26 Structural Parameters in High-Temperature Deformed Metals Fig 3.2 As in Fig 3.1 at the end of the steady-state stage subgrain sizes D (upper curves) and in their misorientations η are presented on the same graph Here and in all following figures each type of symbol corresponds to one crystallite of the same specimen The initial mean size of the subgrains, D, is equal to 3.0µm, in the primary stage of deformation it decreases to 0.8µm and then is almost unchanged during the steady-state creep Fig 3.3 Structural parameters versus time and creep curve for nickel Tests at temperature T = 673K (0.39 Tm ), σ = 130MPa (1.7 × 10−3 µ) 3.1 Evolution of Structural Parameters Fig 3.4 Structural parameters versus time and creep curve for copper Tests at temperature T = 610K (0.45 Tm ); σ = 19.6 MPa (4.0 ì 104 à) The misorientation angle, , increases from to 5–7mrad The change in η is observed during the primary stage The smaller changes occur in the crystallite with the larger initial value of η (open circles) Estimation of the dislocation density in sub-boundaries in conformity with Eq (2.16) gives a quantity of the order of 1013 m−2 Subgrains and sub-boundaries are formed easily in copper, Fig 3.4 and Fig 3.5 The same result is observed under = (1.22.7) ì 104 at all temperatures: the crystallites are reduced to fine cells and sub-boundaries are formed during the primary stage of creep The value D decreases and the angle of misorientation increases The steady-state strain occurs at almost constant mean values of both parameters D and η depend strongly upon stress; the greater the applied stress the greater the misorientation angles and the smaller the sub-boundaries’ dimensions Thus, the substructure is formed inside crystallites during the primary, transitive stage of creep The origin of the steady-state strain coincides with the end of the substructure formation These peculiarities are seen well in Figs 3.4 and 3.5 27 28 Structural Parameters in High-Temperature Deformed Metals Fig 3.5 Structural parameters versus time and creep curve for copper Tests at temperature T = 610K (0.45 Tm ); = 29.4 MPa (6.1 ì 104 à) Processes naturally occur differently in different crystallites Equilibrium values of D and η are somewhat distinct There is a distribution in the size of these values, however, one may consider the mean values The accuracy of the method is of concern We have used the t-distribution for evaluation of the relative error of the average values Accepting a confidence factor of 0.9 we find the minimum number of necessary measurements, n = 12 Under these conditions we obtain a mean relative error of 12% for D and 8% for η In accordance with this result we usually investigated in situ at least to crystallites of or specimens of each material under each set of external conditions (temperature and stress) The substructure formation during high-temperature strain in vanadium is shown in Figs 3.6 and 3.7 The data are obtained at the same temperature 0.6 Tm , but under different stresses The rate of steady strain increases from × 10−7 to × 10−6 s−1 The change in stress leads to a sharper increase in η and decrease in D The values of the structural parameters in this metal are also dependent upon stress 3.1 Evolution of Structural Parameters Fig 3.6 Structural parame- ters and strain as a function of time for vanadium Tests at temperature T = 1318K (0.60 Tm ); σ = 5.9 MPa (1.3 × 10−4 µ) Fig 3.7 Structural parame- ters and strain as a function of time for vanadium Tests at temperature T = 1318K (0.60 Tm ); σ = 9.8 MPa (2.1 × 10−4 µ) The average values of the subgrain size and the subgrain misorientation at the beginning of the steady-state stage for face-centered metals are listed in Table 3.1 29 30 Structural Parameters in High-Temperature Deformed Metals Tab 3.1 Average substructure parameters in nickel and copper at steady-state creep σ/µ, 10−4 σ, MPa D,µm η, mrad ¯ 673 11.0 17.0 20.0 85 130 152 1.9 1.1 0.7 4.4 6.0 5.3 0.51 873 6.7 8.9 9.7 50 66 72 1.4 0.9 0.7 4.5 4.8 4.5 1073 1.3 2.0 2.7 10 14 20 2.0 1.7 1.0 5.3 6.3 7.5 0.45 610 3.0 5.1 6.1 14.7 24.5 29.4 1.5 1.0 0.6 3.1 3.8 4.8 0.50 678 1.8 3.4 4.2 8.8 16.7 20.6 1.8 1.2 0.9 3.1 4.2 4.7 0.55 Cu T, K 0.62 Ni T /Tm 0.39 Metal 746 1.2 2.0 2.8 5.8 9.8 13.7 1.8 1.7 0.8 3.5 3.5 5.4 In Table 3.2 the average values of the parameters at the steady-state creep are presented for three body-centered metals D and η have the same order in various metals D tends to increase with temperature The value of η increases when the applied stress rises In Fig 3.8 one can see the effect of stress on the average subgrain size in nickel The dependence is almost linear Investigations of single-phase two-component alloys Ni–9.5Cr (at.