

(b) The creep strain during the design life can be tolerated by the design.

(c) The design life is less, by a suitable safety factor, than t .

But what does high temperature mean in this context? Tungsten, used for lamp filaments, melts at the very high temperature of 3673 K. Lightbulb filaments typically run at 2600 K and, were they not strengthened with oxide particles, would fail by creep in only minutes. Nickel-based superalloys melt at about 1550 K and cannot be run in gas-turbines at more than about 1220 K. Lead, which melts at 600 K, creeps noticeably at room temperatures of 300 K. And the movement of glaciers and ice caps is controlled by the creep of ice near its melting point. These observations show that the temperature at which materials start to creep depends on their melting point. As a rough guide, we find that creep begins when:

T > 0.3 to 0.4 T for metals (3) M

T > 0.4 to 0.5 T for ceramics (4) M

where T is the melting temperature in degrees Kelvin. However, as our M examples of doped tungsten and superalloys show, specially developed alloys can resist creep up to 0.7 or even 0.8 T .

CREEP DATA

In order to design a component against creep, or to analyze a failure caused by creep, we need to have creep data for the material involved. This is done by putting a specimen in a furnace at the required temperature, loading it to a constant stress and following the build-up of strain with time (Fig. la). The strain can then be plotted against time to give the standard form of creep curve (Fig. lb) (see, for example, Ashby and Jones, 1980; Greenfield, 1972). The curve is divided into four regions. The first, the elastic strain of the specimen under the applied load, is usually negligible. The primary creep strain is essentially a "starting transient" which, again, is usually small. Most creep takes place in the steady-state

region at a steady-state creep rate ε . Finally, structural damage starts

to build up in the creeping material leading to the tertiary region and eventual failure. Because most of the life of the material is taken up by steady-state creep, design requirement (b) is usually satisfied by using data for ε

ss

If tests are done at the same temperature but at different stresses the steady-state strain rates vary with stress in the way shown by Fig. 2. At low stresses, the creep rate varies linearly with stress, and

ε = Ασ. (5) ss

At higher stresses the creep rate varies with stress according to the power law

ε = Á,óç, (6) ss

where n is a constant.

Failure by Creep 237

furnace windings

v stress cr, temperature T strain, ε = [l-lo)/io

Γ~Τ

D

Fig. 1(a). Schematic of experimental set-up for creep testing.

Finally, if tests are done at the same stress but at different temperatures, we find that the strain rate obeys the relation

„ -(O/RT) (7)

where Q is the activation energy for creep, R is the gas constant and T is the temperature in degrees Kelvin. Equation (7) may be rewritten by taking natural logs of each side to give

Ιηε = In B - (§) ^ ss R T (8)

so that, as Fig. 3 shows, a plot of Ιηε against l/T should give a straight line of slope (-Q/R).

Equations (5), (6) and (7) may be combined to give overall rate equations of the form

ε = CGe ss -(O/RT) (9)

for diffusion creep, and

238 D.R.H. J o n e s

e ι cT, T = constant

tertiary creep -

steady - state creep

primary creep instantaneous

I elastic strain

failure

Fig. 1(b). Typical form of creep curve.

= c, an e-(0'/RT) (10)

for power-law creep.

Creep experiments can be long and expensive and the data available are never as comprehensive as one would wish. Reference books (e.g. Smithells, 1976) and suppliers' data sheets often quote strain-rate data simply in terms of the stress needed to produce a 1 % creep strain after 10,000 and 100,000 hours at three or four different temperatures. Equations like (9) and (10) are then of great value for interpolating and extrapolating data. Frost and Ashby (1982) have used the creep-rate equations as the basis for computer fitting creep data for a large number of materials. They present their findings in the form of deformation-mechanism maps (Fig. 4). These summarize data for ε as a function of σ and T, and also show the regions where either ss power-law creep or diffusion creep operate. Creep data are very sensitive to the structural state of the material, and a deformation-mechanism map for a particular material should therefore specify the structural state of the material (e.g. grain size) and give details of any prior mechanical or heat treatments.

