- Email: [email protected]
On the microstructural origin of primary creep in nickel-base superalloys
ELSEVIER
Materials Scienceand EngineeringA234&236 (1997) 501-504
On the microstructural origin of primary creep in nickel-base superalloys M. Heilmaier a,*, B. Reppich b b Institut
fur
a Institut fir FestkiirperWerkstoffwissenschaften,
and Werkstofforschung Lehrstuhl I, Universitiit
Dresden, D-01 171 Dresden, Germany Erlangen-Niirnberg, D-91058 Erlangen,
Germany
Received 3 February 1997;received in revised form 26 March 1997
Abstract The nature of primary creep in nickel-base superalloys is strongly correlated to the different hardening species present in the material. In fine-grained single-phase material the classical assumption of a homogeneous dislocation distribution enables the prediction of the transition from normal via sigmoidal to inverse primary creep with decreasing applied stress 6. In coarse-grained material the back stress ob of hard subgrain boundaries evolving during plastic deformation must be additionally taken into account. Second-phase particles influence creep in a 2-fold manner via reducing the effective stress gefc, namely directly by the stress o,* for particle overcoming, and indirectly by increasing the dislocation density p. The proposed approach accounts for the observed pronounced normal primary creep in particle-strengthened superalloys. 0 1997 Elsevier Science S.A. Keywords:
Superalloys; High-temperature creep; Particle-strengthening
1. Introduction
2. Primary creep in single-phasematerial
The extraordinary strength of superalloys is strictly controlled in terms of the effective stress (a&-model [1,2] by internal back stresses a,; due to: (a) effective metallurgical obstacles (solid solution atoms, dispersoids, precipitates, grain boundaries, in increasing order of size) and; (b) homogeneous and heterogeneous dislocation structures evolving during the deformation and loading history, respectively, and by synergetic effects due to complex interaction between (a) and (b). Under high temperature creep conditions metallic alloy systems approach a dynamic equilibrium of strain hardening and recovery, termed steady-state. The way, however, in which steady-state will be achieved depends on the kinetic and evolution of internal back stresses involved. This will be exemplified in the present study with selected single-phase and particle-strengthened nickel-base superalloys.
Nimonic 75 is essentially a nickel-base solid solution with z 20 wt.% chromium. Therefore, it may serve as an appropriate single-phase matrix reference material for particle strengthened nickel-base superalloys of similar chemical composition.
* Corresponding author.Tel.: + 49 351 4659721; 4659320; e-mail:heilmaier@ifw-dl:esden.de
fax:
+ 49 351
0921-5093/97/$17.00 0 1997Elsc:vierScienceS.A. All rightsreserved. PIISO921-5093(97)00258-X
2.1. Homogeneous dislocation structure In single-phasematerials, pi is composed of the longrange stress field op of free dislocations and the back stress Otub resulting from hard subgrain boundaries. Following Taylor [3] the former can be calculated as dp = clGbM & with CI elastic interaction constant, G shear modulus, b Burgers vector, M Taylor factor, p the mean total dislocation density. However, the latter (orb) can be suppressedby fine grains. The reason for that microstructural pecularity is displayed in Fig. 1 where dislocation spacing pS&O.’and subgrain size w,, at steady-state are plotted vs. normalized stress o/G for various nickel-base alloys. At o/G M 7. lop4 corresponding to 0 z 45 MPa at 850°C the straight line for w intersects the grey-shaded area which represents the grain size distribution of fine-grained material with a
502
M.
