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Influence of microstructure on the mechanical properties of heat-treated cast lamellar structure
pp.1581-1587, 1996 Else&r Science Ltd Copyright 0 1996 Acta Metallurgica Inc. Printed in the USA. All rights reserved 1359-6462/96 $12.00 + .OO
Scripta Materialia, Vol. 34, No. 10,
PI1 S1359-6462(96)00021-8
INFLUENCE OF MICROSTRUCTURE ON THE MECHANICAL PROPERTIES OF HEAT-TREATED CAST LAMELLAR STRUCTURE J.Y. Jung and J.K. Park Department of Materials Science and Engineering Korea Advanced Institute of Science and Technology 373-l Kusung-Dong Yosung-Gu, 305-701 Taejon, S. Korea (Received August 2, 1995) (Revised December 1, 1995) Introduction
The lamellar structure of (a + y) two-phase Ti-Al alloys is known as a promising structure because of its good fracture toughness and creep properties, despite its comparatively low ductility at ambient temperature (1). Low ductility of lamellar structure is partly attributed to its relatively coarse grain size, suggesting that the amelioration of its ductility may be achieved by refining its grain sizes (1). Studies on the mechanical properties of PST (polysynthetically twinned) crystals have indicated that the yield stress of lamellar structure strongly depends on the mode of deformation (2). Namely, the yield stress of PST crystals in a hard mode deformation varies with the interlamellar spacing following a Hall-Petch type equation, whereas that in a easy mode deformation varies with the ordered domain size in a y lamellae again following a Hall-Petch type equation. The strengthening effect of ordered domain was small as compared to that of lamellar boundaries. The purpose of the present work was to investigate the effect of lamellar structure on the mechanical properties of cast lamellar structure by controlling, as precisely as possible, its lamellar grain size, lamellar spacing, and ordered domain sizes. The volume fraction effect of a2 phase has been also investigated. It is normally difficult to obtain a small sized grain(i.e., -3OOpm) in a cast lamellar structure since the grain size of as-cast structure is already large (i.e., -6OOpm). To circumvent this difficulty, we have fully coarsened the cast lamellar structure by discontinuous coarsening before solutionizing it in an CCsingle phase field. This has produced a starting grain size of lo-130pm, lamellae of which are fully coarsened. The tensile yield stress has been measured using a miniaturized disk bend test (MDBT) used by Ardell and his coworkers (3). This method has, in particular, an advantage to monitor the yield stress of alloys using a small amount of specimen and to control precisely the gram and lamellar sizes of testing specimens because of its srnall dimension. ExDeriments
All alloys have been prepared in a vacuum arc melting furnace. The designated composition is a target composition, which is actually turned out to be close to a real composition. 1581
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Figure 1. Optical micrographs showing the variation of grain size of a Ti-45%AI alloy at a fixed lamellar spacing held at 1330°C for (a) 20min and (b) 3min before cooling to 1000°C by 30’Cimin.
34, No. 10
: the alloy was
For the purpose of investigating the effect of a2 volume fraction, alloy composition has been varied from 40 to 45at.?/oAl.The cast alloys have been solution-treated in an a single phase field at temperature, 30°C above T, for 0.5hr and cooled to 1000°C by control cooling with 10°C /min. These alloys were tempered for 4hr at 1000°C before air-cooling to room temperature. This treatment has produced the alloys which have various fractions of a2 phase (0.30-0.71) but have a nearly constant grain size (SO&lOOOpm). In order to control the gram size, in particular, to obtain a small grain size, the as-cast Ti-45Al alloy fust has been subject to a heat treatment at 1200°C for 24hr. This induces a discontinuous coarsening and produces fully coarsened lamellar grains having fine grain sizes of 10 to 130um. These specimens were subsequently solutionized in an a single phase field for various times and cooled to 1000°C at controlled cooling rates from 1 to 3OYYminin order to control the lamellar spacing. They were tempered for 4hr at 1000°C before air-cooling to room temperature. We could obtain, in this way, a wide variation of lamellar grain sizes ranging from 1000um down to 300um at a fixed lamellar spacing (Fig. 1). The variation of cooling rates from 1 to 30”C/min resulted in a variation of lamellar spacing from 2.4 to 0.4um. Fig. 2 shows a schematic diagram of the MDBT apparatus, which was originally designed by Ardell and his coworkers (3). It consists of a punch @0.970mm, a guide cylinder 41.007mm and a lower die $3mm. The load is delivered to the disk specimen by punch through a hardened steel ball $0.983 f 0.0025mm. The test was conducted at a crosshead speed at 0.1-0.2mm/min. The signals from the load cell and LVDT were collected by an IBM-PC computer. The data acquisition rate was 14/s. The thickness of specimens tested was mostly ranged from 190-220um.
