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Optimization of ti-al-v beta phase for dispersed phase transformation toughening of gamma titanium aluminides
Vol. 15, No. 2, pp. 173-178. Printed in the USA.
CALPHAD
0364~59$6/91 $3.00 + .OO (c) 1991 Pergamon Press plc
1991
OPTIMIZATION OF l-i-AI-V BETA PHASE FOR DISPERSED PHASE “lXANSFORMATIQN TOUGHENING OF GAMMA TlTANIUM ALUMINIDES M. Grujicic and C.P. Narayan Departmim of Mechanical Engineering 3 f 8 Riggs Hall, Clemson University Clemson, South Carorma 29634-0921 ABSTRACT
The most important factors affecting the dispersed-phase tmnsfotmation toughening in the gammaTll intermetallic by a dispersion of the beta phase arc the stability of the dispersion, the transformation volume change and the /&r chemical compatibility. A thermodynamics-based, computer-aided analysis was used to design an optimum composition of the @-phasedispersion for the crack-tip ~sf~don hugging. It is found that such an optimum composidon exists in the ternary T&A{V system.
High specific strength and high specific stiffness combined with good oxidation properties and a ready availabiity of titanium and aluminum in the United States make titanium aluminides very attractive materials for aerospace application. However, limited ductility, which is particularly pronounced at lower temperanues, inhibits a wide scale ical room-temperature ductility and fracture toughness of the gammaapplication of these materials. For example, TiAI intermetallic are below 2% and l&W&z rprn I respcctivtly. As a result of the limited ductility and toughness severe problems, such as cracking and fracture also arise during ingot breakdown leading to low yields. Hence in o&r for ~ T~~~n~~~lIc to become a valuable material for advanced high-temperature application, such as aircraft engines, it is imperative to find ways to enhance its ductility and toughness. Among several approaches which are currently being pursued in an attempt to ductilize and toughen titanium alumninides (such as the use of ternary and qumrnary alloy additions, the grain size refinement, the introduction of whiskers and fibers) ilre introduction of fine-scale, dispersed, metastable phases appears to be the most promising. The same approach, the dispersed phase transformation toughening, yielded record ductility and fractun?: toughness levels in high-strength steels and ceramics f&23. The purpose of present paper is to discuss the pomtia8 of defmtion-induceii znartsnsiticiransf~ti~ dispersedE-AI-V beta-phase as a toughening mechanism for gamma-TiAl-base matrix alloys.
in the
It is well-established [3,4] that dispersed-phase transformation toughening is controlled by the stabiIity of the metastable dispersion, i.e. the size and the chemical composition of dispersed particles and by tho sign and magnitude of the transformation volume change. To maximize the transformation toughening effect, the stability of the metastable beta dispersion must be optimized with respect to the crack tip smss state. Such an optimum stability is generally quite high owing to a high t&xl&l&y of the crack tip stress field which through effects of the stress state sensitiviy of marte&tic tnznsfonsation promotes the martensitic ~s~on at a lower effective stress. This condition &en pnsnibes the microstructi re@zments, i.e. average particle size and composition, to obtain the required stability of the beta phase. In the present paper we will be primarily concerned with the effect of chemical composition on the thermodynamic stability of the beta phase. In addition to a high stability, the transformation toughening squires a large positive transformation volum change. The effect of the transformation volume change on the transformation toughening could involve three phenomena: ---_-----__-___“____ Received20 August 1990
174
M. GRUJICIC
and C.P. NARAYAN
(a) the phenomenon of the sness state sensitivity of transformation plasticity, mentioned earlier, which leads to an enlargement of the plastic wne and reductions crack tip stresses; (b) the direct PAV energy dissipation and (c) a modification of the crack tip stress state and effective stress intensity by the volume change. It is clear that the alloy selection procedure outlined above, must be subjected to a constraint that, at the desired level of stability, the @-phase composition ensures a maximum positive transformation volume change. Chemical compositions of the p-phase, associated with the desired levels of stability and transformation volume change must be furthermore subjected to a constraint that the J3-phase is in chemical equilibrium with the ‘y-matrix at a given homogeni~g temperature, say 1073K. This ensures that the toughening effects will not be lost by undesirable chemical mactions at the Bfy interface. Since the problems associated with limited fracture toughness in titanium aluminides are particularly pronounced at room temperature, a quantitative characterization c&austenite~tability c be provided by the free-energy change for martensitic transformation at room temperature, AG (RT) = G (RT) - Gir‘(RT). Clearly, when the TOtemperature, (a temperature at which the &parent p@e and the a-martensite have the same Gibbs free energies) is below room temperature, RT = Tt in Figure 1, AG (RT) is a positive quantity. Conversely, when TOis above room tempemture, RT = T2 in Figure 1, AG (RT) is negative.