Heilmaier,
B. Reppich
/Materials
Science
mean value of d g z 11 urn. Considering that subgrains may form only when the condition w K c - ’ 5 d,/2 is fufilled no complete substructure formation could be expected even at values below 10 ~ 3s/G or 0 x 80 MPa, alternatively. The single parameter (p,) HAI-model according to Haasen-Alexander-Ilschner [ 1,2] yields the following relationship:
&41=MP&o
sinh(p(g
and Engineering
A2346236
1o-3
(1997)
501-504
85OV
Nimonic
75
lo4 7 * 1o-5 . ‘W
1o-6
- aGbM&))
1O-7 10 MPa
The term in the inner parentheses represents crerr. The parameters of dislocation velocity, v0 = 2. 10e9 m s ~ l and /I = 0.08 MPa- ‘, have been determined at ‘constant dislocation structure’ by sudden stress change tests in a former work [4]. The evolution of dislocation spacing p - o.5 (and thus of g,,) with plastic strain is described by a common Avrami kinetics. For a complete derivation of Eq. (1) refer to Heilmaier et al. [6].
In
-81’
I”
.
0
I
I
0.20
0.10
0.30
0.40
Fig. 2. Comparison of true strain rate-true strain curves of fine- and coarse-grained single-phase Nimonic 75. Solid lines: measured; dashed lines: calculated according to the HAI-model, Eq. (1) setting x = 0.2, G = 55.8 GPa, M = 3, b = 0.254 nm. The open and full circles indicate the point of maximum deformation resistance, i.e., minimum creep rate.
2.2. Heterogeneous dislocation structure :‘..:‘.:. ,... i.,.
. . . . . . . :.:.:.:.‘.:.‘-:.:-:-: :.. ->..: ..:\:i. i :‘:‘:::::‘:::‘::~.::‘::~,~:’ :i:I:~:i:i:,.~::i:Iji:ii ;i;i:;;: -.,-‘Y-::‘:::.~i:‘. ,.z.:.>:.: ..:.:: ,:,.:...; .,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .:.:t: .:,.,;:.;: . . . . . .:...: .:, >> ,.,.,.,.,.. /, ..,.., ,. ;.>3,.;>;: ~..,...,.... ,.,. . . . . :........ ,.,., ., . . . . . . ,.,,...,. ., ., . ..,. .,. ..,.. .,., ..,:. ” ‘“-““.:::‘:.:::~ .> ., . . :.:..:.“““” . . . ““. .,., ,. . .,. ..-... :.: ..A:.?..: .;:::;; ,\.::::,:::,:j:**,.> i... .......~.i.:.:,.:..:..~ .:.:.: :...:.,:, :.:.;:.,, .> ,,,
The composite model of plastic creep deformation [7] introduces a long-range back stress 0;“’ due to the evolution of an inhomogeneous dislocation structure consisting of hard subgrain boundaries and soft subgrain interior. If subgrains evolve the amount of exertion of backstress into the subgrain interior can be calculated as gb
sub _
fh 1 -Al
- -cT(kb
- 1)
with fh = fS,,.2a/w x 0.05 for a fully developed substructure; a is the width of subgrains and fsub is the volume fraction of subgrain-containing regions, respec-
loo g 2 5 n ‘c! ?Z Q
MA 754, 85OT
10 -l
h [9]
0 Nimonic75 CD Ni-20Cr-2Th02 0 MA754 q MA6000 0 IN 738 LC 3*10d
...::::::.:::;. .....<.. ‘Y,& ..:.... ,c ,
1o-g
1o-3
o/G(T)
Fig. 1. Dependence of characteristic steady-state dislocation spacings on normalized applied stress for various nickel-base alloys. Comparison with the grain size of single-phase Nimonic 75, dg,fine and the interparticle spacing (channel width) in IN 738 LC, L,, respectively. Data of thoria dispersed Ni-20G taken from Hausselt and Nix [9].
0
0.02
0.04 &PI
Fig. 3. Differentiated creep curves of MA 754. Solid lines: measured; dashed lines: calculated according to the particle-modified HATmodel, Eq. (3); dotted line: calculated, setting or = const. Model parameters G(, G, b, M, v,,, j? have been adopted from Nimonic 75, Section 2.1.