%), Ni–9.9Al, Ni–10.1 Co, Ni–9.5W not show any qualitative differences in the structure evolution from that in the pure metals The formation of substructure inside crystallites also occurs in the substitutional solid solutions at the primary stage However, solid solutions differ in having greater initial values of η In solid solutions one observes, at the stationary deformation, greater values of η than in pure metals 3.2 Dislocation Structure Some regularities are revealed as the result of systematic examination of the bright- and dark-field image pictures and diffraction patterns of a large number of specimens Most of the dislocations in specimens after hightemperature tests are associated in sub-boundaries The parallel sub-boundary 3.2 Dislocation Structure Tab 3.2 Average substructure parameters in niobium, vanadium and α-iron at the steady-state creep σ/µ, 10−4 σ, MPa D,µm η, mrad ¯ 1370 7.8 9.4 12.0 29.4 35.3 44.1 1.3 1.3 1.2 2.9 3.3 3.3 0.55 1508 4.6 7.2 7.6 17.2 27.0 28.4 1.5 1.3 1.1 2.4 2.5 3.4 1645 2.1 2.6 3.1 7.8 9.8 11.8 1.6 1.3 1.1 2.2 2.7 3.2 0.50 1096 5.3 6.3 7.4 24.5 29.4 34.3 1.9 1.5 0.8 3.6 4.1 4.4 0.55 1206 2.6 3.7 4.2 12.8 17.2 19.6 2.2 1.6 1.4 4.3 4.5 4.6 0.60 1318 1.3 1.7 2.1 5.9 7.8 9.8 1.8 1.5 1.2 4.1 5.6 5.1 0.51 923 0.7 1.3 1.7 6.0 11.0 14.0 1.5 1.6 0.8 3.8 4.4 4.5 0.54 V T, K 0.60 Nb T / Tm 0.50 Metal 973 0.4 0.7 1.2 3.0 6.0 10.0 1.5 1.4 1.2 3.5 3.8 3.9 Fe dislocations are situated at an equal distance from each other It follows from the results of the Burgers vector determinations and from the repeating structural configurations that the parallel sub-boundary dislocations have the same sign Two intersected dislocation systems are often observed inside sub-boundaries These systems form the small-angle boundary The electron micrographs of typical subgrains and sub-boundaries in niobium are presented in Fig 3.9 Creep tests were carried out until the second stage of creep was reached In Fig 3.9(a) the Burgers vector of the dislocations is b = a[¯ 100], i.e it is directed along the rib of the elementary cell of the cubic body-centered crystal lattice The plane of the foil is the face (100) Figure 3.10 illustrates the dislocation sub-boundary in α-iron Two systems of dislocations, which intersect each other at right angles, are observed Dislocation lines are parallel to face diagonals, i.e they are directed along crystalline directions [110] and [1¯ One of the systems is inclined noticeably to the foil 10] plane This is the cause of an oscillating contrast in the dislocation images 31 32 Structural Parameters in High-Temperature Deformed Metals Fig 3.8 Subgrain dimensions versus applied stress Nickel tested at 673K, steady-state stage Errors of measurements are shown with vertical bars ¯ The Burgers vectors were determined to be b1 = a/2[111] and b2 = a/2[111] Atomic displacements are directed along the body diagonals of the elementary cubic cell The typical small-angle boundary in α-iron, which consists of pure screw dislocations, is shown in Fig 3.11 Dislocations form a network with cells Fig 3.9 Transmission electron micrographs showing dislocation sub-boundaries in niobium, which are formed in the steady-state creep (a) T = 1370K, σ = 44.1MPa; (b) T = 1233K, σ = 39.2MPa ×39 000 3.2 Dislocation Structure Fig 3.10 Transmission electron micrograph showing the dislocation sub-boundary in α-iron, which is formed in the steady-state creep T = 813K and σ = 49.0MPa The first dislocation system is directed along [110] with b1 = a/2[111], the second along [1¯ with b2 = a/2[1¯ 10] 11] The plane of the foil is (2¯ ×84 000 10) of hexagonal shape The dislocation