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The low cycle fatigue deformation response of a single-crystal superalloy at 650 °C
Materials Science and Engineering, A 108 (1989) 189-202
189
The Low Cycle Fatigue Deformation Response of a Single-crystal Superalioy at 650 °C T. P. GABB
Lewis Research ('enter, National A eronautics and Space Administration, Clevehmd, OH 44135 (U.S.A.) G. WELSCH
Materials Science and Engineering Department, Case Western Reserve Universio,, Cleveland, OH 44100 (U.S.A.) R. V. MINER and J. GAYDA
Lewis Research Center, National Aeronauties and Space Administration, Clevehmd, OH 44135 (U.S.A.) (Received March 3(J, 1988; in revised form June 6, 19881
Abstract
The purpose of this study was to characterize the cyclic stress-strain response, the corresponding deJormation structure and their relationships in the single crystal nickel-base superalloy PWA 1480. The isothermal low cycle fatigue response and deformation structures of specimens oriented near the/001], [2 5 20], l 3 6 lOft lOll], [234] and l]11] crystallographic orientations were characterized at an intermediate temperature (650 °C). The initial yield strength of all these specimens was controlled by the shearing of the 7' precipitates by dislocation pairs. The low cycle fatigue tests exhibited cyclic hardening, which was associated with dislocation interactions in the g matrix. In specimens deforming by slip on a single slip system, dislocations of the primary slip system accumulated in the 7 matrix and formed sessile entanglements. In specimens deforming by slip on several slip systems, the dislocations of the different operative slip systems intersected in the 7 matrix and formed sessile arrangements'.
I. Introduction
Most modern nickel-base superalloys deform by planar slip in low cycle fatigue (LCF) loading at intermediate application temperatures (500800 °C) [1]. In part because of this, the cyclic stress-strain response of superalloy single crystals is dependent on crystallographic orientation [2]. In single-phase copper [3] and two-phase A1-Cu [4] f.c.c, alloys, some aspects of the planar slipinduced orientation dependence have been ac0921-5093/89/$3.50
counted for by resolving the cyclic stress and inelastic strain on the active slip systems [5]. Other aspects of the cyclic hardening response in these alloys have been associated with the number of operative octahedral slip systems. These concepts have also been applied to some extent to the LCF of single-crystal nickel-base superalloys [6]. However, some modern single-crystal nickelbase superalloys with high 7' volume fractions show significant deviations from the well-known planar slip response of f.c.c, alloys at intermediate temperatures. While conventional f.c.c, alloys deform by octahedral slip (slip on {111} planes in (101) directions), single crystals of Ren6 N4 [7] !and PWA 1480 [8] oriented near the [111] crystallographic orientations deform b_y primary cube slip (slip on the (001) plane in the [110] direction). Single crystals of these superalloys oriented to deform by octahedral slip display an orientationdependent tension-compression anisotropy in monotonic yield strength. In both cases, these variations have been attributed to the tendency for cube slip in the V' precipitates. These deviations from f.c.c, alloy response affect the cyclic stress-strain behavior of these superalloys [2, 9, 10]. The purpose of this study was to investigate this cyclic stress-strain response and the associated deformation structures of one of these superalloys, PWA 1480. Single crystals of various crystallographic orientations were tested in LCF at 650 °C. The operative deformation mechanisms were characterized and related to the observed cyclic stress-strain behavior. © Elsevier Sequoia/Printed in The Netherlands
190
2. Materials and experimental procedure
3. Results
The composition of the PWA 1480 test material is listed in Table 1. This material was cast by the withdrawal technique into singlecrystal bars, nominally 21 mm in diameter and 140 mm in length, and single-crystal slabs, nominally 160 mm long, 60 mm wide and 13 mm thick. The growth axis of the bars and slabs were within 10 ° of the [001] crystallographic direction. The bars and slabs were subsequently solution treated in argon at an average temperature of 1270 °C for 4 h, air quenched and then aged in argon at 1080 °C for 4 h and then at 871 °C for 32h. Specimens of [001] crystallographic orientation were machined directly from the bars. Specimen blanks were spark machined at various angles in the slabs in order to obtain specimens with axes oriented near the [001], [2 5 20], [3 6 10], [011], [234] and [i11] crystallographic directions. These specimens were tested at 650 °C in a closed-loop servohydraulic testing machine employing an axial extensometer of 12.7 mm gauge length. The specimens were heated with a three-zone clamshell resistance-heating furnace. The LCF tests were performed at a constant total strain range, with the total axial strain varied sinusoidally at a frequency of 0.1 Hz. Several tensile tests were also performed; these tests were conducted at a constant displacement rate of 8 mm s- '. Further detailed information on these tests has been provided elsewhere
The heat-treated microstructure of both the bars and the slabs was principally constituted of 65 vol.% of cuboidal y' precipitates of 0.55 + 0.18 p m width in a 7 matrix. Additionally, about 3 vol.% of remnant 7-7' eutectic pools about 10-100 p m in diameter was observed, together with about 0.3 vol.% of casting micropores about 5-10 p m in diameter. The operative slip systems of the test specimens at 650 °C were determined by identifying the planes of the slip offsets on the specimen surfaces (Fig. 1), measuring the crystallographic rotations of the tensile specimens' axes towards the slip direction, and by TEM analysis. The [2 5 20], [3 6 10] and [011] specimens deformed predominantly by primary octahedral slip on the (111) plane in the []01] direction. The [001] specimens deformed by octahedral slip on several {111} planes in several (101) directions. The [234] and []11] specimens deformed predominantly by primary cube slip on the (001) plane in the [i 10] direction.
3.1. Mechanical response 3.1.1. Cyclic hardening response The results of the tensile tests at 650 °C are listed in Table 2. The axial stress-strain curves of these tests are shown in Fig. 2. The specimens deforming by primary octahedral slip, [2 5 20], [3 6 10] and [011], had a comparable tensile response, similar to classical f.c.c, single-crystal response for a single operative slip system. On yielding, these specimens initially displayed stage I "easy-glide" flow with very little strain hardening. At an inelastic strain of 0.02-0.03, this was followed by stage II flow of increased strain hardening. The [001] specimens had immediate enhanced strain hardening. The [234] and [ i l 1] specimens both displayed brief stage I flow to an inelastic strain of about 0.01, followed by steep stage II hardening. The initial yield strengths in tension and compression are listed in Table 3. As reported elsewhere [8, 11], the specimens deforming by octahedral slip had an orientationdependent tension-compression anisotropy in
[10]. Foils for transmission electron microscopy (TEM) were prepared normal to the specimens' center-line axes and sometimes also parallel to the operative slip planes. The foils were mechanically polished to 0.1 mm thickness and then electrochemically thinned with a twin-jet thinner using a solution of 10% perchloric acid, 45% acetic acid and 45% butylcellusolve at 0 °C. The foils were examined with a Phillips EM400T transmission electron microscope operated at 120 kV. At least four foils of every specimen selected for TEM analysis were briefly surveyed; one or two of these foils were analyzed in detail. TABLE 1
Composition of the PWA 1480 test material
Element Nominal amount (wt.%) A m o u n t in slabs (wt.%) A m o u n t in bars (wt.%)
AI 5 4.7 5.3
C < 0.02 0.005 0.003
Co 5 4.8 5.3
Cr 10 9.4 10.3
S -0.001 --
Si -0.9 --
Ta 12 11 11.9
Ti 1.5 1.0 1.3
W 4 5.2 4.0
Ni Balance Balance Balance
191
(a)
(b)
(c)
(d)
Fig. 1. Slip offsets of the LCF test specimens at 650 °C: (a) [3 6 10] specimen, Aei, , i < 0 . 0 0 1 0 m m m m i; (b) [3 6 10] specimen, Ac,,, ~= 0.0017 mm m m ~; (c) [001 ] specimen, Aein t = 0.0020 mm mm ~; (d) [i 11 ] specimen, A tin ~= 0.0017 m m mm ~.
TABLE 2
Nominal orientation [hkl ] 00 1 5 20 6 10 0 11 34 11
Tensile test results
Measured orientation [hkl ] i 1 1~33 2~-63 ] 81 3-~97 7-882
lO0 100 100 100 100 100
Symbol in figures II * • '~ II •
Elastic" modulus E (GPa)
Yield strength 0.2% Qffset oV (g'lPa)
Ultimate strength ou (MPa)
True fracture strain (ram mm l)
1()3 133 177 184 238 257
963 855 742 841 755 747
1343 992 951 983 1159 1180
0.033 0.112 0.149 0.112 0.232 0.245
eft
192 1~00
.
