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The dislocation structure of crack tip plastic zones in a cobalt base superalloy
July 1998
Materials Letters 36 Ž1998. 218–222
Short communication
The dislocation structure of crack tip plastic zones in a cobalt base superalloy Z. Lu a
a,)
, Y.B. Xu
a,b
, Z.Q. Hu
a
State Key Laboratory for Fatigue and Fracture of Materials Institute of Metal Research, Chinese Academy of Science, Shenyang 110015, China b Laboratory of Atomic Imaging of Solids, Institute of Metal Research, Chinese Academy of Science, Shenyang 110015, China Received 1 September 1997; revised 19 January 1998; accepted 19 January 1998
Abstract An investigation has been made of the dislocation structure of the plastic zone head of crack tips in a Co-base superalloy during in situ tensile deformation. The results show that the dislocation distribution in the plastic zone depends on both the orientation of the tensile axis and the stress state at the crack tip. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Dislocation structure; Plastic zone; Crack tip; Co-base superalloy; Stress state
1. Introduction The structure of the plastic zone ahead of a crack tip usually depends on the stacking fault energy ŽSFE. of the material. In materials with low SFE, for example, stainless steel w1x and Cu w2x, the plastic zone is narrow and consists of only one array of dislocations which are split into partial dislocations. However, the plastic zones of materials with high SFE ŽAl w3x, Mo w4x, W w4x. are broad and consists of several dislocation arrays, some of which may cross slip out of the original slip plane. Kobayashi and Ohr w5x found that there are two types of dislocation distributions in the plastic zone in nickel with an intermediate SFE value. The dislocations in one type of plastic zone are split into partials, and in the second type, the dislocations are not split, depending on the orientation of the stress axis. )
Corresponding author.
In the present study, the structure of the plastic zone in a Co-base superalloy with very low SFE has been studied using in situ TEM strain technique. It is shown that the dislocations in the plastic zone can be either split or unsplit, depending not only on the orientation of the stress axis but also on the stress state of the crack tip.
2. Experimental Tensile tests were performed in a JOEL 2000FXII transmission electron microscope. The specimens were spark cut from the directionally solidified Cobase superalloy which has a chemical composition of 0.5 C, 11 Ni, 25 Cr, 7.5 W, 0.2 Mo, 0.14 Ta, 0.8 Al, 0.15 Zr, 0.05 B and the balance cobalt. The foils for TEM examination were polished, and thinned in a solution of 90 vol% ethanol and 10 vol% perchloric acid at y308C.
00167-577Xr98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 9 8 . 0 0 0 3 1 - 7
Z. Lu et al.r Materials Letters 36 (1998) 218–222
219
Fig. 1. Partial dislocations emitted from the crack-tip and dislocation extension in plastic zone. Tensile axis w511x.
Fig. 2. Perfect dislocations emitted from the crack-tip first, and then these dislocations extended to partials and stacking faults Ža., enlargement of the crack-tip Žb.. Tensile axis w121x.
220
Z. Lu et al.r Materials Letters 36 (1998) 218–222
3. Results When tensile stress was applied gradually to the specimens, microcracks originated at the edge of the electropolishing hole. Many dislocations were generated at crack tips, forming plastic zones ahead of the cracks. Dislocation emission from the crack tip is discontinuous during loading. Two distinct distributions of dislocations in the plastic zones associated with the cracks were observed, as shown in Figs. 1 and 2. One type of the plastic zone is shown in Fig. 1, where the orientation of tensile axis is w511x. It can be seen that the dislocations emitted from the crack tip were in the form of partial dislocations. The leading partial is emitted first and moves away from the crack tip, forming a stacking fault behind it, as shown in Fig. 1, and then the trailing partial emitted from the crack tip catches up with the leading one quickly, decreasing the width of the stacking fault. From trace analysis, the slip direction of the partials is w101x and the slip plane is identified as Ž111.. The split model of the dislocation in the plastic zone is determined as: 1r2w011x ™ 1r6w112x Žleading. q 1r6w121x Žtrailing.. The direction of dislocation line is w011x, thus the dislocations emitted from the crack tip are screw type. The second type of plastic zone observed is different from the first one, as shown in Fig. 2. The orientation of the tensile axis is w121x. The dislocations emitted from the crack tip are perfect dislocations, slipping along the direction of w011x on a plane Ž111.. The dislocation density is high near the crack tip and decreases gradually away from the crack tip. The dislocations are split into partials with a stacking fault when they move away from the crack tip. The split mode is determined to be 1r2w011x ™ 1r6w112xŽleading. q 1r6w121x Žtrailing.. It is surprising to note that a few dislocations are branched out of the main pile ups in this alloy, which is usually observed in the materials with high SFE only, as shown in Fig. 2b.