Figure 2. Schematic
drawing of a cross section of the MDBT apparatus.
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In order to supplement the MDBT results for the effect of az volume fraction, compression test has been performed using bulk samples treated to the same conditions as the thin disc samples for MDBT test. The specimen dimensions were 3 x 3 x 6mm and the test was conducted at crosshead speed of 3 x 1O-4/s.
Results and Discussion Preliminarv
MDBT Test
We have measured using MDBT the yield stress of specimens cut from the grip sections of previously tested tensile specimens. The finite element modeling predicts that yielding in the MDBT occurs at the onset of the deviation from linearity in the initially linear elastic region of the load-displacement curve (4). The yield stress can be calculated from an analytical solution (3), if one measures the radius of the contact area between the ball and disk specimen. In order to measure the contact radius, the same load at the onset of deviation as in the test was applied to a dummy specimen used only for contact radius measurement in the same testing die. The indentation size was then measured by optical microscopy (3). Tested specimens were ductile Cu and Al alloys, brittle Ni,(Al,Fe) and y-TiAl intermetallic compounds, and high strength ferrous alloy. The results are summarized and compared with those of the tensile test in Table 1. The results using MDBT were quite reproducible and are relatively in good agreement with those from the tensile test, except for the Al-Li alloys. Underestimation of yield stress for Al-Li alloys is probably due to a strong anisotropy of tensile properties of sheet form of these alloys. Testing Results
Fig. 3 illustrates how the yield stress, measured by MDBT, of the lamellar structure of Ti-(40-45)Al alloys depends on the volume fraction of a2 phase. The grain sizes of these alloys were more or less fixed to -(800-1000)pm. However the interlamellar spacing greatly varies with the volume fraction of a2 phase, namely with the variation of Al content : it varies from 0.19pm to 0.63pm (Fig. 4) and its minimum appears at 41-42at.%. Despite of a large variation of lamellar spacing, the yield stress of lamellar structure, measured by MDBT, appears to be linearly dependent on the volume fraction of a1 phase, independently of lamellar spacing. This is somewhat unexpected one since one normally expects a significant yield stress increment at fine lamellar spacing in a hard mode deformation. This could be due to a small ratio of specimen thickness to grain size(t/d -0.23) in our MDBT specimens. Most grains are in a weakly constrained condition and the easy mode deformation can predominantly determine the yielding behavior. To confirm this possibility, bulk samples corresponding to the same conditions have been tested in com-
pression. The results, however, again show the independency of 0.2% offset yield stress on the lamellar spacing. This suggests that the yielding behavior in these alloys is actually governed predominantly by the easy mode deformation. This is in agreement with a conclusion drawn from a tension test of forged TABLE 1
Comparison of Yield Stress Measured by MDBT Apparatus Alloy composition 1 No. of 1 t ) r V Sample (~3 G-4 8 233 88.8 0.330 Cu-l.jNi-0.3Si-O.O3P(wt.%) Ti-jOAl(at.%) 10 223 14.9 0.234 Ni-ZOAi-IOFe-O.ZZr(at.%l I 6 1 196 1 75.2 ._ 1 0.399 Al-2. ILi-25Cu-OSMg-O.l3Zr(wt.%) ) 7 1 185 1 68.9 ) 0.330 Fe-19Mn-13Cr-5.AI-0.2C-O.jSi(wt.%) 7 1 211 1 84.1 ) 0.289 -1 * Estimated from cr, = 175.5 + 0.615MPa-&d.‘“(8.9).
with Tensile Yield Stress 1
1 1 I
Grain size 1
hn) 12 252 148 2-15 36
Tensile Y.S (MPa) 151.4 214.2’ 12660-__._ ( 444.6 I 635.0
1 MDBT Y.S (MPa) 150.5~4 217.6tiO , 247.7flj ( 368.3+13 1 619.8526
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Al
content(al.%)
45 44 43 42 4,
0.0
Vol. 34, No. 10
06
40
0.2
04
Volume
fraclion 01 U, phase
06
01 10
Figure 3. Variation of yield stresses measured by MDBT and by compression test and of interlamellar spacing as a function of volume fraction of 0~)phase. Grain size is nearly constant (80~1000)um. The yield stresses of single a2 and y phases are taken from the literatures(8-10).