,-r~?.-~.~-;~
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~ -
. . . . . . . . . .
initial yield strength, with the [001] and [2 5 20] specimens stronger in tension, and the [3 6 10] and [011] specimens stronger in compression. The results of the LCF tests are given in Table 4. Typical examples of the hardening response are shown in Figs. 3 and 4. Data from different tests on specimens of the same crystallographic orientation are indicated by the open, half-filled and full symbols in order of increasing inelastic strain range. The cyclic stress and inelastic strain hardening responses of the primary octahedral slip specimens, [2 5 20], [3 6 10], and [011], were quite comparable. Comparable cyclic hardening occurred in tension and compression; therefore the cyclic mean stresses produced by the initial yield strength tension-compression anisotropy were sustained and varied with crystallographic orientation. In these strain-controlled tests, the initial stage I easy glide produced "jerky" flow with negligible strain hardening for 10-20 LCF cycles, as shown in the typical hysteresis loops in Fig. 4. The jerky flow then abated as significant stage II strain hardening occurred. The number of fatigue cycles before the onset of stage II hardening varied inversely with initial inelastic strain range. In order to account for this inverse
--~
20C
Fig. 2. The axial stress-strain curves of the tensile tests.
TABLE 3 Average initial yield strengths of the specimens in tension and compression Nominal orientation [hkl]
Average yield strength at ei. = 0.0005 mm mm-
(MPa)
Compression o c (MPa)
883 849 748 825 734 745
832 816 787 919 749 719
Tension o t
00 1 5 20 6 10 0 11 34 ] 11
TABLE 4 Nominal orientation [hkl]
Results of the low cycle fatigue tests Actual orientation [hkl]
Symbol in figures
Schmid factor S
Total strain
001 001 001
Inelastic strain
(mm mm
Cycle 0 . 5 N f
Cycle 1
J)
(mm ram-')
Maximum stress am~x (MPa)
amin (MPa)
Inelastic Maxistrain mum m~'in stress (mm 6rmax rnm-')(MPa)
mEin
Minimum stress
Fatigue life
Minimum stress amin (MPa)
gf
(cycles)
5 8100 4 5100 2 6100
D [] •
0.436 0.427 0.433
0.0145 0.0164 0.0179
0.00026 0.00055 0.00200
798 851 900
798 853 860
0.0002 825 0.00040 870 0.00093 974
782 848 911
1455 1228 215
5 20 2520 ~520 2 5 20
7 22 100 825100 1--430 100 19 13 100
O * * *
0.478 0.482 0.487 0.450
0.0142 0.0149 0.0146 0.0171
0.00033 0.00093 0.00152 0.00266
848 878 846 881
818 822 805 824
0.0002 0.00055 0.00082 0.00130
855 889 879 962
816 841 829 881
872 427 237 165
6 10 ) 6 10 6 10
1 9 5 7 100 1---958 100 3--261 100
o ~ •
0.493 0.492 0.472
0.0092 0.0097 0.0105
0.00128 0.00170 0.00249
758 743 775
784 777 793
0.00069 764 0.00087 789 0.00123 856
807 827 889
1171 971 180
100 100 100 100
o '~ ~' 4)
0.426 0.441 0.435 0.439
0.0089 0.0092 0.0105 0.0115
0.00035 0.00059 0.00150 0.00289
830 854 841 816
897 894 930 896
0.00025 0.00038 0.00080 0.00111
851 861 887 917
884 916 967 1049
1546 824 862 555
34 34 34
4--280 100 4--'066 100 4 3 6 8 100
0 ~ I
0.475 0.470 0.477
0.0074 0.0077 0.0087
0.00082 0.00119 0.00220
741 738 732
755 747 790
0.00034 784 0.00040 795 0.00090 863
818 834 912
2063 1440 281
ill i 11 i 11
7-581100 8--2-86 100 8-894 100
a ~ •
0.497 0.493 0.485
0.0063 0.0072 O.O08O
0.00089 0.00164 0.00249
739 747 749
732 744 771
0.00023 810 0.00056 867 0.00111 917
821 889 956
1884 1010 338
0 0 0 0
1 1 1 1
1 1 1 1
3 2 2 4
94 86 89 88
193
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F.ig. 3. The LCF stress-hardening response of (a) the [3 6 10], (b) the [001 ] and (c) the [111 ] specimens.
/ CYCLE --
dependence and to enable comparisons with the monotonic behavior, the cyclic stress-hardening response was expressed as cyclic shear stress as a function of cumulative inelastic shear strain [3]. Examples of the resulting r vs. 7c curves [10] of typical LCF and tensile tests of these specimens are shown in Fig. 5. These LCF and tensile strain hardening curves all display a comparable stage I easy-glide region extending to a cumulative strain 7g of about 0.07. This maximum easy-glide strain 7g, marking the cessation of easy glide and the onset of more rapid stage II strain hardening, did not vary significantly as a function of inelastic strain range and these strains were of comparable magnitude in the LCF and tensile tests [10]. The subsequent stage II strain hardening was lower in the LCF tests than in the tensile tests. The [001] specimens, deforming on several octahedral slip systems, had rapid cyclic strain hardening to near saturation in 10-20 LCF cycles. The cyclic stress and strain response could not be easily resolved onto the active slip systems,
(YCLE
Nil
II v
~coo
L
01 ~
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Fig. 4. Typical hysteresis loops of the LCF tests.
as several slip systems were operative and the interactions between different slip systems are not easily accounted for. However, in any event the LCF and tensile-hardening responses appeared to be dissimilar. The [234] and [i 11] specimens, deforming by primary cube slip, had comparable cyclic hardening responses. LCF cycling produced immediate and continued strain hardening accompanied by temporary slight jerky flow. The stage I easy glide
194
displayed in the tensile tests of these specimens abated at an inelastic shear strain of about 0.01, which corresponds to the cumulative shear strain produced by only one or two fatigue cycles. The corresponding r vs. ~,~ curves of these LCF and tensile tests therefore did not clearly display comparable stage I regions. 3.1.2. Cyclic stress-strain curves
The stabilized cyclic stress-inelastic strain curves generated from the LCF tests at 650 °C indicated low cyclic strain hardening. The resolved cyclic stress amplitude-inelastic strain amplitude response at half the cyclic life of the specimens deforming on a single slip system was modelled by least-squares analysis with a standard equation of the form Ar 2
K'
m
~ rE~Le ~ST
o •
•
O0
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eo oo°o°~
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I
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I IllLdl 10 i
o
o
c~
,oF TE~T
d__~lllhl
I 100
I
i~lllil ,ol
Fig. 5. The tensile shear stress-cumulative shear strain response of the [) 6 10] LCF and tensile test specimens.
where At/2 and A),m/2 are the resolved cyclic shear stress and inelastic shear strain amplitudes, K' is the cyclic strength constant and m' is the cyclic strain-hardening coefficient. The cyclic strain-hardening coefficients of the [2 5 20], [3 6 10] and [011] primary octahedral slip specimens were 0.021, 0.036 and 0.091 respectively. The [111] and [234] primary cube slip specimens as a group had slightly higher hardening coefficients, 0.071 and 0.116 respectively. The axial cyclic stress amplitude-inelastic strain amplitude response of the [001] specimens produced a cyclic strain-hardening coefficient of 0.104. 3.2. Deformation structure 3.2.1. General characteristics
The deformation structures of the [2 5 20], [3 6 10] and [011] primary octahedral slip specimens were quite comparable and varied as function of the inelastic strain range incurred. Specimens tested to failure at low inelastic strains (Aei, l-~0.001 m m n ] l ~ - 1 ) had irregular illdefined bands of various moderate dislocation densities separated by relatively undeformed regions (Fig. 6). This was consistent with the often widely separated slip offsets observed on the specimen surfaces (Fig. 1). The direction of the bands was parallel to the (111) primary octahedral slip plane trace. About 80% of the dislocations had Burgers vectors corresponding to primary octahedral slip, b=+_½[i01]. The majority of the dislocations were in the 7 phase, sometimes bowed on the (111) plane and sometimes combined in non-planar entanglements.