4. Discussion The stacking fault energy of Co-base superalloy is reported to be about 0.2–4 ergrm2 w6x. Therefore
dislocations are very easily split into the partials with stacking faults. Copley and Kear w7x pointed out that the shear stress acting on the leading and trailing partials are different and the spacing of pairs depends on the orientation of the applied stress. The Schmid factor for a partial dislocation is given by mŽ b . s
bi < b<
ai n j a j
Ž 1.
where a i 4 , bi 4 , n i 4 are the direction cosines of the tensile axis direction, Burgers vector of partial, and slip plane normal referred to 0014 crystallographic axes. The Schmid factors of the partials in the plastic zone are calculated in term of Eq. Ž1. and given in Table 1. It can be seen that the Schmid factors of the leading partials are all higher than those of trailing partials in two cases, thus the dislocations are split into partials with stacking faults w7x. These results are in agreement with the observation in the present study. Kobayashi and Ohr w5x found that dislocations in some plastic zones are split while the dislocations in other plastic zones are unsplit, depending on the orientation of tensile axis. It can be seen clearly that the dislocation structure of the plastic zone near and far away from the crack tip is sometimes different, as shown in Fig. 2. The reason for this is that the shear stresses acting on the leading and trailing partials change with distance from the crack tip. According to the Peach–Koehler equation w8x, the shear stress t acting on a dislocation with Bergers vector b on a slip plane with normal n can be obtained by the following equation:
tsbPsPn
Ž 2.
where s is the stress tensor. The elastic stress
Table 1 Calculation of Schmid factors Tensile axis w511x
Tensile axis w121x
bp
S ŽSchmid factor.
bp
S ŽSchmid factor.
1r6w112x 1r6w121x
0.85 0.21
1r6w112x 1r6w121x
0.16 0.13
Z. Lu et al.r Materials Letters 36 (1998) 218–222
221
components si j at the crack tip can be described by the following relation w9x:
½
sx X x Xs A cos 2c cos
u
u 3u 1 y sin sin 2 2 2
ž
u ycos c cosh sin
½
syX yXs A cos 2c cos
u
/
u 3u 2 q cos cos 2 2 2
ž
u 3u 1 q sin sin 2 2 2
ž
/5
/
u u 3u qcos c cosh sin cos cos 2 2 2
5
szX zX s n Ž sx X x X q syX yX . u u 3u sx X yXs A cos 2c cos sin cos 2 2 2 u u 3u qcos c cosh cos 1 y sin sin 2 2 2
Fig. 3. The shear stresses distribution on w101x Ž111. slip system around the crack tip. Tensile axis: w511x.
½
ž
/5
u sx X zX s yAcos c cos j sin syX zX s yAcos c cos j cos
2 u
Ž 3.
2
where A s s Ž ar2 r .1r2 , h , c and j refer to the angles between the tensile axis and crack tip coordinate axes X X , Y X and ZX , respectively. The X X and Y X axes of crack tip coordinate system refer to the crack growth direction and the normal of the crack plane. The ZX axes is taken to be normal to X X –Y X plane. According to the definition of the crack tip coordinate system mentioned above, the Ž X X , Y X , ZX .
