THE EFFECTS OF GRAIN SIZE REFINEMENT ON THE

MECHANICAL PRO?ERTIES OF UNALLOYED TITANIUM

Robin L. Jones* Senior Research Metallurgist

Franklin Institute Research Laboratories Philadelphia, Pa.

Introduction

In the course of an extensive study of the interrelated effects of thermomechanical processing history, impurity content and sub­stitutional alloying on the mechanical properties of a-titanium (1-4), the grain size dependence of the uniaxial tensile behavior and toughness of unalloyed titanium sheet has been investiga.ted. Wire test samples, made by recrystallization of heavily cold swaged material, were used exclusively in our previous investigations of the low ·temperature deformation mechanism (5-8) and of the origin of the grain size dependence of the strength (8,9) of unalloyed titanium. The question then arises as to the extent to which the observations reported and the conclusions drawn from them were influenced by the crystallographic texture of the wire samples. One objective of the present work was to determine whether or not unalloyed titanium sheet behaved in a similar manner to that reported previously for wire (5-9). The second objective of the program was to investigate, using a modified Kahn-type tear test (10), the effect of grain refinement on the room temperature toughness of the sheet material, since the increase of strength which results from grain refinement is of little utility if it is accompanied by a substantial toughness decrease.

Sample Fabrication and Testing Procedures

The material used in this program was obtained from General Aerospace Materials Corp. in the form of a billet. The billet conforms to ASTM Spec. #B265-58T Grade 3, and the as-received chem­ical analysis is given in Table I. The billet was received in the

*Now associated with the Stanford Research Institute, Menlo Park, Cal.

1033

1034 R. L. JONES

mill annealed condition.

TABLE I: Chemical Analysis of Grade 3 Titanium

0 c N H Fe Ti 0.12 0.02 0.005 <0.01 0.11 Balance

Sheet material with a thickness of 0.06 in. was prepared by unidirectional cold rolling without intermediate annealing of 0.6 in. thick slabs cut from the billet. This rather drastic reduction, which caused considerable amounts of edge cracking, was used so as to permit the attainment of the widest possible range of recrystal­lized grain sizes. Test samples were machined from the as-rolled sheet. Recrystallized samples with grain sizes in the range 0.5-20 microns were prepared by isothermal annealing in the range 823°K -973°K. Grain sizes less than about 2 microns were produced by short annealing treatments in a molten lead bath, while the longer anneals required for coarser grain sizes were performed in a dynamic vacuum of ~ 5 x l0-6 torr. Test samples were surface ground following annealing to a 600 grit final finish, the grinding direction being parallel to the tensile axis of the sample.

Grain sizes were equated to the mean distance between intercepts with grain boundaries on a linear traverse. Three different quanti­tative metallographic techniques were employed which are described elsewhere (4). The three techniques were found to give mutually consistent estimates of grain size to an accuracy of about + 5%. Grain shapes were essentially equiaxed and the grain sizes were quite uniform with no marked tendency for any systematic through­thickness grain size variation.

Quantitative pole figures were generated for selected repre­sentative samples using a semi-automated, modified Schultz technique. The textures observed were similar to those reported in the litera­ture (11-13) for the cold rolled and intermediate annealed state and no systematic variation with grain size was observed. A typical example of the characteristic anisotropic basal texture is shown in Fig. 1. Williams and Eppelsheimer (14) have shown that the aniso­tropy can be explained by supposing that slip occurs during rolling on basal, prism and pyramidal systems in addition to operation of compression twinning modes. The operation of all of the three major slip systems appears reasonable since Churchman (15) has shown that the critical resolved shear stresses differ by only ~ 15% at room temperature in commercially pure titanium.

Tensile tests were performed using an Instron machine at a nominal strain rate of 3.3 x l0-4sec-l. Change-of-strain rate information was generated bl instantaneous changes of nominal strain rate between 3.3 x lo-4sec- and 3.3 x l0-5sec-l. Load sensitivity was improved to about 0.1% of the applied load using a zero sup-

GRAIN SIZE REFINEMENT AND MECHANICAL PROPERTIES OF UNALLOYED Ti 1035

suppression device and plastic elongations were obtained as devia­tions from the extrapolated 'elastic' loading line on the load­displacement chart. Test temperatures below ambient were obtained by immersion in liquid coolants while elevated temperature tests were performed in air.