Fig. 6. The deformation structures of [3 6 10] LCF specimens with a [011] zone axis: (a) Ae~.l<0.001 (b) Aei. ~> 0.002 mm m m - ].
mm m m - J ;
195
These dislocations were often slightly dissociated on {111 } planes. A smaller number were in the 7' precipitates. Specimens cycled at large inelastic strains (Aein 1 "~0.002 m m m m - l ) had deformation throughout the microstructure (Fig. 6). This was consistent with the densely packed slip offsets evident on the specimen surfaces (Fig. 1). Where the dislocations were of a low enough density to enable counting, 95% with a standard deviation of 10% of the dislocations had the primary octahedral slip Burgers vectors. A majority of these dislocations were again in the y phase, where they were again either bowed on {111} planes or combined in non-planar entanglements. A smaller number of dislocations were in the 7' precipitates. The deformation structure of the failed [001] LCF specimens generally consisted of localized dislocation patches rather than bands of deformation. Specimens tested at low inelastic strain ranges had moderately spaced patches of dislocations, while specimens tested at large inelastic strain ranges had more frequent patches of higher dislocation density (Fig. 7). Most of the dislocations observed had Burgers vectors corresponding to octahedral slip: b = _+1[]01], ![101], ½[0i 1] and ½[011]. A majority of these dislocations were again in the ), phase, of various characters and often slightly dissociated on {111} planes. They were often combined in non-planar entanglements, especially in the specimens tested at large inelastic strain ranges. These dislocations were also sometimes arranged in square arrays at the V-y' interfaces. A smaller number of dislocations of these Burgers vectors were in the y' precipitates. The deformation structure of the [234] and [i 11] primary cube slip LCF specimens also varied with cyclic inelastic strain range. Failed specimens tested at low inelastic strain ranges contained irregular ill-defined dislocation bands parallel to the (001) primary cube slip plane, separated by dislocation-free regions (Fig. 8). Only about 65% of the dislocations had Burgers vectors corresponding to primary cube slip, with b = +½[il0]. The first observation of this low percentage in a [ i 11 ] specimen was initially interpreted as evidence of cube slip on other slip systems [10]. However, tensile axis rotation measurements in tensile tests, slip trace analyses and further TEM examinations of various [234] and [] 11] tensile and LCF specimens indicated that primary cube slip did predominate. A
majority of the dislocations were in the 7 phase. Individually occurring 7 dislocations were often bowed and dissociated on the (111) or (] ] 1) planes. This is shown in the tilting experiment of a [234] LCF test specimen interrupted at 13 cycles (Fig. 9). Many of the curved 7 dislocations become straight projected lines parallel to the (111) plane trace when this plane is perpendicular to the electron beam. A smaller number of dislocations were in the 7' precipitates. The [234] and [i 11] specimens fatigue tested to failure at large inelastic strain ranges had deformation throughout the microstructure (Fig. 8). Over 90% of the dislocations observed in these specimens had the primary cube slip Burgers vectors b=½[il0]. They were mostly located in the 7 phase and were sometimes bowed on the (111) or (111) planes when
Fig. 7. T h e d e f o r m a t i o n structures of [0011 L C F specimens: (a) Aei,,t <0.001 m m m m i, [013] zone axis; (b) Ae,, t > 0.002 m m m m ~. [ ] 01 ] zone axis.
196
Fig. 8. The deformation structures of the LCF specimens: (a) [234], A~in i <0.001 mm. mm ], [011] zone axis; (b)[i 11], A ei, ~> 0.002 mm m m - i, [101] zone axis.
singular. The (111) plane is nearly perpendicular to the electron beam in Fig. 8(b). But the dislocations in the 7 matrix were quite often arranged in non-planar entanglements of slightly dissociated dislocations. The dislocations in the 7' precipitates were bowed on the (001) plane. 3.2.2. 7" Dislocation pairs The glide and cross-slip of dislocation pairs in the 7' precipitates are believed to control the yield strength and yield strength tension-compression anisotropy in superalloys. The characteristics of these dislocation pairs in the test specimens (Fig. 10) were therefore examined in detail [12]. To summarize these characteristics briefly, 80%+ 11% of the 7' dislocation pairs in the [2 5 20], [3 6 10] and [011] LCF and tensile specimens had a near-screw character and were
Fig. 9. Typical micrographs of a tilting experiment of a [i34] LCF specimen (Aein i = 0.0018 mm m m - I ) interrupted at 10 cycles: A, [213] zone axis; B, [031 ] zone axis.
on the (010) cube cross-slip plane. A large majority of the 7' dislocation pairs in the [001] LCF and tensile specimens had a near-screw character and were on their respective cube cross-slip planes. Therefore the pairs with b= +½[]01] and ½[101] were on the (010) plane, while pairs having b = +½[0il] and ½[011] were on the (100) plane. The 7' dislocation pairs of the [234] and [111] LCF and tensile specimens were on the (001) primary cube slip plane and of various characters.
197
L : ~L;'2)
I1
Fig. 10. The 7' dislocation pairs of the LCF specimens: (a) [)6 10] specimen, [[21] zone axis: (b)[001] specimen, [012] zone axis: (c)[234] specimen, [001] zone axis.
3.2. 3. 7he generation of deformation struclU res
In order to examine how these deformation structures are generated and their correlation with stress-hardening response, additional interrupted tests and TEM analyses were performed on the primary octahedral slip specimens. LCF (Aai=l>0.002 m m m m - l ) and tensile tests of [) 6 10] specimens were interrupted at a cumulative shear strain of less than 0.07, near the end of
the easy glide stage at 7g, and analyzed. Stage I easy-glide flow was confined to bands parallel to the (111) plane in both the LCF and the tensile specimens. The bands were of varying widths and dislocation densities. At least nine slip bands of each specimen were analyzed in standard nearidentical tilting experiments to determine the Burgers vector and plane of the dislocations. The 7 dislocations (b = +_½[i01]) in both specimens were mostly on the (111) plane, with no significant non-planar entanglements observed. This is illustrated in Fig. 11, where the curved 7 dislocations become nearly straight projected lines when the (111) plane is tilted nearly perpendicular to the electron beam. The 7' dislocation pairs in these specimens had already cross-slipped onto the (010) plane and had a near-screw character. The deformation characteristics of the primary octahedral slip specimens tested to failure showed significant changes compared with the previous interrupted tests. LCF specimens tested at A% 1>0.002 mm mm-~ had deformation throughout the microstructure, while those tested at lower inelastic strain ranges had deformation still confined to slip bands. Tensile specimens tested to failure had a higher density of dislocations throughout the microstructure. At least nine regions of foils from each of the LCF and tensile specimens were analyzed with the same tilting experiments (Fig. 12). The observed dislocations in the y' precipitates of these specimens had the same characteristics as before, with little change. However, the 7 dislocations were greatly increased in number and were no longer predominantly on the (111) plane. As illustrated in Fig. 12, while singular y dislocations were sometimes still on the (111) plane, the dislocations were often combined in non-planar entanglements. Dislocations in these entanglements were often locally dissociated on {111 }planes. In order to learn more about when these changes in deformation structure occurred, an LCF test of an [011] specimen was interrupted during stage II strain hardening at a cumulative shear strain of 0.096. TEM examination of several foils from this specimen indicated that deformation still occurred in bands. These bands were now often very broad and of a relatively consistent dislocation density, but narrow slip bands were also observed. Nine slip bands were analyzed using the same standard tilting experiments. The narrow slip bands had characteristics similar to specimens interrupted at Yc< 0.07, with
198
Fig. 11. Micrographs of typical tilting experiments of [3 6 10] specimens, A, [231] zone axis and B, [0 i 4] zone axis; (upper) LCF, Yc= 0.062 mm mm l; (lower) tensile, Yc= 0.039 mm mm ~.
the 7 dislocations predominantly on the (111) plane. However, the broad slip bands additionally had areas where the ), dislocations were entangled and no longer confined to the (111) plane (Fig. 13). Dislocation segments in these entanglements were locally dissociated on {111} planes. 4. Discussion
The single-crystal specimens deforming by octahedral slip displayed a significant
tension-compression anisotropy in initial yield strength at 650 °C. The [001] and [2 5 20] specimens were stronger in tension, while the [011] and [3 6 10] specimens were stronger in compression. This anisotropy, reported in other studies of PWA 1480 [8, 11] and Ren6 N4 [7] superalloys, has been associated with the shearing of V' precipitates by dislocation pairs. The specific shearing mechanism cited [13] concerned the effect of applied stress in promoting cross-slip of the lead dislocation from the ( 111 ) plane to the (010 ) cube cross-slip plane. An analysis of the 7' dislocation
199
Fig. 12. Micrographs of typical tilting experiments of failed [3 6 10] specimens, A, ['531] zone axis and B, [0[4] zone axis: (upper) LCF; (lower) tensile.