Figure 4. SEM micrographs illustrating the variation of lamellar spacing at a fixed grain size(-900um): (a) Ti-41%AI ahoy; (b) Ti-45%AI alloy. Both specimens were cooled by 10Wmin.
Ti-46Al-2Cr-2Nb alloy (5): no evidence of hard mode deformation could be found in this investigation even up to near fracture. The variation of yield stress of lamellar structure of a Ti-45Al alloy has been tested as a function of lamellar grain size, ranging from 30&1000um, at three different lamellar spacings. The results (Table 2) show a normal strong dependency of yield stress on lamellar grain size (the variation of cooling rate, thus of lamellar spacing (0.41-2.3um), also affects the yield stress to some extent). These data however underestimate the bulk properties because the t/d ratios in the present MDBT specimens are low, ranging from 0.2 to 0.7. The flow stresses are generally known, due to a loss of constraining force near surface (6,7), to diminish with decreasing specimen thickness when the t/d ratio is less than a critical value. Miyazaki et al. (6) have proposed a simple model to evaluate the variation of flow stress at small t/d ratios less than a critical value. The flow stress at thickness t, normalized by bulk value, is given by o’(t) = ui + FI(t)( 1 - ai), where uI, is the flow stress at t/d - 0, normalized by bulk value. W(t) represents for the average fraction of constraining force in the specimen of thickness t with respect to that in the bulk specimen. H(t) reflects the loss of constraining force, due to the cut-off effect by the top and bottom surfaces, in the case of specimens having small t/d ratios. The variation behavior of R(t) with t/d ratio depends on the number of grains, (R - RJd, contained along the radial direction of deformation affected zone (where % and R radii of the grain and of affected zone respectively), which can be determined by fitting the experimentally measured flow stresses at different t/d ratios for a given grain size. The (R RJd value in general depends on the grain size. The various test results for various materials have however shown that this value tends to saturate to a constant value at grain sizes larger than -1OOpm (6). The u’(t) vs. t/d curve then becomes nearly independent of grain size of specimen in this large grain size regime. We have applied this model to the present MDBT data to evaluate the yield stresses of bulk specimens at different grain sizes. For this purpose, we have first evaluated, as a reference state, the bulk yield stress of 45%Al alloy having grain size of-920pm from the compression test data in Fig. 3: the method was just to use our experimentally measured correlation curve between compression and tensile test data for a 47%Al bulk alloy subjected to various heat treatment conditions. The MDBT data for specimens having
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TABLE 2 Yield Stresses Measured by MDBT and Their Corrected Values Using the Model of Miyazaki et al. (6) at Three Different Latnellar Spacings (Three Different Cooling Rates)
The contact radius(r, pm) was esperimentally determined to vary with the specimen thickness (t, 140-270~x11)by r = -130.6 + 36.43 Pn(t). Poisson’s ratio is estimated from Ref. 11.
the same grain size of 920pm, but having different t/d ratios, have then been normalized with the bulk value and are fitted by the model of Miyazaki et al. by varying the (R - %)/d value. The result is shown in Fig. 5, where (R - RJd = 0.5 (with ub = 0.8)gives rise to the best fit. Once this o’(t) vs. t/d curve determined, one can estimate the bulk yield stress at a different grain size from the yield stress a(t) measured by MDBT at that grain size and from its t/d ratio. Here we have implicitly assumed the independency of o’(t) VI;.t/d curve on the grain size, which is actually appeared to be true for large grain sizes (6) as in the present case. The results are summarized in Table 2 and are plotted in Fig. 6 as a function of the inverse of the square root of lamellar grain size, according to the Hall-Petch equation CI= o, + k,d-I’*. The result again suggests that the yield stress is nearly independent of lamellar spacing. The k, value is -4.62MPaG at
: 500 450 400 350 m 250 200
0
2
4
6
5
10
Thickness/Grain size
Figure 5. Variation of yield stress, normalized by bulk value, as a function of thickness/grain size(t/d) ratio of a Ti_45%Al alloy having a constant grain six of 920pm. The theoretical curves are, using the model of Miyazaki et al.(6), calculated as a timction of number of grain size contained along the radial direction of the deformation affected zone. The figure also shows MDBT data for grain size of 400pm.
I
Lamellar grain size, cTIR(m”“)
Figure 6. Variation of yield stress of a Ti-45%Al lamellar structure as a function of lamellar grain size, according to a HaSPetch equation, at three different cooling rates (thus three different interlamellar spat-ings).
