High Temperature Strain of Metals and Alloys Part 3 pdf

It follows from the results of the Burgers vector determinations and from the repeat-ing structural configurations that the parallel sub-boundary dislocations have the same sign.. 3.9 Tr

Fig 3.2 As in Fig 3.1 at the end of the steady-state stage

subgrain sizesD (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 temperatureT = 673K (0.39 Tm),

σ = 130MPa (1.7 × 10 −3 µ).

3.1 Evolution of Structural Parameters 27

Fig 3.4 Structural parameters versus time and creep curve

for copper Tests at temperatureT = 610K (0.45 Tm);

σ = 19.6 MPa (4.0 × 10 −4 µ).

The misorientation angle,η, increases from 2 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 ofη (open circles).

Estimation of the dislocation density in sub-boundaries in conformity with

Eq (2.16) gives a quantity of the order of1013m−2.

Subgrains and sub-boundaries are formed easily in copper, Fig 3.4 and Fig 3.5 The same result is observed under σ = (1.2–2.7) × 10 −4 µ at all

temperatures: the crystallites are reduced to fine cells and sub-boundaries are formed during the primary stage of creep The valueD 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

Fig 3.5 Structural parameters versus time and creep curve

for copper Tests at temperatureT = 610K (0.45 Tm);

σ = 29.4 MPa (6.1 × 10 −4 µ).

Processes naturally occur differently in different crystallites Equilibrium values ofD 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 confi-dence 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 3 to 5 crystallites of 3 or 4 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

9 × 10 −7to5 × 10 −6s−1.

The change in stress leads to a sharper increase inη and decrease in D.

The values of the structural parameters in this metal are also dependent upon stress

3.1 Evolution of Structural Parameters 29

Fig 3.6 Structural parame-ters and strain as a function

of time for vanadium Tests

at temperatureT = 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 temperatureT = 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

Tab 3.1 Average substructure parameters in nickel and copper

at steady-state creep

Metal T /Tm T , K σ/µ, 10 −4 σ, MPa D,µm η, mrad¯

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 do not show any qualitative differences in the structure evolution from that in the pure metals The formation of sub-structure inside crystallites also occurs in the substitutional solid solutions

at the primary stage However, solid solutions differ in having greater initial values ofη In solid solutions one observes, at the stationary deformation,

greater values ofη 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 high-temperature tests are associated in sub-boundaries The parallel sub-boundary

3.2 Dislocation Structure 31 Tab 3.2 Average substructure parameters in niobium, vanadium andα-iron at the

steady-state creep

Metal T / Tm T , K σ/µ, 10 −4 σ, MPa D,µm η, mrad¯

dislocations are situated at an equal distance from each other It follows from the results of the Burgers vector determinations and from the repeat-ing 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 nio-bium 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 inα-iron Two systems

of dislocations, which intersect each other at right angles, are observed Dislo-cation lines are parallel to face diagonals, i.e they are directed along crystalline directions[110] and [1¯10] One of the systems is inclined noticeably to the foil plane This is the cause of an oscillating contrast in the dislocation images

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[1¯11].

Atomic displacements are directed along the body diagonals of the elementary cubic cell

The typical small-angle boundary inα-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 33

Fig 3.10 Transmission electron micrograph showing the

dislocation sub-boundary inα-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¯10] with b2= a/2[1¯11].

The plane of the foil is(2¯10) ×84 000.

of hexagonal shape The dislocation lines are located along directions[1¯11],

[¯111] and [001] The Burgers vectors are b1 = a/2[1¯11] and b2 = a/2[¯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 inα-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.

Distances between Dislocations in Sub-boundaries

The distanceλ between parallel dislocations of the same sign in a small-angle

boundary can be represented (whenη
1, tan η  η) by an expression of

the form:

whereb 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 X-ray data

λ, nm λ, nm

Ni 1073 14.0 42 ± 5 45 ± 3

20.0 34 ± 4 38 ± 3

773 50.0 36 ± 2 34 ± 3

973 11.0 41 ± 2 69 ± 7

Nb 1233 39.2 67 ± 13 74 ± 6

1370 29.4 109 ± 14 107 ± 10

44.1 60 ± 3 94 ± 6

3.4

Sub-boundaries as Dislocation Sources and Obstacles

The sub-boundaries that have been formed seem to be sources of slipping dis-locations 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 inα-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 35

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

α-iron Tests at 813K andσ = 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-tempera-ture deformation, are not associated in sub-boundaries They are located in-side subgrains and have the Burgers vectora/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

Fig 3.14 Dislocations inside subgrains in niobium tested

atT = 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 letters) These dislocations have the Burgers

vectora/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 withj, 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 letterj 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 com-ponents 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 sub-grains in nickel tested atT = 1023K

andσ = 49.0MPa s, Screw

disloca-tions; j, jogs.×48 000.

3.5 Dislocations inside Subgrains 37

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 distancesz0between adjacent bends The histograms

of these density distributions are presented in Fig 3.16 Under the mentioned strain conditions the most probable quantities ofz0in nickel and niobium are 4–5 hn and 9–10 hn, respectively

A comparison of the average distances ¯λ between sub-boundary

disloca-tions, determined by the X-ray method, and the spacingsz0between jogs in mobile dislocations, measured with the aid of electron microscopy, is given

in Table 3.4.n is the number of measurements of z0values Confidence in-tervals 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

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 measurementsn = 129;

(b) niobium, 1645K, 11.8MPa,n = 185.

Tab 3.4 Comparison of average distancesz0between jogs

in mobile dislocations and of average distances ¯λ between

subgrain dislocations.n is the number of measurements.

29.4 107 ± 10 120 ± 10 75

The density of dislocations, which are not associated in sub-boundaries,

N, has been measured, and the results are presented in Table 3.5

Disloca-tion densities during the high-temperature deformaDisloca-tion for the metals under study are estimated to be from1011m−2to1012m−2

Tab 3.5 The density of dislocations inside subgrains

Metal T , K σ, MPa N, 1011 m−2 Metal T , K σ, MPa N, 1011 m−2

3.6 Vacancy Loops and Helicoids 39

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 letterl, 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¯10), but two thirds are in planes (0¯11) and (¯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 vectora[¯110]; the loops are of the

vacancy type One can also see helicoids

Fig 3.17 Transmission electron micro-graphs showing vacancy loops and heli-coids: (a), (b) Iron tested atT = 973K

andσ = 10MPa; ×46 000 (c) Niobium

tested atT = 1508K and σ = 17.3MPa;

×39 000.