pairs of the octahedral slip specimens in the present study suggested that this cube cross-slip process was the dominant dislocation storage mechanism in the )" phase. Specimens deforming by primary cube slip displayed no significant tension-compresison anisotropy in yield strength. The V' dislocation pairs in these specimens appeared to remain gliding on the (001) primary cube slip plane. The initial tension-compression anisotropy in yield strength persisted during LCF cycling. However, the strain hardening produced by LCF
cycling was comparable in tension and compression. The LCF cyclic hardening was associated with major changes in the dislocation structure in the V phase. When slip was confined to the primary octahedral slip system, the initial hardening response in LCF deformation and monotonic tensile deformation was similar. Stage I easy glide initially occurred, with "jerky" flow and little strain hardening. This behavior persisted to a cumulative shear strain of about ),g = 0.07. Over the range of these tests, this maximum easy-glide strain ~'g w a s
200
Fig. 13. Micrographs of a typical tilting experiment of a [011] LCF specimen (yc=0.096 mm mm-l): A, [231] zone axis; B, [012] zone axis.
relatively independent of specific crystallographic orientation, unidirectional or reversed loading path, and LCF inelastic strain range. This suggested that some portion or aspect of this deformation was relatively irreversible, as a characteristic direction-independent amount of slip was necessary to initiate stage II strain hardening. Analysis of the deformation structures generated during the stage I easy glide indicated that
this deformation was confined to planar slip bands, with most of the dislocations in the y phase gliding on the (111) plane. After the onset of stage II strain hardening, the dislocations had accumulated in the V phase and possibly because of cross-slip had begun to combine in non-planar entanglements in the bands, becoming sessile there and providing barriers to other gliding dislocations. Possibly owing to this hardening of the slip bands, deformation spread to some extent to the remaining undeformed regions between the slip bands. In tensile tests and LCF tests of sufficiently large inelastic strains, this resulted in deformation throughout the microstructure at failure. However, in all LCF specimens tested to failure, the dislocations observed in the 7 phase were often in non-planar entanglements, with individual dislocation segments dissociated on {111 } planes. Therefore, the irreversible aspect of the stage I easy glide appeared to be the accumulation of dislocations in the 7 phase, facilitating the formation of non-planar sessile entanglements during stage II strain hardening. This accumulation of 7 dislocations may have been driven by the cube cross-slip of the paired portions of these dislocations penetrating the 7' precipitates. These cross-slipped segments on the (010) plane in the 7' would act as pinning points, hindering the free glide of the adjoining segments on the ( 111 ) plane in the V phase. In this manner, the effective free glide distance of the dislocations would be continually reduced, resulting in their accumulation to give a locally higher dislocation density. This in turn could encourage more crossslip in the 7 matrix, driven by the repulsive forces between dislocations of the same Burgers vectors. Dislocation intersections would then probably occur to produce the sessile entanglements, When slip took place simultaneously on several octahedral slip systems, rapid cyclic strain hardening occurred, and the cyclic stress range approached a saturation value in only 20-30 LCF cycles. This strain hardening was related to the intersection, principally in the 7 phase, of dislocations of the different octahedral slip systems. The dislocations formed non-planar entanglements in the 7 phase after only 10-20 LCF cycles. Additional dislocations were observed in sessile orientations at the 7-7' interfaces, sometimes intersecting to form rectangular networks, as reported in other studies [14, 15]. These dislocations arrangements each act as barriers to dislocation glide in addition to the 7' precipitates.
201 Specimens deforming by macroscopic primary cube slip displayed gradual LCF strain hardening from the first fatigue cycle. This cyclic strain hardening continued for nearly a third of the lives of these tests. Although the IJ_11] specimens have (like the [001] specimens) several highly stressed slip systems, slip only occurred on the primary cube slip system. Therefore intersecting sliphardening mechanisms do not seem to be operative here. TEM analysis of their deformation structures suggested that, while primary cube slip occurred in the y' phase, many dislocations in the 7 phase lay on the (111) or (]11) cross-slip planes. Glide on {111 } planes would occur more easily in the f.c.c, y phase. These conflicting processes may acount for the gradual continual cyclic hardening. Some gliding dislocation pairs on the (001) primary cube slip plane in the y' precipitates appear to glide into the y phase on the (001) plane. However, the observation of dislocations on the octahedral cross-slip planes in the }, phase suggests that some portion of the dislocations may have locally cross-slipped onto octahedral planes in the y phase. These cross-slipped segments could thereafter glide on these octahedral planes to the next y-y' interface. The likelihood that two cross-slipped dislocations arrive at the same interface location in this manner and orientation is rather small. In such cases these dislocations could not easily pair up for further y' shearing but would be pinned at the 7-7' interfaces (Fig. 9) and act as barriers to other dislocations. Additionally, dislocations gliding on the {111 } planes in the y phase could intersect dislocations which are still on the (001) plane and form non-planar entanglements. The entanglements were quite common in these LCF specimens at failure. The cyclic stress-strain curves at saturation of all specimens tested at 650 °C displayed low cyclic strain-hardening coefficients. This was especially evident when only the primary octahedrai slip system was operative. The cyclic stress-strain curve of single-crystal copper displays negligible strain hardening in this strain regime [16]. The constancy of cyclic stress over a range of inelastic strain amplitudes was associated with the stress required to generate persistent slip bands in the undeformed microstructure. A similar explanation appears to be applicable in the present case. In LCF tests of low inelastic strain ranges, the dislocations were in loose bands of deformation separated by
undeformed regions. In fatigue tests of large inelastic strain ranges, deformation occurred throughout the microstructure. It seems that, after the formation of the non-planar entanglements, only a limited amount of inelastic strain could be taken up in a given slip band. Further slip bands were nucleated at about the same stress level to accommodate larger inelastic strains. In tests of sufficiently large inelastic strain ranges, this resulted in the spread of the deformation throughout the entire microstructure. Any further increase in inelastic strain range was then taken up within the entire deformed microstructure. This did occur, at somewhat higher stress levels, producing the dense aggregates of dislocations in the y phase. 5. Conclusions
(1) The initial yield strength of PWA1480 single crystals at 650 °C was controlled by the shearing of y' precipitates by dislocation pairs. When slip occurred on octahedral slip systems, these dislocation pairs were stored in the y' precipitates by a cube cross-slip process, which produced a tension-compression anisotropy in initial yield strength. (2) The LCF cyclic hardening of the crystals was associated with dislocation interactions occurring in the y phase. This was most evident in specimens deforming on the primary octahedral slip system. Stage I easy glide was associated with the planar glide of dislocations in slip bands. Stage II strain hardening to a higher saturation level was related to the formation of dislocation entanglements in the y phase and the spreading of deformation on the same slip system throughout the microstructure. (3) Specimens deforming by octahedral slip on several slip systems exhibited rapid initial cyclic hardening to a stress saturation level. This was related to the intersection of dislocations of the different operative octahedral slip systems in the y phase. (4) Specimens deforming by macroscopic primary cube slip had gradual sustained cyclic hardening. This was associated with the different slip processes occurring in the y and y' phases and the related early formation of non-planar dislocation entanglements in the y phase. (5) The cyclic stress-strain curves of all these specimens had low cyclic strain-hardening coefficients. This was consistent with the fact that LCF
202
deformation spread throughout the microstructure only in the tests of largest inelastic strain ranges.