TEMPERATURE FIG. 1
Schematic Free Energy/Temperature Diagrams for a and p phases. See the text for an explanation of the symbols. Also shown in Figure 1 is the effectitif driving force for martensite nucleation, AGnUC1. which is by convention always positive. A typical value for AG for the @+a martensitic transformation inTi-Al -base alloys is about 1000 J/mole. AGmech in Figure 1, represents the mechanical driving force for transformation due to applied sttess. Defining 0 as the angle between the martensitic habit plane normal and the axis of the maximum magnitude principal stress 01,
OPTIMIZATION OF THE Ti-Al-V BETA PHASE FOR TRANSFORMATION TOUGHENING OF ALUMtNtDES
175
and expressing the applied stress in terms of the maximum and minimum principal stress the mechanical driving force can be expressed as [I]: 1 *loI cil- 031 sin 26 + $V* AG mech = TV”
where
[ai+ 03 + 1ol- 031 COS281
Vm is the molar volume and ‘yeand ~0 are mspectively shear and normal components of the transformation strain expressed as an invarian - plane shape strain.
Setting dAG m~h/de = 0, the habit orientation for maximum AGmcchis given by tan 28 = ye/q For the shape strain of a-martensite in Ti-AZ-V alloys, under consideration hem, ye = 0.08, ~0 = 0.01 [S] and 28=83 . Exgessing stress in terms of the von Mises equivalent tensile stress iz, the driving force contribution of stress aAGm l&r for the crack tip stress state can be calculated as following: o1= 02 = 3a ;a3 = 25 (crack tip), V, = 2.045 x 10-‘m3,&e aAGmch 1 = +~* ao
v
sin 20 + +&
[S] and
[5 + cos 28 ]=
o.67MpaJm,e
Hence the mechanical driving force, A G mech=(aAG m”h/a7i) Ti due to a crack-tip stress state in the gamma - TiA/ matrix with a typical yield stress of 520MPa, is approximately, 34i J/mole. According to Figure 1. the following relation holds.
AGnuff = - AGch i- AG mech Hence the required level of P-phase stability is simply. AC ch = AG ch (R’11= AG mech- AG ” = - 652--&
Figure 2 shows a 1073K isothermal section of the ternary Ti-AI-V phase diagram [6j. In order to comply with the requirement for a chemical compatibility between the beta and gamma phases alloys 1 through 4, with compositions along the B/p + y phase bounw when originally selected. The alloy compositions are listed in Table 1. AGch at room temperature has been next calculated using the THERMGCALC computer program [7] and the Kaufman database [7,gf. The results of the calculation are shown in Figme 3. The optimum alloy composition lies between alloys 2 and 3.The subsquent ~~~ladon yielded the following alloy composition 28Ti 41 AI 3 1 V (at %), allo 2.5, which represents an optimum combination of the @-phase stability, the transformation volume change and the 2;fu chemical compatibility.
M. GRUJICIC and CR NARAYAN
176
A
w 60
40
70 ?.
30
20
10
p&o 7.
weight % Ti FIG. 2 1073K Isothermal Section of the Ti-AI-V Ternary Phase Diagram 161
Table 1.
Chemical Compositions (at %) of the Ti-AI-V alloys analysed in this work.
2
31
41
28
3
22
42
36
4
8
49
54
2.5
I
28
I
41
I
31
I
OPTIMIZATION OF THE Ti-AI-V BETA PHASE FOR TRANSFORMATION TOUGHENING OF ALUMINIDES
177
It must be emphasized that in the case at hand, the transformation volume change (t?,e= + 0.01) was quite insensitive to, and hence ssumed to be independent of, the alloy composition [Q]what made the alloy design procedure relatively s~~~~~d. In general, however, one must consider the composition dependence of ~0.
l
. .
