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Design of TiAlV β phase for transformation toughening of γ-titanium aluminide
Materials Science and Engineering, A 154 (1992) 75-78
75
Design of Ti-A1-V 13 phase for transformation toughening of "/-titanium aluminide Mica Grujicic
Centerfor Advanced Manufacturing, Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921 (USA) (Received September 13, 1991 )
Abstract A thermodynamic analysis is developed to determine the chemical composition of the T i - A I - V [3 phase for dispersed phase transformation toughening of y-titanium aluminide. The analysis takes into account the fact that maximum transformation toughening is associated with an optimum level of thermodynamic stability of the 13 phase with respect to martensitic transformation and with a large positive value of the 13 phase--, martensite transformation volume change. In addition, to prevent deleterious interracial reactions, the two phases 13 and y are required to be in chemical equilibrium. Available thermodynamic and lattice parameter data are used to determine a range of chemical compositions of the/3 phase which ensures maximum transformation toughening. It is found that this range is sufficiently close to the 13-(13+ y) phase boundary and hence guarantees chemical compatibility between the two phases.
1. Introduction
2. Thermodynamic analysis
A combination of attractive properties such as high specific strength, high specific stiffness, good oxidation resistance, ready availability of titanium and aluminum in the United States, etc. makes titanium aluminides a very important class of materials for aerospace application. However, limited ductility and toughness, a problem which is particularly pronounced at temperatures below 900 K, limits a wide-range use of these materials. Among various approaches which are currently being pursued in an attempt to enhance ductility and toughness in titanium aluminides, deformationinduced martensitic transformation associated with a fine-scale, metastable dispersed Ti-A1-V [3 phase appears to be the most promising [1]. The same approach, dispersed phase transformation toughening, yielded record ductility and fracture toughness levels in high strength steels and ceramics [2, 3]. The objective of the present work is (a) to develop a thermodynamic analysis of the deformation-induced martensitic transformation and of the associated toughening enhancement in y-titanium aluminide matrix containing a metastable T i - A I - V [3 phase dispersion and (b) to determine optimum stability and the corresponding chemical composition of the [3 phase which ensures maximum transformation-toughening effects.
It is well established [4-6] that thermodynamic stability of the metastable dispersed phase with respect to martensitic transformation is one of the most important factors affecting the dispersed phase transformation toughening of brittle solids. That is, maximum transformation toughening is generally associated with an optimum level of dispersed phase stability. Such stability is typically quite high owing to a high triaxiality of the crack tip stress field, which, through effects of the stress state sensitivity of martensitic transformation, promotes the martensitic transformation at lower effective stress. While the thermodynamic stability of the dispersed phase depends on both its chemical composition and the particle size (and distribution), only the effect of the former will be analyzed in this paper. The effect of particle size, which is associated with the probability of finding a martensile nucleus in the particle, will be analyzed elsewhere [7]. Since the particle size effect is not considered here, the analysis to be developed is strictly valid only for coarser dispersions where this effect is minor. In addition to high stability of the dispersed phase, transformation toughening requires a large positive martensitic transformation volume change. A volume increase accompanying transformation of dispersed particles surrounding a crack reduces the crack tip
0921-5093/92/$5.00
© 1992--Elsevier Sequoia. All rights reserved
M. Grujicic /
76
Transformation toughening of T-Ti-Al
stress intensity factor and hence enhances material toughness. Various analytical studies (e.g. ref. 6) showed that the toughness enhancement is linearly proportional to the magnitude of the transformation volume change. In materials used in high temperature applications, such as y-titanium aluminide, the chemical compositions of the dispersed phase, associated with the desired levels of thermodynamic stability and the transformation volume change, must also ensure chemical compatibility between the dispersed phase and the matrix. This in turn reduces the tendency for deleterious chemical reactions at the interface between the two phases. Since y-titanium aluminide suffers from a loss of ductility and toughness over a wide temperature range (below 900 K), one would ideally need to have a wide range of dispersed phase stabilities. In practice this can be achieved by having a range of particle sizes. In the present analysis, however, only toughness enhancement at room temperature has been considered. A quantitative characterization of the parent phase stability can then be provided by the free-energy change for martensitic transformation at room temperature (RT), AGch(RT) = G~(RT) - G~(RT), where ct is the martensite phase and [3 the parent (dispersed) phase. Figure 1 shows a schematic diagram of free energy vs. temperature for the two phases. At temperature TOthe two phases have the same Gibbs free energies. When To is below room temperature, RT = T1 in Fig. 1, AGch(RT ) is a positive quantity. Conversely, when TOis below room temperature, R T = T2 in Fig. 1, AGCh(RT) is negative.