M. Heilmaier,
B. Reppich
/Materials
Science
and Engineering
A234-236
(1997)
501P.504
503
tively. Fig. 2 assesses typical differentiated creep curves of fine- and coarse-grained (d, = 650 urn) Nimonic 75. Essentially, in fine-grained material the transition from normal (81 MPa) to sigmoidal (45 MPa) and inverse (18 MPa) primary transient creep with decreasing applied stress CTis properly reflected by the features of the model (compare the corresponding dashed curves according to Eq. (1) and the measured continous curves). In coarse-grained material, however, a continous decrease of 6 resulting from evolving subgrains is obvious. Thus, the increase of otub reduces cefi in Eq. (1) which in turn explains the observed creep deceleration (see the respective 6b-arrows in Fig. 2).
3. Primary
creep in two-phase
materials
Starting point of our refined analysis of primary creep in particle-strengthened nickel-base superalloys are the following experimental evidences compared to single-phase material: (a) the i-decrease during primary creep is extremely high, usually several orders of magnitude [5], (Fig. 3 and Fig. 5a); (b) the steady-state dislocation density pss is seriously increased at equivalent strain rates & (Fig. 1); and (c) in constant strain rate tests the yield stress-increment at E = 0 is significantly lower than the stress-increment at steady-state cp
Fl. Thus, we must revise the sofar simple picture of the original threshold stress concept [8] suggesting that a single parameter op accounts for the total particle hardening contribution. Rather, the effect of particlestrengthening on creep acts 2-fold: firstly, via a constant o,*-value representing the traditional contribution for the mere particle overcoming process (explaining observation c) and secondly, via an additional long-range back stress up,p -term reflecting the evolution of particleinduced dislocations during plastic deformation (satisfying observation (b). Splitting gp = u,* + gp,p as the simplest superposition rule we modify the effective stress model, Eq. (l), to obtain the deformation law for particle-strengthened materials: .i”& = -pbvo M sinh(/?(a - 0, - arb - g*, - o~,~))
(3)
However, closer examination in the following sections will reveal that the origin of op.? depends on the particular type of the particle-matrix interface. 3.1. Oxide dispersion strengthened
MA 754
In comparison with single-phase Nimonic 75 the ODS alloy MA 754 is additionally strengthened by incoherent Y203 dispersoids. The MA process enables an extremely fine distribution of the thermally stable particles resulting in mean values of diameter d = 14
Fig. 4. Particle and dislocation microstructure in IN TEM micrograph of creep deformed IN 738 LC, 0 E = 0.04; (b) scheme of the shell model [I l] reflecting the channels a long-range back stress bp,p in the matrix dislocation networks (dark sketched) around y’-precipitates
738 LC: (a) = 414 MPa, evolution of due to hard (shaded).
nm, volume fraction f = l.O%, and interparticle spacing L, = 83 nm [6]. Fig. 3 displays a set of typical creep curves of MA 754 [5]. Post mortem TEM observations have revealed that subgrain formation is effectively suppressed by the dispersoids during creep. Thus, we assume a homogeneous dislocation distribution, setting oEub = 0 in Eq. (3) (compare Section 2.1): for all creep curves in Fig. 3 a constant fraction of a,* = 0.6 ap has been applied as evaluated from yield stress increment measurements [6]. bp,p approaches its steady-state value of 0.4. gp analogously to G,, ( = aGbM&), but starts from zero using a different Avrami kinetic for the additional dislocation density pp. It is obvious from Fig. 3 that the dashed curves describe the pronounced normal tran-
504
M. Heilmaier,
L 0
B. Reppich
/Materials
Science
I 2
4
6
8
10
12
14
t1103h Fig. 5. (a) Differentiated creep curve of IN 738 LC in log&t-representation. Full circles, measured; solid lines, calculated according to the shell model [ll]; (b and c): stress components and y’-particle coarsening kinetics. Damage accumulation like cavity growth controls the tertiary creep stage which has not been plotted here (time to failure was about 30000 h).
