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Mechanical properties and microstructural evolution of a cobalt base alloy coating
Materials &:ience and Engineering, A 169 (1993) 85-92
85
Mechanical properties and microstructural evolution of a cobalt base alloy coating P. Revel, M. Clavel and G. Beranger Laboratoire de G~nie M~canique pour les Mat&iaux et les Structures (LG2mS), URA 1505 CNRS, Universitd de Technologic de CompiOgne, BP 649, 60206 CompiOgne Cedex (France)
P. Pilvin* ENSMP, Centre des Materiaux, BP 87, 91003 Evry Cedex (France) (Received June 23, 1992; in revised form December 28, 1992)
Abstract Several isothermal mechanical tests have been performed on a cobalt superalloy to determine the parameters of a viscoplastic behavior law in the range (20-700 °C). These parameters have been identified by means of a systematic numerical procedure (a computer program for simulation and identification). The microstructural evolution during the mechanical tests has been examined in relation to the evolution of the internal variables of the viscoplastic model. It was found that the material softens at room temperature, mainly as a result of an isotropic component decrease. However, at high temperatures (500-700 °C), the material hardens, mostly owing to a kinematic component increase. The deformation mode, i.e. the martensitic transformation, has been identified for all the temperatures studied. At high temperatures carbide precipitation on stacking faults and deformation bands has been observed. Complementary tests have shown that, at high temperatures, the further addition of carbide precipitates dissolves by dislocation glide and a diffusion mechanism. At room temperature, after heat treatment at 700 °C, carbides precipitated on deformation bands induced the formation of "hard" zones. These microstructural observations have been correlated with the important part of the kinematic term in the stress increase.
1. Introduction Alloys used at elevated temperatures require two main characteristics: first, adequate resistance to corrosive attack and, secondly, sufficient mechanical strength to resist deformation or fracture under the imposed stresses. These alloys are multiphase alloys, the first phase being called the matrix and the second phase the precipitate. They have two striking features: their rather high limit of elasticity at relatively low temperature (up to about 0.21m); their tendency to preserve fairly high flow stresses up to temperatures close to their melting point (0.9-0.95 Tm). The strengthening of cobalt base alloys is provided by solid solution strengthening of the matrix and by the precipitation of carbides. Solid solution strengthening is principally due to the contents of addition elements, such as chromium, nickel, molybdenum, tungsten etc. The second-phase strengthening in cobalt base alloys is
*Also at: Universit6 Pierre et Marie Curie, Paris Cedex, France. 0921-5093/93/$6.(10
mainly provided by carbides formed from the chromium, which is primarily present to confer corrosion resistance, and from other elements added as carbide formers, e.g. tungsten, molybdenum etc. The carbides form as mixed carbides and the forms present will depend on the balance of metallic composition, on the carbon content and on the thermal history of the alloy. The morphology and the location of the carbide precipitates affect the strengthening effect and, for the optimum improvement, precipitation both at grain boundaries and within the grains is required. Intragranular precipitation strengthens the matrix by providing hard particles, such as carbides, which cannot be sheared by gliding dislocations and which remain stable in size and distribution up to the highest service temperatures [1 ]. During the last 30 years, many microstructural observations have been carried out using transmission electronic microscopy (TEM) to determine the microscopic mechanisms which take place during deformation. Complex dislocation interactions have enabled the metallurgists to develop microscopic models. However, macroscopic models based on © 1993 - Elsevier Sequoia. All tights reserved
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continuum mechanics have been developed with constitutive equations for the viscoplastic behavior of isotropic and anisotropic materials. Often, these models, which required the introduction of a few internal variables, seem to ignore the crystallographic nature of slip and dislocation mechanisms [2]. Understanding and describing the behavior of crystalline solids under alternate loading (tensioncompression) are forcing the mechanical and the metallurgical approaches towards a necessary point of convergence. The material strain hardening (uniaxial tension-compression) could be described by two components: the isotropic strengthening R, which is called forest hardening in the dislocation theory; the kinematic strengthening X (back stress hardening) [2-4]. In the present work, a cobalt base coating (Stellite 21) was deposited using a semitransferred plasma arc technique on a low alloyed steel support in 10 to 12 coats. This cobalt alloy was chosen on account of its good resistance to thermal fatigue. To predict the thermomechanical behavior of the material in the range 20-700 °C, isothermal mechanical experiments were conducted using laboratory samples. The results allow the evaluation of the material parameters of the viscoplastic constitutive model related to the microstructural evolution of the cobalt superalloy during the tests.
Fig. 1. Dendritic structure of the coating.
2. Experimentalprocedure 2.1. Material
The composition of the coating is given in Table 1. The microstructure of this material coating results in a dendritic array, with the primary dendrites axis normal to the surface of the steel support (Figs. 1 and 2). The interdendritic zones are rich in chromium and molybdenum. In fact, an abundant precipitation of a mixture of M7C 3 and MC carbides (M = Cr, Mo) takes place in the interdendritic zones [5, 6]. The grains are 1-2 mm long and 50-200/~m wide. The crystallographic structure of the matrix is face-centered cubic (f.c.c.). Previously [7-9], the cobalt-rich alloys were considered to have low stacking fault energies. Indeed, in the as-received material, a high density of stacking faults and partial dislocations have been observed. Moreover, the martensite phase e was not observed. In TABLE 1. Composition of Stellite 21 Element Amount (wt.%)
Cr 27
Mo 5.5
Ni 3
Si 1
Mn 1
C Co 0.25 Balance
Fig. 2. Micrograph showingthe structure of Stellite 21.
fact, it was observed elsewhere that the M s temperature is below room temperature [10]. 2.2. M e c h a n i c a l isothermal tests
The low cycle fatigue tests were carried out on a Mayes fatigue machine at different temperatures in the range 20-700 °C. They were performed with sawtoothshaped signals, under a constant plastic strain range (0.2%; 0.5%; 1%), with a strain ratio R, = - 1 . The specimens were heated by a Joule-effect furnace. The total strain was measured using a longitudinal capacitive extensometer with ceramic knives. Longitudinal strain control was applied to cylindrical specimens (8 mm in diameter and 10 mm in gauge length). The total strain amplitude was adjusted when necessary by
P. Revel et al. / Mechanicaltesting of cobalt base alloy a computer program. The total constant strain rate was gt = i x 10 -3 s-J. The load and strain evolution were recorded up to failure, to estimate the fatigue life (NF) and to determine the mechanical behavior. Two complementary tests have been carried out. The first one corresponded to Aep/2=0.2% and 1"= 600 °C. It was interrupted twice during half an hour and the stress was held at a zero value. The second test corresponded to Aep/2 = 0.5% and T = 20 °C. It was interrupted at Nv/3. The specimen was placed in a tube furnace in a purified dried argon atmosphere at 700 °C for 1 h. Then, the fatigue test was continued at 20 °C. Other fatigue tests have been carried out. When stabilized cycles were reached, relaxation tests were performed. These tests were performed to characterize the viscous effects.