-3
b I
2 ALLOY
2.5
3
4
NUMBER
FIG. 3 Free ecfergy change for martensitic transformation at room temperature, A Cl (RT), for the Ti-AI-V alloys studies in this work. See Table 1 for the chemical composition of the alloys.
4. Conclusion Beta-alpha martensitic ~sfo~don can be utilized to improve fracture toughness of the g~a-T~~~te~e~ic through the effects of dispersed phase ~sfo~ation toughe~ng. Compu~r-add ~e~~~~ analysis can be used to optimize the composition of the fi -phase dispersion with respect to an optimum ~e~~~~c stability, maximum transformation volume change and a p/y chemical compatibility. Present calculation indicates that such a optimum composition exists in the ternary Ti-AI-V system
This work has been supported by The National Science Foundation, The Small Grant Exploratory Research Grant #DMR-9017214. The authors would like to thank Dr. Bruce A. MacDonald for his continuing interest in this work.
M. GRUJICIC
178
and C.P. NARAYAN
1.
G. B. Olson, in Pefom
Struck
2.
A. G. Evans and A. I-l. Hever, J. Amer. Cer. Sot., 63,24 (1980).
3.
M. Grujicic, Materials Science and Engineering, Al25.453 (1990)..
4.
M, Grujicic, ibid, A 127,975 (1990).
5.
J. C, Williams, in ~
6.
K. Hashimoto, H. Doi and T. Tsujimoto, Trans. JIM, 27,241 (1986).
7.
B. Sundman, B. Jansson, and J. 0. Andersson, Calphad, 9,153 (1985).
and Tech-
.
.
pp. 391-424, ASM, Metals Park. OH, 1983.
eds., R I. Jaffee and II. M. Butte, 3,1433 (1973).
8.
L. Kaufman, in User 1987.
9.
C. P. Narayan, MSc work in Progress, Clemson University, June 1990.
, ed. L. Kaufman, pp. 59-96, ASM International,
CALPHAD
0364~59$6/91 $3.00 + .OO (c) 1991 Pergamon Press plc
1991
OPTIMIZATION OF l-i-AI-V BETA PHASE FOR DISPERSED PHASE “lXANSFORMATIQN TOUGHENING OF GAMMA TlTANIUM ALUMINIDES M. Grujicic and C.P. Narayan Departmim of Mechanical Engineering 3 f 8 Riggs Hall, Clemson University Clemson, South Carorma 29634-0921 ABSTRACT
The most important factors affecting the dispersed-phase tmnsfotmation toughening in the gammaTll intermetallic by a dispersion of the beta phase arc the stability of the dispersion, the transformation volume change and the /&r chemical compatibility. A thermodynamics-based, computer-aided analysis was used to design an optimum composition of the @-phasedispersion for the crack-tip ~sf~don hugging. It is found that such an optimum composidon exists in the ternary T&A{V system.
High specific strength and high specific stiffness combined with good oxidation properties and a ready availabiity of titanium and aluminum in the United States make titanium aluminides very attractive materials for aerospace application. However, limited ductility, which is particularly pronounced at lower temperanues, inhibits a wide scale ical room-temperature ductility and fracture toughness of the gammaapplication of these materials. For example, TiAI intermetallic are below 2% and l&W&z rprn I respcctivtly. As a result of the limited ductility and toughness severe problems, such as cracking and fracture also arise during ingot breakdown leading to low yields. Hence in o&r for ~ T~~~n~~~lIc to become a valuable material for advanced high-temperature application, such as aircraft engines, it is imperative to find ways to enhance its ductility and toughness. Among several approaches which are currently being pursued in an attempt to ductilize and toughen titanium alumninides (such as the use of ternary and qumrnary alloy additions, the grain size refinement, the introduction of whiskers and fibers) ilre introduction of fine-scale, dispersed, metastable phases appears to be the most promising. The same approach, the dispersed phase transformation toughening, yielded record ductility and fractun?: toughness levels in high-strength steels and ceramics f&23. The purpose of present paper is to discuss the pomtia8 of defmtion-induceii znartsnsiticiransf~ti~ dispersedE-AI-V beta-phase as a toughening mechanism for gamma-TiAl-base matrix alloys.