Samples were prepared for tear testing by machining a 5/16 inch deep 60° edge notch in one long side of a 1.5 x 0.8 inch blank. For most samples the root radius of the notch was sharpened to about 0.0005 in. by drawing a razor blade across it. A few samples were tested with as-machined notches (radius ~ .005 in.) to assess the effect of notch sharpness. The samples were pin-loaded in the Instron at a nominal strain rate of 1.1 x l0-3sec-l. The line joining the centers of the loading pins was within 0.0005 in. of the tip of the starting notch and the behavior of the sample during tear failure was followed by a conventional load-deflection chart recorder.

Experimental Results - Tensile Tests

General Features

Unlike the behavior observed previously for fine grain size wire samples of commercial purity titanium (1,9), the present sheet samples showed no evidence of discontinuous yielding at any test temperature, the transition from elastic to plastic behavior being accomplished smoothly without yield drops or yield plateaux. As observed in wire experiments (1,7,8,9), the relation between true stress o and true strain E in the uniform flow portion of the stress strain curve obeyed the relation

o = o(O) + hEl/ 2 . . .1

The hardening coefficient, h, typically showed values of ~ 70 ksi at room temperature and depended slightly, if at all, on grain size. The temperature dependence of h was similar to that observed pre­viously for commercial purity wire samples (7). The values of the intercept stress o(O) were generally in the vicinity of the observed proportional limits. Scanning electron fractography indicated that fracture was entirely ductile in nature at all testing temperatures and for all grain sizes (3).

Effects of Grain Size at Room Temperature

Selected tensile data obtained in room temperature tests are tabulated in Table II to illustrate the effects of grain refinement. All the data in Table II were obtained using longitudinal samples (tensile axis parallel to the rolling direction). The yield stresses tabulated are 0.2% plastic offset flow stresses and the UTS values are true stresses. It is evident in Table II that grain refinement leads to an increase in yield stress, a smaller increase in UTS, a

1036 R. L. JONES

R.O

Fig. 1. Typical basal texture for unidirectionally cold rolled and recrystallized Grade 3 titanium sheet.

100

90

- BO en "' en en

"' ~ 70 en 0 -'

"' ;:: 60

50

ROOM TEMPERATURE TESTS

40L_~~-'-~~-'--~~-'-~~--'~~~L-~~~~~~~~-'-~~---'-~~~

0 10 15 20 25 30 35 40 45 50

GRAIN SIZE -1/2 I mm - 112 )

Fig. 2. Effect of grain size on the 0.2% offset proof stress for Grade 3 titanium sheet. Tests at room temperature at a strain rate of 3.3 x 1Q-4sec-l.

GRAIN SIZE REFINEMENT AND MECHANICAL PROPERTIES OF UNALLOYED Ti 1037

slight increase in reduction in area, a systematic decrease in uniform elongation and little effect on total elongation. The com­plete data for the yield stress are plotted against the inverse square root of the grain size in Fig. 2 and show excellent support for a linear relationship.

TABLE II. Effect of Grain Size on the Room Temperature Tensile Behavior of Grade 3 Titanitun Sheet

Grain Size Yield UTS Uniform Total( Reduction Elongation Elongation of Area

(Microns) (ksi) (ksi) (%) (%) (%) 20 55 89 18 27 50 5.0 62 95 17 30 52 1.2 78 107 16 26 53 0.5 96 118 10 25 57

Effect of Test TemEerature and Strain Rate

The effect of test temperature on the tensile properties was established for samples with 2 grain sizes, 0.5 micron and 5 microns. The data obtained are summarized in Table III and values of the yield stress are plotted against temperature in Fig. 3. Below about 500°K t.he increase in yield stress due to grain refinement is seen to be athermal in nature i.e. the strength increase is .temperature independent. Above 573°K the curves converge and metallographic examination indicated that some grain growth occurred in the 0.5 micron grain size samples during the tests. Total elongations and

TABLE III: Effect of Temperature on the Tensile Behavior of Grade 3 Titanium Sheet

Grain Size Test Temp. Y. Stress UTS Uniform Total (ksi) Elong. Elong.

