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Solubility considerations for threshold stress intensities controlled by hydride fracture
Scripta
METALLURGICA
Vol. iS, pp. 7 0 9 - 7 1 1 , 1981 Printed in t h e U . S . A .
SOLUBILITY
Pergamon P r e s s Ltd. All rights reserved
CONSIDERATIONS FOR THRESHOLD STRESS INTENSITIES CONTROLLED BY HYDRIDE FRACTURE N. R. Moody* and W. W, Gerberich**
*Graduate student, Dept. of Chem. Eng. and Mat. Sci., Univ. of MN, Minneapolis, MN 55455 **Professor, Director of Materials Science, Dept. of Chem. Eng. and Mat. Sci., Univ, of MN, Minneapolis, MN 55455 (Received February 24, 1 9 8 1 )
Many applications of titanium alloys are limited by hydrogen embrittlement. In ~ and ~/B titanium alloys hydrogen embrittlement is due to hydride precipitation. 1,2 When a tensile stress is present, the hydrides are strain-induced forming at hydrogen concentrations considerably less than required for equilibrium precipitation. 1'3 This occurs even at very low initial hydrogen concentrations. Under an externally applied stress, hydrogen migrates to and accumulates in the region of maximum tensile stress, such as in front of a crack. 4'5 To quantitatively characterize the embrittling effects of hydrogen requires determination of the stress intensity necessary for hydride precipitation. A recent approach 6 equated the expression for solubility to that for hydrogen concentration in a stress field. The expression for hydrogen concentration in a stress field, as given by Liu 5, is generally accepted. Hydrogen solubility in hydride formers on the other hand, has not been well defined until recently. Recent works 7-10 provide good quantitative descriptions of hydrogen solubility in hydride forming metals. The descriptions by Dutton 7 and Pardee and Paton 8 differ only slightly from each other. Combining both descriptions results in a complete expression for hydrogen solubility. The stress intensity required for hydride precipitation can be accurately determined using this expression. A Pardee percent sizable
physically accurate description of hydrogen solubility from the works of Dutton 7 and and Paton8will now be discussed. When a hydride forms in a-titanium there is an 18 volume increase which must be accomodated. II,12 This volume increase results in elastic and plastic constraint. 8 This constraint increases solubility as follows
(2)
C s = ~ exp [(-AG ° + Wc)/RT] where ~ is a constant, AG ° is the free energy of formation energy due to constraint. 7
and W c is the total molar strain
An externally applied stress alters the solubility of hydrogen in solution and in the hydride. In solution, hydrogen solubility is increased. This increase is expressed by the term oiiVH/3. 7 An interaction energy also arises from the interaction between the crack tip stress field and the hydride. 7,8 This increases the propensity for hydride precipitation as the stress field does part of the work needed to dilate the lattice. This interaction energy can be expressed as 8
709 0036-9748/81/070709-03502.00/0 Copyright (c) 1 9 8 1 P e r g a m o n Press
Ltd.
710
HYDRIDE
FRACTURE
Vol.
(P ekk - °ij' eij') VH
15,
No.
7
(2)
!
where ei3- = e-.13 - 6"'ekk/313 and ekk are the stress free transformation strains. Pardee and Paton 8 found that the largest effect occurs on the basal plane where the primed term does not contribute. Since observed hydride habit planes generally exhibit a near basal orientation the primed terms can be neglected without significantly changing the result. Plastic work is done during hydride formation by dislocations moving along the basal plane to change the stacking sequence. This work, Wp, can be supplied by the externally applied stress. 8 Combining these effects gives the following equation for the solubility of hydrogen under stress. C s° = ~ exp [(-AG ° + oiiVH/3 + W c - Wp - oiiekkVh/3)/RT ]-
(3)
where Vh is the partial molar volume of the hydride. When strain-induced hydrides precipitate, the hydrogen concentration in the crack tip region equals the solubility limit. The concentration of hydrogen due to an external stress is given by 4 C H = C O exp (oiiVH/3RT)
(4)
Simultaneously solving equations (3) and (4) using mode I elastic stress solutions an equation for the stress intensity at which hydrides form. Kef f = [in s/C o + (-AG ° + W e - Qp)/RT]3(2~r) ½ RT/Vhekk
2(l+v)
gives
(5)