in the
It is well-established [3,4] that dispersed-phase transformation toughening is controlled by the stabiIity of the metastable dispersion, i.e. the size and the chemical composition of dispersed particles and by tho sign and magnitude of the transformation volume change. To maximize the transformation toughening effect, the stability of the metastable beta dispersion must be optimized with respect to the crack tip smss state. Such an optimum stability is generally quite high owing to a high t&xl&l&y of the crack tip stress field which through effects of the stress state sensitiviy of marte&tic tnznsfonsation promotes the martensitic ~s~on at a lower effective stress. This condition &en pnsnibes the microstructi re@zments, i.e. average particle size and composition, to obtain the required stability of the beta phase. In the present paper we will be primarily concerned with the effect of chemical composition on the thermodynamic stability of the beta phase. In addition to a high stability, the transformation toughening squires a large positive transformation volum change. The effect of the transformation volume change on the transformation toughening could involve three phenomena: ---_-----__-___“____ Received20 August 1990
174
M. GRUJICIC
and C.P. NARAYAN
(a) the phenomenon of the sness state sensitivity of transformation plasticity, mentioned earlier, which leads to an enlargement of the plastic wne and reductions crack tip stresses; (b) the direct PAV energy dissipation and (c) a modification of the crack tip stress state and effective stress intensity by the volume change. It is clear that the alloy selection procedure outlined above, must be subjected to a constraint that, at the desired level of stability, the @-phase composition ensures a maximum positive transformation volume change. Chemical compositions of the p-phase, associated with the desired levels of stability and transformation volume change must be furthermore subjected to a constraint that the J3-phase is in chemical equilibrium with the ‘y-matrix at a given homogeni~g temperature, say 1073K. This ensures that the toughening effects will not be lost by undesirable chemical mactions at the Bfy interface. Since the problems associated with limited fracture toughness in titanium aluminides are particularly pronounced at room temperature, a quantitative characterization c&austenite~tability c be provided by the free-energy change for martensitic transformation at room temperature, AG (RT) = G (RT) - Gir‘(RT). Clearly, when the TOtemperature, (a temperature at which the &parent p@e and the a-martensite have the same Gibbs free energies) is below room temperature, RT = Tt in Figure 1, AG (RT) is a positive quantity. Conversely, when TOis above room tempemture, RT = T2 in Figure 1, AG (RT) is negative.
TEMPERATURE FIG. 1
Schematic Free Energy/Temperature Diagrams for a and p phases. See the text for an explanation of the symbols. Also shown in Figure 1 is the effectitif driving force for martensite nucleation, AGnUC1. which is by convention always positive. A typical value for AG for the @+a martensitic transformation inTi-Al -base alloys is about 1000 J/mole. AGmech in Figure 1, represents the mechanical driving force for transformation due to applied sttess. Defining 0 as the angle between the martensitic habit plane normal and the axis of the maximum magnitude principal stress 01,
OPTIMIZATION OF THE Ti-Al-V BETA PHASE FOR TRANSFORMATION TOUGHENING OF ALUMtNtDES
175
and expressing the applied stress in terms of the maximum and minimum principal stress the mechanical driving force can be expressed as [I]: 1 *loI cil- 031 sin 26 + $V* AG mech = TV”
where
[ai+ 03 + 1ol- 031 COS281
Vm is the molar volume and ‘yeand ~0 are mspectively shear and normal components of the transformation strain expressed as an invarian - plane shape strain.
Setting dAG m~h/de = 0, the habit orientation for maximum AGmcchis given by tan 28 = ye/q For the shape strain of a-martensite in Ti-AZ-V alloys, under consideration hem, ye = 0.08, ~0 = 0.01 [S] and 28=83 . Exgessing stress in terms of the von Mises equivalent tensile stress iz, the driving force contribution of stress aAGm l&r for the crack tip stress state can be calculated as following: o1= 02 = 3a ;a3 = 25 (crack tip), V, = 2.045 x 10-‘m3,&e aAGmch 1 = +~* ao
v
sin 20 + +&
[S] and
[5 + cos 28 ]=
o.67MpaJm,e
Hence the mechanical driving force, A G mech=(aAG m”h/a7i) Ti due to a crack-tip stress state in the gamma - TiA/ matrix with a typical yield stress of 520MPa, is approximately, 34i J/mole. According to Figure 1. the following relation holds.