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Figure 8. Optical micrographs illustrating the variation of domain sizes within the r plates in a lamellar grain of Ti-45%AI alloy: (a) cooling rate, 1‘C/min ; (b) cooling rate, I O’Clmin.
Figure 7. Variation of yield stress as a function of the inverse of square root of ordered domain size (d,) and of interlamellar spacing (A).
a moderate to fast furnace cooling rate (1&3O”C/min). This value is unusually high, but is in good agreement with that (-5MPafi) obtained in a tensile test of wrought lamellar structure of Ti-465Al-Xr3Nb-0.3W alloy for grain size ranging from 250~2600pm (1). This is to be compared with that (0.615-l .2 IMPa&) in an a,/y duplex structure (1) and in a single y structure (8,9). This unusually high k, value in lamellar structure has been attributed to a strong anisotropic flow stress behavior of lamellar structure (1). Fig. 6 further indicates that the k, mrther increases to -6.23MPah in an extremely slowly furnace-cooled samples, despite of the increased lamellar spacing by a factor of -6. The reason of this abnormal behavior is not clearly understood. However, we would like to point out, in a closely related matter, two peculiar grain boundary structures of these extremely slowly cooled specimens. The one is that these grain boundaries frequently appear as jagged boundaries, which is believed to be due to the initiation of discontinuous coarsening to some degree during slow cooling. The other is the presence of nearly continuous film of y phase at grain boundaries, which originates from the grain boundary precipitation. The friction stress a0 in the Hall-Petch plot systematically increases with the increase in the cooling rate (Fig. 6), suggesting that the yield stress of a single grain of lamellar structure depends on the cooling rate. The plot of a, vs. L-“2 (Fig. 7) indicates that the slope is -0.05, which is smaller by an order of magnitude than that (0.414.5) in a hard mode deformation of PST crystals (2). The plot of (I, vs. ds-“*, where d, is the ordered domain size (Fig. S), yields a slope (0.17) and intercept (119.4), which are in a reasonable agreement with those (0.27 and 64.0 respectively) obtained in a easy mode deformation of PST crystals (2). This result suggests that the deformation up to the yielding condition mostly occurs through easy mode of deformation. This conclusion is in good agreement with a previous report that the deformation of polycrystalline lamellar structure preferentially occurs in a lamellar grain favorably oriented for easy mode of deformation even up to near fracture (5). Conclusions The yield stress of lamellar structure of Ti-(40-45)Al alloys having a nearly same grain size increases linearly with the volume fraction of a2 phase, despite of a wide variation of az/y lamellar spacing ranging from 0.19 to 0.63um. The yield stress of lamellar structure at a fixed lamellar spacing strongly depends on the grain size, exhibiting a large Hall-Petch slope, -4.62MPaJ;;;. The Hall-Petch slope is nearly independent on the lamellar spacing in a range t?om 0.41 to 2.30pm. This is believed to be due to the fact that the deformation up to the yielding condition in polycrystalline lamellar structure predominantly occurs by easy mode deformation along directions parallel to lamellar boundaries.
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Acknowledvments Authors are grateful to the Agency for Defense Development for their financial support of this research and also grateful to Prof. A.J. Ardell for permitting to duplicate their MDBT apparatus. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
Y-W. Kim, J. h4etals, 46(7), 30 (1994). Y. Umakoshi and T. Nakano, Acta Metall. Mater., 41, 1155 (1993). H. Li, F.C. Chen, and A.J. Ardell, Metall. Trans., 22A, 2601 (1991). M.P. Marx&an, A.E. Browning, A.S. Argon, and O.K. Harling, The Use of Small Scale Specimen for Testing Irradiated Materials, W.F:. Corwin and G.E. Lucas, eds., ASTM STP 888, ASTM, Philadelphia, PA, 17 (1986). G. Malakonaiah, Y-W. Kim, and T. Nicholas, Scripta Metall. Mater., 30,939 (1994). S. Miyazaki, K. Shibata, and H. Fujita, ActaMetall., 27,855 (1975). N. Igata, K. Mi#yahara,T. Uda, and S. Asada, in Ref. 5, 161 (1986). R. Imayev, V. Imayev, and G. Salishichev, Scripta Metall. Mater., 29,719 (1993). S.C. Huang and D.S. Shih, Microstructure/Property Relationships in Titanium Aluminides and Alloys, Y-W. Kim and R.R. Boyer, eds., TMS, Warrendale, PA, 105 (1991). H.A. Lips&, D. Sechtman, and R.E. Schafrik, Metall. Trans., llA, 1369 (1980). R.E. Schafrik, Metall. Trans., 8A, 1003 (1977).
