148 8 Deformation of Some Refractory Metals 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 0.96 T m ). is presented in Fig. 8.9. The authors plot experimental data in log ˙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, σ cr , 10, 20, and 70MPa at 1973, 1633 and 1033 K, respectively. No creep strain with n =1was 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 metals that have a face-centered crystal 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 from 2.2 × 10 −8 to 1.3×10 −8 s −1 . The only visible effect is a shift of the function log ˙ε = f(log σ) to higher stresses. Molybdenum specimens have a random dislocation distribution after creep in the range n =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. under n =1conditions. Only some grains close to the break stress between segments n =1and n =8have sub-boundaries, obviously due to a local overstress. At n =8one 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: P = T [15 + log t 1% ]10 3 (8.1) where T is temperature of the tests, t 1% is the time of 1% deformation of a specimen, 15 is an empirically determined value. 150 8 Deformation of Some Refractory Metals 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]. Curve Alloy Mo Ti Zr Nb Ta W Hf Re C 1 Mo-TZM bal. 1.0 0.75 – – – – – – 2 Nb-1Zr – – 1.0 bal. – – – – – 3 PWC-11 – – 1.0 bal – – – – 0.10 4 T-111 – – – – bal 8.0 2.0 – – 5 ASTAR-811C – – – – bal. 8.0 0.7 1.0 0.025 152 8 Deformation of Some Refractory Metals 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 this log ˙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 of n was obtained from the slope of each straight line, and a least-squares analysis yielded n =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 154 8 Deformation of Some Refractory Metals 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 classesofalloys 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 of L1 2 type. 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) 3 Nb. The steady-state creep rate at 1923 K for the Ir–15Nb–1Ni alloy was 1.2 × 10 −8 s −1 , about three orders of magnitude lower than that of the binary Ir–17Nb alloy (10 −5 s −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 −19 Jat. −1 , for molybdenum Q =(5.59 ± 0.35) ×10 −19 Jat. −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. 157 Supplements Supplement 1: On Dislocations in the Crystal Lattice 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.Itisa 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 of b 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 [...]... dislocation slip in the crystal plane of type {111 } in the < 110 > direction The Burgers vector is e.g b = a/2 [110 ] The dissociation happens according to the reaction a a a [110 ] = [121] + [21¯ 1] (S.1) 2 6 6 Two Shockley dislocations are formed that can slip in the same plane {1¯ 11} The sum of Burgers vectors of two partial dislocations must be equal to the Burgers vector of the complete dislocation: b1... component Supplement 3: Composition of Superalloys Supplement 3: Composition of Superalloys In Table S1 the nominal contents of the main alloying elements are presented Typical third generation alloys include CMSX-4, EI867, ZhS26VI, TMS-75, Rene N6, and the fourth generation include CMSX-10M, TMS-138 Tab S1 Nominal chemical composition (wt.%) of some nickel base superalloys Alloy Cr Al Ti Mo W Co Ta Nb... meander through the crystal This tendency to shorten itself, gives rise to the concept of a dislocation line tension Inherent properties of dislocations are mobility and multiplication Dislocations move easily in their slip plane The stress that a dislocation needs to begin to move is of the order of 10−4 µ, where µ is the shear modulus The velocity of dislocations is related to the applied stress and. .. applied stress and temperature Dislocations can multiply under the effect of external stress The quantity of dislocations in a crystal is measured by the dislocation density: ρ = N/S, where N is the number of dislocations which intersect the area S The strain of a crystal is given by equation ε = bρL, where L is the length of the crystal A dislocation may dissociate into two so-called partial dislocations... perpendicular systems; within each of the networks the dislocations are parallel and equidistant The theorem states that in these conditions dislocations at least of one system have a screw component The notations are illustrated in Fig S4 1 and 2 are planes, in which are located the systems under consideration ξ1 and ξ2 are the unit vectors of dislocation lines b1 and b2 are Burgers vectors e1 = (b1... 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,... vectors of perpendiculars to slip planes N1 and N1 are inverse vectors, they lie in the boundary plane and are perpendicular to dislocation lines By definition Ni = Ni (n × ξi ) (S.2) where i = 1, 2; Ni = 1/ηλi n = (ξ1 × ξ2 ) is the unit vector of the perpendicular to the sub-boundary plane It is known in the theory of low-angle sub-boundaries [18] that N1 = b2 − n(n · b2 ) |b1 × b2 | (S.3) and N2... 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... a minimum energy for the split dislocation and the stacking fault This equilibrium distance depends mostly on the stacking fault energy γ The smaller γ the larger distance d between the partial dislocations; d is equal to four interatomic distances in nickel and ten interatomic distances in copper The dissociation into partial dislocations hinders the climb of the dislocation into parallel slip planes... n(n · b1 ) |b1 × b2 | (S.4) Multiplying vectors N1 and ξ2 as scalars and taking into account Eq (S.2) we obtain N1 · [(n × ξ1 ) · ξ2 ] = (b2 · ξ2 ) − (n · ξ2 )(n · b2 ) |b1 × b2 | (S.5) 161 162 Supplements Fig S4 The dislocation sub-boundary that consists of two crossed systems of parallel equidistant dislocations Similarly multiplying vectors N2 and ξ1 as scalars we obtain N2 · [(n × ξ2 ) · ξ1 ] = . 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. 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. New classesofalloys 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