0~ W Z W
~
Also shown in Fig. 1 is the net driving force required for martensitic nucleation, A G hues, which is the free energy required to surmount the nucleation barrier. By convention this quantity is always positive. To estimate a typical value of A G nucl, experimental To-M S data from ref. 8 have been used. M S is a temperature at which martensitic transformation starts spontaneously on cooling. Using the Thermocalc computer program and the accompanying database [9], the corresponding chemical Gibbs free-energy change in the undercooled [3 phase, A G nucl, was computed. After averaging over a series of alloys, the nucleation driving force has been adopted as 14 000 J mol- 1. AG m¢ch in Fig. 1 represents a mechanical driving force for transformation due to applied stress. Defining 0 as the angle between the martensitic habit plane normal and the axis of the maximum magnitude principal stress ol, and expressing the applied stress in terms of the maximum and minimum principal stresses, the mechanical driving force can be expressed as [2]
AGmech = ½Vm70] (71- (731sin(20)+½Vmeo[(71 + (73 +1(71- (731cos(20)]
(1)
where Vm is the parent phase molar volume and 70 and e0 are the shear and normal components of the (invariant plane) transformation strain respectively. Setting d(A G mech)/d 0 = 0, the "most favorable" habit plane orientation associated with maximum AG mechis given by tan(20)= 70/e0. In the T i - A I - V alloys under consideration here, the magnitude of the shear strain associated with the [3--,(orthorhombic) a"-martensitic transformation is 7o = 0.08 [1]. The normal strain, on the other hand, is a very sensitive function of the chemical composition [1 ]. Expressing the stresses in terms of the von Mises equivalent tensile stress 6,
o1=(72=36,
03=26
(2)
the mechanical driving force contribution 0(AGmCch)/ 06 for the crack tip stress state can be written as ¢h
0(AG mech)
W W n~ U_
cr
", N
M, TZ TO
/ aG'.°"
TI
TEMPERATURE
Fig. 1. Schematic free energy-temperature diagram for ct (martensite) phase and 13 (parent) phase. See text for an explanation of the symbols.
06
-½VmToSin(20)+½Vmeo[5+cos(20)]
(3)
The mechanical driving force A G mech= [0(A Gmech)/ 06] 5 due to a crack tip stress state in the ~/-titanium aluminide matrix can then be obtained by multiplying eqn. (3) by a typical value for the y-Ti-AI yield stress (5 =- 520 MPa). Since the molar volume of the [3 phase, Vm, and the transformation volume change e0 are dependent on the composition of the [3 phase, the mechanical driving force defined above is also dependent on the chemical composition of the 13phase. The chemical driving force AG Chis also a function of the chemical composition and can be readily evaluated
M. Gruficic / Tranfformationtougheningof y-Ti-Al using various solution models and the corresponding lattice stability and interaction parameter data. In the present work a Redlich-Kister-Muggiana (subregular) model [9] was used. According to this model, the Gibbs free energy of mixing for a phase is defined as G m = Z x:'G,+
RT~ x, lnx,+
i
i
given as AGCh(xAI, Xv ) = Gm¢~(XAI, Xv )-- Gmi~(XAI, Xv )
A G nucl = AGCh(XAI, Xv ) + A Gmcch(XAi, Xv)
(4)
i / k
where the summations are taken over j # i, k # i, k ¢ j and i, j, k are the elements (aluminum, titanium, vanadium) given in alphabetical order. °G i represents the standard Gibbs free energy of element i. The twoelement interaction parameters L 8 are defined as the following function of the mole fractions x:
Lij =°Lii + ILo(x i -xj) + 2Ljj(xi-xj) 2 +...