sients (solid curves) adequately. In contrast, applying the original threshold stress concept [8] the dotted model curve for cr= 192 MPa reflects the nature of inverse creep from the corresponding curve of Nimonic 75 at 0 = 10 MPa (Fig. 2). 3.2. Precipitation strengthened in 738 LC
The enhanced Al- und Ti-content in IN 738 LC leads to the additional precipitation of the ordered intermetallic phase Ll,-Ni,(Al,Ti). These 1;‘-particles are coherent and exhibit an average particle diameter d,, in the fully heat-treated condition of z 0.1 ym. Due to the large volume fraction (f= 42%) dislocation motion is mainly concentrated in the narrow matrix channels. In fact, subgrain formation is suppressed in an analogous way to the fine grain size of Nimonic 75 (Section 2.1) as the channel width L, (shaded band in Fig. 1) is always lower than W. Thus, otUb = 0 in Eq. (3). However, TEM observations indicate a particular
and Engineering
A234-236
(1997)
501-504
variant of the particle-induced back stress gp,p introduced in the previous section, Fig. 4a. The shell model [l l] accounts for the built-up of a dislocation network of thickness a at the particle-matrix interface during plastic deformation arising from coherency/misfit dislocations, geometrically necessary dislocations [lo] and glide dislocations, Fig. 4b. Thus, we observe a heterogeneous dislocation structure consisting of hard shells of volume fraction f&, and soft channels of volume fraction f,. Consequently, we evaluate gp,p analogously to arb, Eq. (2), simply replacing.& by fh,,,( K a/&). However, the situation gets more complicated since the y’-particles show pronounced Ostwald ripening such that d:. oc t, Fig, 5b. The observed microstructural changes act twice on geff in Eq. (3): firstly, the particle hardening contribution is reduced assuming an Orowan-type dependence of 0,” cc l/d,.(t) and secondly, the dislocation network evolution around the particles accounts for bp,p ocf(a/d,,(t)), This complex situation is visualized for a technical-relevant long-term creep test in Fig. 5: the shape of the creep curve (Fig. 5a) results from the superimposed effects of dislocation evolution via gp,p (shell formation, Fig. 5c) and dp (not plotted), and of particle coarsening via &J (Fig. 5b) upon geff (Fig. 5~). It exhibits pronounced normal primary creep followed by a convex &increase and, as a transition state a creep minimum in between. References [l] H. Alexander, P. Haasen, Solid State Phys. 22 (1968) 27. [2] B. Ilschner, Hochtemperaturplastizitat, Springer-Verlag, Berlin, 1973. [3] G. Taylor, Proc. Royal Sot. A145 (1934) 362. [4] M. Heilmaier, K. Wetzel, B. Reppich: In: H. Oikawa et al. (Eds.), Proc. 10th Int. Conf. on the Strength of Materials, The Japan Institute of Metals, Sendai, 1994, p. 563. [S] M. Heilmaier, B. Reppich, Met. Mater. Trans. 27A (1996) 3861. [6] M. Heilmaier, J. Wunder, U. Bohm, B. Reppich, Comp. Mater. Sci. 7 (1996) 159. [7] W. Blum: In: R.W. Cahn et al. (Eds.), Materials Science and Technology, Vol. 6: Plastic Deformation and Fracture of Materials (H. Mughrabi, Ed.), VCH-Verlagsgesellschaft, Weinheim, 1992, p. 359. [8] L.M. Brown, R.K. Ham, in: A. Kelly et al. (Eds.), Strengthening Methods in Crystals, Applied Science Publishers, London, 1971, [9] y: iausselt. W.D. Nix, Acta Metall. 25 (1977) 595. [lo] M.F. Ashby: ibid. 8, p. 137. [I l] K.-D, Stein: PhD thesis. In: Fortschritt-Berichte VDI, Reihe 5 Nr. 428, VDIVerlag, Dusseldorf, 1996.