coordinate system of the crack tip in Fig. 1 is given by: X X s w101x, Y X s w111x and ZX s w121x. The Ž X X , Y X , ZX . coordinate system of the crack in Fig. 2 is given by: X X s w101x, Y X s w121x and ZX s w111x. Using the standard formula for the transformation of coordinate systems, the coordinates of the tensile axis vector, the Bergers vector b of partials and the normal vector n of slip plane in the crack tip coordinate system were calculated and given in column II in Table 2. The shear stress given by Eq. Ž2. can be calculated in terms of Eq. Ž3., and the b and n vectors in Table 2. The results calculated are shown in Figs. 3 and 4 which show the angular dependence
Table 2 The Miler indices of the parameters in Eqs. Ž2. and Ž3. in the 0014 and Ž X X , Y X , ZX . coordinate systems X X X Column I 0014 Column II Ž X , Y , Z . coordinate system coordinate system
Tensile axis n
w511x w111x
b. for leading partial b. for trailing partial Tensile axis n b. for leading partial b. for trailing partial
w112x w121x w121x w111x w112x w121x
w4.24 2.89 0.82x w0 1.73 0x wy2.12 0 1.22x w0 0 2.45x w0 2.45 0x wy1.41 0.82 0.58x w0.71 2.04 y1.15x w1.41 1.63 1.15x
Fig. 4. The shear stresses distribution on w011x Ž111. slip system around the crack tip. Tensile axis: w121x.
Z. Lu et al.r Materials Letters 36 (1998) 218–222
222
of shear stress Žt . on the potentially active slip systems. The shear stress Žt . plotted in Figs. 3 and 4 were normalized by s ar2 r . It can be seen from Fig. 3 that t 1 , the shear stress acting on the leading partial, is higher than t 2 , the shear stress acting on the trailing partial, near the crack tip on the w101x Ž111. slip system. Therefore the leading partial should be preferentially generated w7x. The shear stress on the leading partial is still higher than that on the trailing partial at the region away from the crack tip, as shown in Table 1. The dislocations in the plastic zone can all be split into partials. This is in agreement with the observation as shown in Fig. 1. From Fig. 4, however, one can find that t4 , the shear stress exerting on the trailing partial, is higher than t 3 , the stress on exerting the leading partial, on the w011x Ž111. slip system. In this case, the condition for preferential generation of leading partial is not satisfied w7x. This is because when the crack propagates into the specimen, the stress state in the region around the crack tip changes. This leads to the emission of perfect dislocations from the crack tip, with some of them branching out of the main pile up. Away from the crack tip, the shear stress acting on the leading partial is higher than that acting on the trailing one, as shown in Table 1, hence perfect dislocations are split into partials with stacking faults Žsee Fig. 2..
'
5. Conclusion There are two types of dislocation distributions in the plastic zone in the present low SFE alloy, de-
pending on both the orientation of the tensile axis and the stress state at the crack tip. When the tensile axis is w511x, the dislocations in the plastic zone are all split into partials with a stacking fault. When the tensile axis is w121x, however, the dislocation distribution is changed. Dislocations near the crack tip are perfect, with some of them moving out of the main slip plane, and those which are far away from the crack tip in the plastic zone are split into partials with a stacking fault. This is because the change in shear stress state exerted on the dislocations.
Acknowledgements This research was sponsored by the National Nature Science Foundation of China ŽNo. 59671040..
References w1x w2x w3x w4x w5x w6x
S.M. Ohr, J. Narayan, Philos. Mag. A 42 Ž1980. 81. S. Kobayashi, S.M. Ohr, Scr. Metall. 15 Ž1981. 343. J.A. Horton, S.M. Ohr, Scr. Metall. 16 Ž1982. 621. S. Kobayashi, S.M. Ohr, Philos. Mag. A 42 Ž1980. 763. S. Kobayashi, S.M. Ohr, J. Mater. Sci. 19 Ž1984. 2273. F.R. Moral, L. Habraken, D. Coutsouradis, J.M. Drapier, M. Urbain, Metal Eng. Q. 11 Ž1969. 1. w7x S.M. Copley, B.H. Kear, Acta Metall. 16 Ž1968. 227. w8x M.D. Peach, J.S. Koehler, Phys. Rev. 80 Ž1950. 436. w9x P.C. Paris, G.C. Sih, in: Fracture Toughness Testing and its Application, ASTM STP 381, ASTM, Philadelphia, 1965, p. 30.