(Microns) (oK) (ksi) (ksi) (%) (%) 0.5 77. 182 192 2 18

200 123 147 5 22 300 96 118 10 25 373 89 107 6 28 473 71 85 5 28 573 65 72 3.5 27 673 45 55 2.5 36

5.0 77 146 163 6 23 200 90 115 10 24 300 62 95 17 30 373 50 74 16 28 473 38 54 10 27 573 33 42 6 27 673 30 38 3 38

R.A.

(%) 49 55 57 53 55 65

>90

42 45 52 53 52 69

>90

1038 R. L. JONES

reductions in area show a general tendency to increase with increasing test temperature, with the most marked increase occurring at the highest testing temperatures, while the uniform elongations tend to peak at around ambient temperature.

In addition to constant strain rate tests, one sample at each grain size was subjected to change-of-strain rate tests at each test temperature. Values for the change in flow stress resulting from order of magnitude changes in strain rate, which were found to be independent of grain size and strain, increased with test temperature up to 373°K, decreased rapidly at higher test temperatures and reached small values at test temperatures ::._ 573°K.

Experimental Results - Tear Tests

General Features

Longitudinal samples of Grade 3 titanium covering the entire grain size range were tear tested at room temperature. Samples of 2024 aluminum alloy (in the T3 condition) and Ti-6Al-4V (in both the annealed and the solution treated and aged (STA) conditions) were tested to provide comparative data. With the exception of Ti-6Al-4V samples in the STA condition, qualitatively similar load-deflection curves were obtained, typified by the example shown in Fig. 4. The area under the rising portion of the curve is considered to be associ ated with the energy required for tear initiation while the area uncle the falling part of the curve is taken to represent the energy re­quired to propagate the crack (16). Also defined on Fig. 4 are the two most useful parameters which can be obtained from this test -the tear strength (maximum nominal combined tensile and bending stres and the unit propagation energy (UPE). Values of these parameters were calculated for all samples tested, the areas under the load­deflection curves being measured directly with the aid of a plani­meter. Samples of Ti-6Al-4V in the STA condition behaved in a rather different manner, in that propagation occurred catastrophically following a similar initiation curve. For these samples an upper limit estimate of the value of the UPE was made by measuring the elastic energy stored in the loading rig at the maximum load, Pmax• In all cases the tear propagation direction was normal to the loading axis. The root radius of the starting notch was not found to have any effect on the tear properties observed for Grade 3 titanium, probably because extensive plastic deformation in the notch root region occurs prior to the initiation of the tear failure.

The Tear Strength and Unit Propagation Energy

Fig. 5 shows the tear strength data plotted as a function of yield stress. The tear strength is linearly related to yield stress for the unalloyed titanium samples. The tear strength for annealed Ti-6Al-4V lies close to the line defined by the Grade 3 data while the data points for 2024-T3 aluminum and Ti-6Al-4V STA lie far below

GRAIN SIZE REFINEMENT AND MECHANICAL PROPERTIES OF UNALLOYED Ti

180

•60

140

~ 120

"' "' .., ~ 100

0

~ 80 ;::

60

40

20

\

\.O\. 0 0.5 MICRON GRAIN SIZE

"' ~ • 5.0 MICRON GRAIN SIZE

~~o . ~ ~- 0--0

"-· ~ ---- o, ·-­·-·-

TEST TEMPERATURE (°K)

1039

Fig. 3. Effect of temperature on the 0.2% offset proof stress for Grade 3 titanium sheet samtles of two grain sizes •. Nominal strain rate 3.3 x lo-4sec- •

0

" g

t---~~---MAXIMUM LOAD

PMAX

r TEAR STRENGTH"'

4PwAX {PSI) bl

UNIT PROPAGATION ENERGY-= tr- (IN-LB/SC IN)

FINAL FRACTURE-

INITIATION {AREA UNDER CURVE~ PROPAGATION E~NE;-;;R~GY;;A ,)-------------DEFLECTION (IN 1--

Fig. 4. Typical load-deflection curve observed in modified Kahn­type tearing tests. The rising portion preceding final fracture was observed for all Grade 3 titanium samples and indicates that final fracture is tensile rather than tear­ing in nature.