Materials Scienceand EngineeringA234&236 (1997) 501-504
On the microstructural origin of primary creep in nickel-base superalloys M. Heilmaier a,*, B. Reppich b b Institut
fur
a Institut fir FestkiirperWerkstoffwissenschaften,
and Werkstofforschung Lehrstuhl I, Universitiit
Dresden, D-01 171 Dresden, Germany Erlangen-Niirnberg, D-91058 Erlangen,
Germany
Received 3 February 1997;received in revised form 26 March 1997
Abstract The nature of primary creep in nickel-base superalloys is strongly correlated to the different hardening species present in the material. In fine-grained single-phase material the classical assumption of a homogeneous dislocation distribution enables the prediction of the transition from normal via sigmoidal to inverse primary creep with decreasing applied stress 6. In coarse-grained material the back stress ob of hard subgrain boundaries evolving during plastic deformation must be additionally taken into account. Second-phase particles influence creep in a 2-fold manner via reducing the effective stress gefc, namely directly by the stress o,* for particle overcoming, and indirectly by increasing the dislocation density p. The proposed approach accounts for the observed pronounced normal primary creep in particle-strengthened superalloys. 0 1997 Elsevier Science S.A. Keywords:
Superalloys; High-temperature creep; Particle-strengthening
1. Introduction
2. Primary creep in single-phasematerial
The extraordinary strength of superalloys is strictly controlled in terms of the effective stress (a&-model [1,2] by internal back stresses a,; due to: (a) effective metallurgical obstacles (solid solution atoms, dispersoids, precipitates, grain boundaries, in increasing order of size) and; (b) homogeneous and heterogeneous dislocation structures evolving during the deformation and loading history, respectively, and by synergetic effects due to complex interaction between (a) and (b). Under high temperature creep conditions metallic alloy systems approach a dynamic equilibrium of strain hardening and recovery, termed steady-state. The way, however, in which steady-state will be achieved depends on the kinetic and evolution of internal back stresses involved. This will be exemplified in the present study with selected single-phase and particle-strengthened nickel-base superalloys.
Nimonic 75 is essentially a nickel-base solid solution with z 20 wt.% chromium. Therefore, it may serve as an appropriate single-phase matrix reference material for particle strengthened nickel-base superalloys of similar chemical composition.
* Corresponding author.Tel.: + 49 351 4659721; 4659320; e-mail:heilmaier@ifw-dl:esden.de
fax:
+ 49 351
0921-5093/97/$17.00 0 1997Elsc:vierScienceS.A. All rightsreserved. PIISO921-5093(97)00258-X
2.1. Homogeneous dislocation structure In single-phasematerials, pi is composed of the longrange stress field op of free dislocations and the back stress Otub resulting from hard subgrain boundaries. Following Taylor [3] the former can be calculated as dp = clGbM & with CI elastic interaction constant, G shear modulus, b Burgers vector, M Taylor factor, p the mean total dislocation density. However, the latter (orb) can be suppressedby fine grains. The reason for that microstructural pecularity is displayed in Fig. 1 where dislocation spacing pS&O.’and subgrain size w,, at steady-state are plotted vs. normalized stress o/G for various nickel-base alloys. At o/G M 7. lop4 corresponding to 0 z 45 MPa at 850°C the straight line for w intersects the grey-shaded area which represents the grain size distribution of fine-grained material with a
502
M.