Fai lure by Creep 239

T = constant

log €ss

slope n « 3 to 8 L^"power-law creep

log cr

Fig. 2. How the steady-state creep rate depends on the applied stress.

CREEP MECHANISMS

In order to understand how engineering materials can be made more resistant to creep deformation we must look at how creep takes place on an atomic level. We begin by looking at the mechanism of diffusion creep. As Fig. 5 shows, when a polycrystalline material is stressed there is a driving force which tries to make the grains of the material longer and thinner. If the temperature is high enough, atoms can diffuse from the sides of the grains to the ends in order to allow the material to elongate by creep. Q in

_(O/RT) eqn. (9) is, in fact, the activation energy for creep, and the e " term is simply the temperature dependence of the diffusion coefficient. The rate of diffusion creep depends linearly on the applied stress because doubling the stress will double the driving force for diffusion. This, in turn, will double the rate of diffusion and finally the rate of creep elongation will double too. Lastly, the creep rate depends on the grain size. If the grain size is increased, then atoms have to diffuse further when they move from the sides of grains to the ends, and the creep rate is reduced. This dependence of creep rate on grain size d leads to:

.,σ -(O/RT) ss ,2 α

(11)

which shows that diffusion creep is pretty sensitive to grain size (see, example, Frost and Ashby, 1982).

for

In power-law creep the deformation is produced by dislocations which glide


In € s cr = constant

1/T

Fig. 3. How the steady-state creep rate depends on temperature. Note that T is in degrees Kelvin.

under the action of the applied stress. Initially, the dislocations in the material can move fairly easily, and this is why the rate of creep is high at the start of the creep curve. Dislocations moving on converging slip planes will, however, soon begin to run into one another. This interference slows down the rate at which glide can take place, and the creep rate decreases quite rapidly as a result. Steady state is reached when the rate at which the dislocations run into one another is balanced by the rate at which opposing dislocations can climb over one another by diffusion (Weertman, 1957). The complex statistics that govern the collision of dislocations and their subsequent climbing are responsible for the power-law behaviour of eqn. (10). O' in eqn. (10) is, again, the activation energy for diffusion, but this time the diffusion process involves removing atoms from the cores of the climbing dislocations. In many alloys, precipitates provide extra obstacles to dislocation movement, and the statistics become even more complicated. This is why n can be so different for different materials (between about 3 and 8!).

CREEP FAILURE

Times to failure, t , are normally presented as creep-rupture diagrams (Fig. 6). The diagrams show that the time to failure will be reduced at higher stresses and temperatures. Data are often listed (e.g. Smithells, 1976) in terms of the stress needed to produce failure in 10,000 and 100,000 hours at several representative temperatures. As with creep-rate data, creep


- 1

-*-èss = 10"1/sec

melting point

0 0-5 ' , 1-0 T / T M

Fig. 4. Schematic of a typical deformation-mechanism map. The axes are dimensionless: the stress (given as a shear stress) is normalized by the shear modulus y, and the temperature is normalized by the melting temperature T . The data may be M strongly affected by the structural state of the material (e.g. grain size) and by prior mechanical heat treatments.

failure data are rarely as comprehensive as one would like and it is often necessary to interpolate or extrapolate from the limited data available. Penny and Marriott (1971) and Greenfield (1972) review the available methods for doing this. Ashby and co-workers (Ashby, Gandhi and Taplin, 1979? Fields, Weerasooriya and Ashby, 1980; Gandhi and Ashby, 1979) have plotted times to failure in the form of fracture mechanism maps (Fig. 7) which also show regions where the different mechanisms of creep fracture operate. The three most important mechanisms of creep fracture are intergranular, trans-granular and rupture (also called dynamic recrystallization, and not to be confused with the common use of the term "creep rupture" to mean failure by any creep mechanism). Figure 8 shows how the three types of creep failure occur on a microscopic scale. In intergranular failure, voids form and grow at grain boundaries during tertiary creep. Linkage of these voids leads to failure along the grain boundaries, usually with a rather small degree of necking. In transgranular failure voids form throughout the grains instead. In rupture, repeated waves of recrystallization sweep through the material, cleaning up the dislocation networks and preventing void formation. Creep takes place in a succession of primary-creep transients and the specimen ultimately necks down to a point (or a sharp edge in the case of a sheet

