Effect of polycrystal grain size on steady state creep of titanium

Scripta METALLURGICA

Vol. 15, pp. 1107-1110, 1981 Printed in the U.S.A.

Pergamon Press Ltd. All rights reserved

EFFECT OF P O L Y C R ~ T A ~ G~.~AIN SIZE ON STEADY STATE CREEP OF TITANIUM

G.~elakondaiah and P.Rama Rao Department of Metallurgical Engineering, Banaras Hindu University, Varanasi - 221 005, India (Received July 13, 1981) Introduction The effect of polycrystal grain size on steady state creep rate has been studied by a number of investigators. The most comprehensive of these studies, as yet, appears to be that reported by Barrett et al. (1) on high purity OFHC copper whose results show that the creep rate is independent of grain size (TJ, length of mean linear intercept) beyond ,~60 ~m. Below this value the creep rate increases with a decrease in grain size. Confirmation of this behaviour has been obtained in a simple solid solution alloy (2), in highly alloyed stainless steels (3,4) and in a nimonic (5). Even the seemingly contradictory results of Garofalo et al. (6) have been replotted (7) to show a grain size dependence similar to that observed by Barrett et al. within allowable experimental error. Although the general consensus of understanding is in favour of the observations made by Barrett et al. (1), there is no doubt that a great need still exists to obtain further experimental verification in other metals and alloys. In their careful work Barrett et al. have shown that the rise in creep rate at smaller grain sizes is because of larger contribution to total strain from grain boundary shearing which in their treatment included not only the shear deformation in the plane of the boundary but also the highly localised deformation that occurs in the immediate vicinity of grain boundaries due to enhanced dislocation motion. We report here qualitatively a similar observation on the effect of grain size on the steady state creep rate of titanium. However, the important poi1~t of distinction between the reports referred to in the foregoing and the present work lies in the stress at which creep tests are conducted which~ in the present investigation, is considerably low and falls in the range below 10-4 G, where G is shear modulus. Experimental A high sensitive spring specimen geometry (8~9)ghaS b eenl employed in order to measure the resulting low strain rates (~ lO" sec- ) at temperatures around 0.5 Tm, where Tm is the absolute melting temperature, and stresses less than 10-4 G. A range of grain size from 34 to 443 ~m has been developed through various thermal and thermomechanical treatments (lO,11) in titanium wire samples of diameter 1500 ~m procured from Titanium Metal and Alleys Limited, London. Creep tests have been performed, employing the procedure ~ described elsewhere (12), over a range of temperature from 823 to 1088 K (0.43 to 0.56 Tm). The maximum stress was up to 2.0 MN/m 2. Establishment of grain size-temperature-stress regimes of dominance of various creep mechanisms was the principal aim of the earlier repQrt (ll). We shall be concerned here with tests performed at lO00 K with the specific objective of bringing out the effect of grain size on steady state creep rate.

1107 0036-9748/81/101107-04502.00/0 Copyright (c) 1981 Pergamon Press Ltd.

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Results and Discussion Measured creep rate (E) at a constant stress (o-) of 1.3 MN/m 2 is plotted as a function of grain size in Fig.l (Grain size in terms of grain diameter (d=1.776 ~) is also indicated). It is seen from Fig.l (solid curve) that the creep rate is independent of grain size beyond ,~ 70 pm upto N 8 0 0 ~m. At grain sizes less than about 70 pm creep rate increases steeply with decreasing grain size• To identify the dominating creep mechanism under grain size - stress conditions of interest here we wish to make use of the Langdon-type creep mecha*~ism map (18) which we have constructed on the basis of the e~{tensive experimental study reported earlier (ii). Represented in the map for a constant temperature of i000 K (0..52 Tm), reproduced in Fig. l, are fields of dominance of three viscous creep mechanisms (~ocO-i°), namely Coble (14)~ liabarro-Herring (N-H) (15)16) and Harper-Dorn (H-D) (17) creep processes and dislocation climb controlled power-law (Eo¢O -n ) creep (18). The broken line shc~in in the map corresponds to the stress value of interest in the present discussion (0-=1.3 ...'~/~) .. when normalised with respect to shear modulus (O'/G=~.3xlO "°) (Shear modulus data are derived from the young's modulus data reported by Armstrong and Brown (19) using Poisson's ratio of 1/8). It is seen from the map that at the normalised stress of 6.3x10 "6 climb controlled power-law creep dominates beyond a grain size ~ 7 0 pro, the region in which the steady state creep rate is independent of grain size. Steady state creep rate dependence on stress has been found to obey tb~ well-known power-law with a stress exponent,n) between 4 and 8 over the entire grain size range 69 to 249 pm. in substantiation of this fact_ FiN. 2 shows relevant data ~or grain sizes at the two extremes (L=69 and 249 pm) of the range over which creep rate is independent of grain size. It is to be added here that a creep mechanism map represents the fields of dominance of various creep processes. This implies that the mechanism dominating in the adjoining field also contributes to fl~1 in addition to the dominating process indicated in the map. This effect becomes prominent especially under conditions corresponding to the field boundaries. Hence we have corrected climb creep rates for viscous creep contribution while evaluating the stress exponent,n, for grain sizes greater than ~ 7 0 pro. Compensation for viscous creep contribution is effected by extrapolating the linear portion of ~ versus o- plot to higher stresses, beyond the value at which deviation from linearity occurs) and subtracting the extrapolated value from the measured one at the stress of interest. At grain sizes less than about 70 ~m diffusional creep dominates the flow. The viscous nature of this process is evident from a typical plot for ~=69 pm at stresses below the value (1.2 Mid/m2) marking a transition to power-law creep. The creep map in Fig.1 shows, as e~pected from previous studies [10,20), that the transition stress increases with decreasing grain size reflecting dominance of diffusion creep at finer grain sizes (Fig.l). The steep increase in creep rate below a grain size of ~ 7 0 pm is thus due to diffusional creep which is strongly sensitive to grain size. Although the behavlour depicted in Fig.1 is in accordance with the generally held and accepted notions, it is not often that one comes across such clearly supporting evidence. The present conclusion differs from the findings of Barrett et al. (1), who were concerned with normalised stresses more than an order of magnitude higher, that enhanced contribution from grain boundary sliding leads to the increase in creep rate at a given stress below a certain grain size. It is also to be noted from Fig.1 (solid curve) that creep rate tends again to increase at coarser grain sizes i.e. beyond about 800 pm. The recent work of Miyazaki et al. (21) on the effect of specimen thickness on mechanical properties of polycrystalllne aggregates with various grain sizes is Of relevance here,since climb creep is also based on dislocation movement. It has been demonstrated (~l) that the flow stress decreases with decreasing