2.3. Metallographic observations Metallographic observations were carried out, starting by using optical microscopy on the fatigue section. The specimens were cut, mechanically polished and electrolytically etched. Complementary observations, such as mechanically polishing and electropolishing thin foils of cycled specimens were conducted, using a Jeol 100 CX2 transmission electronic microscope.
2.4. Numerical model In the present work, a viscoplastic constitutive model formulated for isothermal conditions is used [3, 4]. A relationship between the elastic strain tensor e~ and the viscoplastic strain tensor gyp has been supposed: et=t~+evp. This model uses the thermodynamics of an irreversible process. The internal variables of strain hardening are the viscoplasticity strain tensor evp , the tensor a and the scalar p, which are related respectively to the associated variables the linear kinematic variable XL, the non-linear kinematic variable X N and the isotropic variable R. R characterizes the evolution of the elastic domain size. The kinematic variable X has two components, i.e. X = X L+ Xy, and characterizes the displacement of the elastic domain center. The internal variables X L and Xy are chosen for modelling the two sources of kinematic hardening in a polycrystal (intergranular and transgranular) [11]. This model has the following basic equations (one-dimensional form). The state laws are o = Eel.
(1)
Xt. = He~p
(2)
xN = c a
(3)
R = k + Q{ 1 - exp( - bp)}
(4)
87
and the evolution laws are
# = (, ' < l ° - X Kl - R ) ) n
(Z) = max(0, Z)
gvp=sign( o - X) p
a = gv -
(5) (6)
ap
(7)
with 7(P) = Y~+ (7,,- 7~) exp( - tip)
(8)
Ten parameters characterize viscoplasticity. These are as follows: K and n the viscosity parameters; k, Q and b the isotropic hardening parameters, such that k =R(0) = or; H, C, V0, V~and/3 the kinematic hardening parameters. To evaluate the material coefficients of the viscoplastic model from experimental results, the constitutive equations of the model have been implemented in the identification-optimization code SiDoLo [12, 13].
3. Results
3.1. Fatigue life results The fatigue life, at the various temperatures studied, is plotted in the classical Manson-Coffin diagrams as a function of the plastic strain amplitude in Fig. 3 (Nv=f(Aep)). T h e fatigue life is lowest at 20°C and highest at 500 °C. The material exhibits a significant reduction in fatigue life for tests conducted at temperatures in the range 600-700 °C. 3.2. Cyclic stress-strain behavior The variation of the maximum stress amplitude with the cumulative applied plastic strain {p =4N(AEp/2)} is shown in Fig. 4 at various temperatures for a plastic
NF
0.001
0.01 AEp
0.1
Fig. 3. Fatigue life N F as a function of the plastic strain a m p l i t u d e
Aep.
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Mechanical testing of cobalt base alloy
900.
test, performed at 20°C, the stress first decreases. Immediately after the heat treatment at 700 °C, a stress increase of 115 MPa is observed and then stress decreases again during cycles at 20 °C.
850. 800. 750
•
Aa/2 700. (MPa) 650.
0 0
0
0
600.
550
500 0
I
I
I
I
I
I
I
I
I
I
I
2
4
6
8
10
12
14
16
18
20
22
P
Fig 4. Stress amplitude Aa/2 as a function of the cumulated strain p; Aep/2 = 5 x 10 -3.
60O 55O
,
".
A6/'2 (MPa) 5OO
I "'''''I •
mn
mi~m
ml m llllull
Ill
450
(a)
0.01
0.1
1
10
P
100
1000
900,
Aft/2 800 (MPa)
000000000000 000000000000000000000
700
(b)
I
I
I
I
I
I
I
0.1
0.2
0.3
0.4
0.5
0.6
0.7
p
Fig. 5. Complementary tests: (a) fatigue test at T= 600 °C and Aep/2=2xl0 -3 interrupted twice during half an hour; (b) fatigue test at T=20°C and A%/2 = 5 × 10 -3 interrupted by a heat treatment at 700 °C for 1 h.
amplitude of 0.5%. At room temperature, the stress amplitude decreases before it stabilizes, i.e. the material softens. At higher temperatures, cyclic hardening of the alloy takes place; a lot of serrations have been observed on the stress-strain loops. The cyclic evolution of complementary tests is plotted in Fig. 5. It can be seen that, during the first test, performed at 600 °C, the stress increases after the interruptions and then decreases after a few cycles to reach the previous level. However, during the second
3.3. Observation of fatigue microstructures Optical observations have shown a reduction in the number of deformation bands as a function of decreasing temperature. It has been also observed that the number of deformation bands increases as a function of the plastic deformation amplitude. The examination of X-ray diffraction diagrams has allowed the identification of the e phase in the specimens tested at all temperatures [14]. Moreover, some observations on specimens cycled at 700 °C were carried out using transmission electron microscopy (TEM). Numerous deformation bands (DBs) and stacking faults (SFs) were observed, decorated by a large amount of M23C 6 carbides about 0.04-0.05/~m in size. These carbides have been identified using a dark-field imaging technique and extraspot reflection (Fig. 6). Nevertheless, their tendency to form columnar arrays suggests that precipitation takes place in the deformation bands: carbide precipitation often occurs in e martensite laths [10, 15-18]. The diffraction pattern taken on the deformation bands shows the presence of e phase (Fig. 7). The orientation relationship of these f.c.c, carbide precipitates with respect to their hexagonal close-packed (h.c.p.) surrounding was identified in previous studies: {111 }fee//{0001 }hcp a n d (110)fcc//(1120)hop [10, 16-18]. Similar observations have been performed on specimens cycled at 500 and 600 °C. At room temperature, the deformation mode remains the same, i.e. the martensitic transformation (Fig. 8). This observation indicates that the M a temperature was above room temperature [10]. At room temperature, carbide precipitation does not occur. In previous work [10, 19], stacking faults and twin formation were considered as precursors to martensite e formation. In the present work, twinning deformation has not been observed. The deformation mode and carbide precipitation are summed up in Table 2. The TEM examination of the specimen of the second complementary test has shown M23C 6 carbide precipitation on deformation bands (Fig. 9). These deformation bands have been the result of mechanical cycles carried out at 20 °C before the heat treatment at 700 °C. 3.4. Identification of the viscoplastic model For each test, two loops were necessary to identify the material parameters: the initial cycle and the stabilized cycle. A good correlation has been found for several steady state loops under different strain
P. Revel et al.
Mechanical testing of cobalt base alloy
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(ht Fig. 7. Micrographs showing e martensitic lath and associated diffraction pattern (TEM).