^s/p | conventional plasticity

.yield strength

10' 10t \ \ | J_\ \ Y_

242 D.R.H. Jones

er

f I

/Tv!

\ \ σ

Fig. 5. Schematic of diffusion creep in a polycrystalline material. Under the driving force of the stress, atoms diffuse from the sides to the ends of the grains and the material elongates.

specimen).

APPLICATIONS OF CREEP TO FAILURE ANALYSIS

Provided that a structure has been correctly designed against creep, and the materials specified for the construction have actually been used, then failure by creep is most likely to occur by either overload or temperature excursion. If the component is operating at relatively high stresses, so that power-law creep dominates (Fig. 4) then eqn. (10) shows that a comparatively small overload can greatly speed up the creep rate. As an example, n for 316 stainless steel is 7.9 (Frost and Ashby, 1982) so that a 30 % overload will give an 8 times increase in creep rate.1 Fortunately, most structures operate in the diffusion creep region (Fig. 4) so that the creep rate is only linearly dependent on the stress (eqn. (9)). However, if an overload takes the component up into the power-law region, then failure may rapidly follow. Turning to temperature excursions, because both the diffusion creep and power-law creep equations involve the temperature in an exponential term, small temperature changes can cause large increases in creep rate. Diffusion creep rates are generally less sensitive to temperature than are power-law creep rates (Frost and Ashby, 1982). In the diffusion creep region, a temperature increase of 100° C will typically increase the creep rate by 5 times. In the power-law region an extra 100° C will typically give a 10


Fig. 6. Creep-rupture diagram. A component operating at a stress σ and temperature T can be expected to fail after time t .

times increase in creep rate.

Creep mechanisms can be very valuable in analyzing a failure. Large reductions in area at the failure strongly suggest a failure by rupture, which, in turn, indicates that the failed component has been grossly overheated. It is more difficult to distinguish between intergranular and transgranular failure simply on the basis of reduction in area. But if metallurgical sections are cut from material near the fracture, the creep cavities can be seen in the light microscope. The fracture can then be classified and placed in the appropriate region on the fracture-mechanism map.

If neither overload nor temperature excursions can give a satisfactory explanation of a creep failure, the material itself may be suspect. Thielsch (1974) gives an example of a boiler tube failure caused by using a plain carbon steel where a 2 1/4 Cr-1 Mo steel was specified. In order to resist power-law creep, materials should be designed to resist the glide and climb of dislocations as effectively as possible. This can be done in the following ways :

(a) Choose a solid with a large lattice resistance: this means covalent bonding (as in many oxides, and in silicates, silicon carbide, silicon nitride, etc.). Unfortunately, this is rarely practicable.


σ/Ε dynamic fracture

-ductile fracture transgranular creep fracture

rupture (dynamic re crystallization)

Fig. 7. Schematic of a typical fracture-mechanism map for an f.c.c. material. The axes are dimension-less: the stress (given as a tensile stress) is normalized by Young's modulus E, and the temperature is normalized by the meltina temperature T . Maps for materials which cleave W also have regions of cleavage fracture in the left-hand part of the diagram. Maps for materials which undergo phase transformations (e.g. a to γ in ferritic steels) show discontinuities at the temperatures of the transformations.

(b) Alloy to give solid solution or dispersion strengthening. Both solutions and precipitates must, of course, be stable at the service temperature.

(c) Choose a material with a high melting point, since diffusion (and thus

rates of climb) scale as T/T . M

(d) Choose a material with low lattice and dislocation-core diffusion coefficients.