Using appropriate values as described below, the effective stress intensity and then the solubility limit under an external stress can be determined. Thresholds and crack growth rates were studied in Ti-6AI-6V-2Sn containing 38 ppm (wt.) hydrogen. 6 To determine the solubility of hydrogen in this material requires appropriate values. The solubility constant ~ was previously determined to be 2.55 x 104 ppm (wt.), 12 AGO to have a value of 18.6 kJ/mole, 13 poissons ratio equal to 0.32 and ekk equal to 0.24. 8 Since hydrides are precipitated either in the ~ or in an interface phase in the el, 2 Co is the concentration of hydrogen in the ~ phase which is primarily dependent on the aluminum content. Peterson et al. ~ found that this alloy had an ~ phase aluminum content of 9%. Following Boyd's equipartition method 15 the initial hydrogen concentration of the phase was estimated to be 23 ppm (wt.) from data with similar aluminum and 8 phase contents.15,16 The work of accomodation also changes with aluminum content and was estimated to be 7.23 kJ/mole from the data of Paton et al. 13 for Ti-9AI. This work is composed of elastic and plastic terms. The plastic term was estimated to be 2.8 kJ/mole 13 and changed insignificantly over the temperature range of interest, 260 to 320 K. The elastic component should vary as the elastic modulus with temperature. 13 As a result W c ranged from 7.04 kJ/mole at 320 K to 7.42 kJ/mole at 260 K. The plastic work done by dislocations during hydride formation, Wp, was estimated to be 0.67 kJ/mole. 17 The partial molar volu~e of hydrogen in e-titanium, VH, is equal to 1.68 cm3/mole, 16 and Vh is equal to 12.5 cm~/mole. Finally, the value of r was taken as the average grain size, 34 ~m. 6 From these values the effective stress intensities for strain-induced hydride precipitation and hydrogen solubility were determined as a function of temperature. These values are given in Table i. Compared to the effective stress intensities calculated from an earlier model 6 th~se values changed only slightly with the largest deviation occurring near 260 K. The small change did not affect the results or conclusions arrived at from use of the earlier model. The advantage of this new approach to the solubility is that it
Vol.
15,
No.
7
HYDRIDE
FRACTURE
711
provides a quantitative result from a physically accurate model. It will also be used in the analysis of hydrogen-induced crack growth rate data as a function of thickness soon to be completed. Acknowledgment The support of the Air Force Office of Scientific Research through contract AFSOR-78-3133 is gratefully acknowledged. TABLE 1 Calculated Stress Intensities and Solubilities for Ti-6A1-6V-2Sn with 38 ppm (wt.) Hydrogen.
T oK
320 300 280 260
Keff MPa-m½ (ref. 6)
34.6 29.8 24.9 20.1
Kef f MPa-m½ (Eq. 5)
34.7 29.4 23.6 17.7
Cs ppm (wt.) (Eq. 3)
89.1 77.8 65.6 53.8
References I. 2. 3. 4. 5. 6. 7. 8. 9. i0. ii. 12. 13. 14. 15. 16.
17.
N.E. Paton and R.A. Spurling, Met. Trans. A, 7A, 1769 (1976). I.W. Hall and C. Hammond, Metal Sci., 12, 339 (1978). G. Sandoz, in Fundamental Aspects of Stress Corrosion Cracking, ed. by R. Staehle, A.J. Forty and D. Van Rooyen, NACE, Houston, 684 (1969). J.C.M. Li, R.A. Oriani and H.S. Darken, Z. Phys. Chem. Neue Folge, 49, 271 (1966). H.W. Liu, ASME J. Basic Eng., 92, 633 (1970). N.R. Moody and W.W. Gerberich~ Met. Trans. A, IIA, 973 (1980). R. Dutton, Hydrogen in Metals, TMS-CIM Annual Volume, 1 (1978). W.J. Pardee and N.E. Paton, Met. Trans. A, 11A (1980). M.L. Grossbeck and H.K. Birnbaum, Acta. Met., 25, 135 (1977). S. Gahr, M.L. Grossbeck and H.K. Birnbaum, Acta. Met. 25, 125 (1977). N.E. Paton and J.C. Williams, in Effect of Hydrogen on the Behavior of Materials, ed. by A.W. Thompson and I.M. Bernstein, AIME, 409 (1976). N°E. Paton, Annual Technical Report, AFSOR Contract F44620-76-C-0025, Rockwell Science Center, Rockwell International (1977). N.E. Paton, B.S. Hickman and D.H. Leslie, Met. Trans., 2, 2791 (1971). K.P. Peterson, J.C. Schwanebeck and W.W. Gerberich, Met. Trans. A., 9A, 1169 (1978). J.D. Boyd, Trans ASM, 62, 977 (1969). W.W. Gerberich, N.R. Moody, C.L. Jensen, C. Hayman and K. Jatavallabhula, Proc. of the Int. Conf. on the Effects of Hydrogen on the Behavior of Materials, Jackson Lake Lodge, Wyoming, 1980. To be published. N.E. Paton, J.C. Williams and G.P. Rausher, in Titanium Science and Technology, 2, ed. by R.I. Jaffee and H.M. Burte, Plenum Press, New York, 1049 (1973).