Heilmaier,
B. Reppich
/Materials
Science
mean value of d g z 11 urn. Considering that subgrains may form only when the condition w K c - ’ 5 d,/2 is fufilled no complete substructure formation could be expected even at values below 10 ~ 3s/G or 0 x 80 MPa, alternatively. The single parameter (p,) HAI-model according to Haasen-Alexander-Ilschner [ 1,2] yields the following relationship:
&41=MP&o
sinh(p(g
and Engineering
A2346236
1o-3
(1997)
501-504
85OV
Nimonic
75
lo4 7 * 1o-5 . ‘W
1o-6
- aGbM&))
1O-7 10 MPa
The term in the inner parentheses represents crerr. The parameters of dislocation velocity, v0 = 2. 10e9 m s ~ l and /I = 0.08 MPa- ‘, have been determined at ‘constant dislocation structure’ by sudden stress change tests in a former work [4]. The evolution of dislocation spacing p - o.5 (and thus of g,,) with plastic strain is described by a common Avrami kinetics. For a complete derivation of Eq. (1) refer to Heilmaier et al. [6].
In
-81’
I”
.
0
I
I
0.20
0.10
0.30
0.40
Fig. 2. Comparison of true strain rate-true strain curves of fine- and coarse-grained single-phase Nimonic 75. Solid lines: measured; dashed lines: calculated according to the HAI-model, Eq. (1) setting x = 0.2, G = 55.8 GPa, M = 3, b = 0.254 nm. The open and full circles indicate the point of maximum deformation resistance, i.e., minimum creep rate.
2.2. Heterogeneous dislocation structure :‘..:‘.:. ,... i.,.
. . . . . . . :.:.:.:.‘.:.‘-:.:-:-: :.. ->..: ..:\:i. i :‘:‘:::::‘:::‘::~.::‘::~,~:’ :i:I:~:i:i:,.~::i:Iji:ii ;i;i:;;: -.,-‘Y-::‘:::.~i:‘. ,.z.:.>:.: ..:.:: ,:,.:...; .,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .:.:t: .:,.,;:.;: . . . . . .:...: .:, >> ,.,.,.,.,.. /, ..,.., ,. ;.>3,.;>;: ~..,...,.... ,.,. . . . . :........ ,.,., ., . . . . . . ,.,,...,. ., ., . ..,. .,. ..,.. .,., ..,:. ” ‘“-““.:::‘:.:::~ .> ., . . :.:..:.“““” . . . ““. .,., ,. . .,. ..-... :.: ..A:.?..: .;:::;; ,\.::::,:::,:j:**,.> i... .......~.i.:.:,.:..:..~ .:.:.: :...:.,:, :.:.;:.,, .> ,,,
The composite model of plastic creep deformation [7] introduces a long-range back stress 0;“’ due to the evolution of an inhomogeneous dislocation structure consisting of hard subgrain boundaries and soft subgrain interior. If subgrains evolve the amount of exertion of backstress into the subgrain interior can be calculated as gb
sub _
fh 1 -Al
- -cT(kb
- 1)
with fh = fS,,.2a/w x 0.05 for a fully developed substructure; a is the width of subgrains and fsub is the volume fraction of subgrain-containing regions, respec-
loo g 2 5 n ‘c! ?Z Q
MA 754, 85OT
10 -l
h [9]
0 Nimonic75 CD Ni-20Cr-2Th02 0 MA754 q MA6000 0 IN 738 LC 3*10d
...::::::.:::;. .....<.. ‘Y,& ..:.... ,c ,
1o-g
1o-3
o/G(T)
Fig. 1. Dependence of characteristic steady-state dislocation spacings on normalized applied stress for various nickel-base alloys. Comparison with the grain size of single-phase Nimonic 75, dg,fine and the interparticle spacing (channel width) in IN 738 LC, L,, respectively. Data of thoria dispersed Ni-20G taken from Hausselt and Nix [9].
0
0.02
0.04 &PI
Fig. 3. Differentiated creep curves of MA 754. Solid lines: measured; dashed lines: calculated according to the particle-modified HATmodel, Eq. (3); dotted line: calculated, setting or = const. Model parameters G(, G, b, M, v,,, j? have been adopted from Nimonic 75, Section 2.1.