Materials Letters 36 Ž1998. 218–222
Short communication
The dislocation structure of crack tip plastic zones in a cobalt base superalloy Z. Lu a
a,)
, Y.B. Xu
a,b
, Z.Q. Hu
a
State Key Laboratory for Fatigue and Fracture of Materials Institute of Metal Research, Chinese Academy of Science, Shenyang 110015, China b Laboratory of Atomic Imaging of Solids, Institute of Metal Research, Chinese Academy of Science, Shenyang 110015, China Received 1 September 1997; revised 19 January 1998; accepted 19 January 1998
Abstract An investigation has been made of the dislocation structure of the plastic zone head of crack tips in a Co-base superalloy during in situ tensile deformation. The results show that the dislocation distribution in the plastic zone depends on both the orientation of the tensile axis and the stress state at the crack tip. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Dislocation structure; Plastic zone; Crack tip; Co-base superalloy; Stress state
1. Introduction The structure of the plastic zone ahead of a crack tip usually depends on the stacking fault energy ŽSFE. of the material. In materials with low SFE, for example, stainless steel w1x and Cu w2x, the plastic zone is narrow and consists of only one array of dislocations which are split into partial dislocations. However, the plastic zones of materials with high SFE ŽAl w3x, Mo w4x, W w4x. are broad and consists of several dislocation arrays, some of which may cross slip out of the original slip plane. Kobayashi and Ohr w5x found that there are two types of dislocation distributions in the plastic zone in nickel with an intermediate SFE value. The dislocations in one type of plastic zone are split into partials, and in the second type, the dislocations are not split, depending on the orientation of the stress axis. )
Corresponding author.
In the present study, the structure of the plastic zone in a Co-base superalloy with very low SFE has been studied using in situ TEM strain technique. It is shown that the dislocations in the plastic zone can be either split or unsplit, depending not only on the orientation of the stress axis but also on the stress state of the crack tip.
2. Experimental Tensile tests were performed in a JOEL 2000FXII transmission electron microscope. The specimens were spark cut from the directionally solidified Cobase superalloy which has a chemical composition of 0.5 C, 11 Ni, 25 Cr, 7.5 W, 0.2 Mo, 0.14 Ta, 0.8 Al, 0.15 Zr, 0.05 B and the balance cobalt. The foils for TEM examination were polished, and thinned in a solution of 90 vol% ethanol and 10 vol% perchloric acid at y308C.
00167-577Xr98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 9 8 . 0 0 0 3 1 - 7
Z. Lu et al.r Materials Letters 36 (1998) 218–222
219
Fig. 1. Partial dislocations emitted from the crack-tip and dislocation extension in plastic zone. Tensile axis w511x.
Fig. 2. Perfect dislocations emitted from the crack-tip first, and then these dislocations extended to partials and stacking faults Ža., enlargement of the crack-tip Žb.. Tensile axis w121x.
220
Z. Lu et al.r Materials Letters 36 (1998) 218–222
3. Results When tensile stress was applied gradually to the specimens, microcracks originated at the edge of the electropolishing hole. Many dislocations were generated at crack tips, forming plastic zones ahead of the cracks. Dislocation emission from the crack tip is discontinuous during loading. Two distinct distributions of dislocations in the plastic zones associated with the cracks were observed, as shown in Figs. 1 and 2. One type of the plastic zone is shown in Fig. 1, where the orientation of tensile axis is w511x. It can be seen that the dislocations emitted from the crack tip were in the form of partial dislocations. The leading partial is emitted first and moves away from the crack tip, forming a stacking fault behind it, as shown in Fig. 1, and then the trailing partial emitted from the crack tip catches up with the leading one quickly, decreasing the width of the stacking fault. From trace analysis, the slip direction of the partials is w101x and the slip plane is identified as Ž111.. The split model of the dislocation in the plastic zone is determined as: 1r2w011x ™ 1r6w112x Žleading. q 1r6w121x Žtrailing.. The direction of dislocation line is w011x, thus the dislocations emitted from the crack tip are screw type. The second type of plastic zone observed is different from the first one, as shown in Fig. 2. The orientation of the tensile axis is w121x. The dislocations emitted from the crack tip are perfect dislocations, slipping along the direction of w011x on a plane Ž111.. The dislocation density is high near the crack tip and decreases gradually away from the crack tip. The dislocations are split into partials with a stacking fault when they move away from the crack tip. The split mode is determined to be 1r2w011x ™ 1r6w112xŽleading. q 1r6w121x Žtrailing.. It is surprising to note that a few dislocations are branched out of the main pile ups in this alloy, which is usually observed in the materials with high SFE only, as shown in Fig. 2b.