lines are located along directions [1¯ 11], ¯ ¯ and b2 = a/2[¯ [111] and [001] The Burgers vectors are b1 = a/2[111] 111] The third side of the network with b3 = a[001] appears to be formed as a result of reaction b3 = b1 + b2 Hexagonal cells of the other sub-boundary in iron are seen in pattern (b) The regular dislocation networks as low-angle sub-boundaries are found to be typical for the high-temperature tested metals Fig 3.11 Sub-boundaries in α-iron tested at T = 923K and σ = 12.0MPa (a) The pure screw sub-boundary formed by dislocations along [1¯ [¯ 11], 111], [001] directions (b) Network with hexagonal cells Plane of foil is (110) ×66 000 33 34 Structural Parameters in High-Temperature Deformed Metals 3.3 Distances between Dislocations in Sub-boundaries The distance λ between parallel dislocations of the same sign in a small-angle boundary can be represented (when η 1, tan η η) by an expression of the form: b λ= (3.1) η where b is the modulus of the Burgers vector Two methods were used in this work in order to measure the average spacing between sub-boundary dislocations Note the satisfactory fit between the electron microscopy results and the X-ray data (Table 3.3) Tab 3.3 Distances between dislocations in sub-boundaries Metal T, K σ, MPa TEM data λ, nm X-ray data λ, nm Ni 1073 14.0 20.0 42 ± 34 ± 45 ± 38 ± Fe 773 813 973 50.0 49.0 11.0 36 ± 59 ± 41 ± 34 ± 73 ± 69 ± Nb 1233 39.2 67 ± 13 74 ± 1370 29.4 44.1 109 ± 14 60 ± 107 ± 10 94 ± 746 7.8 87 ± 83 ± Cu 3.4 Sub-boundaries as Dislocation Sources and Obstacles The sub-boundaries that have been formed seem to be sources of slipping dislocations The process of generation of mobile dislocations by sub-boundaries is readily affected by the applied stress The TEM technique allows one to observe the beginning of a dislocation emission The creation of dislocations occurs as if the sub-boundary blows the dislocations loops like bubbles These loops broaden gradually and move further inside subgrains One can see this effect for nickel in Fig 3.12 The sub-boundary in α-iron that generates dislocations is shown in Fig 3.13 The subsequent dislocation semi-loops are blown by the ordered boundary 3.5 Dislocations inside Subgrains Fig 3.12 Transmission electron micrographs showing the dislocation sub-boundary as a source of mobile dislocations in nickel T = 1073K; σ = 20MPa ×48 000 Fig 3.13 Emission of dislocation loops from the sub-boundary in αiron Tests at 813K and σ = 49MPa ×66 000 At the same time sub-boundaries act as obstacles for moving dislocations One can often observe a sequence of dislocation lines which are pressed to the sub-boundary and these can enter the boundary 3.5 Dislocations inside Subgrains Some dislocations, which are observed in specimens after the high-temperature deformation, are not associated in sub-boundaries They are located inside subgrains and have the Burgers vector a/2 < 111 > in metals with the body-centered crystal lattice, i.e α-iron, vanadium, and niobium The slip plane is generally of the {110} type Screw dislocations are observed, as well 35 36 Structural Parameters in High-Temperature Deformed Metals Fig 3.14 Dislocations inside subgrains in niobium tested at T = 1370K and σ = 44.1MPa s, Screw dislocations; j, jogs; h, helicoids; l, vacancy loops ×26 000 as edge or mixed ones Screw dislocations are located at the left-hand side of Fig 3.14 (marked with the letter s) These dislocations have the Burgers vector a/2 < 111 > and are found to be in the {¯ 110} plane The second family of screw dislocations is seen on the right-hand side Bends and kinks in the dislocations, marked with j, attract one’s attention They give an impression that certain points of mobile dislocations are pinned up This can be easily seen in the left lower corner of Fig 3.14 and in other areas marked with the letter j These kinks at mobile dislocations turn out to be of great importance for our understanding of the physical mechanism of the steady-state creep Figure 3.15 illustrates the dislocation structure in nickel Again screw components with kinks are observed Another effect is the appearance of small dislocation loops The dark-field technique allows one to