Scripta Materialia, Vol. 34, No. 10,
PI1 S1359-6462(96)00021-8
INFLUENCE OF MICROSTRUCTURE ON THE MECHANICAL PROPERTIES OF HEAT-TREATED CAST LAMELLAR STRUCTURE J.Y. Jung and J.K. Park Department of Materials Science and Engineering Korea Advanced Institute of Science and Technology 373-l Kusung-Dong Yosung-Gu, 305-701 Taejon, S. Korea (Received August 2, 1995) (Revised December 1, 1995) Introduction
The lamellar structure of (a + y) two-phase Ti-Al alloys is known as a promising structure because of its good fracture toughness and creep properties, despite its comparatively low ductility at ambient temperature (1). Low ductility of lamellar structure is partly attributed to its relatively coarse grain size, suggesting that the amelioration of its ductility may be achieved by refining its grain sizes (1). Studies on the mechanical properties of PST (polysynthetically twinned) crystals have indicated that the yield stress of lamellar structure strongly depends on the mode of deformation (2). Namely, the yield stress of PST crystals in a hard mode deformation varies with the interlamellar spacing following a Hall-Petch type equation, whereas that in a easy mode deformation varies with the ordered domain size in a y lamellae again following a Hall-Petch type equation. The strengthening effect of ordered domain was small as compared to that of lamellar boundaries. The purpose of the present work was to investigate the effect of lamellar structure on the mechanical properties of cast lamellar structure by controlling, as precisely as possible, its lamellar grain size, lamellar spacing, and ordered domain sizes. The volume fraction effect of a2 phase has been also investigated. It is normally difficult to obtain a small sized grain(i.e., -3OOpm) in a cast lamellar structure since the grain size of as-cast structure is already large (i.e., -6OOpm). To circumvent this difficulty, we have fully coarsened the cast lamellar structure by discontinuous coarsening before solutionizing it in an CCsingle phase field. This has produced a starting grain size of lo-130pm, lamellae of which are fully coarsened. The tensile yield stress has been measured using a miniaturized disk bend test (MDBT) used by Ardell and his coworkers (3). This method has, in particular, an advantage to monitor the yield stress of alloys using a small amount of specimen and to control precisely the gram and lamellar sizes of testing specimens because of its srnall dimension. ExDeriments
All alloys have been prepared in a vacuum arc melting furnace. The designated composition is a target composition, which is actually turned out to be close to a real composition. 1581
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Figure 1. Optical micrographs showing the variation of grain size of a Ti-45%AI alloy at a fixed lamellar spacing held at 1330°C for (a) 20min and (b) 3min before cooling to 1000°C by 30’Cimin.
34, No. 10
: the alloy was
For the purpose of investigating the effect of a2 volume fraction, alloy composition has been varied from 40 to 45at.?/oAl.The cast alloys have been solution-treated in an a single phase field at temperature, 30°C above T, for 0.5hr and cooled to 1000°C by control cooling with 10°C /min. These alloys were tempered for 4hr at 1000°C before air-cooling to room temperature. This treatment has produced the alloys which have various fractions of a2 phase (0.30-0.71) but have a nearly constant grain size (SO&lOOOpm). In order to control the gram size, in particular, to obtain a small grain size, the as-cast Ti-45Al alloy fust has been subject to a heat treatment at 1200°C for 24hr. This induces a discontinuous coarsening and produces fully coarsened lamellar grains having fine grain sizes of 10 to 130um. These specimens were subsequently solutionized in an a single phase field for various times and cooled to 1000°C at controlled cooling rates from 1 to 3OYYminin order to control the lamellar spacing. They were tempered for 4hr at 1000°C before air-cooling to room temperature. We could obtain, in this way, a wide variation of lamellar grain sizes ranging from 1000um down to 300um at a fixed lamellar spacing (Fig. 1). The variation of cooling rates from 1 to 30”C/min resulted in a variation of lamellar spacing from 2.4 to 0.4um. Fig. 2 shows a schematic diagram of the MDBT apparatus, which was originally designed by Ardell and his coworkers (3). It consists of a punch @0.970mm, a guide cylinder 41.007mm and a lower die $3mm. The load is delivered to the disk specimen by punch through a hardened steel ball $0.983 f 0.0025mm. The test was conducted at a crosshead speed at 0.1-0.2mm/min. The signals from the load cell and LVDT were collected by an IBM-PC computer. The data acquisition rate was 14/s. The thickness of specimens tested was mostly ranged from 190-220um.