4. Discussion The stacking fault energy of Co-base superalloy is reported to be about 0.2–4 ergrm2 w6x. Therefore
dislocations are very easily split into the partials with stacking faults. Copley and Kear w7x pointed out that the shear stress acting on the leading and trailing partials are different and the spacing of pairs depends on the orientation of the applied stress. The Schmid factor for a partial dislocation is given by mŽ b . s
bi < b<
ai n j a j
Ž 1.
where a i 4 , bi 4 , n i 4 are the direction cosines of the tensile axis direction, Burgers vector of partial, and slip plane normal referred to 0014 crystallographic axes. The Schmid factors of the partials in the plastic zone are calculated in term of Eq. Ž1. and given in Table 1. It can be seen that the Schmid factors of the leading partials are all higher than those of trailing partials in two cases, thus the dislocations are split into partials with stacking faults w7x. These results are in agreement with the observation in the present study. Kobayashi and Ohr w5x found that dislocations in some plastic zones are split while the dislocations in other plastic zones are unsplit, depending on the orientation of tensile axis. It can be seen clearly that the dislocation structure of the plastic zone near and far away from the crack tip is sometimes different, as shown in Fig. 2. The reason for this is that the shear stresses acting on the leading and trailing partials change with distance from the crack tip. According to the Peach–Koehler equation w8x, the shear stress t acting on a dislocation with Bergers vector b on a slip plane with normal n can be obtained by the following equation:
tsbPsPn
Ž 2.
where s is the stress tensor. The elastic stress
Table 1 Calculation of Schmid factors Tensile axis w511x
Tensile axis w121x
bp
S ŽSchmid factor.
bp
S ŽSchmid factor.
1r6w112x 1r6w121x
0.85 0.21
1r6w112x 1r6w121x
0.16 0.13
Z. Lu et al.r Materials Letters 36 (1998) 218–222
221
components si j at the crack tip can be described by the following relation w9x:
½
sx X x Xs A cos 2c cos
u
u 3u 1 y sin sin 2 2 2
ž
u ycos c cosh sin
½
syX yXs A cos 2c cos
u
/
u 3u 2 q cos cos 2 2 2
ž
u 3u 1 q sin sin 2 2 2
ž
/5
/
u u 3u qcos c cosh sin cos cos 2 2 2
5
szX zX s n Ž sx X x X q syX yX . u u 3u sx X yXs A cos 2c cos sin cos 2 2 2 u u 3u qcos c cosh cos 1 y sin sin 2 2 2
Fig. 3. The shear stresses distribution on w101x Ž111. slip system around the crack tip. Tensile axis: w511x.
½
ž
/5
u sx X zX s yAcos c cos j sin syX zX s yAcos c cos j cos
2 u
Ž 3.
2
where A s s Ž ar2 r .1r2 , h , c and j refer to the angles between the tensile axis and crack tip coordinate axes X X , Y X and ZX , respectively. The X X and Y X axes of crack tip coordinate system refer to the crack growth direction and the normal of the crack plane. The ZX axes is taken to be normal to X X –Y X plane. According to the definition of the crack tip coordinate system mentioned above, the Ž X X , Y X , ZX .