9
References 1 A. Pineau, in R. P. Skelton (ed.), Fatigue at High Temperatures, Applied Science, London, 1983, pp. 305-364. 2 T. P. Gabb, J. Gayda and R. V. Miner, Metall. Trans. A, 17 (1986) 497-506. 3 M.S. Patterson, Acta Metall., 3 (1955) 497-506. 4 A. S. Cheng and C. Laird, Mater. Sci. Eng., 51 (1981) 111-121. 5 E. Schmid and W. Boas, Plasticity of Crystals, E A. Hughs, London, 1960, pp. 57-69. 6 L. G. Fritzemeier, The cyclic stress-strain behavior of nickel-base superalloy poly- and single crystals, Ph.D. Thesis, Columbia University, 1984. 7 R. V. Miner, T. P. Gabb, J. Gayda and K. J. Hemker, Metall. Trans. A, 17(1986) 507-512. 8 D. M. Shah and D. N. Duhl, in M. Gell, C. S. Kortovich, R. H. Bricknell, W. B. Kent and J. E Radavich (eds.),
10 11 12 13 14
15 16
Superalloys 1984, Proc. 5th Int. Symp. on Superalloys, Seven Springs, PA, October 7-ll, 1984, Metallurgical Society of AIME, Warrendale, PA, 1984, pp. 105-114. G.A. Swanson, I. Linask, K. M. Nissley, P. P. Norris, T. G. Meyer and K. P. Walker, Life prediction and constitutive models for engine hot section anis0tropic materials program, NASA Contract. Rep. CR-17495, 1986 (National Aeronautics and Space Administration). T. P. Gabb and G. Welsch, Scr. Metall., 20 (1986) 1049-1054. E E. Heredia and D. P. Pope, Acta Metall., 34 (1986) 279-285. T. P. Gabb, G. Welsch and R. V. Miner, Scr. MetalL, 21 (1987) 987-992. S. S. Ezz, D. P. Pope and V. Paider, Acta Metall., 30 (1982) 921-926. E. Huron, High temperature monotonic and cyclic deformation in a directionally solidified nickel-base superalloy, NASA Contract. Rep. CR-175101, 1986 (National Aeronautics and Space Administration). W. M. Milligan and S. D. Antolovich, Metall. Trans. A, 18 (1987) 85-95. A.T. Winter, Philos. Mag., 30 (1974) 719-738.
189
The Low Cycle Fatigue Deformation Response of a Single-crystal Superalioy at 650 °C T. P. GABB
Lewis Research ('enter, National A eronautics and Space Administration, Clevehmd, OH 44135 (U.S.A.) G. WELSCH
Materials Science and Engineering Department, Case Western Reserve Universio,, Cleveland, OH 44100 (U.S.A.) R. V. MINER and J. GAYDA
Lewis Research Center, National Aeronauties and Space Administration, Clevehmd, OH 44135 (U.S.A.) (Received March 3(J, 1988; in revised form June 6, 19881
Abstract
The purpose of this study was to characterize the cyclic stress-strain response, the corresponding deJormation structure and their relationships in the single crystal nickel-base superalloy PWA 1480. The isothermal low cycle fatigue response and deformation structures of specimens oriented near the/001], [2 5 20], l 3 6 lOft lOll], [234] and l]11] crystallographic orientations were characterized at an intermediate temperature (650 °C). The initial yield strength of all these specimens was controlled by the shearing of the 7' precipitates by dislocation pairs. The low cycle fatigue tests exhibited cyclic hardening, which was associated with dislocation interactions in the g matrix. In specimens deforming by slip on a single slip system, dislocations of the primary slip system accumulated in the 7 matrix and formed sessile entanglements. In specimens deforming by slip on several slip systems, the dislocations of the different operative slip systems intersected in the 7 matrix and formed sessile arrangements'.
I. Introduction
Most modern nickel-base superalloys deform by planar slip in low cycle fatigue (LCF) loading at intermediate application temperatures (500800 °C) [1]. In part because of this, the cyclic stress-strain response of superalloy single crystals is dependent on crystallographic orientation [2]. In single-phase copper [3] and two-phase A1-Cu [4] f.c.c, alloys, some aspects of the planar slipinduced orientation dependence have been ac0921-5093/89/$3.50
counted for by resolving the cyclic stress and inelastic strain on the active slip systems [5]. Other aspects of the cyclic hardening response in these alloys have been associated with the number of operative octahedral slip systems. These concepts have also been applied to some extent to the LCF of single-crystal nickel-base superalloys [6]. However, some modern single-crystal nickelbase superalloys with high 7' volume fractions show significant deviations from the well-known planar slip response of f.c.c, alloys at intermediate temperatures. While conventional f.c.c, alloys deform by octahedral slip (slip on {111} planes in (101) directions), single crystals of Ren6 N4 [7] !and PWA 1480 [8] oriented near the [111] crystallographic orientations deform b_y primary cube slip (slip on the (001) plane in the [110] direction). Single crystals of these superalloys oriented to deform by octahedral slip display an orientationdependent tension-compression anisotropy in monotonic yield strength. In both cases, these variations have been attributed to the tendency for cube slip in the V' precipitates. These deviations from f.c.c, alloy response affect the cyclic stress-strain behavior of these superalloys [2, 9, 10]. The purpose of this study was to investigate this cyclic stress-strain response and the associated deformation structures of one of these superalloys, PWA 1480. Single crystals of various crystallographic orientations were tested in LCF at 650 °C. The operative deformation mechanisms were characterized and related to the observed cyclic stress-strain behavior. © Elsevier Sequoia/Printed in The Netherlands
190
2. Materials and experimental procedure
3. Results
The composition of the PWA 1480 test material is listed in Table 1. This material was cast by the withdrawal technique into singlecrystal bars, nominally 21 mm in diameter and 140 mm in length, and single-crystal slabs, nominally 160 mm long, 60 mm wide and 13 mm thick. The growth axis of the bars and slabs were within 10 ° of the [001] crystallographic direction. The bars and slabs were subsequently solution treated in argon at an average temperature of 1270 °C for 4 h, air quenched and then aged in argon at 1080 °C for 4 h and then at 871 °C for 32h. Specimens of [001] crystallographic orientation were machined directly from the bars. Specimen blanks were spark machined at various angles in the slabs in order to obtain specimens with axes oriented near the [001], [2 5 20], [3 6 10], [011], [234] and [i11] crystallographic directions. These specimens were tested at 650 °C in a closed-loop servohydraulic testing machine employing an axial extensometer of 12.7 mm gauge length. The specimens were heated with a three-zone clamshell resistance-heating furnace. The LCF tests were performed at a constant total strain range, with the total axial strain varied sinusoidally at a frequency of 0.1 Hz. Several tensile tests were also performed; these tests were conducted at a constant displacement rate of 8 mm s- '. Further detailed information on these tests has been provided elsewhere
The heat-treated microstructure of both the bars and the slabs was principally constituted of 65 vol.% of cuboidal y' precipitates of 0.55 + 0.18 p m width in a 7 matrix. Additionally, about 3 vol.% of remnant 7-7' eutectic pools about 10-100 p m in diameter was observed, together with about 0.3 vol.% of casting micropores about 5-10 p m in diameter. The operative slip systems of the test specimens at 650 °C were determined by identifying the planes of the slip offsets on the specimen surfaces (Fig. 1), measuring the crystallographic rotations of the tensile specimens' axes towards the slip direction, and by TEM analysis. The [2 5 20], [3 6 10] and [011] specimens deformed predominantly by primary octahedral slip on the (111) plane in the []01] direction. The [001] specimens deformed by octahedral slip on several {111} planes in several (101) directions. The [234] and []11] specimens deformed predominantly by primary cube slip on the (001) plane in the [i 10] direction.
3.1. Mechanical response 3.1.1. Cyclic hardening response The results of the tensile tests at 650 °C are listed in Table 2. The axial stress-strain curves of these tests are shown in Fig. 2. The specimens deforming by primary octahedral slip, [2 5 20], [3 6 10] and [011], had a comparable tensile response, similar to classical f.c.c, single-crystal response for a single operative slip system. On yielding, these specimens initially displayed stage I "easy-glide" flow with very little strain hardening. At an inelastic strain of 0.02-0.03, this was followed by stage II flow of increased strain hardening. The [001] specimens had immediate enhanced strain hardening. The [234] and [ i l 1] specimens both displayed brief stage I flow to an inelastic strain of about 0.01, followed by steep stage II hardening. The initial yield strengths in tension and compression are listed in Table 3. As reported elsewhere [8, 11], the specimens deforming by octahedral slip had an orientationdependent tension-compression anisotropy in
[10]. Foils for transmission electron microscopy (TEM) were prepared normal to the specimens' center-line axes and sometimes also parallel to the operative slip planes. The foils were mechanically polished to 0.1 mm thickness and then electrochemically thinned with a twin-jet thinner using a solution of 10% perchloric acid, 45% acetic acid and 45% butylcellusolve at 0 °C. The foils were examined with a Phillips EM400T transmission electron microscope operated at 120 kV. At least four foils of every specimen selected for TEM analysis were briefly surveyed; one or two of these foils were analyzed in detail. TABLE 1
Composition of the PWA 1480 test material
Element Nominal amount (wt.%) A m o u n t in slabs (wt.%) A m o u n t in bars (wt.%)
AI 5 4.7 5.3
C < 0.02 0.005 0.003
Co 5 4.8 5.3
Cr 10 9.4 10.3
S -0.001 --
Si -0.9 --
Ta 12 11 11.9
Ti 1.5 1.0 1.3
W 4 5.2 4.0
Ni Balance Balance Balance
191
(a)
(b)
(c)
(d)
Fig. 1. Slip offsets of the LCF test specimens at 650 °C: (a) [3 6 10] specimen, Aei, , i < 0 . 0 0 1 0 m m m m i; (b) [3 6 10] specimen, Ac,,, ~= 0.0017 mm m m ~; (c) [001 ] specimen, Aein t = 0.0020 mm mm ~; (d) [i 11 ] specimen, A tin ~= 0.0017 m m mm ~.