In order to resist diffusion creep one should:

(a) Choose a material with a high melting point.

(b) Choose a material with low lattice and grain-boundary diffusion coefficients.


I I

I I Transgranular Rupture

(dynamic recrystallization)

Fig. 8. Microscopic details of the main creep-fracture mechanisms.

(c) Have a large grain size (eqn. (11)).

(d) Arrange to have precipitates at grain boundaries to resist grain boundary movement.

It is obvious from these requirements why creep is so sensitive to material composition and microstructure. And it is equally obvious that departures from the specified materials are inadvisable!

Shortage of data presents a problem for the designer. Most components are designed to operate at low stresses for long times, yet data is most easily obtained from short-term tests carried out at high stresses. As Figs. 2 and 4 show, if power-law creep data are extrapolated into the diffusion creep region, the data will suggest a creep rate that is slower, often by orders of magnitude, than the actual creep rate. Extrapolation of creep rates can, therefore, be very hazardous. Similar problems arise when creep-failure times are extrapolated across the boundaries that separate regions having different creep-fracture mechanisms (Fig. 7 ) .

Special difficulties are presented by welds : the structures of welds and heat-affected zones may be quite different from the structure of the parent metal, and may give quite different creep properties. The phenomenon of reheat cracking is an excellent example of the application of creep analysis. High-performance welds are invariably reheated to 500-650° C in order to relieve the residual stresses (which, initially, are of the order of the

246 D.R.H. Jones

yield strength). Intergranular cracking is frequently observed in the heat affected zones of reheated creep resisting alloys such as austenitic stainless and ferritic steels and nickel-based alloys (Easterling, 1983). Precipitation of carbides such as VC and NbC in the heat-affected zone suppresses power-law creep so that the dominant creep mechanism becomes diffusion creep. The grain boundary sliding that occurs during diffusion creep is then thought to lead to the nucleation and growth of voids at the grain boundaries. Heat affected zones frequently have large grain sizes due to grain coarsening. The localization of the creep damage to a very small region of the material then leads to a low overall creep ductility - less than that needed to relieve the residual strains in the weldment.

A FINAL NOTE

Creep is an inescapable feature of high-temperature design. But few practical situations involve creep alone; and many failures at high temperature, even if they involve creep at some stage, are due primarily to other causes. Thermal fatigue is a common source of failure; and situations involving rapid temperature changes, mechanical restraint, poorly conducting materials and badly matched expansion coefficients should always be suspect. Oxidation and corrosion are obvious problems. Less obvious perhaps are the direct consequences of diffusion at high temperature: diffusional contamination, carburization, decarburization, interdiffusion between mixed materials, microstructural degradation (grain and precipitate coarsening) and unwanted transformations. And one last complication - creep processes are sensitive to environment and can be directly affected by oxidation and corrosion.

REFERENCES

Ashby, M. F., C. Gandhi, and D. M. R. Taplin (1979). Fracture-mechanism maps and their construction for f.c.c. metals and alloys. Acta Met., 27, 699-729.

Ashby, M. F., and D. R. H. Jones (1980). Engineering Materials. Pergamon, Oxford.

Easterling, K. (1983). Introduction to the Physical Metallurgy of Welding. Butterworths, London.

Fields, R. J., T. Weerasooriya, and M. F. Ashby (1980). Fracture-mechanisms in pure iron, two austenitic steels and one ferritic steel. Met. Trans., HA, 333-347.

Frost, H. J., and M. F. Ashby (1982). Deformation-Mechanism Maps. Pergamon, Oxford.

Gandhi, C , and M. F. Ashby (1979). Fracture-mechanism maps for materials which cleave: f.c.c, b.c.c, and h.c.p. metals and ceramics. Acta Met. , _27, 1565-1602.

Greenfield, P. (1972). Creep of Metals at High Temperatures. Mills and Boon, London.

fracture and fracture mechanics || failure by creep

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