High Temperature Strain of Metals and Alloys Part 11 docx

8.2 Alloys of Refractory Metals A review of the creep behavior of refractory metal alloys has been published [53].. 8.10 the typical creep behavior of the refractory metal alloys.. The c

Fig 8.5 The logarithm of strain rate versus stress in

molybdenum The testing temperatures are B, 1973; C, 2173;

D, 2373; E, 2573; F, 2773 K (from 0.68 to 0.96Tm)

is presented in Fig 8.9 The authors plot experimental data inlog ˙ε − log σ

coordinates Two segments of straight lines are observed at every test temper-ature At low stresses the creep rate is directly proportional to stress, so that the factor in the power-law equation (1.1),n = 1 At higher stresses factor n

increases abruptly to 8–9 The slope of the curves changes at critical stresses,

σcr, 10, 20, and 70MPa at 1973, 1633 and 1033 K, respectively

No creep strain withn = 1 was observed earlier In Ref [26] the authors

call it a high-temperature power-like creep The primary stage covers nearly 80% of the strain to rupture The polished surface of specimens exhibits slip bands, thus, the slip of dislocations occurs

The creep mechanism of molybdenum, which has a body-centered crys-tal lattice, differs from the creep in mecrys-tals that have a face-centered cryscrys-tal lattice Unlike face-centered metals the minimum creep rate of molybde-num depends weakly on temperature The critical creep rates in the studied temperature range (changes of flection coordinates) are from2.2 × 10 −8 to 1.3×10 −8s−1 The only visible effect is a shift of the functionlog ˙ε = f(log σ)

to higher stresses

Molybdenum specimens have a random dislocation distribution after creep

in the rangen = 1 The ordered dislocation sub-boundaries cannot be formed

8.2 Alloys of Refractory Metals 149

Fig 8.6 The logarithm of strain rate versus the inverse

abso-lute temperature for molybdenum The applied stress,MPa,

is equal to: B, 9.81; C, 19.62; D, 29.43; E, 39.24; F, 49.05

undern = 1 conditions Only some grains close to the break stress between

segments n = 1 and n = 8 have sub-boundaries, obviously due to a local

overstress Atn = 8 one can observe well formed sub-boundaries With

in-creasing stress the dislocation density in both sub-boundaries and subgrains increases, and the structure eventually becomes cellular

8.2

Alloys of Refractory Metals

A review of the creep behavior of refractory metal alloys has been published [53]

A so called Larsom-Miller parameter,P , is widely used to estimate the creep

strength of alloys:

whereT is temperature of the tests, t1%is the time of 1% deformation of a specimen, 15 is an empirically determined value

Fig 8.7 The measured activation energy of high-temperature strain for molybdenum

Fig 8.8 The strain rate map for molybdenum with a grain size of 100µm Reprinted from Ref [26]

8.2 Alloys of Refractory Metals 151

Fig 8.9 The effect of stress on the steady-state creep in molybdenum at temperatures: 1, 1973; 2, 1633; 3, 1303 K Experimental data from Ref [52]

One can see in Fig 8.10 the typical creep behavior of the refractory metal alloys The corresponding nominal compositions of alloys are presented in Table 8.3 Molybdenum-, niobium- and tantalum-based alloys have been de-veloped, studied and utilized

The creep properties of the refractory alloys are very sensitive to composi-tion, structural features, and test environment Small quantities of interstitial atoms such as C, O and N may also have an important effect on the proper-ties Moreover, additional factors are possible, such as even the geographic location from which the metal ore was obtained and technological features during the production process

Other factors affecting creep behavior include grain size, which can be attributed to the annealing temperature (Fig 8.11)

Many studies have been devoted to the search for potential strengtheners of refractory metals Incoherent or semi-coherent particles have been the most commonly investigated These precipitates are based on carbides Hafnium

Tab 8.3 Nominal composition of some refractory alloys

Data from [53]

1 Mo-TZM bal 1.0 0.75 – – – – – –

3 PWC-11 – – 1.0 bal – – – – 0.10

5 ASTAR-811C – – – – bal 8.0 0.7 1.0 0.025

Fig 8.10 Applied stress to produce 1% creep strain in some

refractory alloys Composition of alloys given in Table 8.3

Reprinted from Ref [53] with permission from Elsevier Science

Ltd

carbide possesses the highest melting point Tungsten–rhenium–hafnium carbide alloys seem to be promising for operation at high temperatures

Fig 8.11 Effect of annealing temperature on applied stress

to produce 1% creep in ASTAR-81C alloy 1, annealed at

1923 K; 2, annealed at 2273 K Reprinted from Ref [53]

8.2 Alloys of Refractory Metals 153

Fig 8.12 Logarithm steady-stage creep rate versus the

logarithm stress for W–4Re–0.32HfC alloy The testing

temperatures are B, 2200; C, 2300; D, 2400 K Experimental

data from Ref [54]