3. Computational procedure and results
(5)
Lattice stability and interaction parameter data assessed and compiled by researchers at the Royal Institute of Technology, Stockholm, Sweden [10] were used as coefficients in the Redlich-Kister-Muggianu polynomial for the chemical driving force A Gchem(XAl, XV ), eqn. (4). Chemical composition dependences of the [3 phase molar volume and the transformation volume change
where °Lo, tL,j, etc. are temperature-dependent coefficients. The three-element interaction parameters Lsjk are temperature dependent and R and T have their usual meanings. For a given alloy composition XAI, Xv, XTi = 1 -- XA~- Xv the chemical free-energy change accompanying martensitic transformation at room temperature is simply
90
I0
\
7O &o x,.
60
(7)
where XA~ and Xv are the mole fractions of aluminum and vanadium in the alloy respectively. Equation (7) defines a series of T i - A I - V alloy compositions which satisfy the requirement regarding the stability of the [3 phase with respect to martensitic transformation in [3 phase particles subject to the crack tip stress state, eqn. (2).
j
+ E ~" E x,xjxkLok
(6)
According to Fig. 1, the following relation holds:
Z 7. x,x/L o i
77
-,/
o "-6"
40 -l
~x-- 50
50 40
60
••///
P
/
20
X
I0
"~70 "80 '90
/ Ti 90
80
70
60
50
40
30
20
I0
WEIGHT % Ti
Fig. 2. Locus of 13 phase chemical compositions associated with an ideal level of [3 phase stability with respect to martensitic transformation (dotted line). Contour lines indicate the magnitude of the [3-¢t" transformation volume change in percentages Ill. The 1073 K ternary Ti-A1-V phase diagram is taken from ref. 12.
78
M. Gruficic /
Transformation toughening of T-Ti-Al
have recently been determined using X-ray diffraction by Narayan [1] and are used here. To determine the locus of alloy compositions defined by eqn. (4), the mole fraction of aluminum in the [3 phase, XAI, was chosen and the resulting nonlinear algebraic equation solved for the mole fraction of vanadium, Xv, using the TK Solver Plus computer program [11]. The value of XAI was next incremented and the procedure repeated. Subsequently the results were expressed in terms of weight percentages. Figure 2 shows a 1073 K isothermal section of the ternary T i - A I - V phase diagram [12]. As discussed earlier, to achieve chemical compatibility between the dispersed [3 phase and the y matrix, the chemical composition of the 13 phase should be in the vicinity of the 13-([3 + y) phase boundary. The results of our calculation (dotted line) are superimposed on the ternary phase diagram in Fig. 2. Also shown in Fig. 2 are the contour lines of the constant transformation volume change determined by Narayan [1]. The results shown in Fig. 2 can be summarized as follows. (1) The locus of the [3 phase compositions possessing the required level of [3 phase stability with respect to martensitic transformation intersects the contour line corresponding to the 4% volume increase. This means that a range of Ti-A1-V [3 phase compositions exists which simultaneously meets the requirements regarding both an optimum level of thermodynamic stability and a large positive value of the transformation volume change. (2) This [3 phase composition range is within 10wt.% of the 13-(13+ y) phase boundary and, in light of a significant experimental scatter observed during determination of this boundary [12], the two phases [3 and 7 are expected to be fairly compatible chemically.