TABLE 2
Nominal orientation [hkl ] 00 1 5 20 6 10 0 11 34 11
Tensile test results
Measured orientation [hkl ] i 1 1~33 2~-63 ] 81 3-~97 7-882
lO0 100 100 100 100 100
Symbol in figures II * • '~ II •
Elastic" modulus E (GPa)
Yield strength 0.2% Qffset oV (g'lPa)
Ultimate strength ou (MPa)
True fracture strain (ram mm l)
1()3 133 177 184 238 257
963 855 742 841 755 747
1343 992 951 983 1159 1180
0.033 0.112 0.149 0.112 0.232 0.245
eft
192 1~00
.
,-r~?.-~.~-;~
--~--
~ -
. . . . . . . . . .
initial yield strength, with the [001] and [2 5 20] specimens stronger in tension, and the [3 6 10] and [011] specimens stronger in compression. The results of the LCF tests are given in Table 4. Typical examples of the hardening response are shown in Figs. 3 and 4. Data from different tests on specimens of the same crystallographic orientation are indicated by the open, half-filled and full symbols in order of increasing inelastic strain range. The cyclic stress and inelastic strain hardening responses of the primary octahedral slip specimens, [2 5 20], [3 6 10], and [011], were quite comparable. Comparable cyclic hardening occurred in tension and compression; therefore the cyclic mean stresses produced by the initial yield strength tension-compression anisotropy were sustained and varied with crystallographic orientation. In these strain-controlled tests, the initial stage I easy glide produced "jerky" flow with negligible strain hardening for 10-20 LCF cycles, as shown in the typical hysteresis loops in Fig. 4. The jerky flow then abated as significant stage II strain hardening occurred. The number of fatigue cycles before the onset of stage II hardening varied inversely with initial inelastic strain range. In order to account for this inverse
--~
20C
Fig. 2. The axial stress-strain curves of the tensile tests.
TABLE 3 Average initial yield strengths of the specimens in tension and compression Nominal orientation [hkl]
Average yield strength at ei. = 0.0005 mm mm-
(MPa)
Compression o c (MPa)
883 849 748 825 734 745
832 816 787 919 749 719
Tension o t
00 1 5 20 6 10 0 11 34 ] 11
TABLE 4 Nominal orientation [hkl]
Results of the low cycle fatigue tests Actual orientation [hkl]
Symbol in figures
Schmid factor S
Total strain
001 001 001
Inelastic strain
(mm mm
Cycle 0 . 5 N f
Cycle 1
J)
(mm ram-')
Maximum stress am~x (MPa)
amin (MPa)
Inelastic Maxistrain mum m~'in stress (mm 6rmax rnm-')(MPa)
mEin
Minimum stress
Fatigue life
Minimum stress amin (MPa)
gf
(cycles)
5 8100 4 5100 2 6100
D [] •
0.436 0.427 0.433
0.0145 0.0164 0.0179
0.00026 0.00055 0.00200
798 851 900
798 853 860
0.0002 825 0.00040 870 0.00093 974
782 848 911
1455 1228 215
5 20 2520 ~520 2 5 20
7 22 100 825100 1--430 100 19 13 100
O * * *
0.478 0.482 0.487 0.450
0.0142 0.0149 0.0146 0.0171
0.00033 0.00093 0.00152 0.00266
848 878 846 881
818 822 805 824
0.0002 0.00055 0.00082 0.00130
855 889 879 962
816 841 829 881
872 427 237 165
6 10 ) 6 10 6 10
1 9 5 7 100 1---958 100 3--261 100
o ~ •
0.493 0.492 0.472
0.0092 0.0097 0.0105
0.00128 0.00170 0.00249
758 743 775
784 777 793
0.00069 764 0.00087 789 0.00123 856
807 827 889
1171 971 180
100 100 100 100
o '~ ~' 4)
0.426 0.441 0.435 0.439
0.0089 0.0092 0.0105 0.0115
0.00035 0.00059 0.00150 0.00289
830 854 841 816
897 894 930 896
0.00025 0.00038 0.00080 0.00111
851 861 887 917
884 916 967 1049
1546 824 862 555
34 34 34
4--280 100 4--'066 100 4 3 6 8 100
0 ~ I
0.475 0.470 0.477
0.0074 0.0077 0.0087
0.00082 0.00119 0.00220
741 738 732
755 747 790
0.00034 784 0.00040 795 0.00090 863
818 834 912
2063 1440 281
ill i 11 i 11
7-581100 8--2-86 100 8-894 100
a ~ •
0.497 0.493 0.485
0.0063 0.0072 O.O08O
0.00089 0.00164 0.00249
739 747 749
732 744 771
0.00023 810 0.00056 867 0.00111 917
821 889 956
1884 1010 338
0 0 0 0
1 1 1 1
1 1 1 1
3 2 2 4
94 86 89 88
193
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/ CYCLE --
dependence and to enable comparisons with the monotonic behavior, the cyclic stress-hardening response was expressed as cyclic shear stress as a function of cumulative inelastic shear strain [3]. Examples of the resulting r vs. 7c curves [10] of typical LCF and tensile tests of these specimens are shown in Fig. 5. These LCF and tensile strain hardening curves all display a comparable stage I easy-glide region extending to a cumulative strain 7g of about 0.07. This maximum easy-glide strain 7g, marking the cessation of easy glide and the onset of more rapid stage II strain hardening, did not vary significantly as a function of inelastic strain range and these strains were of comparable magnitude in the LCF and tensile tests [10]. The subsequent stage II strain hardening was lower in the LCF tests than in the tensile tests. The [001] specimens, deforming on several octahedral slip systems, had rapid cyclic strain hardening to near saturation in 10-20 LCF cycles. The cyclic stress and strain response could not be easily resolved onto the active slip systems,
(YCLE
Nil
II v
~coo
L
01 ~
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Fig. 4. Typical hysteresis loops of the LCF tests.
as several slip systems were operative and the interactions between different slip systems are not easily accounted for. However, in any event the LCF and tensile-hardening responses appeared to be dissimilar. The [234] and [i 11] specimens, deforming by primary cube slip, had comparable cyclic hardening responses. LCF cycling produced immediate and continued strain hardening accompanied by temporary slight jerky flow. The stage I easy glide
194
displayed in the tensile tests of these specimens abated at an inelastic shear strain of about 0.01, which corresponds to the cumulative shear strain produced by only one or two fatigue cycles. The corresponding r vs. ~,~ curves of these LCF and tensile tests therefore did not clearly display comparable stage I regions. 3.1.2. Cyclic stress-strain curves
The stabilized cyclic stress-inelastic strain curves generated from the LCF tests at 650 °C indicated low cyclic strain hardening. The resolved cyclic stress amplitude-inelastic strain amplitude response at half the cyclic life of the specimens deforming on a single slip system was modelled by least-squares analysis with a standard equation of the form Ar 2
K'
m
~ rE~Le ~ST
o •
•
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o
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I 100
I
i~lllil ,ol
Fig. 5. The tensile shear stress-cumulative shear strain response of the [) 6 10] LCF and tensile test specimens.
where At/2 and A),m/2 are the resolved cyclic shear stress and inelastic shear strain amplitudes, K' is the cyclic strength constant and m' is the cyclic strain-hardening coefficient. The cyclic strain-hardening coefficients of the [2 5 20], [3 6 10] and [011] primary octahedral slip specimens were 0.021, 0.036 and 0.091 respectively. The [111] and [234] primary cube slip specimens as a group had slightly higher hardening coefficients, 0.071 and 0.116 respectively. The axial cyclic stress amplitude-inelastic strain amplitude response of the [001] specimens produced a cyclic strain-hardening coefficient of 0.104. 3.2. Deformation structure 3.2.1. General characteristics
The deformation structures of the [2 5 20], [3 6 10] and [011] primary octahedral slip specimens were quite comparable and varied as function of the inelastic strain range incurred. Specimens tested to failure at low inelastic strains (Aei, l-~0.001 m m n ] l ~ - 1 ) had irregular illdefined bands of various moderate dislocation densities separated by relatively undeformed regions (Fig. 6). This was consistent with the often widely separated slip offsets observed on the specimen surfaces (Fig. 1). The direction of the bands was parallel to the (111) primary octahedral slip plane trace. About 80% of the dislocations had Burgers vectors corresponding to primary octahedral slip, b=+_½[i01]. The majority of the dislocations were in the 7 phase, sometimes bowed on the (111) plane and sometimes combined in non-planar entanglements.