Fig. 6. Micrographs of a specimen strained to A%/2=2 x 10 -~ at 700 °C: (a) bright-field; (b) dark-field showing M:3C~, carbides with a size of about 50 nm (TEM).
amplitudes and at various temperatures between the experimental response (symbols) and the numerical simulation (solid line) (Fig. 10). T h e results of the numerical identification have shown an evolution of the p a r a m e t e r s as a function of the temperature. T h e p a r a m e t e r s of the second c o m p l e m e n t a r y test have been identified separately before and after heat treatment. This was to establish the effect of carbide precipitation on the internal variables of the model. T h e material p a r a m e t e r s at various temperatures are given in Table 3. 4. Discussion
T h e main result of the study is the relationship between the evolution of the microstructural internal variables.
4.1. Mechanical behavior of Stellite 21 First, concerning the deformation mode, it has been established that martensitic transformation takes place
Fig. 8. Micrographs of a specimen strained to Aep/2 = 10 2 at 20 °C: martensitic laths sheared (TEM).
TABLE 2. Deformation mode and carbide precipitation (%)
700 °c
600 °C
500 °c
20 °C
1
SFs
SFs
SFs
SFs + DBs(e)
0.5
+ DBs(e)
+ DBs(e)
+ DBs(e)
SFs + DBs(e)
0.2
+carbides (M>C,,)
+carbides (M:3C,,)
+carbides (M:~C<,)
SFs+DBs
2
SFs, stacking faults: DBs, deformation bands: & martensite phase.
during tests, regardless of the temperature. Furthermore, it should be noted that, for the mechanical tests carried out at high temperatures, a great amount of carbide precipitation takes place in martensitic laths and stacking fault ribbons. T h e fact that carbides have
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Mechanical testing of cobalt base alloy
precipitated in the d e f o r m a t i o n bands in particular, the observation of serrations on fatigue loops and also previous studies on cobalt alloys [16, 18] suggest a Suzuki effect. It seems reasonable to conclude f r o m the numerical identification that the uniaxial mechanical behavior of Stellite 21 in the range 2 0 - 7 0 0 ° C could be well described by this viscoplastic model. Therefore, the associated variables (R, X ) have b e e n calculated with the help of the identified p a r a m e t e r values for each test with the value ep--0.5%. We can then c o m p a r e their evolution as a function of the t e m p e r a t u r e and n u m b e r of cycles.
ing. This could be illustrated by the negative value of the t e r m R - k . T h e increase in stress at high t e m p e r a tures result f r o m the evolution of the kinematic t e r m X, as shown by the value 70 > 72 and the variation of the t e r m X - X i (where X i is the value of X after the first quarter of the first cycle with 7(P) = 70 or the X value at the stabilized cycle with 7(P) = 7s)) (Table 4).
O 11300
500
4
4.1.1. Evolution of internal variables as function of number of cycles It is shown at 20 °C that m o s t of the softening is related to the decrease in the isotropic strain harden-
O ~,~)
80o
Fig. 9. Micrographs of a specimen strained to Aep/2 = 5 × 10 -3 at 20 °C. Heat treatment at 700 °C. Deformation bands can be seen decorated by M23C 6 carbides (TEM).
Fig. 10. Comparison between model (full lines) and experimental responses (symbols) at (a) 20°C and (b) 600 °C. Thick lines, initial loop; thin lines, stabilized loop.
TABLE 3. Values of material parameters Parameter
E(GPa) k(MPa) K (MPas ~/') n H(GPa) Yl} Q (MPa) b C(MPa) y~ fl
20 °C
165 357 50 20 199 656 - 123 0.97 26000 674 0.98
300 °C
160 206 70 14 163 415 3 1 17800 628 1.0
500 °C
143 208 90 11 103 488 21 0.95 14750 400 1.0
aparameters identified before and after heat treatment at 700 °C.
600 °C
141 247 467 3.6 102 475 19 0.9 9585 405 1.03
700 °C
123 169 1940 3.2 44 408 26 0.9 6470 330 0.9
20 °Ca Be~re
After
175 304 50 20 218 702 -108 0.88 41100 801 1.5
175 304 50 20 250 645 -105 0.88 40350 659 1.2
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Mechanical testing of cobalt base alloy
q-,
TABLE 4. Respectiveparts of kinematicand isotropic variables in hardening ( + ) or softening( - ) evolution T (°C)
X (%)
500 + 46 +21 69
600 + 37 + 19 66
700 + 25 +25 50
20 - 6 -86 7
R (%)
31
34
50
93
X-X~ (MPa) R - k (MPa)
91
m
(a) X,k, Gv
(MPa) 500 o.t¢
400
•
k
o
X[
K
30O
P
--
200
&~
_
•
,
-
/~,d
%
100
(b) 0
•
0
,
200
-
400
,
-
,
600 800 TeL3
Fig. 1 1. X~, k and ov as functions of temperature.
At room temperature, the material softens. The stress decrease during the fatigue tests could be correlated with the relaxation of residual stresses, as evaluated in previous studies [20, 21]. The relaxation of residual stresses is generally related to the evolution of the internal stress and its associated tensor X. Therefore, it may be suggested that, at room temperature, the contribution of the isotropic component R in the stress decrease is too high. Nevertheless, this could be explained by the decrease in the partial dislocation density in the matrix compared with their high density in the as-received material. At high temperatures, carbide precipitation takes place in the matrix and in particular on deformation bands. This phenomenon could be correlated with the significant contribution of X in the stress increase. The first complementary test has shown that, when the test has continued, after breaks, the excess carbide precipitation has been dissolved by dislocation glide [22].