1040

220

200

180 v; " ~ 160 Cl z "' 0:: ~ 140

a: <I

"' .... 120

100

80

TEAR UPE STRENGTH

0 • t:. " "'

,. 0 •

t

MATERIAL

GRADE 3 Ti

2024-T3 Al

Ti -6AI -4V (ANNEALED I

Ti - 6 Al-4V (STA l

R. L. JONES

0

T

3200

2800~ 0 11'1

' m 2400-;'

~

,_ 2000~

"' z "'

1600 i5 ~ ~

1200 0 0:: 0..

.... 800 ~

400

60'--~---'~~-'-~~--'-~~-'-~~'--~---'~~-'-~~--'-~~-'-~~'--~---'~~~o

40 50 60 70 80 90 100 110 120 130 140 150 160 YIELD STRESS ( KSI l

Fig. S. Variation of tear strength and unit propagation energy with yield stress for three materials tear tested at room tem­perature.

GRAIN SIZE REFINEMENT AND MECHANICAL PROPERTIES OF UNALLOYED Ti 1041

the line. Mean values of the unit propagation energy (UPE) obtained are also plotted in Fig. 5. The error bars indicate the maximum experimentally observed scatter for nominally identical samples and the mean values are for two or more tests. Although the data show considerable scatter, there appears to be a peak in UPE for Grade 3 titanium at a yield strength of ~ 70 ksi. The aluminum and titanium alloys both show very much lower values of UPE than the unalloyed material.

Discussion - Tensile Tests

Apart from the absence of yield points, the effects of grain size, testing temperature and strain rate on tensile properties of longitudinal sheet samples are qualitatively identical to the effects previously reported for wire specimens (5-9). Fig. 2 shows that the effect of grain size on the room temperature yield strength obeys the commonly observed Hall-Petch (17,18) relation, namely:

0 y

= o. + kd-112 1

•••• 2

where o is the yield stress, o. is the 'friction stress',d is the grain size and k is the Hall-Pefch constant. The previous results (1,8,9) showed that for unalloyed titanium both o. and k increased with increasing interstitial content. The data piotted in Fig. 2 indicate values of o. and k for Grade 3 sheet of 47ksi and 1.1 ksi­mml/2. Both values Iie within the range reported previously (1,8,9) and are close to those .expected on the basis of the interstitial content of the present material given in Table I.

The reduction in uniform elongation which accompanies grain refinement can be explained as follows. In well-behaved poly­crystalline materials the strain hardening rate decreases as the flow stress increases with increasing strain, and it is easy to show (17) that since deformation occurs at almost constant volume, necking will begin when the values of the strain hardening rate and flow stress are equal, i.e.

(do/dE) = 0 u u

•••• 3

where (do/dE) and o are respectively the strain hardening rate and flow streMs at tMe UTS, and o and E are true stress and strain. If equation 1 is an accurate representation of the.uniform flow behavior, we can use it to substitute for Ou and, after differen­tiating, for (do/dE)u in equation 3, obtaining a relation for Eu• the true strain at the UTS which can be solved obtaining:

2

•••• 4

We can then use the observed values of o(O) and h to predict ex-

1042 R. l. JONES

pected values of Eu as a function of grain size. This is done in Table IV, the value of h used (70 ksi) being the mean value observed in room temperature tests. The agreement between the calculated and observed values of Eu is surprisingly good and serves to show that the decrease in uniform elongation which accompanies grain refinement arises because decreasing the grain size increases the strength of a-titanium while having little effect on the strain hardening behavior. A similar argument can be used to explain the temperature variation of Eu•