Figure 2. Schematic
drawing of a cross section of the MDBT apparatus.
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In order to supplement the MDBT results for the effect of az volume fraction, compression test has been performed using bulk samples treated to the same conditions as the thin disc samples for MDBT test. The specimen dimensions were 3 x 3 x 6mm and the test was conducted at crosshead speed of 3 x 1O-4/s.
Results and Discussion Preliminarv
MDBT Test
We have measured using MDBT the yield stress of specimens cut from the grip sections of previously tested tensile specimens. The finite element modeling predicts that yielding in the MDBT occurs at the onset of the deviation from linearity in the initially linear elastic region of the load-displacement curve (4). The yield stress can be calculated from an analytical solution (3), if one measures the radius of the contact area between the ball and disk specimen. In order to measure the contact radius, the same load at the onset of deviation as in the test was applied to a dummy specimen used only for contact radius measurement in the same testing die. The indentation size was then measured by optical microscopy (3). Tested specimens were ductile Cu and Al alloys, brittle Ni,(Al,Fe) and y-TiAl intermetallic compounds, and high strength ferrous alloy. The results are summarized and compared with those of the tensile test in Table 1. The results using MDBT were quite reproducible and are relatively in good agreement with those from the tensile test, except for the Al-Li alloys. Underestimation of yield stress for Al-Li alloys is probably due to a strong anisotropy of tensile properties of sheet form of these alloys. Testing Results
Fig. 3 illustrates how the yield stress, measured by MDBT, of the lamellar structure of Ti-(40-45)Al alloys depends on the volume fraction of a2 phase. The grain sizes of these alloys were more or less fixed to -(800-1000)pm. However the interlamellar spacing greatly varies with the volume fraction of a2 phase, namely with the variation of Al content : it varies from 0.19pm to 0.63pm (Fig. 4) and its minimum appears at 41-42at.%. Despite of a large variation of lamellar spacing, the yield stress of lamellar structure, measured by MDBT, appears to be linearly dependent on the volume fraction of a1 phase, independently of lamellar spacing. This is somewhat unexpected one since one normally expects a significant yield stress increment at fine lamellar spacing in a hard mode deformation. This could be due to a small ratio of specimen thickness to grain size(t/d -0.23) in our MDBT specimens. Most grains are in a weakly constrained condition and the easy mode deformation can predominantly determine the yielding behavior. To confirm this possibility, bulk samples corresponding to the same conditions have been tested in com-
pression. The results, however, again show the independency of 0.2% offset yield stress on the lamellar spacing. This suggests that the yielding behavior in these alloys is actually governed predominantly by the easy mode deformation. This is in agreement with a conclusion drawn from a tension test of forged TABLE 1
Comparison of Yield Stress Measured by MDBT Apparatus Alloy composition 1 No. of 1 t ) r V Sample (~3 G-4 8 233 88.8 0.330 Cu-l.jNi-0.3Si-O.O3P(wt.%) Ti-jOAl(at.%) 10 223 14.9 0.234 Ni-ZOAi-IOFe-O.ZZr(at.%l I 6 1 196 1 75.2 ._ 1 0.399 Al-2. ILi-25Cu-OSMg-O.l3Zr(wt.%) ) 7 1 185 1 68.9 ) 0.330 Fe-19Mn-13Cr-5.AI-0.2C-O.jSi(wt.%) 7 1 211 1 84.1 ) 0.289 -1 * Estimated from cr, = 175.5 + 0.615MPa-&d.‘“(8.9).
with Tensile Yield Stress 1
1 1 I
Grain size 1
hn) 12 252 148 2-15 36
Tensile Y.S (MPa) 151.4 214.2’ 12660-__._ ( 444.6 I 635.0
1 MDBT Y.S (MPa) 150.5~4 217.6tiO , 247.7flj ( 368.3+13 1 619.8526
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Al
content(al.%)
45 44 43 42 4,
0.0
Vol. 34, No. 10
06
40
0.2
04
Volume
fraclion 01 U, phase
06
01 10
Figure 3. Variation of yield stresses measured by MDBT and by compression test and of interlamellar spacing as a function of volume fraction of 0~)phase. Grain size is nearly constant (80~1000)um. The yield stresses of single a2 and y phases are taken from the literatures(8-10).
Figure 4. SEM micrographs illustrating the variation of lamellar spacing at a fixed grain size(-900um): (a) Ti-41%AI ahoy; (b) Ti-45%AI alloy. Both specimens were cooled by 10Wmin.
