Creep-resistant alloy design

7.9.4 Creep-resistant alloy design

The problem of the design of engineering creep- resistant alloys is complex, and the optimum alloy for

a given service usually contains several constituents in various states of solution and precipitation. Never- theless, it is worth considering some of the principles underlying creep-resistant behaviour in the light of the preceding theories.

First, let us consider the strengthening of the solid solution by those mechanisms which cause disloca- tion locking and those which contribute to lattice friction hardening. The former include solute atoms interacting with (1) the dislocation or (2) the stacking fault. Friction hardening can arise from (1) the stress fields around individual atoms (i.e. the Mott –Nabarro effect), (2) clusters of solute atoms in solid solutions, (3) by increasing the separation of partial dislocations and so making climb, cross-slip and intersection more difficult, (4) by the solute atoms becoming attached to jogs and thereby impeding climb, and (5) by influ- encing the energies of formation and migration of vacancies. The alloy can also be hardened by precipi- tation, and it is significant that many of the successful industrial creep-resistant alloys are of this type (e.g. the nickel alloys, and both ferritic and austenitic steels).

The effectiveness of these various methods of con- ferring strength on the alloy will depend on the con- ditions of temperature and stress during creep. All the effects should play some part during fast primary creep, but during the slow secondary creep stage the impeding of dislocation movement by solute locking effects will probably be small. This is because modern creep-resistant alloys are in service up to tempera- tures of about two-thirds the absolute melting point

⊲T/T m ' 2 3 ⊳ of the parent metal, whereas above about T/T m ' 1 2 solute atoms will migrate as fast as dis-

locations. Hardening which relies on clusters will be more difficult to remove than that which relies upon single atoms and should be effective up to higher tem- peratures. However, for any hardening mechanism to

be really effective, whether it is due to solute atom clusters or actual precipitation, the rate of climb and cross-slip past the barriers must be slow. Accordingly, the most probable role of solute alloying elements in modern creep-resistant alloys is in reducing the rate of climb and cross-slip processes. The three hardening mechanisms listed as 3, 4 and 5 above are all effective in this way. From this point of view, it is clear that the best parent metals on which to base creep-resistant alloys will be those in which climb and cross-slip

250 Modern Physical Metallurgy and Materials Engineering is difficult; these include the fcc and cph metals of

hinder a dislocation and force it to climb and cross- low stacking-fault energy, for which the slip disloca-

slip. Second, and more important, is the retarding tions readily dissociate. Generally, the creep rate is

effect on recovery as shown by some dispersions, described by the empirical relation

Cu–Al 2 O 3 (extruded), SAP (sintered alumina powder), P

⊲ ⊳ m D (7.58)

and Ni –ThO which retain their hardness almost to

2 the melting point. A comparison of SAP with a

where A is a constant, n, m stress and fault energy ‘conventional’ complex aluminium alloy shows that exponents, respectively, and D the diffusivity; for

C there is little to choose between them but fcc materials m ³ 3 and n ³ 4. The reason for the

at 250 °

C SAP is several times stronger. Generally, good creep strength of austenitic and Ni-base materials

at 400 °

the dislocation network formed by strain-hardening containing Co, Cr, etc. arises from their low fault

interconnects the particles and is thereby anchored energy and also because of their relatively high melting

by them. To do this effectively, the particle must be point when D is small.

stable at the service temperature and remain finely From the above discussion it appears that a suc-

dispersed. This depends on the solubility C, diffusion cessful creep-resistant material would be an alloy, the

coefficient D and interfacial energy 1 , since the composition of which gives a structure with a hardened

time to dissolve the particle is t D r 4 kT/DC 1 R 2 . In solid–solution matrix containing a sufficient number

precipitation-hardening alloys, C is appreciable, and D of precipitated particles to force glissile partial dis-

offers little scope for adjustment; great importance is locations either to climb or to cross-slip to circum-

therefore placed on 1 as for the Ni 3 (TiAl) phase in vent them. The constitution of the Nimonic alloys,

Nimonics where it is very low. which consist of a nickel matrix containing dissolved

Figure 7.63 shows that n ³ 4 both above and below chromium, titanium, aluminium and cobalt, is in accor-

0.5T m for the Ni –Al 2 O 3 and Ni–Co–Al 2 O 3 alloys dance with these principles, and since no large atomic

that were completely recrystallized, which contrasts size factors are involved it appears that one of the func-

with values very much greater than 4 for extruded TD tions of these additions is to lower the stacking-fault

nickel and other dispersion-strengthened alloys 1 con- energy and thus widen the separation of the partial

taining a dislocation substructure. This demonstrates dislocations. A second object of the titanium and alu-

the importance of substructure and probably indicates minium alloy additions 1 is to produce precipitation,

that in completely recrystallized alloys containing a and in the Nimonic alloys much of the precipitate is

dispersoid, the particles control the creep behaviour, Ni 3 Al. This precipitate is isomorphous with the matrix,

whereas in alloys containing a substructure the dis-

location content is more important. Since n ³ 4 for enough to give a low interfacial energy, it is, neverthe-

and while it has a parameter difference ⊲³ 1 2 %⊳ small

the Ni– and Ni–Co–Al 2 O 3 alloys in both tempera- less, sufficiently large to give a source of hardening.