conclude that these are vacancy loops There are good reasons to assume that kinks and bends that have been described by us are jogs A jog is known to be a segment of a screw dislocation, which does not lie in its plane of slipping In fact, the jog is a segment of the Fig 3.15 Dislocations inside subgrains in nickel tested at T = 1023K and σ = 49.0MPa s, Screw dislocations; j, jogs ×48 000 3.5 Dislocations inside Subgrains edge extra-plane and therefore it can move with the slipping screw dislocation only with emission or absorption of point defects (vacancies or interstitial atoms) During movement the jog slows the dislocation and lags behind Even the highest resolution of the electron microscope is not sufficient for direct observation of jogs, since their length is of the order of one interatomic distance However, kinks and loops that have been observed in this work for different metals show convincingly that the formation of jogs takes place during high-temperature deformation Assuming that the kinks and bends in dislocation lines are produced by jogs we have measured distances z0 between adjacent bends The histograms of these density distributions are presented in Fig 3.16 Under the mentioned strain conditions the most probable quantities of z0 in nickel and niobium are 4–5 hn and 9–10 hn, respectively ¯ A comparison of the average distances λ between sub-boundary dislocations, determined by the X-ray method, and the spacings z0 between jogs in mobile dislocations, measured with the aid of electron microscopy, is given in Table 3.4 n is the number of measurements of z0 values Confidence intervals by probability 0.95 are also shown in the table The two values are close to each other In our opinion, the new experimental result that has been obtained ¯ z0 ≈ λ ¯ (3.2) is of great importance for our understanding of the physical mechanism of high-temperature deformation Fig 3.16 Histograms of the distribution of distances between jogs in screw components of dislocations: (a) nickel, 1073K, 14.0MPa, number of measurements n = 129; (b) niobium, 1645K, 11.8MPa, n = 185 37 38 Structural Parameters in High-Temperature Deformed Metals Tab 3.4 Comparison of average distances z0 between jogs ¯ in mobile dislocations and of average distances λ between subgrain dislocations n is the number of measurements T, K n 29.4 35.3 44.1 107 ± 10 94 ± 94 ± 120 ± 10 100 ± 97 ± 12 75 94 24 17.2 28.4 130 ± 10 92 ± 120 ± 10 95 ± 11 120 37 9.8 11.8 120 ± 10 97 ± 93 ± 95 ± 68 185 1096 24.5 34.3 80 ± 67 ± 90 ± 60 ± 115 35 673 110.0 140.0 55 ± 50 ± 56 ± 48 ± 85 211 873 50.0 58.0 72.0 63 ± 58 ± 58 ± 67 ± 54 ± 46 ± 60 125 75 1073 10.0 14.0 20.0 54 ± 45 ± 38 ± 65 ± 48 ± 45 ± 96 129 85 873 25.0 30.0 64 ± 60 ± 63 ± 53 ± 78 88 923 6.0 71 ± 76 ± 12 45 746 Ni z0 , nm 1645 V ¯ λ, nm 1508 Nb σ, MPa 1370 Metal 7.8 87 ± 83 ± 46 Fe Cu The density of dislocations, which are not associated in sub-boundaries, N , has been measured, and the results are presented in Table 3.5 Dislocation densities during the high-temperature deformation for the metals under study are estimated to be from 1011 m−2 to 1012 m−2 Tab 3.5 The density of dislocations inside subgrains Metal T, K 873 Ni 1023 Cu 678 σ, MPa N , 1011 m−2 29.4 68.7 98.1 9.8 40.0 2.4 5.7 9.5 1.3 6.3 8.8 20.6 2.2 9.6 Metal T, K 1370 Nb 1508 V 1096 σ, MPa N , 1011 m−2 24.9 29.4 35.3 17.2 28.4 1.6 3.1 3.8 2.9 5.3 29.4 34.3 1.6 1.4 3.6 Vacancy Loops and Helicoids 3.6 Vacancy Loops and Helicoids Closed dislocation loops as well as helicoids are observed very often in the structure of the high-temperature tested metals Dark-field analysis makes it possible to determine the sign and the type of loops The loops have been found to be of the vacancy type Helicoids are known to be formed usually by screw dislocations under conditions of volume supersaturation by point crystalline defects We can see the loops, marked with the letter l, in Fig 3.14 and also in 3.15 In Fig 3.17 the typical structures of helixes and vacancy loops are presented The helicoid looks like a spiral in electron patterns The foil in Fig 3.17(a) and (b) coincides with the crystal plane (111) One third of the loops lie in the plane (1¯ but two thirds