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Study of the crack tip plastic strain in a nickel-based superalloy
M E T A L L O G R A P H Y 17:139-148 (1984)
139
Study of the Crack Tip Plastic Strain in a Nickel-Based Superalloy
J. S. CROMPTON* AND J. W. MARTIN
Department (ff" Metallurgy and Science (~f Materials, University c~f Oxford, Parks Road. Oxford OXl 3PH, England
Selected area channeling patterns (SACPs) of high quality have been obtained from a single crystal nickel-based superalloy, and the effect of plastic strain upon the patterns has been analyzed. Analysis of the pattern quality enables strains of approximately 1% to be readily detected, thus permitting the mapping of a crack tip plastic zone associated with a fatigue crack. A systematic deterioration in SACP quality with strain has also been demonstrated and the technique applied to the determination of the strain distribution within the plastic zone.
Introduction The mechanisms of fracture which determine the rate at which a crack advances in a metal during either cyclic or static loading occur within a region of plastically deforming material at the crack tip. Many models have been proposed in which the size of this zone and the stresses and strains within it are related to the fracture behavior. Numerous techniques have evolved to investigate the plastic zone, many of them limited in their inherent sensitivity and applicability. Techniques such as the use of a brittle lacquer, strain gauges [1], and photoelectron microscopy [2] may only demonstrate the existence of plastic deformation at a free surface. The plane strain plastic zone has also been extensively investigated, most notably by the use of etching procedures [3, 4], microhardness [5], and recrystallization [6]. Although successful in detecting plasticity, these methods are generally limited to specific materials or are of limited sensitivity. For example, microhardness indentations may be large relative to the plastic zone size and often only detect relatively high levels of strain. * Present address: Department of Metallurgy and Materials Engineering, Lehigh University, Bethlehem, PA 18015, U.S.A. © Elsevier Science Publishing Co., Inc., 1984 52 Vanderbilt Ave., New York, NY 10017
0026-0800/84/$03.00
140
J. S. Crompton and J. W. Martin
The accurate determination of plastic zone sizes is generally limited by two parameters, (1) the minimum detectable level of strain associated with the technique and (2) the area of material with which this strain level is associated. Recent investigations [7, 8] have successfully employed the effect of deformation on channeling patterns produced in the SEM to detect crack tip plasticity. Channeling patterns may be produced from small selected areas (SACPs) by rocking the beam about a point on the specimen surface. Geometrical arrays of bands are then produced due to changes in the electron intensity as the beam rocks over the specimen surface [9]. A departure from lattice perfection within the interaction volume of the beam gives rise to a deterioration in the pattern, thus enabling detection of local strains. Lankford et al. [7] have reported the detection of levels of strain of approximately 0.4%. In the present work we report an extension of the technique allowing the crack tip plastic zones and levels of strain within the plastic zone to be determined. Materials and Methods The material used in this work was single crystal MM002, the composition of which is given in Table 1. The material was heat-treated for I h at I I00°C followed by 16 h at 860°C, giving a microstructure consisting of approximately 60 vol % of 0.5-p~m edge cuboidal 3", and a small volume fraction of spherical 3" of approximately 15-nm radius. Approximately 6 vol % of 3' - 3" eutectic and a number of interdendritic script carbides were also present (Fig. I). The effect of deformation on the SACPs in the present work was determined using a series of specimens deformed in compression along the (100) crystal growth direction. Cylindrical specimens 2.3 mm in diameter and 4.6 mm in height were prepared by spark erosion and centerless grinding. These were then subjected to uniaxial compression to produce samples of known strain. The surfaces of both transverse midheight section and longitudinal {100} section were mechanically ground and electropolished prior to examination by channeling patterns. The conditions for electropolishing are given in Table 2. Channeling patterns were obtained on a JEOL 100C electron microscope with an EM-AS 10-40 scanning attachment operating at 100 kV and with a 100-1xm condenser aperture. The size of the selected area from TABLE 1 Material Composition (wt. %) 10.0Co 8.8Cr 0.15 C 0.012 B
5.5A1 1.4Ti 9.8W 0.07 Zr Balance Ni
2.5Ta
1.5Hf
20pm FIG. I. The microstructure of the material used in this investigation: (a) cuboidal ",/', (b) "y "y' eutectic at A, interdendvilic script carbides a! B.