ture regimes, the operative deformation mechanism is Thus, since the energy of the interface provides the

likely to be the same, but it is clear from the activation driving force for particle growth, this low-energy inter-

energies, listed in Table 7.4, that the rate-controlling face between particle and matrix ensures a low rate of

thermally activated process changes with temperature. particle growth and hence a high service temperature.

The activation energy is greater at the higher tem- Grain boundary precipitation is advantageous in

perature when it is also, surprisingly, composition (or reducing grain boundary sliding. Alternatively, the

stacking-fault energy) independent. weakness of the grain boundaries may be eliminated

Such behaviour may be explained, if it is assumed altogether by using single-crystal material. Nimonic

that the particles are bypassed by cross-slip (see alloys used for turbine blades have been manufactured

Chapter 8) and this process is easy at all temperatures, in single-crystal form by directional solidification (see

but it is the climb of the edge segments of the cross- Chapters 3 and 10).

slipped dislocations that is rate-controlling. At low Dispersions are effective in conferring creep

temperatures, climb would proceed by pipe-diffusion strength by two mechanisms. First the particle will 1 To analyse these it is generally necessary to introduce a 1 The chromium forms a spinel with NiO and hence

0 , so that the effective stress improves the oxidation resistance.

Table 7.4 Experimentally-determined parameters from creep of Ni –Al 2 O 3 and Ni –Co–Al 2 O 3 alloys

temperature Alloy

Q⊲kJ mol ⊳

A⊲s ⊳

Q⊲kJ mol ⊳

1.1 ð 10 28 5.5 ð 10 28 Ni–67% Co

Mechanical behaviour of materials 251

Figure 7.67 Schematic diagram showing the distribution of second-phase particles before and after diffusion creep .

so that the composition-dependence relates to the vari-

a PFZ. Such a structural change has been observed in ation in the ease of pipe-diffusion along dislocations

C and is accom- of different widths. At high temperatures, climb occurs

Mg–0.5%Zr (Magnox ZR55 ) at 400 °

panied by a reduced creep rate. It is not anticipated by bulk diffusion and the absence of any composition-

that diffusion is significantly affected by the presence dependence is due to the fact that in these alloys

of particles and hence the effect is thought to be due to the jog distribution is determined mainly by disloca-

the particles affecting the vacancy-absorbing capabil- tion/particle interactions and not, as in single-phase

ities of the grain boundaries. Whatever mechanism is alloys and in dispersion-strengthened alloys containing

envisaged for the annihilation of vacancies at a grain

a substructure, by the matrix stacking-fault energy. The boundary, the climb-glide of grain boundary disloca- optimum creep resistance of dispersion-strengthened

tions is likely to be involved and such a process will alloys is produced when a uniform dislocation net-

be hindered by the presence of particles. work in a fibrous grain structure is anchored by the

particles and recovery is minimized. Such a structure can reduce the creep rate by several orders of mag- nitude from that given in Figure 7.63, but it depends

7.10 Deformation mechanism maps

critically upon the working and heat-treatment used in fabricating the alloy.

The discussion in this chapter has emphasized that Second-phase particles can also inhibit diffusion

over a range of stress and temperature an alloy is creep. Figure 7.67 shows the distribution of particles

capable of deforming by several alternative and inde- before and after diffusion creep and indicates that

pendent mechanisms, e.g. dislocation creep with either the longitudinal boundaries tend to collect precipi-

pipe diffusion at low temperatures and lattice diffusion tates as vacancies are absorbed and the boundaries

at high temperatures being the rate-controlling mecha- migrate inwards, while the tensile boundaries acquire

nism, and diffusional creep with either grain-boundary

252 Modern Physical Metallurgy and Materials Engineering

Figure 7.68 Deformation-mechanism maps for (a) nickel, (b) nickel-based superalloy (after M. F. Ashby) .

diffusion or lattice diffusion being important. In a par- to poor design of the component, but in some can ticular range of temperature, one of these mechanisms

be ascribed to the condition of the material. Conse- is dominant and it is therefore useful in engineering

quently, the treatment of fatigue may be conveniently application to identify the operative mechanism for a

divided into three aspects: (1) engineering consider- given stress–temperature condition, since it is ineffec-

ations, (2) gross metallurgical aspects, and (3) fine- tive to change the metallurgical factors to influence, for

scale structural and atomic changes. example, a component deforming by power-law creep