4.1.2. Evolution of internal variables as function of temperature The effects of temperature on the evolution of internal variables, X, k and ov, where o v= Io - X[ - R is the viscosity component of the stress, have been illustrated in Fig. 11. For all temperatures, X, k and Ov have been evaluated at the beginning of the fatigue test. It should
Fig. 12. Schematic diagram of the evolution of the elastic domain at (a) 20 °C and (b) 700 °C. Full lines, initial cycle; b r o k e n lines, stabilized cycle.
be noted that, in the range 600-700 °C, the mechanical behavior of the material evolves, with the component ov becoming greater than the X and k components. Moreover, it is worth noting about the kinematic component X that the relative part of the non-linear term X N is more important than the linear term XL in the range 500-700 °C. At room temperature, the relative part of X L is higher than that of X N. The mechanical behavior of Stellite 21 in the range 20-700 °C is illustrated in Fig. 12.
4.2. Evolution of the internal variables during the second complementary test The calculation of the internal variables before and after heat treatment has shown that 80% of the stress increase (115 MPa) results from the kinematic component X and 20% from the isotropic component R. It could be reasonably deduced that the important carbide precipitation results depend on the X increase. Therefore, the increase in X is entirely due to the nonlinear term X N. Classically, an increase in the isotropic component is due to an increasing density of statistically stored dislocations. The kinematic component reflects intergranular deformation or incompatibility deformation between different phases, emphasized by a stable dislocation configuration [23], i.e. a "soft" phase (the f.c.c, matrix) or a "hard" phase (carbides on deformation bands and stacking faults).
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Furthermore, we have observed that, after the heat treatment, the stress decreases identically as that which occurs during the first part of the test and it is essentially the isotropic c o m p o n e n t R which decreases. T h e decrease in R was not affected by the heat treatment (carbide precipitation).
Acknowledgments T h e Stellite 21 coatings were supplied by H. Michaud and R. Leveque from IRSID Unieux (UsinorSacilor Co.). T h e authors would like to thank Dr. G. Cailletaud from E N M S P for his help in the writing of the paper.
References 5. Conclusions T h e systematic isothermal mechanical tests allow the identification of the material parameters of the viscoplastic model at five temperatures in the range 2 0 - 7 0 0 °C. Then, an anisothermal constitutive model could be introduced into the numerical procedure. T h e numerical procedure permits, by a finite element method, the calculation of the thermomechanical effects of thermal fatigue on a structure. We have observed that, at r o o m temperature, at the start of the tests, the kinematic c o m p o n e n t is greater than the isotropic c o m p o n e n t and during cycling the isotropic term decreases. At high temperature, Le. at 700 °C, the kinematic c o m p o n e n t is lower than the isotropic component. T h e y increase together during fatigue cycling, especially the X term in relation to carbide precipitation on deformation bands. T h e second complementary test has shown that, when the carbides have precipitated on deformation bands and when the effects of diffusion were insignificant (at 20 °C), the carbides induced the formation of "hard" zones. T h e s e microstructural observations could be correlated with the macrostructural calculation which determines the increasing of kinematic term X. It seems a reasonable deduction that the evolution of each c o m p o n e n t of the kinematic term, i.e. X N and X L , could be related to carbide precipitation on deformation bands. Therefore, it could be suggested that the linear c o m p o n e n t X L accounts for intergranular deformation and the non-linear c o m p o n e n t XN corresponds to transgranular deformation, because the X N term is related to carbide precipitation. T h e viscoplastic model chosen in this study has allowed us to describe well not only the macrostructural study results, but also microstructural evolutions of the material.
1 W. Betteridge, Cobalt and its alloys, in Industrial Metals, Ellis Horwood, 1981. 2 J. L. Strudel, in R. W. Cahn and P. Haasen (eds.), Physical Metallurgy, North-Holland, Amsterdam, 1983, pp. 1411-1440. 3 J. Lemaitre and J. L. Chaboche, M~canique des Matdriaux Solides, Dunod, Paris, 1985. 4 J. L. Chaboche, Int. J. Plast., 5 (1989) 247-302. 5 C. T. Sims, in C. T. Sims and W. C. Hagel (eds.), The Superalloys, Wiley, 1972, pp. 145-174. 6 N. Ben Salah, S. Tawfiq, M. Clavel, P. Fluzin, G. Beranger and A. Boucher, J. Int. Printemps, Paris (June 1986) 302-316. 7 L. Farcy, R. Rahouadj, M. Clavel, P. Fluzin and G. Beranger, Mdm. Sci. Rev. Met., 84 (2)(1987) 107-114. 8 P.S. Kotwal, Trans. AIME, 242 (1968) 1651. 9 L. Remy, E Lecroisey and A. Pineau, M~m. Sci. Rev. Met., 7-8 (1973) 589-595. 10 P.A. Beaven, E R. Swann and D.R.F. West, J. Mater. Sci., 14 (1979) 354-364. 11 P. Pilvin and G. Cailletaud, Proc. 1UTAM Creep in Structures IV, Cracow, 1990, September 1990, pp. 171-178. 12 P. Pilvin, Proc. MECAMAT, Besan¢on, September 1988, pp. 155-164. 13 P. Pilvin, Doctorate Thesis, Universit6 Paris VI, 1990. 14 P. Revel, Doctorate Thesis, Universit6 de Technologie de Compi~gne, 1991. 15 W.V. Youdelis and O. Kwon, Met. Sci., 17(1983) 379-384. 16 R. N. J. Taylor and R. B. Waterhouse, J. Mater. Sci., 21 (1986) 1990-1996. 17 J. B. Vander Sande, J. R. Coke and J. Wulff, Metall. Trans. A, 7(1976) 389-397. 18 R. N. J. Taylor and R. B. Waterhouse, J. Mater. Sci., 18 (1983) 3265-3280. 19 K. Rajan and J. B. Vander Sande, J. Mater. Sci., 17 (1982) 769-778. 20 J. J. Olivera, R. Baccino and D. Brenet, paper presented at 1AEA Specialists Meeting, Buenos Aires, October 1989.
21 J. Hernandez, Doctorate Thesis, INSA de Lyon, November 1986. 22 M. J. Deleury, J. R. Donati and J. L. Strudel, Ann. Chim. Franc., 6 (1981) 59. 23 J.L. Chaboche, Rech. Akrospatiale, 5 (1983) 363-375.