METALLURGICA
Vol. iS, pp. 7 0 9 - 7 1 1 , 1981 Printed in t h e U . S . A .
SOLUBILITY
Pergamon P r e s s Ltd. All rights reserved
CONSIDERATIONS FOR THRESHOLD STRESS INTENSITIES CONTROLLED BY HYDRIDE FRACTURE N. R. Moody* and W. W, Gerberich**
*Graduate student, Dept. of Chem. Eng. and Mat. Sci., Univ. of MN, Minneapolis, MN 55455 **Professor, Director of Materials Science, Dept. of Chem. Eng. and Mat. Sci., Univ, of MN, Minneapolis, MN 55455 (Received February 24, 1 9 8 1 )
Many applications of titanium alloys are limited by hydrogen embrittlement. In ~ and ~/B titanium alloys hydrogen embrittlement is due to hydride precipitation. 1,2 When a tensile stress is present, the hydrides are strain-induced forming at hydrogen concentrations considerably less than required for equilibrium precipitation. 1'3 This occurs even at very low initial hydrogen concentrations. Under an externally applied stress, hydrogen migrates to and accumulates in the region of maximum tensile stress, such as in front of a crack. 4'5 To quantitatively characterize the embrittling effects of hydrogen requires determination of the stress intensity necessary for hydride precipitation. A recent approach 6 equated the expression for solubility to that for hydrogen concentration in a stress field. The expression for hydrogen concentration in a stress field, as given by Liu 5, is generally accepted. Hydrogen solubility in hydride formers on the other hand, has not been well defined until recently. Recent works 7-10 provide good quantitative descriptions of hydrogen solubility in hydride forming metals. The descriptions by Dutton 7 and Pardee and Paton 8 differ only slightly from each other. Combining both descriptions results in a complete expression for hydrogen solubility. The stress intensity required for hydride precipitation can be accurately determined using this expression. A Pardee percent sizable
physically accurate description of hydrogen solubility from the works of Dutton 7 and and Paton8will now be discussed. When a hydride forms in a-titanium there is an 18 volume increase which must be accomodated. II,12 This volume increase results in elastic and plastic constraint. 8 This constraint increases solubility as follows
(2)
C s = ~ exp [(-AG ° + Wc)/RT] where ~ is a constant, AG ° is the free energy of formation energy due to constraint. 7
and W c is the total molar strain
An externally applied stress alters the solubility of hydrogen in solution and in the hydride. In solution, hydrogen solubility is increased. This increase is expressed by the term oiiVH/3. 7 An interaction energy also arises from the interaction between the crack tip stress field and the hydride. 7,8 This increases the propensity for hydride precipitation as the stress field does part of the work needed to dilate the lattice. This interaction energy can be expressed as 8
709 0036-9748/81/070709-03502.00/0 Copyright (c) 1 9 8 1 P e r g a m o n Press
Ltd.
710
HYDRIDE
FRACTURE
Vol.
(P ekk - °ij' eij') VH
15,
No.
7
(2)
!
where ei3- = e-.13 - 6"'ekk/313 and ekk are the stress free transformation strains. Pardee and Paton 8 found that the largest effect occurs on the basal plane where the primed term does not contribute. Since observed hydride habit planes generally exhibit a near basal orientation the primed terms can be neglected without significantly changing the result. Plastic work is done during hydride formation by dislocations moving along the basal plane to change the stacking sequence. This work, Wp, can be supplied by the externally applied stress. 8 Combining these effects gives the following equation for the solubility of hydrogen under stress. C s° = ~ exp [(-AG ° + oiiVH/3 + W c - Wp - oiiekkVh/3)/RT ]-
(3)
where Vh is the partial molar volume of the hydride. When strain-induced hydrides precipitate, the hydrogen concentration in the crack tip region equals the solubility limit. The concentration of hydrogen due to an external stress is given by 4 C H = C O exp (oiiVH/3RT)
(4)
Simultaneously solving equations (3) and (4) using mode I elastic stress solutions an equation for the stress intensity at which hydrides form. Kef f = [in s/C o + (-AG ° + W e - Qp)/RT]3(2~r) ½ RT/Vhekk
2(l+v)
gives
(5)
