On the grain boundary conditions for grain boundary sliding in superplastic deformation

Materials Science and Engineering, 80 (1986) L l l - L 1 4

Lll

Letter

On the grain boundary conditions for grain boundary sliding in superplastic deformation R. A. VARIN

Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada) K. J. KURZYDLOWSKI

Institute of Materials Science and Engineering, Warsaw Technical University, 02-524 Warsaw, Narbutta 85 (Poland) K. TANGRI

Metallurgical Sciences Laboratories, University of Manitoba, Winnipeg, Manitoba R3T 2N2 (Canada)

(Received September 4, 1985; in revised form December 30, 1985)

controlled by grain boundary diffusion [2], the annihilation of a specific number of dislocations in grain boundaries should somehow affect grain boundary sliding, especially in ultrafine-grained materials exhibiting a superplasticity effect. It is well known that, in superplastic deformation, 50%-70% of the total deformation is produced by grain boundary sliding [3]. Therefore, the above-mentioned relationship between the formation and spreading of EGBDs is being pursued in the present letter in more detail to explore the specific grain boundary conditions necessary to achieve substantial grain boundary sliding in superplastic materials. However, before these conditions are discussed, a brief discussion regarding the physical mechanisms of grain boundary sliding is necessary.

ABSTRACT

Grain boundary sliding (GBS) is analysed in terms o f the rate o f formation and the rate o f spreading o f extrinsic grain boundary dislocations (EGBDs). It is calculated employing a mathematical model derived in such a way that in superplastic alloys, where GBS is a primary deformation mode, the rate o f EGBD spreading is at least equal to or higher than the rate o f EGBD formation, right from the onset o f superplastic deformation. This condition seems to be a necessary condition to achieve a substantial a m o u n t o f GBS.

1. INTRODUCTION

In the previous letter [ 1 ], evidence was presented that the mechanical behaviour of polycrystalline austenitic stainless steel at elevated temperatures (short-term properties) was strongly affected by the relative rate of the formation and spreading of extrinsic grain boundary dislocations (EGBDs) during plastic deformation. Since the spreading of EGBDs during plastic deformation at elevated temperatures is 0025-5416[86/$3.50

2. STRUCTURE-DEPENDENT GRAIN BOUNDARY SLIDING

It is now widely accepted that grain boundary sliding is a direct result of the movement in the boundary plane of structural grain boundary dislocations (SGBDs) with the Burgers vectors characterized in the DSC lattice (see for instance ref. 4). Any large-angle (random) grain boundary can be formally described as deviating from a specific coincident site lattice misorientation (designated by Z) and as such it can contain a network of SGBDs (see the recent review by Gleiter [5] ). It is argued that lattice dislocations can lower their elastic energy by dissociation in the boundary to form SGBDs which contribute to grain boundary sliding. One of the formal models of grain boundary sliding based on the movement of SGBDs developed by Ashby [6] predicts that the sliding r a t e / ] is directly proportional to the Burgers vector bb of SGBDs: = PbbV

(1)

where p is the linear density of SGBDs and v their velocity. As the Burgers vector bb gener© Elsevier Sequoia/Printed in The Netherlands

L12 ally decreases with increasing Z value (see ref. 7), it could be expected in accord with eqn. (1) that low Z boundaries (large bb) should slide more easily than random grain boundaries with large ~ misorientations and very small bb vectors. However, at this point a strong discrepancy with the experimental observations arises. There is ample experimental evidence provided recently by Kokawa et al. [8, 9] and Watanabe [10] that the amount of sliding at grain boundaries close to coincidence misorientations is much smaller than that at random (general) boundaries. Following Kokawa et al. [8] it could be argued that a random boundary might absorb more lattice dislocations per unit strain than a special boundary at the same deformation temperature because the spreading is generally easier in random boundaries. This, in turn, might compensate (larger p in eqn. (1)) for a smaller bb value in random boundaries. However, at some transition temperature the efficiency for absorption of both types of boundary should become the same. Such a behaviour is not observed experimentally. According to recent results of Watanabe et al. [11] obtained on zinc bicrystals, the average sliding rate for special boundaries is always substantially lower than that for random boundaries up to the melting temperature. It seems therefore that the description o f grain b o u n d a r y sliding at random boundaries by the movement of SGBDs cannot satisfactorily explain the largest amount of sliding observed experimentally. It is suggested here that grain boundary sliding is a direct consequence of the spreading of the cores of a large number of EGBDs as they are formed, for example, from lattice dislocations impinging on grain boundaries at elevated temperatures. The atomistic model of this mechanism may be similar either to that presented by Johannesson and Th51en [12] or to that given more recently by Lojkowski [13] and Lojkowski and Grabski [14]. However, both of these models yield essentially similar equations to describe the kinetics of the spreading process. In view of the above discussion, it is concluded that random grain boundaries, rather than special boundaries, play a major role in superplastic deformation as they can provide a substantial amount of grain boundary sliding.