TABLE IV: Predicted and Observed Values of Uniform Strain at Room Temperature

Grain Size o(O) h Eu(calculated) Eu(observed) (Microns) (ksi) (ksi)

20 52 70 .18 .17 5 59 70 .16 .16

1.2 75 70 .12 .15 0.5 93 70 .09 .095

The increase in reduction in area which accompanies grain refinement probably occurs because the fracture stress is more sensitive to grain size than are the yield and flow stresses. Larger values of k for fracture than for yield have been reported for unalloyed titanium (9) as well as zirconium (20) and mild steel (21). The almost constant total elongation observed for specimens of differing grain sizes is not believed to have any fundamental significance. The elongation during necking is very sensitive to specimen geometry and its observed insensitivity to grain size is most probably coincidental.

In order to determine whether or not the deformation mechanism in the present sheet samples is the same as that deduced for wire (1,8), the change-of-strain rate and yield strength vs. temperature data, have been subjected to a brief thermal activation analysis. Following the same approach as before (1,8) the present data for the yield stress have been separated into two components, the short range (strain rate and temperature dependent) thermal component a* and the long range (strain rate and temperature independent) compon­ent aµ• As noted earlier the effect of grain size primarily resides in oµ• It has been confirmed that a* varies linearly with the square root of the absolute temperature (1,5,8) and that a* (the extra­polated value of a* at 0°K) is in accordance with the previously published relation between this parameter and the interstitial content (1,8). The change-of-strain rate data have been used in conjunction with the temperature dependence data to deduce values of H, the activation enthalpy for the operative, rate - controlling, thermally activated deformation process, at each testing temperature. The values obtained are independent of strain and grain size and are plotted against temperature in Fig. 6. The line plotted through the data shows the relation previously obtained for wire samples of

GRAIN SIZE REFINEMENT AND MECHANICAL PR()PERTIES OF UNALLOYED Ti

1.4..------.----r----.,..----,.-----,----...,

> 41

J:

1.2.

1.0

f; 0.8 a: w z w z Qo.6 I-

~ ~ u <(

0.4

0.2

GRADE 3 TITANIUM SHEET

l::i. 0.5 MICRON GRAIN SIZE 'V 5.0 MICRON GRAIN SIZE

100 200 300 400 500 600 TEMPERATURE (°KJ

1043

Fig, 6. Temperature dependence of the activat.ion enthalpy for de­formation of Grade 3 titanium sheet. The line through the data is replotted from reference 1.

1044 R. l. JONES

a range of purities (1,8). The linear relation indicates a single rate controlling process and the value of the activation enthalpy at 500°K (the temperature at which the relation between 0* and T extrapolates to 0* = O) is about 1.2 ev.

The analysis indicates that the rate controlling deformation mechanism in fine grained unalloyed titanium sheet is the same as that previously observed in wire samples. On the basis of the more detailed analysis for wire samples (1,8) it is believed that this mechanism is dislocation glide on firstorder prism planes opposed by obstacles associated with individual interstitial atoms. The magnitude of the activation energy suggests that the interaction is not due to elastic repulsion between the strain fields of the dislocation and interstitial (22), but rather arises due to inter­ference by the interstitials vith the smooth motion of atoms in the dislocation core (23).

It should be noted that the test samples used here were all tested in the longitudinal direction i.e. with the tensile axis parallel to the rolling direction. The anisotropy of the basal texture shown in Fig. 1 is such that the longitudinal test direction favors prism slip at the expense of basal in the same kind of way as occurs in swaged and recrystallized wire samples. Sheet samples tested transverse to the rolling direction are found to show some­what different tensile behavior (3). The most striking difference is that transverse samples show much lower strain hardening rates than longitudinal samples, which leads to low values of uniform elongation and, more indirectly, to a lower value of k, the Hall­Petch constant. The origin of this low strain hardening rate has not yet been investigated. The increased importance of basal slip may be significant, or possibly deformation twinning (which was not observed in deformed longitudinal samples) may occur. Interestingly, strain rate change experiments lead to values of the stress acti­vation volume which are indistinguishable for the two test directions (3), suggesting that the marked difference in strain hardening behavior does not reflect any change in the rate controlling deforma­tion mechanism.