Ti-46Al-2Cr-2Nb alloy (5): no evidence of hard mode deformation could be found in this investigation even up to near fracture. The variation of yield stress of lamellar structure of a Ti-45Al alloy has been tested as a function of lamellar grain size, ranging from 30&1000um, at three different lamellar spacings. The results (Table 2) show a normal strong dependency of yield stress on lamellar grain size (the variation of cooling rate, thus of lamellar spacing (0.41-2.3um), also affects the yield stress to some extent). These data however underestimate the bulk properties because the t/d ratios in the present MDBT specimens are low, ranging from 0.2 to 0.7. The flow stresses are generally known, due to a loss of constraining force near surface (6,7), to diminish with decreasing specimen thickness when the t/d ratio is less than a critical value. Miyazaki et al. (6) have proposed a simple model to evaluate the variation of flow stress at small t/d ratios less than a critical value. The flow stress at thickness t, normalized by bulk value, is given by o’(t) = ui + FI(t)( 1 - ai), where uI, is the flow stress at t/d - 0, normalized by bulk value. W(t) represents for the average fraction of constraining force in the specimen of thickness t with respect to that in the bulk specimen. H(t) reflects the loss of constraining force, due to the cut-off effect by the top and bottom surfaces, in the case of specimens having small t/d ratios. The variation behavior of R(t) with t/d ratio depends on the number of grains, (R - RJd, contained along the radial direction of deformation affected zone (where % and R radii of the grain and of affected zone respectively), which can be determined by fitting the experimentally measured flow stresses at different t/d ratios for a given grain size. The (R RJd value in general depends on the grain size. The various test results for various materials have however shown that this value tends to saturate to a constant value at grain sizes larger than -1OOpm (6). The u’(t) vs. t/d curve then becomes nearly independent of grain size of specimen in this large grain size regime. We have applied this model to the present MDBT data to evaluate the yield stresses of bulk specimens at different grain sizes. For this purpose, we have first evaluated, as a reference state, the bulk yield stress of 45%Al alloy having grain size of-920pm from the compression test data in Fig. 3: the method was just to use our experimentally measured correlation curve between compression and tensile test data for a 47%Al bulk alloy subjected to various heat treatment conditions. The MDBT data for specimens having
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TABLE 2 Yield Stresses Measured by MDBT and Their Corrected Values Using the Model of Miyazaki et al. (6) at Three Different Latnellar Spacings (Three Different Cooling Rates)
The contact radius(r, pm) was esperimentally determined to vary with the specimen thickness (t, 140-270~x11)by r = -130.6 + 36.43 Pn(t). Poisson’s ratio is estimated from Ref. 11.
the same grain size of 920pm, but having different t/d ratios, have then been normalized with the bulk value and are fitted by the model of Miyazaki et al. by varying the (R - %)/d value. The result is shown in Fig. 5, where (R - RJd = 0.5 (with ub = 0.8)gives rise to the best fit. Once this o’(t) vs. t/d curve determined, one can estimate the bulk yield stress at a different grain size from the yield stress a(t) measured by MDBT at that grain size and from its t/d ratio. Here we have implicitly assumed the independency of o’(t) VI;.t/d curve on the grain size, which is actually appeared to be true for large grain sizes (6) as in the present case. The results are summarized in Table 2 and are plotted in Fig. 6 as a function of the inverse of the square root of lamellar grain size, according to the Hall-Petch equation CI= o, + k,d-I’*. The result again suggests that the yield stress is nearly independent of lamellar spacing. The k, value is -4.62MPaG at
: 500 450 400 350 m 250 200
0
2
4
6
5
10
Thickness/Grain size
Figure 5. Variation of yield stress, normalized by bulk value, as a function of thickness/grain size(t/d) ratio of a Ti_45%Al alloy having a constant grain six of 920pm. The theoretical curves are, using the model of Miyazaki et al.(6), calculated as a timction of number of grain size contained along the radial direction of the deformation affected zone. The figure also shows MDBT data for grain size of 400pm.
I
Lamellar grain size, cTIR(m”“)
Figure 6. Variation of yield stress of a Ti-45%Al lamellar structure as a function of lamellar grain size, according to a HaSPetch equation, at three different cooling rates (thus three different interlamellar spat-ings).
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Figure 8. Optical micrographs illustrating the variation of domain sizes within the r plates in a lamellar grain of Ti-45%AI alloy: (a) cooling rate, 1‘C/min ; (b) cooling rate, I O’Clmin.