4. Conclusions According to the current understanding of the phenomenon of transformation toughening, the most important factors controlling the extent of toughening in y-titanium aluminide by dispersion of the T i - A I - V [3 phase are (a) thermodynamic stabifity of the [3 phase with respect to martensitic transformation, (b) the [3--, martensite transformation volume change and (c)
chemical compatibility of the two phases which prevents deleterious chemical reactions at the 13-y interface. In general there are no guarantees that in a phase alloy system a chemical composition range exists which meets all the above requirements. Our calculation shows, however, that in the Ti-AI-V system a composition range exists which provides the required level of [3 phase stability and a significant (4%) increase in volume during martensitic transformation. In addition, the composition range is sufficiently close to the [3-([3 + y) phase boundary to reduce the tendency for interfacial reactions.
Acknowledgments This work has been supported by the National Science Foundation, Small Grant Exploratory Research Grant DMR-9017214 and by the Center for Advanced Manufacturing, Clemson University. The author would like to thank Dr. Bruce A. MacDonald of NSF for his encouragement and continuing interest in this work. The author also acknowledges helpful discussions with C. P. Narayan.
References 1 C. P. Narayan, Dispersed-phase transformation toughening of titanium aluminides, M.Sc. Thesis, Clemson University, 1991. 2 G. B. Olson, in Deformation Processing and Structures, ASM, Metals Park, OH, 1983, pp. 391-424. 3 A. G. Evans and A. H. Heuer, J. Am. Ceram. Soc., 63 (1980) 24. 4 M. Grujicic, Mater. Sci. Eng. A, 125 (1990) 453; 127(1990) 975. 5 M. Grujicic and C. P. Narayan, Calphad, 15 (1991) 173. 6 A. G. Evans and R. M. Cannon, Acta Metall., 34 (1986) 761. 7 M. Grujicic,Clemson University,work in progress, 1992. 8 D. L. Moffat and D. C. Larbalestier, Metall. Trans. A, 19 (1985) 153. 9 B. Sundman, B. Jansson and J. O. Andersson, Calphad, 9 (1985) 153. 10 SGTE Database, The Royal Institute of Technology,Stockholm, December 1990. 11 TK Solver Plus Computer Program, Universal Technical Systems, Rockford, IL, 1989. 12 K. Hashimoto, H. Doi and T. Tsujimoto, Trans. Jpn. Inst. Met., 27(1986) 241.
75
Design of Ti-A1-V 13 phase for transformation toughening of "/-titanium aluminide Mica Grujicic
Centerfor Advanced Manufacturing, Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921 (USA) (Received September 13, 1991 )
Abstract A thermodynamic analysis is developed to determine the chemical composition of the T i - A I - V [3 phase for dispersed phase transformation toughening of y-titanium aluminide. The analysis takes into account the fact that maximum transformation toughening is associated with an optimum level of thermodynamic stability of the 13 phase with respect to martensitic transformation and with a large positive value of the 13 phase--, martensite transformation volume change. In addition, to prevent deleterious interracial reactions, the two phases 13 and y are required to be in chemical equilibrium. Available thermodynamic and lattice parameter data are used to determine a range of chemical compositions of the/3 phase which ensures maximum transformation toughening. It is found that this range is sufficiently close to the 13-(13+ y) phase boundary and hence guarantees chemical compatibility between the two phases.
1. Introduction
2. Thermodynamic analysis
A combination of attractive properties such as high specific strength, high specific stiffness, good oxidation resistance, ready availability of titanium and aluminum in the United States, etc. makes titanium aluminides a very important class of materials for aerospace application. However, limited ductility and toughness, a problem which is particularly pronounced at temperatures below 900 K, limits a wide-range use of these materials. Among various approaches which are currently being pursued in an attempt to enhance ductility and toughness in titanium aluminides, deformationinduced martensitic transformation associated with a fine-scale, metastable dispersed Ti-A1-V [3 phase appears to be the most promising [1]. The same approach, dispersed phase transformation toughening, yielded record ductility and fracture toughness levels in high strength steels and ceramics [2, 3]. The objective of the present work is (a) to develop a thermodynamic analysis of the deformation-induced martensitic transformation and of the associated toughening enhancement in y-titanium aluminide matrix containing a metastable T i - A I - V [3 phase dispersion and (b) to determine optimum stability and the corresponding chemical composition of the [3 phase which ensures maximum transformation-toughening effects.