141
142
J. S. Crompton and J. W. Martin TABLE 2 Electropolishing Conditions 45% Butoxyethanol 45% Acetic Acid 10% Perchloric Acid Temperature -20°C Current Density I A cm -2 Stainless Steel Cathode
which patterns are obtained may be varied by adjusting the rocking angle of the beam. In the present work, rocking angles of _+ 10° and _+5° were used, giving selected area sizes of approximately 15-txm and 3-~m diameter, respectively. SACPs were imaged using a backscattered electron detector and the effect of deformation quantified using a travelling microscope to measure the increase in width of specific lower order lines. To allow the crack tip plastic zone to be studied, fatigue tests were conducted on center cracked tension specimens having faces close to {100}. Crack growth tests were interrupted prior to failure at known values of cyclic stress intensity (AK), and the specimen was rapidly removed from the testing rig to minimize relaxation effects not characteristic of the propagating crack. The crack tip region and surrounding material were cut from the specimen by spark erosion and sectioned to reveal the longitudinal midplane. The area containing the crack tip was then mechanically ground and electropolished. The extent of crack tip plasticity was measured using the digital display of specimen position as a coordinate system for the area adjacent to the crack tip. SACPs characteristic of undeformed material were obtained at a region remote from the crack tip. Examination of patterns closer to the crack tip revealed positions at which the pattern altered to one of a deformed specimen. Initial estimates of these points were made with 0 = _+ 10°; more accurate values were obtained by using 0 = _+5°. Several estimates of these points were made and an accuracy of better than _ 5 p.m obtained for each point. In this manner a representation of the crack tip plastic zone size and shape could be plotted. In addition, SACPs from areas within the plastic zone were recorded at known distances from the crack tip. Detailed measurement of the deterioration of these channeling patterns was made, and comparison with the calibration specimens enabled us to associate known strains with discrete points ahead of the crack tip. Results
EFFECTS OF DEFORMATION ON SACPS The effect of deformation on the SACPs may be seen in Fig. 2. It is apparent that in the undeformed specimen [Fig. 2(a)] high order lines, typically the fourth order of {200}, are visible. As deformation increases,
F16.2. The effect of deformation on {100} selected area channeling pattern, with 0 - + 10c. Differentiated b a c k s c a t t e r e d electron signal. (a) Unstrained material; (b) true strain - 2.9~7~. T h e pattern degradation m a y be appreciated by considering the {800} and {660} lines in Ca) which are absent in the pattern from the deformed specimen. The degradation m a y also be seen in the n u m b e r of b a c k g r o u n d lines which are absent after deformation. 143
J. S. Crompton and J. W. Martin
144
the acuity of the lines diminishes and the higher order lines are lost. From these changes, strains of approximately I% may be accurately detected, so that the plastic zone boundaries reported here represent strictly the elastic 1% plastic interface. The deterioration may be more quantitatively assessed in terms of the angular resolution of specific lines. The measurement of the angular resolution of {200} and {220} lines as a function of strain are presented in Fig. 3. Relatively little scatter is associated with the results, permitting the accurate determination of strain to within -+0.25%.
PLASTIC ZONE EFFECTS The plastic zone associated with a fatigue crack at AK = 23.4 M P a V ~ , R = 0.1, T = 600°C, and v = I Hz is represented in Fig. 4. The plastic zone extends 223 i~m in a direction directly ahead of the crack tip. Perpendicular to the crack propagation direction, plastic zone dimensions of 127 ~m above and 132 ~m below the crack plane were experimentally observed. Several continuum calculations of the monotonic plastic zone size are
10
o
o
c_
6 x
g o (%1
o
• (220}
True Strain , %
FiG. 3. Variationof angular resolution of {200}and {220}SACP lines with specimen strain for MM002 single crystals.
Crack Tip Plastic Strain in Ni Superalloy
999999
145
-o -'-El
--£3
"-El -t3
Fatigue
"CI
Crack
--[3 "H
F~c;. 4. Plastic zone size at 600°C, a s s o c i a l e d with a fatigue crack at ~ K MPaVm, R 0.1, and f r e q u e n c y I Hz.
