88 6 High-temperature Deformation of Superalloys 6.2 Changes in the Matrix of Alloys during Strain The specimens of industrial superalloys (see Table 2.1) were investigated in situ by means of the X-ray method described above; transmission electron mi- croscopy studies were also carried out. For this purpose the high-temperature tests were interrupted and thin films were prepared from the specimens (Fig. 6.4). EI437B is a nickel-based superalloy widely used in gas turbine jet engines and also in various applications up to 1023K (750 ◦ C) such as turbine blades, wheels and afterburner parts. The specimens were solution treated for 1h at 1273K, air cooled and aged for 16h at 973K. Figure 6.6 presents the results of X-ray investigations on this superalloy. The loading of specimens results in an increase in the misorientation angle, η, and a decrease in the average subgrain size, D. The mean values of the parameters under investigation are almost unchangedatthesteady-statestage and are equal to 3mrad and 0.6µm, respectively. Consequently, fragmentation of the γ crystallites is also intrinsic to superalloys. This is due to the formation Fig. 6.6 Dependence of the elongation, average subgrain size and subgrain misorientation angle on time for the EI437B superalloy. T = 973K. ◦, •: σ = 570MPa; : σ = 700MPa. 6.3 Interaction of Dislocations and Particles 89 Fig. 6.7 Dislocation sub-boundaries in the matrix of the tested EI437 superalloy. The steady-state stage of creep. T = 973K; σ = 450MPa. ×150000. of dislocation sub-boundaries in the γ matrix. Decrease in D and increase in η is observed when the applied stress increases. Transmission electron microscopy is difficult to apply to the alloy because it contains many small coherent γ  particles. The contrast at the matrix–particle boundary is known to have a deformation origin and hence the borders of the particles seem to be fuzzy. The average particle size in EI437B superalloy was found to be 14nm after the initial heat treatment. The dimensions of the particles increase to 22nm after creep tests and the borders of the particles become more distinct. One can see the dislocation sub-boundaries in Fig. 6.7. The dimensions of the subgrains are about 0.3–0.5µm. This is close to the values estimated with the X-ray method. 6.3 Interaction of Dislocations and Particles of the Hardening Phase Typical pairs of deforming dislocations are seen in Fig. 6.8. The dislocation lines, which slip under the effect of the applied stress, are parallel and inter- sect the particles. Transmission electron microscopy evidence supports the cutting of γ  particles by slipping dislocations. The dislocations cut the coher- ent particles of the γ  phase without changing the slip plane which is mainly of the type {111}. However, during the tertiary stage of creep the particles coarsen and their coherent bond with the matrix is broken. Orowan bowing 90 6 High-temperature Deformation of Superalloys Fig. 6.8 Electron microphotographs of the EI437 superalloy during the steady-state stage of creep. T = 973K; σ = 450MPa. ×150000 (a), ×200000 (b). occurs as the rate-controlling strain mechanism. It is the Orowan mechanism that dominates in tertiary creep deformation. In Fig. 6.9 one can see that dislocations cut small particles and bow the big ones. The dislocation loops around particles remain when the dislocation lines have passed. The bowing of particles takes place till cavitation occurs and the specimen ruptures. EI 867 is a superalloy strengthened by chromium, aluminum, molybde- num, tungsten and cobalt. The standard heat treatment consists of solution treatment at 1493K for 2h, quenching in air and ageing at 1223K for 8h. This heat treatment produces cuboidal γ  particles, which are on average 130 nm in size along the cube edge. The edges of the cubes are oriented along the < 100 > direction (Fig.6.10). The electron micrographs taken during the steady-state stage of creep are presented in Figs. 6.11–6.13. Parallel deforming dislocations are seen. They move inside the ordered zones one after the other. It is at once apparent from Fig. 6.11 that the particles are obstacles for the moving dislocations. A plane sequence of dislocations is pressed to the edge of the γ  particle. The spacing between successive dislocations decreases as the distance to the particle is reduced, as if the dislocations “are waiting” to enter the particle. After entering the particle the dislocations continue to move. The dislocation loops that expand from the interface of the phases are seen in Fig. 6.13. 