Creep-resistant alloy design

6.9.4 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. Nevertheless, it is worth considering some of the principles underlying creep-resistant behavior in the light of the preceding theories.

First, let us consider the strengthening of the solid solution by those mechanisms which cause dislocation 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 influencing the energies of formation and migration of vacancies. The alloy can also be hardened by precipitation, 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 conferring strength on the alloy will depend on the conditions 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 temperatures of about two-thirds the absolute melting point (T /T

m ≈ 3 ) of the parent metal, whereas above about T /T

m ≈ 2 solute atoms will migrate as fast as dislocations. 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 temperatures. 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 are difficult; these include the fcc and cph metals of low stacking-fault energy, for which the slip dislocations readily dissociate. Generally, the creep rate is described by the empirical relation

˙ε = A(σ/E) n (γ) m D, (6.58) where A is a constant, n and m stress and fault energy exponents respectively, and D the diffusivity;

for fcc materials m ≈ 3 and n ≈ 4. The reason for the good creep strength of austenitic and Ni-based

Mechanical properties I 369 materials containing Co, Cr, etc. arises from their low fault energy and also because of their relatively

high melting point when D is small.

From the above discussion it appears that a successful creep-resistant material would be an alloy, the composition of which gives a structure with a hardened solid–solution matrix containing a sufficient number of precipitated particles to force glissile partial dislocations either to climb or to cross-slip to circumvent them. The constitution of the Nimonic alloys, which consist of a nickel matrix containing dissolved chromium, titanium, aluminum and cobalt, is in accordance with these principles, and since no large atomic size factors are involved it appears that one of the functions of these additions is to lower the stacking-fault energy and thus widen the separation of the partial dislocations. A second

object of the titanium and aluminum alloy additions 7 is to produce precipitation, and in the Nimonic alloys much of the precipitate is Ni 3 Al. This precipitate is isomorphous with the matrix, and while it has a parameter difference ( 1 ≈ 2 %) small enough to give a low interfacial energy, it is nevertheless sufficiently large to give a source of hardening. Thus, since the energy of the interface provides the driving force for particle growth, this low-energy interface between particle and matrix ensures a low rate of particle growth and hence a high service temperature.

Grain boundary precipitation is advantageous in reducing grain boundary sliding. Alternatively, the weakness of the grain boundaries may be eliminated altogether by using single-crystal material. Nimonic alloys used for turbine blades have been manufactured in single-crystal form by directional solidification (see Chapters 2 and 8).

Dispersions are effective in conferring creep strength by two mechanisms. First, the particle will hinder a dislocation and force it to climb and cross-slip. Second, and more important, is the retarding effect on recovery as shown by some dispersions, Cu–Al 2 O 3 (extruded), SAP (sintered alumina pow- der) and Ni–ThO 2 , which retain their hardness almost to the melting point. A comparison of SAP with

C there is little to choose between them but at 400 ◦

a ‘conventional’complex aluminum alloy shows that at 250 ◦

C SAP is several times stronger. Generally, the dislocation network formed by strain hardening interconnects the particles and is thereby anchored by them. To do this effectively, the particle must be stable at the service temperature and remain finely dispersed. This depends on the solubility C, diffu-

sion coefficient D and interfacial energy γ 1 , since the time to dissolve the particle is t =r 4 kT /DCγ 1 R 2 . In precipitation-hardening alloys, C is appreciable and D offers little scope for adjustment; great importance is therefore placed on γ 1 as for the Ni 3 (TiAl) phase in Nimonics, where it is very low. Figure 6.62 shows that n ≈ 4 both above and below 0.5T m for the Ni–Al 2 O 3 and Ni–Co–Al 2 O 3 alloys that were completely recrystallized, which contrasts with values very much greater than 4 for extruded TD nickel and other dispersion-strengthened alloys 8 containing a dislocation substructure. This demonstrates the importance of substructure and probably indicates that in completely recrys- tallized alloys containing a dispersoid, the particles control the creep behavior, whereas in alloys containing a substructure the dislocation content is more important. Since n ≈ 4 for the Ni– and

Ni–Co–Al 2 O 3 alloys in both temperature regimes, the operative deformation mechanism is likely to

be the same, but it is clear from the activation energies, listed in Table 6.4, that the rate-controlling thermally activated process changes with temperature. The activation energy is greater at the higher temperature when it is also, surprisingly, composition (or stacking-fault energy) independent.

Such behavior may be explained, if it is assumed that the particles are bypassed by cross-slip (see Chapter 7) and this process is easy at all temperatures, but it is the climb of the edge segments of the cross-slipped dislocations that is rate controlling. At low temperatures, climb would proceed by pipe diffusion so that the composition dependence relates to the variation in the ease of pipe diffusion along dislocations of different widths. At high temperatures, climb occurs by bulk diffusion and the

7 The chromium forms a spinel with NiO and hence improves the oxidation resistance. 8 To analyze these it is generally necessary to introduce a threshold (or friction) stress σ 0 , so that the effective stress is

370 Physical Metallurgy and Advanced Materials Table 6.4 Experimentally determined parameters from creep of Ni–Al 2 O 3 and Ni–Co–Al 2 O 3

alloys. Alloy

Test temperature

5.5 × 10 28 Ni–67% Co

absence of any composition dependence is due to the fact that in these alloys the jog distribution is determined mainly by dislocation/particle interactions and not, as in single-phase alloys and in dispersion-strengthened alloys containing a substructure, by the matrix stacking-fault energy. The optimum creep resistance of dispersion-strengthened alloys is produced when a uniform dislocation network 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 magnitude from that given in Figure 6.62, but it depends critically upon the working and heat treatment used in fabricating the alloy.

Second-phase particles can also inhibit diffusion creep. Figure 6.66 shows the distribution of particles before and after diffusion creep, and indicates that the longitudinal boundaries tend to collect precipitates as vacancies are absorbed and the boundaries migrate inwards, while the tensile boundaries acquire a PFZ. Such a structural change has been observed in Mg–0.5% Zr (Magnox ZR55) at 400 ◦

C and is accompanied by a reduced creep rate. It is not anticipated that diffusion is significantly affected by the presence of particles and hence the effect is thought to be due to the particles affecting the vacancy-absorbing capabilities of the grain boundaries. Whatever mechanism is envisaged for the annihilation of vacancies at a grain boundary, the climb-glide of grain boundary dislocations is likely to be involved and such a process will be hindered by the presence of particles.