M. Heilmaier,
B. Reppich
/Materials
Science
and Engineering
A234-236
(1997)
501P.504
503
tively. Fig. 2 assesses typical differentiated creep curves of fine- and coarse-grained (d, = 650 urn) Nimonic 75. Essentially, in fine-grained material the transition from normal (81 MPa) to sigmoidal (45 MPa) and inverse (18 MPa) primary transient creep with decreasing applied stress CTis properly reflected by the features of the model (compare the corresponding dashed curves according to Eq. (1) and the measured continous curves). In coarse-grained material, however, a continous decrease of 6 resulting from evolving subgrains is obvious. Thus, the increase of otub reduces cefi in Eq. (1) which in turn explains the observed creep deceleration (see the respective 6b-arrows in Fig. 2).
3. Primary
creep in two-phase
materials
Starting point of our refined analysis of primary creep in particle-strengthened nickel-base superalloys are the following experimental evidences compared to single-phase material: (a) the i-decrease during primary creep is extremely high, usually several orders of magnitude [5], (Fig. 3 and Fig. 5a); (b) the steady-state dislocation density pss is seriously increased at equivalent strain rates & (Fig. 1); and (c) in constant strain rate tests the yield stress-increment at E = 0 is significantly lower than the stress-increment at steady-state cp
Fl. Thus, we must revise the sofar simple picture of the original threshold stress concept [8] suggesting that a single parameter op accounts for the total particle hardening contribution. Rather, the effect of particlestrengthening on creep acts 2-fold: firstly, via a constant o,*-value representing the traditional contribution for the mere particle overcoming process (explaining observation c) and secondly, via an additional long-range back stress up,p -term reflecting the evolution of particleinduced dislocations during plastic deformation (satisfying observation (b). Splitting gp = u,* + gp,p as the simplest superposition rule we modify the effective stress model, Eq. (l), to obtain the deformation law for particle-strengthened materials: .i”& = -pbvo M sinh(/?(a - 0, - arb - g*, - o~,~))
(3)
However, closer examination in the following sections will reveal that the origin of op.? depends on the particular type of the particle-matrix interface. 3.1. Oxide dispersion strengthened
MA 754
In comparison with single-phase Nimonic 75 the ODS alloy MA 754 is additionally strengthened by incoherent Y203 dispersoids. The MA process enables an extremely fine distribution of the thermally stable particles resulting in mean values of diameter d = 14
Fig. 4. Particle and dislocation microstructure in IN TEM micrograph of creep deformed IN 738 LC, 0 E = 0.04; (b) scheme of the shell model [I l] reflecting the channels a long-range back stress bp,p in the matrix dislocation networks (dark sketched) around y’-precipitates
738 LC: (a) = 414 MPa, evolution of due to hard (shaded).
nm, volume fraction f = l.O%, and interparticle spacing L, = 83 nm [6]. Fig. 3 displays a set of typical creep curves of MA 754 [5]. Post mortem TEM observations have revealed that subgrain formation is effectively suppressed by the dispersoids during creep. Thus, we assume a homogeneous dislocation distribution, setting oEub = 0 in Eq. (3) (compare Section 2.1): for all creep curves in Fig. 3 a constant fraction of a,* = 0.6 ap has been applied as evaluated from yield stress increment measurements [6]. bp,p approaches its steady-state value of 0.4. gp analogously to G,, ( = aGbM&), but starts from zero using a different Avrami kinetic for the additional dislocation density pp. It is obvious from Fig. 3 that the dashed curves describe the pronounced normal tran-
504
M. Heilmaier,
L 0
B. Reppich
/Materials
Science
I 2
4
6
8
10
12
14
t1103h Fig. 5. (a) Differentiated creep curve of IN 738 LC in log&t-representation. Full circles, measured; solid lines, calculated according to the shell model [ll]; (b and c): stress components and y’-particle coarsening kinetics. Damage accumulation like cavity growth controls the tertiary creep stage which has not been plotted here (time to failure was about 30000 h).