=
._ .4
available [7] which relate the plastic zone size r v to the applied stress intensity Kmax through equations of the form rp =
~ ( K m a x / O - y ) 2,
(1)
where O-y is the monotonic yield stress and c, is a dimensionless constant. H o w e v e r , such calculations fail to consider the effects of microstructure [10] and testing conditions [11]. In the present material, values of the plastic zone size extrapolated from room temperature measurements [ I I I suggested that a plastic zone size of approximately 170 p.m directly ahead of the crack would be associated with a plastic zone developed at 600°C. Clearly this behavior was not observed, indicating that the plastic zone size at elevated temperatures cannot be expressed by relationships based on simple continuum interpretations of a material deformation behavior [ll]. The variation of plastic strain with the distance directly ahead of the crack tip, dpz, was determined by analyzing the deterioration in the SACPs in terms of the strain (Fig. 3). An example of this deterioration is shown in Fig. 5. The analysis was conducted on SACPs with 0 = --5 °, thus allowing the determination of strain associated with material having a surface diameter of approximately 3 p,m. As the distance d,~ from the crack tip decreases, a degradation in the SACPs is observed. Analysis of the angular resolution of specific lines on the SACPs obtained at known positions within the plastic zone enables the strain at that point to be determined. The resulting distribution of strain within the plastic zone of Fig. 4 may be seen in Fig. 6. The straindistribution within the plastic zone indicates that the strain at the crack tip may be estimated to be 12%-
J. S. Crompton and J. W. Martin
146
dpz= 297Hm
227pm
207pro
1871Jm
147pm
87pm
FIG. 5. SACPs at various distances from the crack tip in the plastic zone developed at 600°C and 1 Hz.
Crack Tip Plastic Strain in Ni Superalloy
147
'f,
E
2:
dp~ Ilnl 0
Fl(;. 6.
510
I
100
i
150
I
200
2150
Variation of strain within the plastic zone directly ahead of the crack tip at 600°C.
13%. In addition, the strain at the plastic zone boundary is approximately 1%, indicating good agreement with the values of strain previously estimated in a qualitative manner.
Conclusions The effect of deformation on the SACPs in the present work is in agreement with that of other workers [12, 13]. Observations of the quality of SACPs from material with a surface diameter of approximately 3 #.m enable strains of approximately 1% to be readily determined. This has allowed the accurate detection of the plastic zone boundary. The SACPs also indicate a quantifiable degradation with increasing strain, in broad agreement with that of other workers [12, 13], although in the present case a considerably lower degree of scatter was associated with the results. This latter observation may in part be due to the higher accelerating voltage and greater system stability used here, but may also be related to the elimination of incompatibility effects associated with the presence of grain boundaries.
148
J. S. Crompton and J. W. Martin
On a theoretical basis the pattern degradation may be more correctly correlated with the dislocation density [13]. However, experimental measurements of dislocation densities are often difficult, and since the sampling volume of the beam is large in comparison to the individual defect size an averaging effect will be observed. The pattern degradation may, therefore, be adequately correlated with the strain and this observation has been applied in the present work, When considering the fracture process, which determines crack advance, the value of these strains may be of more significance than the local dislocation density. The use of single crystal material has enabled the constant orientation SACPs from within the plastic zone to be analyzed in terms of the strain. Therefore, levels of strain may be accurately associated with small volumes of material at discrete points within the plastic zone, allowing for more extensive investigations of the micromechanisms determining crack advance. The authors are grateful to Professor Sir P. B. Hirsch, F.R.S., for the provision of laboratory facilities, and also to the S.E.R.C. and the Procurement Executive of the Ministry of Defence for their support. The authors would also like to thank Major J. A. Blind, Ph.D., U.S.A.F., for many useful discussions. References I. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
S. I. Kwum and M. E. Fine, Scr. Metall. 14:155 (1980). W. J. Baxter and S. R. Rouze, Met. Trans. 7A:647 (1976). G. T. Hahn, R. G. Hoagland, and A. R. Rosenfield, Met. Trans. 3A:1189 (1972). M. Clavel, D. Fournier, and A. Pineau, Met. Trans. 6A:2305, (1975). C. Bathias and R. M. Pelloux, Met. Trans. 4A:1265 (1973). Y. lino, Met. Sci. 10:159 (1976). J. Lankford, D. L. Davidson, and T. S. Cook, A S T M STP 637:36 (1977). J. S. Crompton and J. W. Martin, Metallography 13:225 (1980). D. C. Joy and G. R. Booker, Proe. 5th Annual Stereoscan Colloquium~ 77 (1972). J. A. Blind and J. W. Martin, Mater. Sci. Eng. 57:49, (1983). J. S. Crompton and J. W. Martin, to be published in Mater. Sei. Eng. (1984). R. Stickler, C. W. Hughes, and G. R. Booker, Proc. 4th Annual SEM Symp., I.I.T.R.I., 473 (1971). 13. J. P. Spencer, G. R. Booker, C. J. Humphreys, and D. C. Joy, Proc. 7th SEM Symp., I.I.T.R.I., 919 (1974).