coordinate system of the crack tip in Fig. 1 is given by: X X s w101x, Y X s w111x and ZX s w121x. The Ž X X , Y X , ZX . coordinate system of the crack in Fig. 2 is given by: X X s w101x, Y X s w121x and ZX s w111x. Using the standard formula for the transformation of coordinate systems, the coordinates of the tensile axis vector, the Bergers vector b of partials and the normal vector n of slip plane in the crack tip coordinate system were calculated and given in column II in Table 2. The shear stress given by Eq. Ž2. can be calculated in terms of Eq. Ž3., and the b and n vectors in Table 2. The results calculated are shown in Figs. 3 and 4 which show the angular dependence
Table 2 The Miler indices of the parameters in Eqs. Ž2. and Ž3. in the 0014 and Ž X X , Y X , ZX . coordinate systems X X X Column I 0014 Column II Ž X , Y , Z . coordinate system coordinate system
Tensile axis n
w511x w111x
b. for leading partial b. for trailing partial Tensile axis n b. for leading partial b. for trailing partial
w112x w121x w121x w111x w112x w121x
w4.24 2.89 0.82x w0 1.73 0x wy2.12 0 1.22x w0 0 2.45x w0 2.45 0x wy1.41 0.82 0.58x w0.71 2.04 y1.15x w1.41 1.63 1.15x
Fig. 4. The shear stresses distribution on w011x Ž111. slip system around the crack tip. Tensile axis: w121x.
Z. Lu et al.r Materials Letters 36 (1998) 218–222
222
of shear stress Žt . on the potentially active slip systems. The shear stress Žt . plotted in Figs. 3 and 4 were normalized by s ar2 r . It can be seen from Fig. 3 that t 1 , the shear stress acting on the leading partial, is higher than t 2 , the shear stress acting on the trailing partial, near the crack tip on the w101x Ž111. slip system. Therefore the leading partial should be preferentially generated w7x. The shear stress on the leading partial is still higher than that on the trailing partial at the region away from the crack tip, as shown in Table 1. The dislocations in the plastic zone can all be split into partials. This is in agreement with the observation as shown in Fig. 1. From Fig. 4, however, one can find that t4 , the shear stress exerting on the trailing partial, is higher than t 3 , the stress on exerting the leading partial, on the w011x Ž111. slip system. In this case, the condition for preferential generation of leading partial is not satisfied w7x. This is because when the crack propagates into the specimen, the stress state in the region around the crack tip changes. This leads to the emission of perfect dislocations from the crack tip, with some of them branching out of the main pile up. Away from the crack tip, the shear stress acting on the leading partial is higher than that acting on the trailing one, as shown in Table 1, hence perfect dislocations are split into partials with stacking faults Žsee Fig. 2..
'
5. Conclusion There are two types of dislocation distributions in the plastic zone in the present low SFE alloy, de-
pending on both the orientation of the tensile axis and the stress state at the crack tip. When the tensile axis is w511x, the dislocations in the plastic zone are all split into partials with a stacking fault. When the tensile axis is w121x, however, the dislocation distribution is changed. Dislocations near the crack tip are perfect, with some of them moving out of the main slip plane, and those which are far away from the crack tip in the plastic zone are split into partials with a stacking fault. This is because the change in shear stress state exerted on the dislocations.
Acknowledgements This research was sponsored by the National Nature Science Foundation of China ŽNo. 59671040..
References w1x w2x w3x w4x w5x w6x
S.M. Ohr, J. Narayan, Philos. Mag. A 42 Ž1980. 81. S. Kobayashi, S.M. Ohr, Scr. Metall. 15 Ž1981. 343. J.A. Horton, S.M. Ohr, Scr. Metall. 16 Ž1982. 621. S. Kobayashi, S.M. Ohr, Philos. Mag. A 42 Ž1980. 763. S. Kobayashi, S.M. Ohr, J. Mater. Sci. 19 Ž1984. 2273. F.R. Moral, L. Habraken, D. Coutsouradis, J.M. Drapier, M. Urbain, Metal Eng. Q. 11 Ž1969. 1. w7x S.M. Copley, B.H. Kear, Acta Metall. 16 Ž1968. 227. w8x M.D. Peach, J.S. Koehler, Phys. Rev. 80 Ž1950. 436. w9x P.C. Paris, G.C. Sih, in: Fracture Toughness Testing and its Application, ASTM STP 381, ASTM, Philadelphia, 1965, p. 30.