6.3 Interaction of Dislocations and Particles 91 Fig. 6.9 Electron micrographs of the tested EI437 superalloy during the tertiary stage of creep. T = 973K; σ = 450MPa. ×200000. Fig. 6.10 Electron micrographs of the EI867 superalloy in the initial state. Particles of γ  phase. (a) Replica, ×20000; (b) thin film, ×100000. At the stage of the tertiary, accelerating creep the shape of the particles becomes irregular. A rafting process of the γ  structure occurs because of development of diffusion coarsening. Now the incoherent irregular rafted 92 6 High-temperature Deformation of Superalloys Fig. 6.11 Electron micrographs of the EI867 superalloy during the steady-state stage of creep. T = 1173K; σ = 215MPa. Interaction of deforming dislocations with γ  particles. ×130000. Fig. 6.12 Interaction of deforming dislocations with γ  precipitates in the EI867 superalloy. ×90000 (a); ×40000 (b). Fig. 6.13 Interaction of deforming dislocations with particles in the EI867 alloy. ×60000. 6.3 Interaction of Dislocations and Particles 93 particles cannot be obstacles for deforming dislocations. As a result disloca- tion networks are formed (Fig. 6.14). The networks fill the volume between the particles and spread inside the particles. At the same time the strain rate of the specimen increases. Fig. 6.14 Dislocation networks during the tertiary stage of creep in the EI867 superalloy. ×90 000. Electron micrographs of the EP199 superalloy (Table 2.1) are shown in Fig. 6.15. Parallel dislocations can be observed. The dislocations move one after the other and intersect particles of the γ  phase ((a), (b)). The dislocation sets are formed at the tertiary stage of creep ((c), (d)). Electron microstructural examination of the crept test specimens of super- alloys has indicated that a rate-controlling process is the precipitate cutting, or shearing. During high-temperature exposure the precipitates coarsen, and the rate-controlling mechanism becomes dislocation bowing. It follows from the obtained data that deforming dislocations are slowed by the coherent particles and then cut them. Hence, the thermally activated overcoming of particles is the process that controls the constant strain rate. However, under the effect of applied stress and high temperature the raft- ing of particles occurs and the deforming dislocations can bow between the obstacles. This results in accelerating tertiary creep and rupture. 94 6 High-temperature Deformation of Superalloys Fig. 6.15 Electron micrographs of the EP199 superalloy. T = 1173K; σ = 110MPa. (a), (b) At the end of the steady-state stage of creep; ×65000. (c), (d) The stage of the tertiary creep; ×48000. 6.4 Creep Rate. Length of Dislocation Segments 95 6.4 Dependence of Creep Rate on Stress. The Average Length of the Activated Dislocation Segments The experimental dependences of the minimum creep rate, ˙ε, on the applied stress for five superalloys are presented in Fig. 6.16, where ln ˙ε is plotted against σ. Results for three alloys are shown in Fig. 6.17. A linear dependence is observed for all superalloys. Hence, the minimum creep rate is dependent exponentially on stress. The activation volume v of an elementary deformation event can be cal- culated from these data according to Eq. (1.5). Further, we may compute the average length of a dislocation segment ¯ l that must be activated in order that the dislocation can move ahead: ¯ l = v b 2 (6.3) In Table 6.2 the values of l and the average particle dimensions 2¯r are listed. The lengths of the activated dislocation segments are one order less than the average particle sizes. Values of the ratio of ¯ l/2¯r lie within the range 0.07 to 0.14, more precisely 0.12 ± 0.04. Fig. 6.16 Logarithm of strain rate versus stress for superalloys: B, Ni+18Cr+2 .6Al. T = 1023K. Data from Ref. [35]. C, Ni + 19Cr + 0.8Al + 2.1Ti. T = 1023K. Data from Ref. [35]. D, Ni+9Cr+4.5Al + 5W + 14Co (EI867). T = 1173K. Data of the present au- thor. E, Ni + 19Cr + 0.8Al + 2.5Ti. T = 973K. Data from Ref. [35]. F, Ni+ 20Cr+2 .2Al +2.0Ti+3.3W+5Fe. T = 1023K. Data from Ref. [32]. 