The fatigue conditions which occur in service controlled by pipe diffusion if the operative mechanism

are usually extremely complex. Common failures is one of Herring–Nabarro creep.

are found in axles where the eccentric load at a The various alternative mechanisms are displayed

wheel or pulley produces a varying stress which is conveniently on a deformation-mechanism map in

a maximum in the skin of the axle. Other examples, which the appropriate stress, i.e. shear stress or equiv-

such as the flexure stresses produced in aircraft wings alent stress, compensated by modulus on a log scale,

and in undercarriages during ground taxi-ing, do, is plotted against homologous temperature T/T m as

however, emphasize that the stress system does not shown in Figure 7.68 for nickel and a nickel-based

necessarily vary in a regular sinusoidal manner. The superalloy with a grain size of 100 µ m. By comparing

series of aircraft disasters attributed to pressurized- the diagrams it is evident that solid solution strength-

cabin failures is perhaps the most spectacular example ening and precipitation-hardening have raised the yield

of this type of fatigue failure. stress and reduced the dislocation creep field. The

shaded boxes shown in Figure 7.68 indicate the typi- cal stresses and temperatures to which a turbine blade

7.11.2 Engineering aspects of fatigue

would be subjected; it is evident that the mechanism In laboratory testing of materials the stress system is of creep during operation has changed and, indeed, the

usually simplified, and both the Woehler and push-pull creep rate is reduced by several orders of magnitude.

type of test are in common use. The results are usually plotted on the familiar S–N curve (i.e. stress versus the number of cycles to failure, usually plotted on a

7.11 Metallic fatigue

logarithmic scale). Ferritic steels may be considered to exhibit a genuine fatigue limit with a fatigue ratio

S/ TS ³ 0.5. However, other materials, such as alu- The term fatigue applies to the behaviour of a metal

7.11.1 Nature of fatigue failure

minium or copper-based alloys, certainly those of the which, when subjected to a cyclically variable stress

age-hardening variety, definitely do not show a sharp of sufficient magnitude (often below the yield stress)

discontinuity in the S–N curve. For these materials produces a detectable change in mechanical properties.

no fatigue limit exists and all that can be specified is In practice, a large number of service failures are due

the endurance limit at N cycles. The importance of to fatigue, and so engineers are concerned mainly with

the effect is illustrated by the behaviour of commer- fatigue failure where the specimen is actually separated

cial aluminium-based alloys containing zinc, magne- into two parts. Some of these failures can be attributed

sium and copper. Such an alloy may have a TS of

Mechanical behaviour of materials 253 617 MN/m 2 but the fatigue stress for a life of 10 8 show that the normal speed effect is reversed in a

cycles is only 154 MN/m 2 (i.e. a fatigue ratio at 10 8 certain temperature range and the number of cycles cycles of 0.25).

to failure increases with decrease in the frequency The amplitude of the stress cycle to which the spec-

of the stress cycle. This effect may be correlated imen is subjected is the most important single variable

with the influence of temperature and strain-rate in determining its life under fatigue conditions, but the

on the TS. The temperature at which the tensile performance of a material is also greatly affected by

strength reaches a maximum depends on the rate various other conditions, which may be summarized

of strain, and it is, therefore, not surprising that the as follows:

temperature at which the fatigue strength reaches a maximum depends on the cyclic frequency.

4. Mean stress For conditions of fatigue where the start at or near the surface of the component, the

1. Surface preparation Since fatigue cracks frequently

mean stress, i.e.

surface condition is an important consideration in

min fatigue life. The removal of machining marks and ⊳/ 2 other surface irregularities invariably improves the

f max

y , then the rela- fatigue properties. Putting the surface layers under

tionship

compression by shot peening or surface treatment improves the fatigue life. a

f D const.

2. Effect of temperature Temperature affects the fatigue known as Basquin’s law, holds over the range 10 properties in much the same way as it does the ten- 2 to ³10 sile strength (TS); the fatigue strength is highest at 5 cycles, i.e. N less than the knee of the S–N

curve, where a ³ low temperatures and decreases gradually with ris- 1 10 and N f the number of cycles ing temperature. For mild steel the ratio of fatigue

y then limit to TS remains fairly constant at about 0.5,

Basquin’s law no longer holds, but a reasonable while the ratio of fatigue limit to yield stress varies

relationship

over much wider limits. However, if the tempera-

(7.60) ture is increased above about 100

ε N b p D D f b D const.