It is well established [4-6] that thermodynamic stability of the metastable dispersed phase with respect to martensitic transformation is one of the most important factors affecting the dispersed phase transformation toughening of brittle solids. That is, maximum transformation toughening is generally associated with an optimum level of dispersed phase stability. Such stability is typically quite high owing to a high triaxiality of the crack tip stress field, which, through effects of the stress state sensitivity of martensitic transformation, promotes the martensitic transformation at lower effective stress. While the thermodynamic stability of the dispersed phase depends on both its chemical composition and the particle size (and distribution), only the effect of the former will be analyzed in this paper. The effect of particle size, which is associated with the probability of finding a martensile nucleus in the particle, will be analyzed elsewhere [7]. Since the particle size effect is not considered here, the analysis to be developed is strictly valid only for coarser dispersions where this effect is minor. In addition to high stability of the dispersed phase, transformation toughening requires a large positive martensitic transformation volume change. A volume increase accompanying transformation of dispersed particles surrounding a crack reduces the crack tip
0921-5093/92/$5.00
© 1992--Elsevier Sequoia. All rights reserved
M. Grujicic /
76
Transformation toughening of T-Ti-Al
stress intensity factor and hence enhances material toughness. Various analytical studies (e.g. ref. 6) showed that the toughness enhancement is linearly proportional to the magnitude of the transformation volume change. In materials used in high temperature applications, such as y-titanium aluminide, the chemical compositions of the dispersed phase, associated with the desired levels of thermodynamic stability and the transformation volume change, must also ensure chemical compatibility between the dispersed phase and the matrix. This in turn reduces the tendency for deleterious chemical reactions at the interface between the two phases. Since y-titanium aluminide suffers from a loss of ductility and toughness over a wide temperature range (below 900 K), one would ideally need to have a wide range of dispersed phase stabilities. In practice this can be achieved by having a range of particle sizes. In the present analysis, however, only toughness enhancement at room temperature has been considered. A quantitative characterization of the parent phase stability can then be provided by the free-energy change for martensitic transformation at room temperature (RT), AGch(RT) = G~(RT) - G~(RT), where ct is the martensite phase and [3 the parent (dispersed) phase. Figure 1 shows a schematic diagram of free energy vs. temperature for the two phases. At temperature TOthe two phases have the same Gibbs free energies. When To is below room temperature, RT = T1 in Fig. 1, AGch(RT ) is a positive quantity. Conversely, when TOis below room temperature, R T = T2 in Fig. 1, AGCh(RT) is negative.
0~ W Z W
~
Also shown in Fig. 1 is the net driving force required for martensitic nucleation, A G hues, which is the free energy required to surmount the nucleation barrier. By convention this quantity is always positive. To estimate a typical value of A G nucl, experimental To-M S data from ref. 8 have been used. M S is a temperature at which martensitic transformation starts spontaneously on cooling. Using the Thermocalc computer program and the accompanying database [9], the corresponding chemical Gibbs free-energy change in the undercooled [3 phase, A G nucl, was computed. After averaging over a series of alloys, the nucleation driving force has been adopted as 14 000 J mol- 1. AG m¢ch in Fig. 1 represents a mechanical driving force for transformation due to applied stress. Defining 0 as the angle between the martensitic habit plane normal and the axis of the maximum magnitude principal stress ol, and expressing the applied stress in terms of the maximum and minimum principal stresses, the mechanical driving force can be expressed as [2]
AGmech = ½Vm70] (71- (731sin(20)+½Vmeo[(71 + (73 +1(71- (731cos(20)]
(1)
where Vm is the parent phase molar volume and 70 and e0 are the shear and normal components of the (invariant plane) transformation strain respectively. Setting d(A G mech)/d 0 = 0, the "most favorable" habit plane orientation associated with maximum AG mechis given by tan(20)= 70/e0. In the T i - A I - V alloys under consideration here, the magnitude of the shear strain associated with the [3--,(orthorhombic) a"-martensitic transformation is 7o = 0.08 [1]. The normal strain, on the other hand, is a very sensitive function of the chemical composition [1 ]. Expressing the stresses in terms of the von Mises equivalent tensile stress 6,
o1=(72=36,
03=26
(2)
the mechanical driving force contribution 0(AGmCch)/ 06 for the crack tip stress state can be written as ¢h
0(AG mech)
W W n~ U_
cr
", N
M, TZ TO
/ aG'.°"
TI
TEMPERATURE
Fig. 1. Schematic free energy-temperature diagram for ct (martensite) phase and 13 (parent) phase. See text for an explanation of the symbols.