Discussion - Tear Tests

The objective of the tear testing portion of the program was to establish the effect of grain size on the toughness of unalloyed titanium. Undoubtedly the best method of doing this would be to measure the plane strain fracture toughness Kic as a function of grain size. Unfortunately the specimen size required for a valid Kic test on a material as tough as unalloyed titanium makes the performance of such a program extremely difficult, if not impossible. In ASTM Method E399-70T the plastic enclave factor R, defined as (Kicl0y)2, where 0y is the 0.2% proof stress, must, for a valid test, be less than the smaller of 0.4a0 or 0.4B where a0 is the initial c·rack size and B is the specimen thickness. Taking typical

GRAIN SIZE REFINEMENT AND MECHANICAL PROPERTIES OF UNALLOYED Ti 1045

handbook values for Grade 3 unalloyed titanium of 80 ksi /in and 60 ksi we obtain R = 1.78 inches, and therefore for a valid test B > 4.45 inches. To investigate the effect of grain size on Kic• we are thus faced with the necessity for obtaining a wide range of equiaxed, uniform grain sizes in material > 4.45 inches thick - a daunting prospect indeed.

In view of this problem it seemed most reasonable to use instead of Kic some other toughness indicator with less stringent size requirements, preferably one which previous work has shown to give a reasonable correlation with Kic• Such a parameter is the unit propagation energy (UPE) obtained from the modified Kahn tear test. Kaufman and Hunsicker (16) have made extensive use of this parameter as a toughness indicator for aluminum alloys in sheet form, and have reported a correlation between their measurements of Kic and UPE. Although the material available dictated the use of a smaller sample in the present work than that used by Kaufman and Hunsicker, a qualitative relation between UPE and Kic is evidenced by the data in Table V where the present values of UPE are compared with typical values of Kic obtained from the literature. Fig. 5 shows that the UPE for Grade 3 titanium rises initially as the yield strength is increased by grain refinement, and subsequently falls as grain refinement is continued. However the value of the UPE remains very high over the entire grain size range investigated and is probably equivalent to Kic values of 2:._ 80 ksi /in at all grain sizes. The highest values of UPE are observed at a yield stress of ~ 70 ksi, equivalent to a grain size of about 2 microns.

TABLE V: Correlation of UPE and Krc

Material Condition UPE Kic (in-lb/sq inch) (ksi lin)

Grade 3 Ti Recrystallized 1850 >80 (10-20µ)

2024 Al T3 400 40 Ti-6Al-4V Annealed 510 50 Ti-6A-4V STA <200 30

The other parameter obtained from the tear test, the tear strength, is generally used as an indicator of notch sensitivity in much the same way as the notched tensile strength is used in the notched tensile test (16). It is seen in Fig. 5 that the tear strength is a linear function of yield strength for Grade 3 titanium samples, indicative of notch insensitive behavior. This conclusion is supported by the absence of any effect of notch root radius on tear strength and by the notch insensitive behavior shown by Grade 3 titanium in notched tensile tests (3). The other materials tested fall below the relation between tear strength and yield 5trength defined by the Grade 3 data, indicating varying degrees Jf notch sensitivity.

1046 R. L. JONES

Conclusions

Grain size refinement increases the yield strength of Grade 3 titanium sheet according to the Hall-Petch relation. The magnitude of the grain size effect in sheet samples is similar to that expected on the basis of the results of previous work using wire specimens and the interstitial content of the Grade 3 material. The decrease in uniform elongation which accompanies grain refine­ment can be explained in terms of the interrelation between flow stress and strain hardening rate at the onset of necking. Thermal activation analysis of the effects of temperature and strain rate on the yield and flow stresses indicates that the rate controlling, thermally activated deformation process at temperatures below 700°K is identical for both sheet and wire test specimens.