Using appropriate values as described below, the effective stress intensity and then the solubility limit under an external stress can be determined. Thresholds and crack growth rates were studied in Ti-6AI-6V-2Sn containing 38 ppm (wt.) hydrogen. 6 To determine the solubility of hydrogen in this material requires appropriate values. The solubility constant ~ was previously determined to be 2.55 x 104 ppm (wt.), 12 AGO to have a value of 18.6 kJ/mole, 13 poissons ratio equal to 0.32 and ekk equal to 0.24. 8 Since hydrides are precipitated either in the ~ or in an interface phase in the el, 2 Co is the concentration of hydrogen in the ~ phase which is primarily dependent on the aluminum content. Peterson et al. ~ found that this alloy had an ~ phase aluminum content of 9%. Following Boyd's equipartition method 15 the initial hydrogen concentration of the phase was estimated to be 23 ppm (wt.) from data with similar aluminum and 8 phase contents.15,16 The work of accomodation also changes with aluminum content and was estimated to be 7.23 kJ/mole from the data of Paton et al. 13 for Ti-9AI. This work is composed of elastic and plastic terms. The plastic term was estimated to be 2.8 kJ/mole 13 and changed insignificantly over the temperature range of interest, 260 to 320 K. The elastic component should vary as the elastic modulus with temperature. 13 As a result W c ranged from 7.04 kJ/mole at 320 K to 7.42 kJ/mole at 260 K. The plastic work done by dislocations during hydride formation, Wp, was estimated to be 0.67 kJ/mole. 17 The partial molar volu~e of hydrogen in e-titanium, VH, is equal to 1.68 cm3/mole, 16 and Vh is equal to 12.5 cm~/mole. Finally, the value of r was taken as the average grain size, 34 ~m. 6 From these values the effective stress intensities for strain-induced hydride precipitation and hydrogen solubility were determined as a function of temperature. These values are given in Table i. Compared to the effective stress intensities calculated from an earlier model 6 th~se values changed only slightly with the largest deviation occurring near 260 K. The small change did not affect the results or conclusions arrived at from use of the earlier model. The advantage of this new approach to the solubility is that it
Vol.
15,
No.
7
HYDRIDE
FRACTURE
711
provides a quantitative result from a physically accurate model. It will also be used in the analysis of hydrogen-induced crack growth rate data as a function of thickness soon to be completed. Acknowledgment The support of the Air Force Office of Scientific Research through contract AFSOR-78-3133 is gratefully acknowledged. TABLE 1 Calculated Stress Intensities and Solubilities for Ti-6A1-6V-2Sn with 38 ppm (wt.) Hydrogen.
T oK
320 300 280 260
Keff MPa-m½ (ref. 6)
34.6 29.8 24.9 20.1
Kef f MPa-m½ (Eq. 5)
34.7 29.4 23.6 17.7
Cs ppm (wt.) (Eq. 3)
89.1 77.8 65.6 53.8
References I. 2. 3. 4. 5. 6. 7. 8. 9. i0. ii. 12. 13. 14. 15. 16.
17.
N.E. Paton and R.A. Spurling, Met. Trans. A, 7A, 1769 (1976). I.W. Hall and C. Hammond, Metal Sci., 12, 339 (1978). G. Sandoz, in Fundamental Aspects of Stress Corrosion Cracking, ed. by R. Staehle, A.J. Forty and D. Van Rooyen, NACE, Houston, 684 (1969). J.C.M. Li, R.A. Oriani and H.S. Darken, Z. Phys. Chem. Neue Folge, 49, 271 (1966). H.W. Liu, ASME J. Basic Eng., 92, 633 (1970). N.R. Moody and W.W. Gerberich~ Met. Trans. A, IIA, 973 (1980). R. Dutton, Hydrogen in Metals, TMS-CIM Annual Volume, 1 (1978). W.J. Pardee and N.E. Paton, Met. Trans. A, 11A (1980). M.L. Grossbeck and H.K. Birnbaum, Acta. Met., 25, 135 (1977). S. Gahr, M.L. Grossbeck and H.K. Birnbaum, Acta. Met. 25, 125 (1977). N.E. Paton and J.C. Williams, in Effect of Hydrogen on the Behavior of Materials, ed. by A.W. Thompson and I.M. Bernstein, AIME, 409 (1976). N°E. Paton, Annual Technical Report, AFSOR Contract F44620-76-C-0025, Rockwell Science Center, Rockwell International (1977). N.E. Paton, B.S. Hickman and D.H. Leslie, Met. Trans., 2, 2791 (1971). K.P. Peterson, J.C. Schwanebeck and W.W. Gerberich, Met. Trans. A., 9A, 1169 (1978). J.D. Boyd, Trans ASM, 62, 977 (1969). W.W. Gerberich, N.R. Moody, C.L. Jensen, C. Hayman and K. Jatavallabhula, Proc. of the Int. Conf. on the Effects of Hydrogen on the Behavior of Materials, Jackson Lake Lodge, Wyoming, 1980. To be published. N.E. Paton, J.C. Williams and G.P. Rausher, in Titanium Science and Technology, 2, ed. by R.I. Jaffee and H.M. Burte, Plenum Press, New York, 1049 (1973).