Received September 1983; accepted December 1983.
139
Study of the Crack Tip Plastic Strain in a Nickel-Based Superalloy
J. S. CROMPTON* AND J. W. MARTIN
Department (ff" Metallurgy and Science (~f Materials, University c~f Oxford, Parks Road. Oxford OXl 3PH, England
Selected area channeling patterns (SACPs) of high quality have been obtained from a single crystal nickel-based superalloy, and the effect of plastic strain upon the patterns has been analyzed. Analysis of the pattern quality enables strains of approximately 1% to be readily detected, thus permitting the mapping of a crack tip plastic zone associated with a fatigue crack. A systematic deterioration in SACP quality with strain has also been demonstrated and the technique applied to the determination of the strain distribution within the plastic zone.
Introduction The mechanisms of fracture which determine the rate at which a crack advances in a metal during either cyclic or static loading occur within a region of plastically deforming material at the crack tip. Many models have been proposed in which the size of this zone and the stresses and strains within it are related to the fracture behavior. Numerous techniques have evolved to investigate the plastic zone, many of them limited in their inherent sensitivity and applicability. Techniques such as the use of a brittle lacquer, strain gauges [1], and photoelectron microscopy [2] may only demonstrate the existence of plastic deformation at a free surface. The plane strain plastic zone has also been extensively investigated, most notably by the use of etching procedures [3, 4], microhardness [5], and recrystallization [6]. Although successful in detecting plasticity, these methods are generally limited to specific materials or are of limited sensitivity. For example, microhardness indentations may be large relative to the plastic zone size and often only detect relatively high levels of strain. * Present address: Department of Metallurgy and Materials Engineering, Lehigh University, Bethlehem, PA 18015, U.S.A. © Elsevier Science Publishing Co., Inc., 1984 52 Vanderbilt Ave., New York, NY 10017
0026-0800/84/$03.00
140
J. S. Crompton and J. W. Martin
The accurate determination of plastic zone sizes is generally limited by two parameters, (1) the minimum detectable level of strain associated with the technique and (2) the area of material with which this strain level is associated. Recent investigations [7, 8] have successfully employed the effect of deformation on channeling patterns produced in the SEM to detect crack tip plasticity. Channeling patterns may be produced from small selected areas (SACPs) by rocking the beam about a point on the specimen surface. Geometrical arrays of bands are then produced due to changes in the electron intensity as the beam rocks over the specimen surface [9]. A departure from lattice perfection within the interaction volume of the beam gives rise to a deterioration in the pattern, thus enabling detection of local strains. Lankford et al. [7] have reported the detection of levels of strain of approximately 0.4%. In the present work we report an extension of the technique allowing the crack tip plastic zones and levels of strain within the plastic zone to be determined. Materials and Methods The material used in this work was single crystal MM002, the composition of which is given in Table 1. The material was heat-treated for I h at I I00°C followed by 16 h at 860°C, giving a microstructure consisting of approximately 60 vol % of 0.5-p~m edge cuboidal 3", and a small volume fraction of spherical 3" of approximately 15-nm radius. Approximately 6 vol % of 3' - 3" eutectic and a number of interdendritic script carbides were also present (Fig. I). The effect of deformation on the SACPs in the present work was determined using a series of specimens deformed in compression along the (100) crystal growth direction. Cylindrical specimens 2.3 mm in diameter and 4.6 mm in height were prepared by spark erosion and centerless grinding. These were then subjected to uniaxial compression to produce samples of known strain. The surfaces of both transverse midheight section and longitudinal {100} section were mechanically ground and electropolished prior to examination by channeling patterns. The conditions for electropolishing are given in Table 2. Channeling patterns were obtained on a JEOL 100C electron microscope with an EM-AS 10-40 scanning attachment operating at 100 kV and with a 100-1xm condenser aperture. The size of the selected area from TABLE 1 Material Composition (wt. %) 10.0Co 8.8Cr 0.15 C 0.012 B
5.5A1 1.4Ti 9.8W 0.07 Zr Balance Ni
2.5Ta
1.5Hf
20pm FIG. I. The microstructure of the material used in this investigation: (a) cuboidal ",/', (b) "y "y' eutectic at A, interdendvilic script carbides a! B.