06
-½VmToSin(20)+½Vmeo[5+cos(20)]
(3)
The mechanical driving force A G mech= [0(A Gmech)/ 06] 5 due to a crack tip stress state in the ~/-titanium aluminide matrix can then be obtained by multiplying eqn. (3) by a typical value for the y-Ti-AI yield stress (5 =- 520 MPa). Since the molar volume of the [3 phase, Vm, and the transformation volume change e0 are dependent on the composition of the [3 phase, the mechanical driving force defined above is also dependent on the chemical composition of the 13phase. The chemical driving force AG Chis also a function of the chemical composition and can be readily evaluated
M. Gruficic / Tranfformationtougheningof y-Ti-Al using various solution models and the corresponding lattice stability and interaction parameter data. In the present work a Redlich-Kister-Muggiana (subregular) model [9] was used. According to this model, the Gibbs free energy of mixing for a phase is defined as G m = Z x:'G,+
RT~ x, lnx,+
i
i
given as AGCh(xAI, Xv ) = Gm¢~(XAI, Xv )-- Gmi~(XAI, Xv )
A G nucl = AGCh(XAI, Xv ) + A Gmcch(XAi, Xv)
(4)
i / k
where the summations are taken over j # i, k # i, k ¢ j and i, j, k are the elements (aluminum, titanium, vanadium) given in alphabetical order. °G i represents the standard Gibbs free energy of element i. The twoelement interaction parameters L 8 are defined as the following function of the mole fractions x:
Lij =°Lii + ILo(x i -xj) + 2Ljj(xi-xj) 2 +...
3. Computational procedure and results
(5)
Lattice stability and interaction parameter data assessed and compiled by researchers at the Royal Institute of Technology, Stockholm, Sweden [10] were used as coefficients in the Redlich-Kister-Muggianu polynomial for the chemical driving force A Gchem(XAl, XV ), eqn. (4). Chemical composition dependences of the [3 phase molar volume and the transformation volume change
where °Lo, tL,j, etc. are temperature-dependent coefficients. The three-element interaction parameters Lsjk are temperature dependent and R and T have their usual meanings. For a given alloy composition XAI, Xv, XTi = 1 -- XA~- Xv the chemical free-energy change accompanying martensitic transformation at room temperature is simply
90
I0
\
7O &o x,.
60
(7)
where XA~ and Xv are the mole fractions of aluminum and vanadium in the alloy respectively. Equation (7) defines a series of T i - A I - V alloy compositions which satisfy the requirement regarding the stability of the [3 phase with respect to martensitic transformation in [3 phase particles subject to the crack tip stress state, eqn. (2).
j
+ E ~" E x,xjxkLok
(6)
According to Fig. 1, the following relation holds:
Z 7. x,x/L o i
77
-,/
o "-6"
40 -l
~x-- 50
50 40
60
••///
P
/
20
X
I0
"~70 "80 '90
/ Ti 90
80
70
60
50
40
30
20
I0
WEIGHT % Ti
Fig. 2. Locus of 13 phase chemical compositions associated with an ideal level of [3 phase stability with respect to martensitic transformation (dotted line). Contour lines indicate the magnitude of the [3-¢t" transformation volume change in percentages Ill. The 1073 K ternary Ti-A1-V phase diagram is taken from ref. 12.