85
Mechanical properties and microstructural evolution of a cobalt base alloy coating P. Revel, M. Clavel and G. Beranger Laboratoire de G~nie M~canique pour les Mat&iaux et les Structures (LG2mS), URA 1505 CNRS, Universitd de Technologic de CompiOgne, BP 649, 60206 CompiOgne Cedex (France)
P. Pilvin* ENSMP, Centre des Materiaux, BP 87, 91003 Evry Cedex (France) (Received June 23, 1992; in revised form December 28, 1992)
Abstract Several isothermal mechanical tests have been performed on a cobalt superalloy to determine the parameters of a viscoplastic behavior law in the range (20-700 °C). These parameters have been identified by means of a systematic numerical procedure (a computer program for simulation and identification). The microstructural evolution during the mechanical tests has been examined in relation to the evolution of the internal variables of the viscoplastic model. It was found that the material softens at room temperature, mainly as a result of an isotropic component decrease. However, at high temperatures (500-700 °C), the material hardens, mostly owing to a kinematic component increase. The deformation mode, i.e. the martensitic transformation, has been identified for all the temperatures studied. At high temperatures carbide precipitation on stacking faults and deformation bands has been observed. Complementary tests have shown that, at high temperatures, the further addition of carbide precipitates dissolves by dislocation glide and a diffusion mechanism. At room temperature, after heat treatment at 700 °C, carbides precipitated on deformation bands induced the formation of "hard" zones. These microstructural observations have been correlated with the important part of the kinematic term in the stress increase.
1. Introduction Alloys used at elevated temperatures require two main characteristics: first, adequate resistance to corrosive attack and, secondly, sufficient mechanical strength to resist deformation or fracture under the imposed stresses. These alloys are multiphase alloys, the first phase being called the matrix and the second phase the precipitate. They have two striking features: their rather high limit of elasticity at relatively low temperature (up to about 0.21m); their tendency to preserve fairly high flow stresses up to temperatures close to their melting point (0.9-0.95 Tm). The strengthening of cobalt base alloys is provided by solid solution strengthening of the matrix and by the precipitation of carbides. Solid solution strengthening is principally due to the contents of addition elements, such as chromium, nickel, molybdenum, tungsten etc. The second-phase strengthening in cobalt base alloys is
*Also at: Universit6 Pierre et Marie Curie, Paris Cedex, France. 0921-5093/93/$6.(10
mainly provided by carbides formed from the chromium, which is primarily present to confer corrosion resistance, and from other elements added as carbide formers, e.g. tungsten, molybdenum etc. The carbides form as mixed carbides and the forms present will depend on the balance of metallic composition, on the carbon content and on the thermal history of the alloy. The morphology and the location of the carbide precipitates affect the strengthening effect and, for the optimum improvement, precipitation both at grain boundaries and within the grains is required. Intragranular precipitation strengthens the matrix by providing hard particles, such as carbides, which cannot be sheared by gliding dislocations and which remain stable in size and distribution up to the highest service temperatures [1 ]. During the last 30 years, many microstructural observations have been carried out using transmission electronic microscopy (TEM) to determine the microscopic mechanisms which take place during deformation. Complex dislocation interactions have enabled the metallurgists to develop microscopic models. However, macroscopic models based on © 1993 - Elsevier Sequoia. All tights reserved
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Mechanical testing of cobalt base alloy
continuum mechanics have been developed with constitutive equations for the viscoplastic behavior of isotropic and anisotropic materials. Often, these models, which required the introduction of a few internal variables, seem to ignore the crystallographic nature of slip and dislocation mechanisms [2]. Understanding and describing the behavior of crystalline solids under alternate loading (tensioncompression) are forcing the mechanical and the metallurgical approaches towards a necessary point of convergence. The material strain hardening (uniaxial tension-compression) could be described by two components: the isotropic strengthening R, which is called forest hardening in the dislocation theory; the kinematic strengthening X (back stress hardening) [2-4]. In the present work, a cobalt base coating (Stellite 21) was deposited using a semitransferred plasma arc technique on a low alloyed steel support in 10 to 12 coats. This cobalt alloy was chosen on account of its good resistance to thermal fatigue. To predict the thermomechanical behavior of the material in the range 20-700 °C, isothermal mechanical experiments were conducted using laboratory samples. The results allow the evaluation of the material parameters of the viscoplastic constitutive model related to the microstructural evolution of the cobalt superalloy during the tests.
Fig. 1. Dendritic structure of the coating.
2. Experimentalprocedure 2.1. Material
The composition of the coating is given in Table 1. The microstructure of this material coating results in a dendritic array, with the primary dendrites axis normal to the surface of the steel support (Figs. 1 and 2). The interdendritic zones are rich in chromium and molybdenum. In fact, an abundant precipitation of a mixture of M7C 3 and MC carbides (M = Cr, Mo) takes place in the interdendritic zones [5, 6]. The grains are 1-2 mm long and 50-200/~m wide. The crystallographic structure of the matrix is face-centered cubic (f.c.c.). Previously [7-9], the cobalt-rich alloys were considered to have low stacking fault energies. Indeed, in the as-received material, a high density of stacking faults and partial dislocations have been observed. Moreover, the martensite phase e was not observed. In TABLE 1. Composition of Stellite 21 Element Amount (wt.%)
Cr 27
Mo 5.5
Ni 3
Si 1
Mn 1
C Co 0.25 Balance
Fig. 2. Micrograph showingthe structure of Stellite 21.
fact, it was observed elsewhere that the M s temperature is below room temperature [10]. 2.2. M e c h a n i c a l isothermal tests
The low cycle fatigue tests were carried out on a Mayes fatigue machine at different temperatures in the range 20-700 °C. They were performed with sawtoothshaped signals, under a constant plastic strain range (0.2%; 0.5%; 1%), with a strain ratio R, = - 1 . The specimens were heated by a Joule-effect furnace. The total strain was measured using a longitudinal capacitive extensometer with ceramic knives. Longitudinal strain control was applied to cylindrical specimens (8 mm in diameter and 10 mm in gauge length). The total strain amplitude was adjusted when necessary by
P. Revel et al. / Mechanicaltesting of cobalt base alloy a computer program. The total constant strain rate was gt = i x 10 -3 s-J. The load and strain evolution were recorded up to failure, to estimate the fatigue life (NF) and to determine the mechanical behavior. Two complementary tests have been carried out. The first one corresponded to Aep/2=0.2% and 1"= 600 °C. It was interrupted twice during half an hour and the stress was held at a zero value. The second test corresponded to Aep/2 = 0.5% and T = 20 °C. It was interrupted at Nv/3. The specimen was placed in a tube furnace in a purified dried argon atmosphere at 700 °C for 1 h. Then, the fatigue test was continued at 20 °C. Other fatigue tests have been carried out. When stabilized cycles were reached, relaxation tests were performed. These tests were performed to characterize the viscous effects.