3. CONDITIONS FOR DISLOCATION FORMATION AND SPREADING DURING GRAIN BOUNDARY SLIDING

It was shown in a previous letter [1] that a significant decay (down to about 10% of the original plateau stress) in the yield stress of t y p e 316 austenitic steel occurred when the condition EGBDsI~ead ~ pEGBDformed

(2)

was fulfilled. The physical meaning of this condition is that grain boundaries become perfect sinks for lattice dislocations. Now, it is interesting to know what are the conditions for dislocation formation and spreading when substantial grain boundary sliding occurs during superplastic deformation. Using the relationship detailed in ref. 1 and given b y

td=ATd exP(R~db ) --- the spreading time of EGBDs

(3)

where h =

11ks

(4)

IG~Do b

~ EGBDfonned ----

eg 3b

the rate of formation of EGBDs (5)

~EGBns~ea d = pEGBD d~ v dt -

-

the rate of spreading of EGBDs

(6)

pEGBDv = Pm

= e g _ the density of EGBDs per unit bd volume (7) the values o f ~5EGsD~o~m~aand ~EGBDs~eaa (for e = 0.002) were both calculated for several superplastic alloys on the assumption that the core of the EGBD is spread o u t up to Sm = 5 × 10 -8 m. The results of these calculations are listed in Table 1. There is a lack of diffu, sion data for superplastic alloys and therefore the diffusion parameters for pure elements were taken for calculations. However, employ-

L13 TABLE 1 Parameters of superplastic deformation and the data on the rate of formation of extrinsic grain boundary dislocations and the rate of their spreading for several superplastic alloys Material (wt.%)

Mean grain size (pro)

Temperature Strain rate M a x i m u m ofsuperplastic (× 10-4 s-1) deformation deformation (%) (K)

pEGBDo pEGBDspread Reference (m-1 S-~ tlled (e = 0.002) (m-1 s-1 )

500

5.5 X 105

4850

1.5 X105

Pb-62Sn

3

298

5

Pb-62Sn

6.9

413

1.33

Zn-22A1

2.5

473

66

2900

Mg-33A1

2.2

673

330

Mg-33A1

2.2

673 673

Mg-l.5Mn0.3Ce Al-33Cu

10 1.5

743

4.1 X 102 (Pb) 3.1 X 106 (Sn) 2.1x105(Pb) 8.8 x 107 (Sn)

[15]

7.3×106

2.9×107(Zn) 1.3 X 10 s (A1)

[17]

2100

3.7 X107

3330

830

3.7X10 s

7.2x 107(Mg) [18] 1.5 X 109 (A1) 7.2X107(Mg) [18] 1.5 X 109 (A1)

84

310

9.3X106

1.6 X107(Mg) [19]

1200

2.2X103

3.5x 109(A1)

0.02

[16]

[20]