141
142
J. S. Crompton and J. W. Martin TABLE 2 Electropolishing Conditions 45% Butoxyethanol 45% Acetic Acid 10% Perchloric Acid Temperature -20°C Current Density I A cm -2 Stainless Steel Cathode
which patterns are obtained may be varied by adjusting the rocking angle of the beam. In the present work, rocking angles of _+ 10° and _+5° were used, giving selected area sizes of approximately 15-txm and 3-~m diameter, respectively. SACPs were imaged using a backscattered electron detector and the effect of deformation quantified using a travelling microscope to measure the increase in width of specific lower order lines. To allow the crack tip plastic zone to be studied, fatigue tests were conducted on center cracked tension specimens having faces close to {100}. Crack growth tests were interrupted prior to failure at known values of cyclic stress intensity (AK), and the specimen was rapidly removed from the testing rig to minimize relaxation effects not characteristic of the propagating crack. The crack tip region and surrounding material were cut from the specimen by spark erosion and sectioned to reveal the longitudinal midplane. The area containing the crack tip was then mechanically ground and electropolished. The extent of crack tip plasticity was measured using the digital display of specimen position as a coordinate system for the area adjacent to the crack tip. SACPs characteristic of undeformed material were obtained at a region remote from the crack tip. Examination of patterns closer to the crack tip revealed positions at which the pattern altered to one of a deformed specimen. Initial estimates of these points were made with 0 = _+ 10°; more accurate values were obtained by using 0 = _+5°. Several estimates of these points were made and an accuracy of better than _ 5 p.m obtained for each point. In this manner a representation of the crack tip plastic zone size and shape could be plotted. In addition, SACPs from areas within the plastic zone were recorded at known distances from the crack tip. Detailed measurement of the deterioration of these channeling patterns was made, and comparison with the calibration specimens enabled us to associate known strains with discrete points ahead of the crack tip. Results
EFFECTS OF DEFORMATION ON SACPS The effect of deformation on the SACPs may be seen in Fig. 2. It is apparent that in the undeformed specimen [Fig. 2(a)] high order lines, typically the fourth order of {200}, are visible. As deformation increases,
F16.2. The effect of deformation on {100} selected area channeling pattern, with 0 - + 10c. Differentiated b a c k s c a t t e r e d electron signal. (a) Unstrained material; (b) true strain - 2.9~7~. T h e pattern degradation m a y be appreciated by considering the {800} and {660} lines in Ca) which are absent in the pattern from the deformed specimen. The degradation m a y also be seen in the n u m b e r of b a c k g r o u n d lines which are absent after deformation. 143
J. S. Crompton and J. W. Martin
144
the acuity of the lines diminishes and the higher order lines are lost. From these changes, strains of approximately I% may be accurately detected, so that the plastic zone boundaries reported here represent strictly the elastic 1% plastic interface. The deterioration may be more quantitatively assessed in terms of the angular resolution of specific lines. The measurement of the angular resolution of {200} and {220} lines as a function of strain are presented in Fig. 3. Relatively little scatter is associated with the results, permitting the accurate determination of strain to within -+0.25%.
PLASTIC ZONE EFFECTS The plastic zone associated with a fatigue crack at AK = 23.4 M P a V ~ , R = 0.1, T = 600°C, and v = I Hz is represented in Fig. 4. The plastic zone extends 223 i~m in a direction directly ahead of the crack tip. Perpendicular to the crack propagation direction, plastic zone dimensions of 127 ~m above and 132 ~m below the crack plane were experimentally observed. Several continuum calculations of the monotonic plastic zone size are
10
o
o
c_
6 x
g o (%1
o
• (220}
True Strain , %
FiG. 3. Variationof angular resolution of {200}and {220}SACP lines with specimen strain for MM002 single crystals.
Crack Tip Plastic Strain in Ni Superalloy
999999
145
-o -'-El
--£3
"-El -t3
Fatigue
"CI
Crack
--[3 "H
F~c;. 4. Plastic zone size at 600°C, a s s o c i a l e d with a fatigue crack at ~ K MPaVm, R 0.1, and f r e q u e n c y I Hz.