2.3. Metallographic observations Metallographic observations were carried out, starting by using optical microscopy on the fatigue section. The specimens were cut, mechanically polished and electrolytically etched. Complementary observations, such as mechanically polishing and electropolishing thin foils of cycled specimens were conducted, using a Jeol 100 CX2 transmission electronic microscope.
2.4. Numerical model In the present work, a viscoplastic constitutive model formulated for isothermal conditions is used [3, 4]. A relationship between the elastic strain tensor e~ and the viscoplastic strain tensor gyp has been supposed: et=t~+evp. This model uses the thermodynamics of an irreversible process. The internal variables of strain hardening are the viscoplasticity strain tensor evp , the tensor a and the scalar p, which are related respectively to the associated variables the linear kinematic variable XL, the non-linear kinematic variable X N and the isotropic variable R. R characterizes the evolution of the elastic domain size. The kinematic variable X has two components, i.e. X = X L+ Xy, and characterizes the displacement of the elastic domain center. The internal variables X L and Xy are chosen for modelling the two sources of kinematic hardening in a polycrystal (intergranular and transgranular) [11]. This model has the following basic equations (one-dimensional form). The state laws are o = Eel.
(1)
Xt. = He~p
(2)
xN = c a
(3)
R = k + Q{ 1 - exp( - bp)}
(4)
87
and the evolution laws are
# = (, ' < l ° - X Kl - R ) ) n
(Z) = max(0, Z)
gvp=sign( o - X) p
a = gv -
(5) (6)
ap
(7)
with 7(P) = Y~+ (7,,- 7~) exp( - tip)
(8)
Ten parameters characterize viscoplasticity. These are as follows: K and n the viscosity parameters; k, Q and b the isotropic hardening parameters, such that k =R(0) = or; H, C, V0, V~and/3 the kinematic hardening parameters. To evaluate the material coefficients of the viscoplastic model from experimental results, the constitutive equations of the model have been implemented in the identification-optimization code SiDoLo [12, 13].
3. Results
3.1. Fatigue life results The fatigue life, at the various temperatures studied, is plotted in the classical Manson-Coffin diagrams as a function of the plastic strain amplitude in Fig. 3 (Nv=f(Aep)). T h e fatigue life is lowest at 20°C and highest at 500 °C. The material exhibits a significant reduction in fatigue life for tests conducted at temperatures in the range 600-700 °C. 3.2. Cyclic stress-strain behavior The variation of the maximum stress amplitude with the cumulative applied plastic strain {p =4N(AEp/2)} is shown in Fig. 4 at various temperatures for a plastic
NF
0.001
0.01 AEp
0.1
Fig. 3. Fatigue life N F as a function of the plastic strain a m p l i t u d e
Aep.
88
P. Revel et al. /
Mechanical testing of cobalt base alloy
900.
test, performed at 20°C, the stress first decreases. Immediately after the heat treatment at 700 °C, a stress increase of 115 MPa is observed and then stress decreases again during cycles at 20 °C.
850. 800. 750
•
Aa/2 700. (MPa) 650.
0 0
0
0
600.
550
500 0
I
I
I
I
I
I
I
I
I
I
I
2
4
6
8
10
12
14
16
18
20
22
P
Fig 4. Stress amplitude Aa/2 as a function of the cumulated strain p; Aep/2 = 5 x 10 -3.
60O 55O
,
".
A6/'2 (MPa) 5OO
I "'''''I •
mn
mi~m
ml m llllull
Ill
450
(a)
0.01
0.1
1
10
P
100
1000
900,
Aft/2 800 (MPa)
000000000000 000000000000000000000
700
(b)
I
I
I
I
I
I
I
0.1
0.2
0.3
0.4
0.5
0.6
0.7
p
Fig. 5. Complementary tests: (a) fatigue test at T= 600 °C and Aep/2=2xl0 -3 interrupted twice during half an hour; (b) fatigue test at T=20°C and A%/2 = 5 × 10 -3 interrupted by a heat treatment at 700 °C for 1 h.
amplitude of 0.5%. At room temperature, the stress amplitude decreases before it stabilizes, i.e. the material softens. At higher temperatures, cyclic hardening of the alloy takes place; a lot of serrations have been observed on the stress-strain loops. The cyclic evolution of complementary tests is plotted in Fig. 5. It can be seen that, during the first test, performed at 600 °C, the stress increases after the interruptions and then decreases after a few cycles to reach the previous level. However, during the second
3.3. Observation of fatigue microstructures Optical observations have shown a reduction in the number of deformation bands as a function of decreasing temperature. It has been also observed that the number of deformation bands increases as a function of the plastic deformation amplitude. The examination of X-ray diffraction diagrams has allowed the identification of the e phase in the specimens tested at all temperatures [14]. Moreover, some observations on specimens cycled at 700 °C were carried out using transmission electron microscopy (TEM). Numerous deformation bands (DBs) and stacking faults (SFs) were observed, decorated by a large amount of M23C 6 carbides about 0.04-0.05/~m in size. These carbides have been identified using a dark-field imaging technique and extraspot reflection (Fig. 6). Nevertheless, their tendency to form columnar arrays suggests that precipitation takes place in the deformation bands: carbide precipitation often occurs in e martensite laths [10, 15-18]. The diffraction pattern taken on the deformation bands shows the presence of e phase (Fig. 7). The orientation relationship of these f.c.c, carbide precipitates with respect to their hexagonal close-packed (h.c.p.) surrounding was identified in previous studies: {111 }fee//{0001 }hcp a n d (110)fcc//(1120)hop [10, 16-18]. Similar observations have been performed on specimens cycled at 500 and 600 °C. At room temperature, the deformation mode remains the same, i.e. the martensitic transformation (Fig. 8). This observation indicates that the M a temperature was above room temperature [10]. At room temperature, carbide precipitation does not occur. In previous work [10, 19], stacking faults and twin formation were considered as precursors to martensite e formation. In the present work, twinning deformation has not been observed. The deformation mode and carbide precipitation are summed up in Table 2. The TEM examination of the specimen of the second complementary test has shown M23C 6 carbide precipitation on deformation bands (Fig. 9). These deformation bands have been the result of mechanical cycles carried out at 20 °C before the heat treatment at 700 °C. 3.4. Identification of the viscoplastic model For each test, two loops were necessary to identify the material parameters: the initial cycle and the stabilized cycle. A good correlation has been found for several steady state loops under different strain
P. Revel et al.
Mechanical testing of cobalt base alloy
89
(ht Fig. 7. Micrographs showing e martensitic lath and associated diffraction pattern (TEM).