78
M. Gruficic /
Transformation toughening of T-Ti-Al
have recently been determined using X-ray diffraction by Narayan [1] and are used here. To determine the locus of alloy compositions defined by eqn. (4), the mole fraction of aluminum in the [3 phase, XAI, was chosen and the resulting nonlinear algebraic equation solved for the mole fraction of vanadium, Xv, using the TK Solver Plus computer program [11]. The value of XAI was next incremented and the procedure repeated. Subsequently the results were expressed in terms of weight percentages. Figure 2 shows a 1073 K isothermal section of the ternary T i - A I - V phase diagram [12]. As discussed earlier, to achieve chemical compatibility between the dispersed [3 phase and the y matrix, the chemical composition of the 13 phase should be in the vicinity of the 13-([3 + y) phase boundary. The results of our calculation (dotted line) are superimposed on the ternary phase diagram in Fig. 2. Also shown in Fig. 2 are the contour lines of the constant transformation volume change determined by Narayan [1]. The results shown in Fig. 2 can be summarized as follows. (1) The locus of the [3 phase compositions possessing the required level of [3 phase stability with respect to martensitic transformation intersects the contour line corresponding to the 4% volume increase. This means that a range of Ti-A1-V [3 phase compositions exists which simultaneously meets the requirements regarding both an optimum level of thermodynamic stability and a large positive value of the transformation volume change. (2) This [3 phase composition range is within 10wt.% of the 13-(13+ y) phase boundary and, in light of a significant experimental scatter observed during determination of this boundary [12], the two phases [3 and 7 are expected to be fairly compatible chemically.
4. Conclusions According to the current understanding of the phenomenon of transformation toughening, the most important factors controlling the extent of toughening in y-titanium aluminide by dispersion of the T i - A I - V [3 phase are (a) thermodynamic stabifity of the [3 phase with respect to martensitic transformation, (b) the [3--, martensite transformation volume change and (c)
chemical compatibility of the two phases which prevents deleterious chemical reactions at the 13-y interface. In general there are no guarantees that in a phase alloy system a chemical composition range exists which meets all the above requirements. Our calculation shows, however, that in the Ti-AI-V system a composition range exists which provides the required level of [3 phase stability and a significant (4%) increase in volume during martensitic transformation. In addition, the composition range is sufficiently close to the [3-([3 + y) phase boundary to reduce the tendency for interfacial reactions.
Acknowledgments This work has been supported by the National Science Foundation, Small Grant Exploratory Research Grant DMR-9017214 and by the Center for Advanced Manufacturing, Clemson University. The author would like to thank Dr. Bruce A. MacDonald of NSF for his encouragement and continuing interest in this work. The author also acknowledges helpful discussions with C. P. Narayan.
References 1 C. P. Narayan, Dispersed-phase transformation toughening of titanium aluminides, M.Sc. Thesis, Clemson University, 1991. 2 G. B. Olson, in Deformation Processing and Structures, ASM, Metals Park, OH, 1983, pp. 391-424. 3 A. G. Evans and A. H. Heuer, J. Am. Ceram. Soc., 63 (1980) 24. 4 M. Grujicic, Mater. Sci. Eng. A, 125 (1990) 453; 127(1990) 975. 5 M. Grujicic and C. P. Narayan, Calphad, 15 (1991) 173. 6 A. G. Evans and R. M. Cannon, Acta Metall., 34 (1986) 761. 7 M. Grujicic,Clemson University,work in progress, 1992. 8 D. L. Moffat and D. C. Larbalestier, Metall. Trans. A, 19 (1985) 153. 9 B. Sundman, B. Jansson and J. O. Andersson, Calphad, 9 (1985) 153. 10 SGTE Database, The Royal Institute of Technology,Stockholm, December 1990. 11 TK Solver Plus Computer Program, Universal Technical Systems, Rockford, IL, 1989. 12 K. Hashimoto, H. Doi and T. Tsujimoto, Trans. Jpn. Inst. Met., 27(1986) 241.