C, both the tensile

strength and the fatigue strength of mild steel show known as the Coffin–Manson law, is found where an increase, reaching a maximum value between

ε p is the plastic strain range, b ³ 0.6, and D is the 200 °

C. This increase, which is not com- ductility of the material. If the mean stress becomes monly found in other materials, has been attributed

C and 400 °

tensile a lowering of the fatigue limit results. Several to strain-ageing.

relationships between fatigue limit and mean stress

3. Frequency of stress cycle In most metals the fre- have been suggested, as illustrated in Figure 7.69a. quency of the stress cycle has little effect on the

However, there is no theoretical reason why a mate- fatigue life, although lowering the frequency usually

rial should follow any given relationship and the results in a slightly reduced fatigue life. The effect

only safe rule on which to base design is to carry out becomes greater if the temperature of the fatigue

prior tests on the material concerned to determine its test is raised, when the fatigue life tends to depend

behaviour under conditions similar to those it will on the total time of testing rather than on the num-

meet in service. Another common engineering rela- ber of cycles. With mild steel, however, experiments

tionship frequently used, known as Miner’s concept

Figure 7.69 Fatigue relationships .

254 Modern Physical Metallurgy and Materials Engineering of cumulative damage, is illustrated in Figure 7.69b.

This hypothesis states that damage can be expressed in terms of the number of cycles applied divided by the number to produce failure at a given stress level.

Thus, if a maximum stress of value S 1 is applied to a

specimen for n 1 cycles which is less than the fatigue life N 1 , and then the maximum stress is reduced to

a value equal to S 2 , the specimen is expected to fail after n 2 cycles, since according to Miner the following relationship will hold

n 1 /N 1 Cn 2 /N 2 C . . . D n/N D 1

5. Environment Fatigue occurring in a corrosive envi- ronment is usually referred to as corrosion fatigue. It is well known that corrosive attack by a liquid medium can produce etch pits which may act as notches, but when the corrosive attack is simultane- ous with fatigue stressing, the detrimental effect is far greater than just a notch effect. Moreover, from microscopic observations the environment appears to have a greater effect on crack propagation than on crack initiation. For most materials even atmo- spheric oxygen decreases the fatigue life by influ- encing the speed of crack propagation, and it is possible to obtain a relationship between fatigue life and the degree of vacuum in which the specimen has been held.

It is now well established that fatigue starts at the surface of the specimen. This is easy to understand in the Woehler test because, in this test, it is there that the stress is highest. However, even in push–pull fatigue, the surface is important for several reasons: (1) slip is easier at the surface than in the interior of the grains, (2) the environment is in contact with the surface, and (3) any specimen misalignment will always give higher stresses at the surface. Accordingly, any alteration in surface properties must bring about

a change in the fatigue properties. The best fatigue resistance occurs in materials with a worked surface layer produced by polishing with emery, shot-peening or skin-rolling the surface. This beneficial effect of a worked surface layer is principally due to the fact that the surface is put into compression, but the increased TS as a result of work hardening also plays a part. Electropolishing the specimen by removing the sur- face layers usually has a detrimental effect on the fatigue properties, but other common surface prepara- tions such as nitriding and carburizing, both of which produce a surface layer which is in compression, may

be beneficial. Conversely, such surface treatments as the decarburizing of steels and the cladding of alu- minium alloys with pure aluminium, increase their susceptibility to fatigue.

The alloy composition and thermal and mechanical history of the specimen are also of importance in the fatigue process. Any treatment which increases the hardness or yield strength of the material will increase the level of the stress needed to produce slip and, as we shall see later, since the fundamental processes

of fatigue are largely associated with slip, this leads directly to an increase in fatigue strength. It is also clear that grain size is a relevant factor: the smaller the grain size, the higher is the fatigue strength at a given temperature.

The fatigue processes in stable alloys are essen- tially the same as those of pure metals but there is, of course, an increase in fatigue strength. However, the processes in unstable alloys and in materials exhibit- ing a yield point are somewhat different. In fatigue, as in creep, structural instability frequently leads to enhancement of the fundamental processes. In all cases the approach to equilibrium is more complete, so that in age-hardening materials, solution-treated speci- mens become harder and fully aged specimens become softer. The changes which occur are local rather than general, and are associated with the enhanced diffusion brought about by the production of vacancies during the fatigue test. Clearly, since vacancy mobility is a thermally activated process such effects can be sup- pressed at sufficiently low temperatures.

In general, non-ferrous alloys do not exhibit the type of fatigue limit shown by mild steel. One exception to this generalization is the alloy aluminium 2–7% magnesium, 0.5% manganese, and it is interesting to note that this alloy also has a sharp yield point and shows L¨uders markings in an ordinary tensile test. Accordingly, it has been suggested that the fatigue limit occupies a similar place in the field of alternat- ing stresses to that filled by the yield point in uni- directional stressing. Stresses above the fatigue limit readily unlock the dislocations from their solute atom atmospheres, while below the fatigue limit most dis- locations remain locked. In support of this view, it is found that when the carbon and nitrogen content of mild steel is reduced, by annealing in wet hydro- gen, striking changes take place in the fatigue limit (Figure 7.5) as well as in the sharp yield point.