Figure 7. Variation of yield stress as a function of the inverse of square root of ordered domain size (d,) and of interlamellar spacing (A).
a moderate to fast furnace cooling rate (1&3O”C/min). This value is unusually high, but is in good agreement with that (-5MPafi) obtained in a tensile test of wrought lamellar structure of Ti-465Al-Xr3Nb-0.3W alloy for grain size ranging from 250~2600pm (1). This is to be compared with that (0.615-l .2 IMPa&) in an a,/y duplex structure (1) and in a single y structure (8,9). This unusually high k, value in lamellar structure has been attributed to a strong anisotropic flow stress behavior of lamellar structure (1). Fig. 6 further indicates that the k, mrther increases to -6.23MPah in an extremely slowly furnace-cooled samples, despite of the increased lamellar spacing by a factor of -6. The reason of this abnormal behavior is not clearly understood. However, we would like to point out, in a closely related matter, two peculiar grain boundary structures of these extremely slowly cooled specimens. The one is that these grain boundaries frequently appear as jagged boundaries, which is believed to be due to the initiation of discontinuous coarsening to some degree during slow cooling. The other is the presence of nearly continuous film of y phase at grain boundaries, which originates from the grain boundary precipitation. The friction stress a0 in the Hall-Petch plot systematically increases with the increase in the cooling rate (Fig. 6), suggesting that the yield stress of a single grain of lamellar structure depends on the cooling rate. The plot of a, vs. L-“2 (Fig. 7) indicates that the slope is -0.05, which is smaller by an order of magnitude than that (0.414.5) in a hard mode deformation of PST crystals (2). The plot of (I, vs. ds-“*, where d, is the ordered domain size (Fig. S), yields a slope (0.17) and intercept (119.4), which are in a reasonable agreement with those (0.27 and 64.0 respectively) obtained in a easy mode deformation of PST crystals (2). This result suggests that the deformation up to the yielding condition mostly occurs through easy mode of deformation. This conclusion is in good agreement with a previous report that the deformation of polycrystalline lamellar structure preferentially occurs in a lamellar grain favorably oriented for easy mode of deformation even up to near fracture (5). Conclusions The yield stress of lamellar structure of Ti-(40-45)Al alloys having a nearly same grain size increases linearly with the volume fraction of a2 phase, despite of a wide variation of az/y lamellar spacing ranging from 0.19 to 0.63um. The yield stress of lamellar structure at a fixed lamellar spacing strongly depends on the grain size, exhibiting a large Hall-Petch slope, -4.62MPaJ;;;. The Hall-Petch slope is nearly independent on the lamellar spacing in a range t?om 0.41 to 2.30pm. This is believed to be due to the fact that the deformation up to the yielding condition in polycrystalline lamellar structure predominantly occurs by easy mode deformation along directions parallel to lamellar boundaries.
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Acknowledvments Authors are grateful to the Agency for Defense Development for their financial support of this research and also grateful to Prof. A.J. Ardell for permitting to duplicate their MDBT apparatus. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
Y-W. Kim, J. h4etals, 46(7), 30 (1994). Y. Umakoshi and T. Nakano, Acta Metall. Mater., 41, 1155 (1993). H. Li, F.C. Chen, and A.J. Ardell, Metall. Trans., 22A, 2601 (1991). M.P. Marx&an, A.E. Browning, A.S. Argon, and O.K. Harling, The Use of Small Scale Specimen for Testing Irradiated Materials, W.F:. Corwin and G.E. Lucas, eds., ASTM STP 888, ASTM, Philadelphia, PA, 17 (1986). G. Malakonaiah, Y-W. Kim, and T. Nicholas, Scripta Metall. Mater., 30,939 (1994). S. Miyazaki, K. Shibata, and H. Fujita, ActaMetall., 27,855 (1975). N. Igata, K. Mi#yahara,T. Uda, and S. Asada, in Ref. 5, 161 (1986). R. Imayev, V. Imayev, and G. Salishichev, Scripta Metall. Mater., 29,719 (1993). S.C. Huang and D.S. Shih, Microstructure/Property Relationships in Titanium Aluminides and Alloys, Y-W. Kim and R.R. Boyer, eds., TMS, Warrendale, PA, 105 (1991). H.A. Lips&, D. Sechtman, and R.E. Schafrik, Metall. Trans., llA, 1369 (1980). R.E. Schafrik, Metall. Trans., 8A, 1003 (1977).