In modified Kahn-type tear tests, Grade 3 unalloyed titanium sheet behaves in a notch insensitive manner at all grain sizes, and consequently shows high values of tear strength which depend on grain size in a similar manner to the yield stress. The unit propa­gation energy for tear propagation is somewhat dependent on grain size, showing maximum values for grain sizes around 2 microns. Grade 3 titanium of any grain size is very resistant to tear propa­gation; values of the UPE observed were much larger than those for tear failure of 2024-T3 aluminum and Ti-6Al-4V, which were tested for comparison. The results show that substantial increases in strength can be obtained by grain refinement in unalloyed titanium without sacrificing the high toughness of the material. It is thus possible to fabricate unalloyed titanium sheet which combines a yield strength close to 100 ksi with high toughness, probably equivalent to a Kic .:::_ 80 ksi /in.

Acknowledgements

The work described was supported by the Department of the Navy, Naval Air Sy.sterns Command under contract number N00019-71-C-0133. The author is indebted to Dr. J. D. Meakin of FIRL, Mr. R. Schmidt of NASC and Dr. J. M. Krafft of NRL for helpful comments regarding various aspects of the program.

References

1. R. L. Jones, F. W. Cooke, H. Conrad and B. R. Banerjee, AFML-TR-68-28 (Feb. 1969).

2. R. L. Jones, FIRL Rept. F-C2470, NASC Contract N00019-69-0437 (Jan. 1970).

3. R. L. Jones, FIRL Rept. F-C2739, NASC Contract N00019-70-C-0206 (March 1971).

4. R. L. Jones, FIRL Rept. F-C3013, NASC Contract N00019-71-c~Ol33 (March 1972).

GRAIN SIZE REFINEMENT AND MECHANICAL PROPERTIES OF UNALLOYED Ti

5. R. L. Jones and H. Conrad, Acta Met. 15, 4 (196 7)' pp.

6. R. L. Jones and H. Conrad, ScriEta Met. 2, (1968), pp.

7. R. L. Jones, ScriEta Met. 2, (1968)' pp. 345-349.

8. H. Conrad and R. L. Jones, The Science 2 Technolog)'. and cation of Titanium, Eds. Jaffee and Promisel, Pergamon N. York (1970), pp. 489-501.

9. R. L. Jones and H. Conrad, Trans. TMS-AIME, 245 (1969), pp. 779-789.

1047

649-650.

239-242.

Apf!li-Press,

10. N. A. Kahn and E. A. Imbembo, Welding Journal 27, (1948), pp. 169s-182s.

11. C. J. McHargue and J. P. Hammond, Trans. TMS-AIME 197, (1953), P• 57.

12. H. T. Clark, Trans. TMS-AIME 188, (1950), p. 1154.

13. D. N. Williams and D. S. Eppelsheimer, Trans. TMS-AIME 197, (1953)' p. 1378.

14. D. N. Williams and D. S. Eppelsheimer, J. Inst. Met. 81, (1953), p. 5 33.

15. A. T. Churchman, Proc. Roy. Soc. A226, (1954), p. 216.

16. J. G. Kaufman and H. Y. Hunsicker, ASTM STP 381 (1965), pp. 290-307.

17. E. O. Hall, Proc. Phys. Soc. (London) B64 (1951) p. 747.

LB. N. J. Petch, J. Iron and Steel Inst. 2 174 (1953) p. 25.

L9. A. H. Cottrell, Introduction to Metallurgy, St. Martin's, N.Y. (1967), pp. 388-389.

~O. c. E. Coleman and D. Hardie, J. Inst. Met. 94 (1966), p. 387.

'.l. N. J. Petch, Phil. Mag. 1 (1956), p. 186.

:2. R. Tang, J. Kratochvil and H. Conrad, ScriEta Met. 2 (1969), p. 485.

3. W. R. Tyson, Canad. Met. Quarterly 6 (1968), p. 307.