sients (solid curves) adequately. In contrast, applying the original threshold stress concept [8] the dotted model curve for cr= 192 MPa reflects the nature of inverse creep from the corresponding curve of Nimonic 75 at 0 = 10 MPa (Fig. 2). 3.2. Precipitation strengthened in 738 LC
The enhanced Al- und Ti-content in IN 738 LC leads to the additional precipitation of the ordered intermetallic phase Ll,-Ni,(Al,Ti). These 1;‘-particles are coherent and exhibit an average particle diameter d,, in the fully heat-treated condition of z 0.1 ym. Due to the large volume fraction (f= 42%) dislocation motion is mainly concentrated in the narrow matrix channels. In fact, subgrain formation is suppressed in an analogous way to the fine grain size of Nimonic 75 (Section 2.1) as the channel width L, (shaded band in Fig. 1) is always lower than W. Thus, otUb = 0 in Eq. (3). However, TEM observations indicate a particular
and Engineering
A234-236
(1997)
501-504
variant of the particle-induced back stress gp,p introduced in the previous section, Fig. 4a. The shell model [l l] accounts for the built-up of a dislocation network of thickness a at the particle-matrix interface during plastic deformation arising from coherency/misfit dislocations, geometrically necessary dislocations [lo] and glide dislocations, Fig. 4b. Thus, we observe a heterogeneous dislocation structure consisting of hard shells of volume fraction f&, and soft channels of volume fraction f,. Consequently, we evaluate gp,p analogously to arb, Eq. (2), simply replacing.& by fh,,,( K a/&). However, the situation gets more complicated since the y’-particles show pronounced Ostwald ripening such that d:. oc t, Fig, 5b. The observed microstructural changes act twice on geff in Eq. (3): firstly, the particle hardening contribution is reduced assuming an Orowan-type dependence of 0,” cc l/d,.(t) and secondly, the dislocation network evolution around the particles accounts for bp,p ocf(a/d,,(t)), This complex situation is visualized for a technical-relevant long-term creep test in Fig. 5: the shape of the creep curve (Fig. 5a) results from the superimposed effects of dislocation evolution via gp,p (shell formation, Fig. 5c) and dp (not plotted), and of particle coarsening via &J (Fig. 5b) upon geff (Fig. 5~). It exhibits pronounced normal primary creep followed by a convex &increase and, as a transition state a creep minimum in between. References [l] H. Alexander, P. Haasen, Solid State Phys. 22 (1968) 27. [2] B. Ilschner, Hochtemperaturplastizitat, Springer-Verlag, Berlin, 1973. [3] G. Taylor, Proc. Royal Sot. A145 (1934) 362. [4] M. Heilmaier, K. Wetzel, B. Reppich: In: H. Oikawa et al. (Eds.), Proc. 10th Int. Conf. on the Strength of Materials, The Japan Institute of Metals, Sendai, 1994, p. 563. [S] M. Heilmaier, B. Reppich, Met. Mater. Trans. 27A (1996) 3861. [6] M. Heilmaier, J. Wunder, U. Bohm, B. Reppich, Comp. Mater. Sci. 7 (1996) 159. [7] W. Blum: In: R.W. Cahn et al. (Eds.), Materials Science and Technology, Vol. 6: Plastic Deformation and Fracture of Materials (H. Mughrabi, Ed.), VCH-Verlagsgesellschaft, Weinheim, 1992, p. 359. [8] L.M. Brown, R.K. Ham, in: A. Kelly et al. (Eds.), Strengthening Methods in Crystals, Applied Science Publishers, London, 1971, [9] y: iausselt. W.D. Nix, Acta Metall. 25 (1977) 595. [lo] M.F. Ashby: ibid. 8, p. 137. [I l] K.-D, Stein: PhD thesis. In: Fortschritt-Berichte VDI, Reihe 5 Nr. 428, VDIVerlag, Dusseldorf, 1996.