Fig. 6. Micrographs of a specimen strained to A%/2=2 x 10 -~ at 700 °C: (a) bright-field; (b) dark-field showing M:3C~, carbides with a size of about 50 nm (TEM).
amplitudes and at various temperatures between the experimental response (symbols) and the numerical simulation (solid line) (Fig. 10). T h e results of the numerical identification have shown an evolution of the p a r a m e t e r s as a function of the temperature. T h e p a r a m e t e r s of the second c o m p l e m e n t a r y test have been identified separately before and after heat treatment. This was to establish the effect of carbide precipitation on the internal variables of the model. T h e material p a r a m e t e r s at various temperatures are given in Table 3. 4. Discussion
T h e main result of the study is the relationship between the evolution of the microstructural internal variables.
4.1. Mechanical behavior of Stellite 21 First, concerning the deformation mode, it has been established that martensitic transformation takes place
Fig. 8. Micrographs of a specimen strained to Aep/2 = 10 2 at 20 °C: martensitic laths sheared (TEM).
TABLE 2. Deformation mode and carbide precipitation (%)
700 °c
600 °C
500 °c
20 °C
1
SFs
SFs
SFs
SFs + DBs(e)
0.5
+ DBs(e)
+ DBs(e)
+ DBs(e)
SFs + DBs(e)
0.2
+carbides (M>C,,)
+carbides (M:3C,,)
+carbides (M:~C<,)
SFs+DBs
2
SFs, stacking faults: DBs, deformation bands: & martensite phase.
during tests, regardless of the temperature. Furthermore, it should be noted that, for the mechanical tests carried out at high temperatures, a great amount of carbide precipitation takes place in martensitic laths and stacking fault ribbons. T h e fact that carbides have
P. Revel et al. /
90
Mechanical testing of cobalt base alloy
precipitated in the d e f o r m a t i o n bands in particular, the observation of serrations on fatigue loops and also previous studies on cobalt alloys [16, 18] suggest a Suzuki effect. It seems reasonable to conclude f r o m the numerical identification that the uniaxial mechanical behavior of Stellite 21 in the range 2 0 - 7 0 0 ° C could be well described by this viscoplastic model. Therefore, the associated variables (R, X ) have b e e n calculated with the help of the identified p a r a m e t e r values for each test with the value ep--0.5%. We can then c o m p a r e their evolution as a function of the t e m p e r a t u r e and n u m b e r of cycles.
ing. This could be illustrated by the negative value of the t e r m R - k . T h e increase in stress at high t e m p e r a tures result f r o m the evolution of the kinematic t e r m X, as shown by the value 70 > 72 and the variation of the t e r m X - X i (where X i is the value of X after the first quarter of the first cycle with 7(P) = 70 or the X value at the stabilized cycle with 7(P) = 7s)) (Table 4).
O 11300
500
4
4.1.1. Evolution of internal variables as function of number of cycles It is shown at 20 °C that m o s t of the softening is related to the decrease in the isotropic strain harden-
O ~,~)
80o
Fig. 9. Micrographs of a specimen strained to Aep/2 = 5 × 10 -3 at 20 °C. Heat treatment at 700 °C. Deformation bands can be seen decorated by M23C 6 carbides (TEM).
Fig. 10. Comparison between model (full lines) and experimental responses (symbols) at (a) 20°C and (b) 600 °C. Thick lines, initial loop; thin lines, stabilized loop.
TABLE 3. Values of material parameters Parameter
E(GPa) k(MPa) K (MPas ~/') n H(GPa) Yl} Q (MPa) b C(MPa) y~ fl
20 °C
165 357 50 20 199 656 - 123 0.97 26000 674 0.98
300 °C
160 206 70 14 163 415 3 1 17800 628 1.0
500 °C
143 208 90 11 103 488 21 0.95 14750 400 1.0
aparameters identified before and after heat treatment at 700 °C.
600 °C
141 247 467 3.6 102 475 19 0.9 9585 405 1.03
700 °C
123 169 1940 3.2 44 408 26 0.9 6470 330 0.9
20 °Ca Be~re
After
175 304 50 20 218 702 -108 0.88 41100 801 1.5
175 304 50 20 250 645 -105 0.88 40350 659 1.2
P. Revel et al.
/
Mechanical testing of cobalt base alloy
q-,
TABLE 4. Respectiveparts of kinematicand isotropic variables in hardening ( + ) or softening( - ) evolution T (°C)
X (%)
500 + 46 +21 69
600 + 37 + 19 66
700 + 25 +25 50
20 - 6 -86 7
R (%)
31
34
50
93
X-X~ (MPa) R - k (MPa)
91
m
(a) X,k, Gv
(MPa) 500 o.t¢
400
•
k
o
X[
K
30O
P
--
200
&~
_
•
,
-
/~,d
%
100
(b) 0
•
0
,
200
-
400
,
-
,
600 800 TeL3
Fig. 1 1. X~, k and ov as functions of temperature.
At room temperature, the material softens. The stress decrease during the fatigue tests could be correlated with the relaxation of residual stresses, as evaluated in previous studies [20, 21]. The relaxation of residual stresses is generally related to the evolution of the internal stress and its associated tensor X. Therefore, it may be suggested that, at room temperature, the contribution of the isotropic component R in the stress decrease is too high. Nevertheless, this could be explained by the decrease in the partial dislocation density in the matrix compared with their high density in the as-received material. At high temperatures, carbide precipitation takes place in the matrix and in particular on deformation bands. This phenomenon could be correlated with the significant contribution of X in the stress increase. The first complementary test has shown that, when the test has continued, after breaks, the excess carbide precipitation has been dissolved by dislocation glide [22].