Park [54] compares some creep models with the experimental data on the creep behavior of W–4Re–0.32HfC alloy He obtained strain–time creep curves of the tested alloy at 2200 K Three regions of a creep curve are nor-mally observed: primary, secondary and tertiary strain The secondary creep rate is assumed by the author to be expressed as ˙ε ∼ σ n[see Eq (1.1)] Three

straight parallel lines were obtained from thislog ˙ε − log σ plot, Fig 8.12,

im-plying that the secondary creep rate and the applied stress have a power-law relationship The value ofn was obtained from the slope of each straight line,

and a least-squares analysis yieldedn = 5.2 Three creep models for

second-phase particle-strengthened alloys were applied to the creep behavior of the alloy in this research Park [54] studied the Ansell-Weertman, the Langeborg, and the Roesler-Arzt models (the reader can find references in the quoted ar-ticle) The conclusion was as follows: “The results showed that none of these models predicted the creep behavior of the alloy” Some models predicted the secondary creep rate approximately five orders of magnitude different from the value obtained experimentally

However, the same experimental data satisfy another dependence, for ex-ample, an exponential one In Fig 8.13 the same strain rates are plotted as

log ˙ε−σ We also obtain straight lines which imply the dependence ˙ε ∼ exp σ.

We have noted (Chapter 1) that a functional dependence only makes it not possible to conclude unequivocally about a physical mechanism of strain The orientation relationship between a matrix structure and a precipitate structure have a dramatic effect on the creep deformation The preferred

Fig 8.13 Logarithm steady-stage creep rate versus the stress

for W–4Re–0.32HfC alloy The same experimental data as in

Fig 8.12 from Ref [54] are used

orientation relationships between coherent and semi-coherent precipitates and matrix may result in an improved resistance against slip of deforming dislocations

A niobium–titanium-based alloy has been investigated by Allamen et al [55] The alloy under study contains 44Nb–35Ti–6Al–5Cr–8V–1W–0.5Mo– 0.3Hf The microstructure of extruded and recrystallized material consists of

a solid solution and of particles of titanium carbide, TiC The particle sizes are between 200 and 500 nm Creep curves were obtained at 977 K

At relatively low stress, 103MPa, the slipping dislocations were attracted

to TiC particles The attraction is energetically favored when the modulus mismatch between the phases is decreased by diffusion In contrast, a higher density of dislocations is observed at the higher stress 172MPa, along with bowed dislocations that are pinned by carbide particles

The lattice periodicity in the [200]-type direction of the cubic body centered matrix is about 0.33 nm On the other hand, for the [220]-type direction of the cubic face-centered precipitate, the lattice periodicity is about 0.32 nm The misfit is about 3% This may explain why these two directions are nearly parallel at the precipitate/matrix interface A specific orientation relationship, namely: [100](110) matrix parallel to [220](111) precipitates, was observed in the specimens subjected to the highest stress level

The development of superalloys for operation at temperatures up to 2073 K continues New classes of alloys attract investigators and engineers Refractory superalloys based on the platinum group metals have a cubic face centered crystal lattice, high melting temperature, and a coherent two-phase structure

8.3 Summary 155

A two-phase iridium-based refractory superalloy has been proposed re-cently [56] The alloy is strengthened by a coherent phase ofL12type This structure is similar to that of nickel-based superalloys The authors investi-gated the strength behavior and the structure of some binary iridium-based alloys The systems Ir–Nb and Ir–Zr are found to be the most promising alloys for study at temperatures up to 1473 K

The rupture life of Ir–Nb alloys was found to be increased dramatically

by the addition of nickel The strengthening phase was determined to be

(Ni, Ir)3Nb The steady-state creep rate at 1923 K for the Ir–15Nb–1Ni alloy was1.2 × 10 −8s−1, about three orders of magnitude lower than that of the

binary Ir–17Nb alloy(10−5s−1)

This shows that the iridium-based alloys may possibly be regarded as ultra-high temperature materials However there is a lot of work ahead before new alloys of this type can be used practically

8.3

Summary

The physical properties of refractory metals are related to their high melting points They look very promising from the practical point of view The most refractory metals have, however, drawbacks such as poor low-temperature fabricability and an extreme high-temperature oxidizability When used they need a protective atmosphere or a coating

The minimum strain rate of niobium and molybdenum is dependent ex-ponentially on the applied stress at high temperatures

The mean value of the activation energy of the high-temperature strain for niobium is found to be Q = (7.5 ± 0.6) × 10 −19Jat.−1, for molybdenum

Q = (5.59 ± 0.35) × 10 −19Jat.−1.