are in planes (0¯ and (¯ 10), 11) 101) Thus, vacancy loops are generated in the dislocation slip planes In Fig 3.17(c) a very interesting effect can be observed Three chains of loops have been left behind two segments of screw dislocations These moved in the slip plane (110) The dislocations have the Burgers vector a[¯ 110]; the loops are of the vacancy type One can also see helicoids Fig 3.17 Transmission electron micro- graphs showing vacancy loops and helicoids: (a), (b) Iron tested at T = 973K and σ = 10MPa; ×46 000 (c) Niobium tested at T = 1508K and σ = 17.3MPa; ×39 000 39 40 Structural Parameters in High-Temperature Deformed Metals 3.7 Total Combination of Structural Peculiarities of High-temperature Deformation The structural peculiarities can be generalized from the observed facts Our experimental data have led to the conclusion that there are several distinctive structural features of strain (creep) at high temperatures and it turns out that these features are caused by a certain physical mechanism The first distinctive feature is the simultaneous formation of sub-boundaries within crystallites and a decrease in the strain rate ε to an approximately ˙ constant value Each of the three curves [ε(t), η(t) and D(t)] have a “nearlinear” segment The abscissae at the start of these segments coincide with each other The following conclusion look obvious: it is the process of substructure formation that is the cause of the decrease in the plastic strain rate The subgrain dimensions are of the order of micrometers, one or two orders less than the grain size in polycrystalline materials Subgrains are separated from each other by small-angle boundaries, which give a rotation angle of the order of several milliradians ¯ The relative constancy of the average structural parameters D and η during ¯ the steady-state period is the second essential feature that is intrinsic for facecentered metals at temperatures of (0.40–0.70) Tm , and for body-centered ¯ metals at (0.45–0.65) Tm The values of D and η depend upon external pa¯ ¯ rameters, especially stress D decreases, and η increases when σ increases ¯ One should distinguish between the immobile dislocations associated in sub-boundaries and the mobile dislocations inside subgrains Dislocation sub-boundaries that have been formed are regular networks or ordered junctions Usually one or two system of parallel equidistant dislocations have been observed inside small-angle boundaries The results of the Burgers vector, b, determination indicate that the parallel sub-boundary dislocations are of the same sign Sub-boundaries contain dislocations with a considerable screw component Mixed dislocations along [110] with b = a/2[111] are characteristic for body-centered metals Pure screw sub-boundaries have also been found with b1 = a/2[¯ 111] and b2 = a/2[1¯ Screw dislocations and 60-degree dis11] locations have been observed in the structure of face-centered metals The presence of a screw component in the boundary structure is the third distinctive feature of the structure of the high-temperature deformed metals The fourth peculiarity is as follows It is obvious from our investigations that sub-boundaries play a double role They are both the sources and the obstacles (sinks) for mobile dislocations Only the mobile dislocations are known to make a contribution to the elementary events leading to the deformation of the specimen Some dislocations are located inside subgrains They move in slip planes i.e in planes of the {111} type for the cubic face-centered and the {110} ... 1 .3 6 .3 8.8 20.6 2.2 9.6 Metal T, K 137 0 Nb 1508 V 1096 σ, MPa N , 1011 m−2 24.9 29.4 35 .3 17.2 28.4 1.6 3. 1 3. 8 2.9 5 .3 29.4 34 .3 1.6 1.4 3. 6 Vacancy Loops and Helicoids 3. 6 Vacancy Loops and. .. 2.1 2.6 3. 1 7.8 9.8 11.8 1.6 1 .3 1.1 2.2 2.7 3. 2 0.50 1096 5 .3 6 .3 7.4 24.5 29.4 34 .3 1.9 1.5 0.8 3. 6 4.1 4.4 0.55 1206 2.6 3. 7 4.2 12.8 17.2 19.6 2.2 1.6 1.4 4 .3 4.5 4.6 0.60 131 8 1 .3 1.7 2.1... vanadium and α-iron at the steady-state creep σ/µ, 10−4 σ, MPa D,µm η, mrad ¯ 137 0 7.8 9.4 12.0 29.4 35 .3 44.1 1 .3 1 .3 1.2 2.9 3. 3 3. 3 0.55 1508 4.6 7.2 7.6 17.2 27.0 28.4 1.5 1 .3 1.1 2.4 2.5 3. 4