AGnuff = - AGch i- AG mech Hence the required level of P-phase stability is simply. AC ch = AG ch (R’11= AG mech- AG ” = - 652--&
Figure 2 shows a 1073K isothermal section of the ternary Ti-AI-V phase diagram [6j. In order to comply with the requirement for a chemical compatibility between the beta and gamma phases alloys 1 through 4, with compositions along the B/p + y phase bounw when originally selected. The alloy compositions are listed in Table 1. AGch at room temperature has been next calculated using the THERMGCALC computer program [7] and the Kaufman database [7,gf. The results of the calculation are shown in Figme 3. The optimum alloy composition lies between alloys 2 and 3.The subsquent ~~~ladon yielded the following alloy composition 28Ti 41 AI 3 1 V (at %), allo 2.5, which represents an optimum combination of the @-phase stability, the transformation volume change and the 2;fu chemical compatibility.
M. GRUJICIC and CR NARAYAN
176
A
w 60
40
70 ?.
30
20
10
p&o 7.
weight % Ti FIG. 2 1073K Isothermal Section of the Ti-AI-V Ternary Phase Diagram 161
Table 1.
Chemical Compositions (at %) of the Ti-AI-V alloys analysed in this work.
2
31
41
28
3
22
42
36
4
8
49
54
2.5
I
28
I
41
I
31
I
OPTIMIZATION OF THE Ti-AI-V BETA PHASE FOR TRANSFORMATION TOUGHENING OF ALUMINIDES
177
It must be emphasized that in the case at hand, the transformation volume change (t?,e= + 0.01) was quite insensitive to, and hence ssumed to be independent of, the alloy composition [Q]what made the alloy design procedure relatively s~~~~~d. In general, however, one must consider the composition dependence of ~0.
l
. .
-3
b I
2 ALLOY
2.5
3
4
NUMBER
FIG. 3 Free ecfergy change for martensitic transformation at room temperature, A Cl (RT), for the Ti-AI-V alloys studies in this work. See Table 1 for the chemical composition of the alloys.
4. Conclusion Beta-alpha martensitic ~sfo~don can be utilized to improve fracture toughness of the g~a-T~~~te~e~ic through the effects of dispersed phase ~sfo~ation toughe~ng. Compu~r-add ~e~~~~ analysis can be used to optimize the composition of the fi -phase dispersion with respect to an optimum ~e~~~~c stability, maximum transformation volume change and a p/y chemical compatibility. Present calculation indicates that such a optimum composition exists in the ternary Ti-AI-V system
This work has been supported by The National Science Foundation, The Small Grant Exploratory Research Grant #DMR-9017214. The authors would like to thank Dr. Bruce A. MacDonald for his continuing interest in this work.
M. GRUJICIC
178
and C.P. NARAYAN
1.
G. B. Olson, in Pefom
Struck
2.
A. G. Evans and A. I-l. Hever, J. Amer. Cer. Sot., 63,24 (1980).
3.
M. Grujicic, Materials Science and Engineering, Al25.453 (1990)..
4.
M, Grujicic, ibid, A 127,975 (1990).
5.
J. C, Williams, in ~
6.
K. Hashimoto, H. Doi and T. Tsujimoto, Trans. JIM, 27,241 (1986).
7.
B. Sundman, B. Jansson, and J. 0. Andersson, Calphad, 9,153 (1985).
and Tech-
.
.
pp. 391-424, ASM, Metals Park. OH, 1983.
eds., R I. Jaffee and II. M. Butte, 3,1433 (1973).
8.
L. Kaufman, in User 1987.
9.
C. P. Narayan, MSc work in Progress, Clemson University, June 1990.
, ed. L. Kaufman, pp. 59-96, ASM International,