It follows from the experimental data that the rate-controlling mechanism

of strain for niobium is the slip of deforming dislocations with one-signed jogs

Molybdenum-, niobium- and tantalum-based alloys have been developed These alloys are able to operate at temperatures up to 1900 K The creep properties of the refractory alloys are very sensitive to composition, structural features, and test environment Other factors have yet to be studied in any detail

The alloys of the systems Ir–Nb and Ir–Zr are found to be the promising for future study

The concept of dislocations is known to be important in the theory of strength and plasticity [18, 20, 21] Let us recall the main theses of the theory of dislo-cations

A crystal lattice is not ideal The arrangement of atoms differs from a reg-ular order This is the immediate cause of the great discrepancy between the theoretical strength of materials and the measured values The practical strength is about three orders less than the strength that would follow from the concept of a regular atomic lattice Any crystal lattice contains defects, i.e there are areas where the structure is irregular

The point is that atoms on a slip plane do not displace simultaneously under the effect of the applied stress The atomic bonds do not break all at the same time The dislocation lines move along slip planes A dislocation is

a one-dimensional defect This means that the dislocation extent is compared with the crystal size in only one dimension In the two other dimensions the dislocation has the extents of the interatomic order The crystal lattice is disturbed along the dislocation line So the dislocation is the line defect in the crystal lattice It is like a stretched string

There are two vectors, which determine the dislocation line at any point

The dislocation line vector is denoted by
ξ The Burgers vector is denoted by
b The unit vector
ξ is directed along the tangent to the dislocation line at every

point It may be directed in a different way at different points of the same

dislocation line The Burgers vector
b is related to the atomic displacements,

which the dislocation causes in the crystal lattice The Burgers vector is the same along a given dislocation, i.e it does not change with the coordinates The magnitude of the Burgers vector is the interatomic distance b It is a

measure of deformation associated with the dislocation The Burgers vector is always directed along a close-packed crystallographic direction This provides

High Temperature Strain of Metals and Alloys, Valim Levitin (Author)

Copyright c
2006 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim

ISBN: 3-527-313389-9

158 Supplements

Fig S1 Motion of the edge dislocation (⊥) in a crystal lattice

under the effect of shear stress

the smallest value ofb and, therefore, the lowest energy per unit length of

dislocation

Dislocations move under the influence of external forces, which cause an internal stress in a crystal slip plane The force per unit length of dislocation,

F , exerted on the dislocation by the shear stress τ is F = bτ The area swept

by the dislocation movement defines a slip plane, which always (by definition)

contains the vector
ξ.

In Fig S1 the edge dislocation formation and its movement is shown Figure S1(a) demonstrates the generation of an edge dislocation by a shear stress, dislocation is denoted as⊥ In Fig.S1(b) movement of the dislocation

through the crystal occurs and an extra-plane appears above the slip plane The shift of the upper half of the crystal takes place after the dislocation emerges from the crystal (Fig.S1(c)) The relative displacement of the two crystal halves is normal to the dislocation The Burgers vector of the edge dislocation is perpendicular to the line vector, so the scalar product

(
b ·
ξ) = 0

The edge dislocation can change its slip plane by means of a climb process

In this connection completion of the extra-plane occurs A diffusion flow of vacancies or interstitial atoms is needed for the climb of the edge dislocation The climb is a slower process than the slip

In Fig S2 screw dislocation is shown, for screw dislocation vector
b is parallel to vector
ξ:

(
b ·
ξ) = b

All dislocations have a character that is either pure edge, pure screw or a combination of the two In fact a dislocation is a boundary of a slip area It separates the area where the slip has occurred from the area where the slip has not yet occurred Dislocation lines may be arbitrarily curved In Fig S3 the arrangement of atoms in a mixed dislocation is shown Atoms denoted

circles are situated under the diagram plane We observe a transfer from the pure screw to the pure edge dislocation

In the general case one may consider the edge and screw components of the mixed dislocation In reality dislocation lines can have any shape, they can form loops and networks and they can contain jogs, nodes, junctions, kinks The dislocation possesses an energy The total energy per unit length is the sum of the energy contained in the elastic field and the energy in the dislocation core The self-energy per unit length of dislocation,Eel, depends upon the magnitude of the Burgers vector and the shear modulus of the material,µ, as Eel≈ µb2

The atoms nearest to the dislocation core are displaced most from their equilibrium positions and therefore they have the highest energy In order

to minimize this dislocation self-energy, the dislocation tries to be as short

as possible That is, a dislocation prefers to minimize its length rather than

Fig S3 A mixed dislocation

in a crystal lattice