Fig. 6. The deformation structures of [3 6 10] LCF specimens with a [011] zone axis: (a) Ae~.l<0.001 (b) Aei. ~> 0.002 mm m m - ].
mm m m - J ;
195
These dislocations were often slightly dissociated on {111 } planes. A smaller number were in the 7' precipitates. Specimens cycled at large inelastic strains (Aein 1 "~0.002 m m m m - l ) had deformation throughout the microstructure (Fig. 6). This was consistent with the densely packed slip offsets evident on the specimen surfaces (Fig. 1). Where the dislocations were of a low enough density to enable counting, 95% with a standard deviation of 10% of the dislocations had the primary octahedral slip Burgers vectors. A majority of these dislocations were again in the y phase, where they were again either bowed on {111} planes or combined in non-planar entanglements. A smaller number of dislocations were in the 7' precipitates. The deformation structure of the failed [001] LCF specimens generally consisted of localized dislocation patches rather than bands of deformation. Specimens tested at low inelastic strain ranges had moderately spaced patches of dislocations, while specimens tested at large inelastic strain ranges had more frequent patches of higher dislocation density (Fig. 7). Most of the dislocations observed had Burgers vectors corresponding to octahedral slip: b = _+1[]01], ![101], ½[0i 1] and ½[011]. A majority of these dislocations were again in the ), phase, of various characters and often slightly dissociated on {111} planes. They were often combined in non-planar entanglements, especially in the specimens tested at large inelastic strain ranges. These dislocations were also sometimes arranged in square arrays at the V-y' interfaces. A smaller number of dislocations of these Burgers vectors were in the y' precipitates. The deformation structure of the [234] and [i 11] primary cube slip LCF specimens also varied with cyclic inelastic strain range. Failed specimens tested at low inelastic strain ranges contained irregular ill-defined dislocation bands parallel to the (001) primary cube slip plane, separated by dislocation-free regions (Fig. 8). Only about 65% of the dislocations had Burgers vectors corresponding to primary cube slip, with b = +½[il0]. The first observation of this low percentage in a [ i 11 ] specimen was initially interpreted as evidence of cube slip on other slip systems [10]. However, tensile axis rotation measurements in tensile tests, slip trace analyses and further TEM examinations of various [234] and [] 11] tensile and LCF specimens indicated that primary cube slip did predominate. A
majority of the dislocations were in the 7 phase. Individually occurring 7 dislocations were often bowed and dissociated on the (111) or (] ] 1) planes. This is shown in the tilting experiment of a [234] LCF test specimen interrupted at 13 cycles (Fig. 9). Many of the curved 7 dislocations become straight projected lines parallel to the (111) plane trace when this plane is perpendicular to the electron beam. A smaller number of dislocations were in the 7' precipitates. The [234] and [i 11] specimens fatigue tested to failure at large inelastic strain ranges had deformation throughout the microstructure (Fig. 8). Over 90% of the dislocations observed in these specimens had the primary cube slip Burgers vectors b=½[il0]. They were mostly located in the 7 phase and were sometimes bowed on the (111) or (111) planes when
Fig. 7. T h e d e f o r m a t i o n structures of [0011 L C F specimens: (a) Aei,,t <0.001 m m m m i, [013] zone axis; (b) Ae,, t > 0.002 m m m m ~. [ ] 01 ] zone axis.
196
Fig. 8. The deformation structures of the LCF specimens: (a) [234], A~in i <0.001 mm. mm ], [011] zone axis; (b)[i 11], A ei, ~> 0.002 mm m m - i, [101] zone axis.
singular. The (111) plane is nearly perpendicular to the electron beam in Fig. 8(b). But the dislocations in the 7 matrix were quite often arranged in non-planar entanglements of slightly dissociated dislocations. The dislocations in the 7' precipitates were bowed on the (001) plane. 3.2.2. 7" Dislocation pairs The glide and cross-slip of dislocation pairs in the 7' precipitates are believed to control the yield strength and yield strength tension-compression anisotropy in superalloys. The characteristics of these dislocation pairs in the test specimens (Fig. 10) were therefore examined in detail [12]. To summarize these characteristics briefly, 80%+ 11% of the 7' dislocation pairs in the [2 5 20], [3 6 10] and [011] LCF and tensile specimens had a near-screw character and were
Fig. 9. Typical micrographs of a tilting experiment of a [i34] LCF specimen (Aein i = 0.0018 mm m m - I ) interrupted at 10 cycles: A, [213] zone axis; B, [031 ] zone axis.
on the (010) cube cross-slip plane. A large majority of the 7' dislocation pairs in the [001] LCF and tensile specimens had a near-screw character and were on their respective cube cross-slip planes. Therefore the pairs with b= +½[]01] and ½[101] were on the (010) plane, while pairs having b = +½[0il] and ½[011] were on the (100) plane. The 7' dislocation pairs of the [234] and [111] LCF and tensile specimens were on the (001) primary cube slip plane and of various characters.
197
L : ~L;'2)
I1
Fig. 10. The 7' dislocation pairs of the LCF specimens: (a) [)6 10] specimen, [[21] zone axis: (b)[001] specimen, [012] zone axis: (c)[234] specimen, [001] zone axis.
3.2. 3. 7he generation of deformation struclU res
In order to examine how these deformation structures are generated and their correlation with stress-hardening response, additional interrupted tests and TEM analyses were performed on the primary octahedral slip specimens. LCF (Aai=l>0.002 m m m m - l ) and tensile tests of [) 6 10] specimens were interrupted at a cumulative shear strain of less than 0.07, near the end of
the easy glide stage at 7g, and analyzed. Stage I easy-glide flow was confined to bands parallel to the (111) plane in both the LCF and the tensile specimens. The bands were of varying widths and dislocation densities. At least nine slip bands of each specimen were analyzed in standard nearidentical tilting experiments to determine the Burgers vector and plane of the dislocations. The 7 dislocations (b = +_½[i01]) in both specimens were mostly on the (111) plane, with no significant non-planar entanglements observed. This is illustrated in Fig. 11, where the curved 7 dislocations become nearly straight projected lines when the (111) plane is tilted nearly perpendicular to the electron beam. The 7' dislocation pairs in these specimens had already cross-slipped onto the (010) plane and had a near-screw character. The deformation characteristics of the primary octahedral slip specimens tested to failure showed significant changes compared with the previous interrupted tests. LCF specimens tested at A% 1>0.002 mm mm-~ had deformation throughout the microstructure, while those tested at lower inelastic strain ranges had deformation still confined to slip bands. Tensile specimens tested to failure had a higher density of dislocations throughout the microstructure. At least nine regions of foils from each of the LCF and tensile specimens were analyzed with the same tilting experiments (Fig. 12). The observed dislocations in the y' precipitates of these specimens had the same characteristics as before, with little change. However, the 7 dislocations were greatly increased in number and were no longer predominantly on the (111) plane. As illustrated in Fig. 12, while singular y dislocations were sometimes still on the (111) plane, the dislocations were often combined in non-planar entanglements. Dislocations in these entanglements were often locally dissociated on {111 }planes. In order to learn more about when these changes in deformation structure occurred, an LCF test of an [011] specimen was interrupted during stage II strain hardening at a cumulative shear strain of 0.096. TEM examination of several foils from this specimen indicated that deformation still occurred in bands. These bands were now often very broad and of a relatively consistent dislocation density, but narrow slip bands were also observed. Nine slip bands were analyzed using the same standard tilting experiments. The narrow slip bands had characteristics similar to specimens interrupted at Yc< 0.07, with
198
Fig. 11. Micrographs of typical tilting experiments of [3 6 10] specimens, A, [231] zone axis and B, [0 i 4] zone axis; (upper) LCF, Yc= 0.062 mm mm l; (lower) tensile, Yc= 0.039 mm mm ~.