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specimen thickness (t) when the valne of t/d becomes smaLt=,r tnc~ a c~z't]c~ ~ value. It was concluded (91) that the constrainin~3 _rorce~ caus~d by the int.raction among grained.acts only near the grain boun]
C.R. Barrett~ J.L. Lytton and O.D. Sherby~ Trans. AIl fE 889~ 17~ (1967). W.R.Johnson~ C.R.Barrett and W.D.i;ix~ "let. Trans. S~ 695. (197;h). R.Lagneborg~ j.ffron Steel inst. 207~ 1803 (iG69). V. Kutumba RaG and P.Rama Rao~ Scripts Ibt. 7 : i 0 0 3 (Ii)TS). R.Y~rownsword and H.R.Koar~ Scripta Met. 7~ 6~3 (1973). F.Garofalo~ W.Domis and F.Von Cemmingen~ ~ a n o . AI:I~ ,~ou~ Ii60 (1964). J.E.Bird~ A.K. Mukherjee and J.E.Dorn~ ~ a n t i t a t i v e ~%~lation between Properties

and

Hicrostructure

(edited

bj

D.G.;'ran~on

Israel Universities Press~ Jerusalem (1969). 8. I•G. Crossland~ R•B. Jones and O.W.Lewthwaite~

~n
F .... ),~

J.Hiys. ~: !u ~.~ . P h y s .

6~ i0:~0.

(1973).

9. i0. ii. 18.

13. 14. 15. 16. 17. 18. 19. 20. 21. ~Z. 23.

D.J.T~,~Ie and i!.Jones~ Acta }let. Z-I~ 399 (1976). G. Halakondaiah~ Ph.D. Thesis~ Banaras iIindu University~ India (19,30). G. Malakondaiah and P.Rama Rao~ Acta Het. (in press). G. Halakondalah and P.Rama Rao~ Trans. indian Institute of l~ta[s 31, ;361 (1978). F.A.Mohamed and T.G. Lan~]don~ Iiet. Trans.A 5~ £SSO (I~74). R.L. Coble~ J.Appl. Phys. 34~ 1679(i°63). F.R.N. Nabarro~ Rep. Conf. on Strength of So!ids~ The Physical ~ociety~ London~ p. TS (1948). C.Herring~ J.Appl. Phys. 81~ 487 (1950). J.G.Harper and J.E. Dorn~ Acta Het. 5~ 65% (1057). A.K. Hukherjee~ J.E.Bird and J.E.Dorn~ Trans.AdH 62~ 155 (!969). P.E.Armstron~] and }l.L.Br~,m~ Trans. AiHE z30~ 962 (1264). H.S.Seltzer~ A.H. Clauer and B.A.WiLcox~ J.19~cL.Mat. 3 ~ 351 (I070}. S.Miyazaki~ K.Shibata and l{.Fujita~ Acts Net. ZT~ 858 (I~)79). G. Malakondaiah and P.Rama ~ao~ Scripts i;et. 13, ii~7 (1979). F •A. Mohamed~ K.L. Murthv. and J....~'orrlo "~ Jr.~ I{ate i rocess~s in Flastic Deformation (edited by J.C.M. Li and A.K.~[rkherjee) p.459~ ACH (1375).

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STEADY STATE CREEP

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TITANIUM T=IOOOK (0"52 Tin)

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MEASURED __a. CORRECTED FOR VISCOUS CREEP CONTRIBUTION

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Fig.1. Steady state creep rate as a function of grain size at constant temperature (1000 K) and stress (I-3 MN m -k) for titanium.

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