96 6 High-temperature Deformation of Superalloys Fig. 6.17 Logarithm of strain rate versus stress for superalloys: B, Ni + 9Cr + 5.0Al + 2.0Ti + 1Nb + 12W + 10Co. T = 1144K. Data from Ref. [36]. C, Ni + 21Cr + 0.8Al + 2.5Ti (EI437B). T = 973K. Data of the present author. F, superalloy C263. T = 973K. Data from Ref. [37]. Tab. 6.2 The length of activated dislocation segments. Alloying elements in Ni-based alloy T ,K l,nm 2¯r, nm Particle shape Ref. 19Cr + 0.8Al + 2.1Ti 973 4.8 42 cub. 18Cr + 2.6Al 1023 8.3 65 spher. 35 19Cr + 0.8Al + 2.1Ti 1023 7.8 65 spher. 21Cr + 0.8Al + 2.5Ti 973 4.7 22 spher. author 9Cr + 4.5Al + 5W + 4Co 1173 10.7 133 cub. author 20Cr + 2.2Al + 2.0Ti + 3.3W + 5Fe 1023 8.9 100 spher. 32 9Cr + 5Al + 2.5Ti + 12W + 10Co 1144 5.7 83 cub. 36 Superalloy C263 973 7.6 54 spher. 37 6.5 Mechanism of Strain and the Creep Rate Equation The applied stress is insufficient to let a dislocation cut aparticle under normal creep conditions. The ordered structure of the γ  phase requires that two dislocations in the γ phase must combine in order to enter the γ  phase as a superdislocation. The associated anti-phase energy in γ  posseses a large barrier to the dislocation entry. A mechanism involving diffusion-controlled movement of dislocations in the ordered γ  phase seems to be the most probable one. There is good reason to believe that, in these conditions, the slip of the deforming dislocations is 6.5 Mechanism of Strain and the Creep Rate Equation 97 controlled by diffusion processes, indeed, with ordering, the activation energy of diffusion increases as well as the creep strength. A mechanism of diffusion-controlled dislocation displacement through the ordered γ  phase is presented in Fig. 6.18. An arrangement of atoms in a su- perdislocation is shown. The superdislocation is dissociated into two partial dislocations that are separated by the band of the anti-phase boundary. A va- cancy approaches the first partial dislocation as a result of thermal activation. The atomic row shears under the effect of the applied stress, and a relaxation in the vacancy area occurs, thus, a double bend is formed in the dislocation line and the adjacent rows displace. This is equivalent to the expansion of both Fig. 6.18 The atomic mechanism of the dislocation diffusion displacement in γ  phase. Arrangement of atoms in two par- allel slip planes of [111] is shown. (a) Ideal crystal lattice. Twelve rows are shown. Along the face diagonal [10 ¯ 1] atoms of aluminum and nickel are altered. Atoms of Ni that are denoted as 1 and of Al that are denoted as 3 are located in the first slip plane. Atoms of Ni 2 and of Al 4 are located in the second parallel slip plane. (b) Partial dislocations and the anti-phase-boundary (APhB). The Burgers vector (arrows) is [10 ¯ 1]. At the row 11 a vacancy 5 () is formed. (c) The shear of the atomic row. The vacancy  has migrated to the next atom. A double bend has been formed at the moving superdislocation. [...]... results of measurements of the particle sizes and the data of the strain rate tests 99 100 6 High- temperature Deformation of Superalloys Finally, the minimum strain rate of a superalloy is supposed to be directly proportional to the dislocation velocity, V , and to the dislocation density, N : ε = bf (c)N ˙ ∆U νb2 exp − 0.24 · 2r kT exp 0.12τ b2 · 2r kT (6.13) where f (c) is a decreasing function of concentration... presented for temperatures from 953K to 1 673 K in seven publications Thus, the value of the activation energy ∆U for superalloys is somewhat greater than the energy of self-diffusion in nickel 1) The activation energy of an elementary event of the high- temperature strain (creep) is denoted differently by different authors, as Q, Qc , ∆Qapp , ∆U 101 102 6 High- temperature Deformation of Superalloys Manonukul... is the initial strain rate at the temperature T1 and ε2 is the final strain ˙ ˙ rate at temperature T2 This method has an essential drawback: an instability of structure during the temperature change results in too high measured values of Qapp If the differential change of temperature did not modify the substructure the authors [39] obtained Qapp = 5.08 × 10−19 Jat.