The following parameters were taken for the calculations: 6 = 5 × 10-10 m;Sm = 5 X 10-s m (500/~); for lead, zk/-/b = 65.7 kJ tool -1 [21], D 0 b = 0.81 × 10 -4 m 2 s-1, G = 0.56 × 1010 N m-2 [22] and ~ = 30.3 X 10-30 m 3 ; for tin, ZM-/b= 39.96 kJ tool -1 [21], D0b = 6.44 X 10- 6 m 2 s-1 [21], G = 1.84 × 1010 N m-2 [22] and ~ = 27.05 X 10-30 m3; for zinc, zSJ-/b= 60.7 kJ tool -1 [21], D0b ~ 0.3 x 10-4 m 2 s-1 (an average of the values in ref. 21), G = 4.2 X 1010 N m -2 [22] and ~ = 15.2 x 10 -30 m 3 ; for aluminum, ~ / b = 35 kJ tool -1 [23], D0 b ~ 0.003 X 10 -4 m 2 s-1 [23], G = 2.6 X 101° N m-2 [22] and ~'~ = 16.61 X 10-3o m3; for magnesium, 5Db = 15 X 10-21 m 3 s-1 [19], G = l . 7 3 X 1 0 l ° N m - 2 [ 2 2 ] a n d s = 23 X 10- 3 ° m 3.

ing the d a t a f o r alloys (if available) w o u l d n o t significantly c h a n g e t h e c o n c l u s i o n s d r a w n as t h e values o f pEGBDformed and pEGBDspread f o r d i f f u s i o n in alloys s h o u l d lie s o m e w h e r e in bet w e e n t h e values for p u r e elements. 4. DISCUSSION T h e striking f e a t u r e o f the results p r e s e n t e d in Table 1 is t h a t f r o m t h e very beginning o f superplastic d e f o r m a t i o n (e = 0 . 0 0 2 ) t h e rate ~sEGSDs~ead o f spreading o f E G B D s is at least equal to or higher t h a n t h e rate pEGBDformed o f their f o r m a t i o n . Physically, this m e a n s t h a t grain b o u n d a r i e s act as p e r f e c t sinks f o r dislocations right f r o m t h e o n s e t o f superplastic d e f o r m a t i o n . These results t h e r e f o r e seem t o indicate clearly t h a t the pEGBDsPread pEGBDforraed c o n d i t i o n w h i c h is fulfilled right f r o m t h e beginning o f d e f o r m a t i o n is in fact a necessary c o n d i t i o n f o r achieving a substantial a m o u n t o f grain b o u n d a r y sliding. O b v i o u s l y , t h e a m o u n t o f sliding o b t a i n e d will d e p e n d m a c r o s c o p i c a l l y on t h e grain size. Ultrafinegrained materials have a high d e n s i t y o f sur-

faces per unit v o l u m e and as such a large area f o r E G B D s to spread and to result in grain b o u n d a r y sliding. Also, it is seen f r o m eqns. (6) and (7) t h a t the rate ~bEGBDs~ead o f spreading increases with decreasing grain size and t h e c o n d i t i o n expressed b y eqn. (2) is fulfilled m o r e easily. Finally, it s h o u l d be p o i n t e d o u t t h a t the p r e s e n t e d h y p o t h e s i s o f grain b o u n d a r y sliding as a c o n s e q u e n c e o f E G B D s is in g o o d qualitative a g r e e m e n t with such e x p e r i m e n t a l o b s e r v a t i o n s as t h e absence o f a n y grain shape c h a n g e and associated grain r o t a t i o n during superplastic d e f o r m a t i o n . Beere [24, 25] analysed the d e f o r m a t i o n o f an aggregate o f cube grains as having d i f f e r e n t resistances t o sliding at t h e boundaries. It was s h o w n that, if one set o f interfaces had a greater resistance to sliding, t h e n a given strain c o u l d be achieved o n l y b y allowing the grains t o rotate. Within t h e f r a m e w o r k o f o u r m o d e l , grain b o u n d a r i e s with a greater resistance to sliding are special b o u n d a r i e s at w h i c h the E G B D spreading process is k n o w n t o be m o r e difficult t h a n t h a t at r a n d o m grain b o u n d a r i e s [26, 27].

L14 ACKNOWLEDGMENT

This work has been supported by Natural Sciences and Engineering Research Council of Canada grants which are gratefully acknowledged.

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