=
._ .4
available [7] which relate the plastic zone size r v to the applied stress intensity Kmax through equations of the form rp =
~ ( K m a x / O - y ) 2,
(1)
where O-y is the monotonic yield stress and c, is a dimensionless constant. H o w e v e r , such calculations fail to consider the effects of microstructure [10] and testing conditions [11]. In the present material, values of the plastic zone size extrapolated from room temperature measurements [ I I I suggested that a plastic zone size of approximately 170 p.m directly ahead of the crack would be associated with a plastic zone developed at 600°C. Clearly this behavior was not observed, indicating that the plastic zone size at elevated temperatures cannot be expressed by relationships based on simple continuum interpretations of a material deformation behavior [ll]. The variation of plastic strain with the distance directly ahead of the crack tip, dpz, was determined by analyzing the deterioration in the SACPs in terms of the strain (Fig. 3). An example of this deterioration is shown in Fig. 5. The analysis was conducted on SACPs with 0 = --5 °, thus allowing the determination of strain associated with material having a surface diameter of approximately 3 p,m. As the distance d,~ from the crack tip decreases, a degradation in the SACPs is observed. Analysis of the angular resolution of specific lines on the SACPs obtained at known positions within the plastic zone enables the strain at that point to be determined. The resulting distribution of strain within the plastic zone of Fig. 4 may be seen in Fig. 6. The straindistribution within the plastic zone indicates that the strain at the crack tip may be estimated to be 12%-
J. S. Crompton and J. W. Martin
146
dpz= 297Hm
227pm
207pro
1871Jm
147pm
87pm
FIG. 5. SACPs at various distances from the crack tip in the plastic zone developed at 600°C and 1 Hz.
Crack Tip Plastic Strain in Ni Superalloy
147
'f,
E
2:
dp~ Ilnl 0
Fl(;. 6.
510
I
100
i
150
I
200
2150
Variation of strain within the plastic zone directly ahead of the crack tip at 600°C.
13%. In addition, the strain at the plastic zone boundary is approximately 1%, indicating good agreement with the values of strain previously estimated in a qualitative manner.
Conclusions The effect of deformation on the SACPs in the present work is in agreement with that of other workers [12, 13]. Observations of the quality of SACPs from material with a surface diameter of approximately 3 #.m enable strains of approximately 1% to be readily determined. This has allowed the accurate detection of the plastic zone boundary. The SACPs also indicate a quantifiable degradation with increasing strain, in broad agreement with that of other workers [12, 13], although in the present case a considerably lower degree of scatter was associated with the results. This latter observation may in part be due to the higher accelerating voltage and greater system stability used here, but may also be related to the elimination of incompatibility effects associated with the presence of grain boundaries.
148
J. S. Crompton and J. W. Martin
On a theoretical basis the pattern degradation may be more correctly correlated with the dislocation density [13]. However, experimental measurements of dislocation densities are often difficult, and since the sampling volume of the beam is large in comparison to the individual defect size an averaging effect will be observed. The pattern degradation may, therefore, be adequately correlated with the strain and this observation has been applied in the present work, When considering the fracture process, which determines crack advance, the value of these strains may be of more significance than the local dislocation density. The use of single crystal material has enabled the constant orientation SACPs from within the plastic zone to be analyzed in terms of the strain. Therefore, levels of strain may be accurately associated with small volumes of material at discrete points within the plastic zone, allowing for more extensive investigations of the micromechanisms determining crack advance. The authors are grateful to Professor Sir P. B. Hirsch, F.R.S., for the provision of laboratory facilities, and also to the S.E.R.C. and the Procurement Executive of the Ministry of Defence for their support. The authors would also like to thank Major J. A. Blind, Ph.D., U.S.A.F., for many useful discussions. References I. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
S. I. Kwum and M. E. Fine, Scr. Metall. 14:155 (1980). W. J. Baxter and S. R. Rouze, Met. Trans. 7A:647 (1976). G. T. Hahn, R. G. Hoagland, and A. R. Rosenfield, Met. Trans. 3A:1189 (1972). M. Clavel, D. Fournier, and A. Pineau, Met. Trans. 6A:2305, (1975). C. Bathias and R. M. Pelloux, Met. Trans. 4A:1265 (1973). Y. lino, Met. Sci. 10:159 (1976). J. Lankford, D. L. Davidson, and T. S. Cook, A S T M STP 637:36 (1977). J. S. Crompton and J. W. Martin, Metallography 13:225 (1980). D. C. Joy and G. R. Booker, Proe. 5th Annual Stereoscan Colloquium~ 77 (1972). J. A. Blind and J. W. Martin, Mater. Sci. Eng. 57:49, (1983). J. S. Crompton and J. W. Martin, to be published in Mater. Sei. Eng. (1984). R. Stickler, C. W. Hughes, and G. R. Booker, Proc. 4th Annual SEM Symp., I.I.T.R.I., 473 (1971). 13. J. P. Spencer, G. R. Booker, C. J. Humphreys, and D. C. Joy, Proc. 7th SEM Symp., I.I.T.R.I., 919 (1974).
Received September 1983; accepted December 1983.