−1 The energy of self-diffusion... tests of the same superalloy under two stresses σ1 and σ2 and denoting the sums of the first three terms as A1 and A2 one can write ∆U = A1 + kT ln[f (c)N1 ] (6.15) ∆U = A2 + kT ln[f (c)N2 ] (6.16) Thus, the logarithm of the ratio of the dislocation densities is given by ln A1 − A2 N2 = N1 kT (6. 17) 6.5 Mechanism of Strain and the Creep Rate Equation Tab 6.3 The calculated activation energies of the... is n (all the atoms that take part in overcoming the potential barrier are considered) The values of νj are (n − 1) frequencies of oscillations in the activated state at the peak of the potential barrier The increment of the thermodynamic potential, ∆Φ, (of the Gibbs free energy) is given by ∆Φ = ∆U − T ∆S − τ v (6.6) where ∆S is the increment of entropy, ∆U the increment of internal energy as the segment... electrolytically from aged superalloys An X-ray technique for the measurement of mean-square amplitudes separately for each of the two sublattices of a γ phase has been developed [ 17] We determined the chemical compositions of the γ phases by chemical analysis and X-ray diffractometer studies of the specimens were also carried out We measured the intensities, I, of the (100) and (200) reflections and compared the... event in the γ phase of superalloys The values of f (c)N that have been assumed (m−2 ) are shown above columns 4 to 6 ∆U , 10−19 Jat.−1 σ2 /σ1 , T, K MPa/MPa 923 1023 973 1023 1 173 1144 600/400 280/80 360/280 320/200 280/120 520/280 Ref N2 /N1 1010 1011 1012 30.3 115.1 6.0 10.3 32.0 7. 2 3.56 3.68 3. 97 4.11 4.45 4.50 3. 87 4.01 4.28 4.44 4.82 4.86 4.18 4.33 4.59 4 .76 5.19 5.22 author 35 37 32 author 36 One... pre-exponential factor Hence there is an optimal size of particles 2r0 , which is dependent on T and σ Taking the derivative and solving ∂V /∂(2r) = 0 we find that for EI437B superalloy at 973 K and σ = 400MPa the value of 2r0 = 12.2 nm The result fits the measured value 14 nm satisfactorily It is of importance to estimate the energy ∆U Taking the logarithm of Eq (6.13) we obtain ∆U = −kT ln ε + 0.12τ b2... been calculated for the distribution of all kinds of elements between the γ sublattices, B and A The ratio under study is dependent on the average factors of the X-ray ¯ ¯ scattering in the sublattices, fB and fA , respectively The final formulas of the phases have been established by us under the condition of a coincidence of the experimental and calculated values of this ratio The obtained data are...98 6 High- temperature Deformation of Superalloys branches of the double bend in opposite directions parallel to the dislocation line When the bend passes the particle the leading dislocation displaces The shift is equal to the Burgers vector length b In such a way the elementary event of plastic strain occurs One vacancy is enough to displace all atoms in the particle section It is . used the results of measurements of the particle sizes and the data of the strain rate tests. 100 6 High- temperature Deformation of Superalloys Finally, the minimum strain rate of a superalloy. 88 6 High- temperature Deformation of Superalloys 6.2 Changes in the Matrix of Alloys during Strain The specimens of industrial superalloys (see Table 2.1) were investigated in situ by means of. subgrain size and subgrain misorientation angle on time for the EI437B superalloy. T = 973 K. ◦, •: σ = 570 MPa; : σ = 70 0MPa. 6.3 Interaction of Dislocations and Particles 89 Fig. 6 .7 Dislocation