4.1.2. Evolution of internal variables as function of temperature The effects of temperature on the evolution of internal variables, X, k and ov, where o v= Io - X[ - R is the viscosity component of the stress, have been illustrated in Fig. 11. For all temperatures, X, k and Ov have been evaluated at the beginning of the fatigue test. It should
Fig. 12. Schematic diagram of the evolution of the elastic domain at (a) 20 °C and (b) 700 °C. Full lines, initial cycle; b r o k e n lines, stabilized cycle.
be noted that, in the range 600-700 °C, the mechanical behavior of the material evolves, with the component ov becoming greater than the X and k components. Moreover, it is worth noting about the kinematic component X that the relative part of the non-linear term X N is more important than the linear term XL in the range 500-700 °C. At room temperature, the relative part of X L is higher than that of X N. The mechanical behavior of Stellite 21 in the range 20-700 °C is illustrated in Fig. 12.
4.2. Evolution of the internal variables during the second complementary test The calculation of the internal variables before and after heat treatment has shown that 80% of the stress increase (115 MPa) results from the kinematic component X and 20% from the isotropic component R. It could be reasonably deduced that the important carbide precipitation results depend on the X increase. Therefore, the increase in X is entirely due to the nonlinear term X N. Classically, an increase in the isotropic component is due to an increasing density of statistically stored dislocations. The kinematic component reflects intergranular deformation or incompatibility deformation between different phases, emphasized by a stable dislocation configuration [23], i.e. a "soft" phase (the f.c.c, matrix) or a "hard" phase (carbides on deformation bands and stacking faults).
92
P. Revel et al.
/
Mechanical testing of cobalt base alloy
Furthermore, we have observed that, after the heat treatment, the stress decreases identically as that which occurs during the first part of the test and it is essentially the isotropic c o m p o n e n t R which decreases. T h e decrease in R was not affected by the heat treatment (carbide precipitation).
Acknowledgments T h e Stellite 21 coatings were supplied by H. Michaud and R. Leveque from IRSID Unieux (UsinorSacilor Co.). T h e authors would like to thank Dr. G. Cailletaud from E N M S P for his help in the writing of the paper.
References 5. Conclusions T h e systematic isothermal mechanical tests allow the identification of the material parameters of the viscoplastic model at five temperatures in the range 2 0 - 7 0 0 °C. Then, an anisothermal constitutive model could be introduced into the numerical procedure. T h e numerical procedure permits, by a finite element method, the calculation of the thermomechanical effects of thermal fatigue on a structure. We have observed that, at r o o m temperature, at the start of the tests, the kinematic c o m p o n e n t is greater than the isotropic c o m p o n e n t and during cycling the isotropic term decreases. At high temperature, Le. at 700 °C, the kinematic c o m p o n e n t is lower than the isotropic component. T h e y increase together during fatigue cycling, especially the X term in relation to carbide precipitation on deformation bands. T h e second complementary test has shown that, when the carbides have precipitated on deformation bands and when the effects of diffusion were insignificant (at 20 °C), the carbides induced the formation of "hard" zones. T h e s e microstructural observations could be correlated with the macrostructural calculation which determines the increasing of kinematic term X. It seems a reasonable deduction that the evolution of each c o m p o n e n t of the kinematic term, i.e. X N and X L , could be related to carbide precipitation on deformation bands. Therefore, it could be suggested that the linear c o m p o n e n t X L accounts for intergranular deformation and the non-linear c o m p o n e n t XN corresponds to transgranular deformation, because the X N term is related to carbide precipitation. T h e viscoplastic model chosen in this study has allowed us to describe well not only the macrostructural study results, but also microstructural evolutions of the material.
1 W. Betteridge, Cobalt and its alloys, in Industrial Metals, Ellis Horwood, 1981. 2 J. L. Strudel, in R. W. Cahn and P. Haasen (eds.), Physical Metallurgy, North-Holland, Amsterdam, 1983, pp. 1411-1440. 3 J. Lemaitre and J. L. Chaboche, M~canique des Matdriaux Solides, Dunod, Paris, 1985. 4 J. L. Chaboche, Int. J. Plast., 5 (1989) 247-302. 5 C. T. Sims, in C. T. Sims and W. C. Hagel (eds.), The Superalloys, Wiley, 1972, pp. 145-174. 6 N. Ben Salah, S. Tawfiq, M. Clavel, P. Fluzin, G. Beranger and A. Boucher, J. Int. Printemps, Paris (June 1986) 302-316. 7 L. Farcy, R. Rahouadj, M. Clavel, P. Fluzin and G. Beranger, Mdm. Sci. Rev. Met., 84 (2)(1987) 107-114. 8 P.S. Kotwal, Trans. AIME, 242 (1968) 1651. 9 L. Remy, E Lecroisey and A. Pineau, M~m. Sci. Rev. Met., 7-8 (1973) 589-595. 10 P.A. Beaven, E R. Swann and D.R.F. West, J. Mater. Sci., 14 (1979) 354-364. 11 P. Pilvin and G. Cailletaud, Proc. 1UTAM Creep in Structures IV, Cracow, 1990, September 1990, pp. 171-178. 12 P. Pilvin, Proc. MECAMAT, Besan¢on, September 1988, pp. 155-164. 13 P. Pilvin, Doctorate Thesis, Universit6 Paris VI, 1990. 14 P. Revel, Doctorate Thesis, Universit6 de Technologie de Compi~gne, 1991. 15 W.V. Youdelis and O. Kwon, Met. Sci., 17(1983) 379-384. 16 R. N. J. Taylor and R. B. Waterhouse, J. Mater. Sci., 21 (1986) 1990-1996. 17 J. B. Vander Sande, J. R. Coke and J. Wulff, Metall. Trans. A, 7(1976) 389-397. 18 R. N. J. Taylor and R. B. Waterhouse, J. Mater. Sci., 18 (1983) 3265-3280. 19 K. Rajan and J. B. Vander Sande, J. Mater. Sci., 17 (1982) 769-778. 20 J. J. Olivera, R. Baccino and D. Brenet, paper presented at 1AEA Specialists Meeting, Buenos Aires, October 1989.
21 J. Hernandez, Doctorate Thesis, INSA de Lyon, November 1986. 22 M. J. Deleury, J. R. Donati and J. L. Strudel, Ann. Chim. Franc., 6 (1981) 59. 23 J.L. Chaboche, Rech. Akrospatiale, 5 (1983) 363-375.