the 7 dislocations predominantly on the (111) plane. However, the broad slip bands additionally had areas where the ), dislocations were entangled and no longer confined to the (111) plane (Fig. 13). Dislocation segments in these entanglements were locally dissociated on {111} planes. 4. Discussion
The single-crystal specimens deforming by octahedral slip displayed a significant
tension-compression anisotropy in initial yield strength at 650 °C. The [001] and [2 5 20] specimens were stronger in tension, while the [011] and [3 6 10] specimens were stronger in compression. This anisotropy, reported in other studies of PWA 1480 [8, 11] and Ren6 N4 [7] superalloys, has been associated with the shearing of V' precipitates by dislocation pairs. The specific shearing mechanism cited [13] concerned the effect of applied stress in promoting cross-slip of the lead dislocation from the ( 111 ) plane to the (010 ) cube cross-slip plane. An analysis of the 7' dislocation
199
Fig. 12. Micrographs of typical tilting experiments of failed [3 6 10] specimens, A, ['531] zone axis and B, [0[4] zone axis: (upper) LCF; (lower) tensile.
pairs of the octahedral slip specimens in the present study suggested that this cube cross-slip process was the dominant dislocation storage mechanism in the )" phase. Specimens deforming by primary cube slip displayed no significant tension-compresison anisotropy in yield strength. The V' dislocation pairs in these specimens appeared to remain gliding on the (001) primary cube slip plane. The initial tension-compression anisotropy in yield strength persisted during LCF cycling. However, the strain hardening produced by LCF
cycling was comparable in tension and compression. The LCF cyclic hardening was associated with major changes in the dislocation structure in the V phase. When slip was confined to the primary octahedral slip system, the initial hardening response in LCF deformation and monotonic tensile deformation was similar. Stage I easy glide initially occurred, with "jerky" flow and little strain hardening. This behavior persisted to a cumulative shear strain of about ),g = 0.07. Over the range of these tests, this maximum easy-glide strain ~'g w a s
200
Fig. 13. Micrographs of a typical tilting experiment of a [011] LCF specimen (yc=0.096 mm mm-l): A, [231] zone axis; B, [012] zone axis.
relatively independent of specific crystallographic orientation, unidirectional or reversed loading path, and LCF inelastic strain range. This suggested that some portion or aspect of this deformation was relatively irreversible, as a characteristic direction-independent amount of slip was necessary to initiate stage II strain hardening. Analysis of the deformation structures generated during the stage I easy glide indicated that
this deformation was confined to planar slip bands, with most of the dislocations in the y phase gliding on the (111) plane. After the onset of stage II strain hardening, the dislocations had accumulated in the V phase and possibly because of cross-slip had begun to combine in non-planar entanglements in the bands, becoming sessile there and providing barriers to other gliding dislocations. Possibly owing to this hardening of the slip bands, deformation spread to some extent to the remaining undeformed regions between the slip bands. In tensile tests and LCF tests of sufficiently large inelastic strains, this resulted in deformation throughout the microstructure at failure. However, in all LCF specimens tested to failure, the dislocations observed in the 7 phase were often in non-planar entanglements, with individual dislocation segments dissociated on {111 } planes. Therefore, the irreversible aspect of the stage I easy glide appeared to be the accumulation of dislocations in the 7 phase, facilitating the formation of non-planar sessile entanglements during stage II strain hardening. This accumulation of 7 dislocations may have been driven by the cube cross-slip of the paired portions of these dislocations penetrating the 7' precipitates. These cross-slipped segments on the (010) plane in the 7' would act as pinning points, hindering the free glide of the adjoining segments on the ( 111 ) plane in the V phase. In this manner, the effective free glide distance of the dislocations would be continually reduced, resulting in their accumulation to give a locally higher dislocation density. This in turn could encourage more crossslip in the 7 matrix, driven by the repulsive forces between dislocations of the same Burgers vectors. Dislocation intersections would then probably occur to produce the sessile entanglements, When slip took place simultaneously on several octahedral slip systems, rapid cyclic strain hardening occurred, and the cyclic stress range approached a saturation value in only 20-30 LCF cycles. This strain hardening was related to the intersection, principally in the 7 phase, of dislocations of the different octahedral slip systems. The dislocations formed non-planar entanglements in the 7 phase after only 10-20 LCF cycles. Additional dislocations were observed in sessile orientations at the 7-7' interfaces, sometimes intersecting to form rectangular networks, as reported in other studies [14, 15]. These dislocations arrangements each act as barriers to dislocation glide in addition to the 7' precipitates.
201 Specimens deforming by macroscopic primary cube slip displayed gradual LCF strain hardening from the first fatigue cycle. This cyclic strain hardening continued for nearly a third of the lives of these tests. Although the IJ_11] specimens have (like the [001] specimens) several highly stressed slip systems, slip only occurred on the primary cube slip system. Therefore intersecting sliphardening mechanisms do not seem to be operative here. TEM analysis of their deformation structures suggested that, while primary cube slip occurred in the y' phase, many dislocations in the 7 phase lay on the (111) or (]11) cross-slip planes. Glide on {111 } planes would occur more easily in the f.c.c, y phase. These conflicting processes may acount for the gradual continual cyclic hardening. Some gliding dislocation pairs on the (001) primary cube slip plane in the y' precipitates appear to glide into the y phase on the (001) plane. However, the observation of dislocations on the octahedral cross-slip planes in the }, phase suggests that some portion of the dislocations may have locally cross-slipped onto octahedral planes in the y phase. These cross-slipped segments could thereafter glide on these octahedral planes to the next y-y' interface. The likelihood that two cross-slipped dislocations arrive at the same interface location in this manner and orientation is rather small. In such cases these dislocations could not easily pair up for further y' shearing but would be pinned at the 7-7' interfaces (Fig. 9) and act as barriers to other dislocations. Additionally, dislocations gliding on the {111 } planes in the y phase could intersect dislocations which are still on the (001) plane and form non-planar entanglements. The entanglements were quite common in these LCF specimens at failure. The cyclic stress-strain curves at saturation of all specimens tested at 650 °C displayed low cyclic strain-hardening coefficients. This was especially evident when only the primary octahedrai slip system was operative. The cyclic stress-strain curve of single-crystal copper displays negligible strain hardening in this strain regime [16]. The constancy of cyclic stress over a range of inelastic strain amplitudes was associated with the stress required to generate persistent slip bands in the undeformed microstructure. A similar explanation appears to be applicable in the present case. In LCF tests of low inelastic strain ranges, the dislocations were in loose bands of deformation separated by
undeformed regions. In fatigue tests of large inelastic strain ranges, deformation occurred throughout the microstructure. It seems that, after the formation of the non-planar entanglements, only a limited amount of inelastic strain could be taken up in a given slip band. Further slip bands were nucleated at about the same stress level to accommodate larger inelastic strains. In tests of sufficiently large inelastic strain ranges, this resulted in the spread of the deformation throughout the entire microstructure. Any further increase in inelastic strain range was then taken up within the entire deformed microstructure. This did occur, at somewhat higher stress levels, producing the dense aggregates of dislocations in the y phase. 5. Conclusions
(1) The initial yield strength of PWA1480 single crystals at 650 °C was controlled by the shearing of y' precipitates by dislocation pairs. When slip occurred on octahedral slip systems, these dislocation pairs were stored in the y' precipitates by a cube cross-slip process, which produced a tension-compression anisotropy in initial yield strength. (2) The LCF cyclic hardening of the crystals was associated with dislocation interactions occurring in the y phase. This was most evident in specimens deforming on the primary octahedral slip system. Stage I easy glide was associated with the planar glide of dislocations in slip bands. Stage II strain hardening to a higher saturation level was related to the formation of dislocation entanglements in the y phase and the spreading of deformation on the same slip system throughout the microstructure. (3) Specimens deforming by octahedral slip on several slip systems exhibited rapid initial cyclic hardening to a stress saturation level. This was related to the intersection of dislocations of the different operative octahedral slip systems in the y phase. (4) Specimens deforming by macroscopic primary cube slip had gradual sustained cyclic hardening. This was associated with the different slip processes occurring in the y and y' phases and the related early formation of non-planar dislocation entanglements in the y phase. (5) The cyclic stress-strain curves of all these specimens had low cyclic strain-hardening coefficients. This was consistent with the fact that LCF
202
deformation spread throughout the microstructure only in the tests of largest inelastic strain ranges.
9
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