Slip transfer across low-angle grain boundaries of deformed Titanium

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etMatmialia, Vol. 33, No. 12, pp. 1883-1888.1995 Elswier Science Ltd czopyi&.o 1995 Acta h4ddlulgica Inc. Pm&d IIIthe USA AU rights reserved 09%-716x/95 $9.50 + .co

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SLIP TRANSFER ACROSS LOW-ANGLE GRAIN BOUNDARIES OF DEFORMED TITANIUM Th. Kehagias, Ph. Komninou, G.P. Dimitrakopulos, J.G. Antonopoulos, and Th. Karakostas Physics Department,

Solid State Section 3 13-l) Aristotle University of Thessaloniki, GR-540 06 Thessaloniki, Greece (Received May 2, 1994) (Revised November 25,1994) Introduction

In a study concerning mechanical deformation of hexagonal close-packed metals at room temperature, observations of 25% deformed Ti revealed a slip transfer mechanism across twin boundaries and have been analysed by the authors [I]. Continuing the investigation to other types of grain boundaries (GBs), we present here experiments on low-angle GBs. Subgrain boundaries have been excluded from the investigation, since it is rather obvious that slip transmission across subboundaries occurs in a manner similar to the one of a single crystal. Slip criteria 12-41 were used in order to fmd the most probable slip systems where slip transmission could occur. ExDerimental Thin foils of polyuystalline Titanium had undergone annealing for 1 hour at 800°C in argon atmosphere and then were reduced 25% in thickness by cold rolling, at room temperature. Three millimeu-e discs for Tmnsmis&on Electron Microscopy (TEM) were cut I&n the foils and thinned by electropolishing in a twin-jet Tenupol apparatus, using a bath of 60% Methanol, 38% Butanol and 2% Perchloric acid at -40°C. The TEM specimens were examined in a Jeol 120 CX electron microscope operating at 120 kV. Results and Discussion In Figure 1 a low-angle boundary of a mixed character is presented. Extensive slip is observed on one slip system of grain Gl and on another slip system of grain G2. This slip is visually real&d corn the slip traces that are clearly visible in Figure 1. In order to reveal these slip systems, the line directions of the piled-up dislocations in both sides of the boundary, arrays 1A and 2A of Figures 2a and 2b respectively, were examined and found to belong to equivalent (liO0) planes of the two crystals. Applying the g - b = 0 criterion the Burgers vector of the arrays was found to be equal to l/3 [ 11201 in both grains of the bicrystal. The experimental determination of the two slip systems, namely the (l-rOO)[llZO],, and the (lTO0) [ 1l?O], ahow us to assume that there is a slip transmission mechanism across the GB that could be described as follows: when the stress field of deformation is high enough, the (ITOO) plane of grain Gl

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Figure 1. Extensive slip ebserved_in a low-angle GB of deformed Ti. The traces of two slip systems, i.e.-he (liOO)[l l;O] in grain G 1 and the equivalent (1 lOO)[ 11201 in grain G2 are clearly visible. The micrograph is taken with the 10 11 and the 2201 reflections of grains Gl and G2 respectively.

is activated forcing the l/3 [ 11201 mixed type dislocations gliding on it (Array 1A) to approach and finally cross the interface. These dislocations (Array 2A) continue to glide on the equivalent (1TOO) slip plane of gram G2 without any change on their Burgers vector. This slip transfer process seems highly favourable, since the angle between the intersections of the boundary plane with the slip planes of the incoming and the outgoing dislocations is only OS”, facilitating the transition of dislocations from one slip plane to the other. This can

Fig&e 2. The same low-angle GB in deform* Ti; a) Array 1A of 1/3[1 ljO] perfect dislocations gliding on the (liO0) ~1% of grain Gl moving towards the GB; reflection 1122 is operated in Gl, w&eas G2 is out of contrast. b) Array 2A of 1/3[1120] perfect dislocations come out of the same GB and glide on the equivalent (1100) slip plane of grain G2; here reflection 1011 is operated in G2, whereas Gl is out of contrast.

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SLIP TRANSFER

be explained as follows: Due to the specilic geometry of the bicrystal, on the intersection of the boundary plane with the two active slip planes both the piled-up and the emerging dislocations become of a nearly pure edge type. the motion of the incoming dislocations for meeting the emerging slip plane can be analysed in a glide and a climb component. Since this rearrangement is performed almost parallel to the Burgers vectors, the climb component is small and is just&d from the elevated stress field of deformation. Relaxation of the energy in the GB is real&d by the creation of residual dislocations let? in the GB after the incoming dislocations move into the emerging slip plane. This result should be verified from the three slip criteria proposed by Livingstone et al. [2], by Shen et al. [3] and by Lee et al. [4]. According to the first criterion, slip is transferred to the slip system with the maximum resolved shear stress. Such a slip system yields the highest transmission factor T, where T = (d, - d,) * (n, - n,) + (d, - nJ * (n, * d,) and the subscripts 1 and 2 denote crystals Gl and G2 respectively, 4 (i = 12) is the unit normal to the slip plane and d = hi/l bit, where bi is the Burgers vector of the dislocations entering or leaving the GB, accordingly. It has to be noted that several authors [5,6] consider that the application of the first criterion is insticient to predict the emerging slip system. According to the second criterion, slip is favoured when the factor M is maximum, where M = cosa *cosS, a is the angle between the Burgers vectors in the two crystal components and l3 is the angle between the lines of intersection with the interface of the Gl and G2 active slip planes. Obviously cosa = d, - d,. Additionally, the resolved shear stress acting on the emerging slip system Corn the stress field of the piled-up dislocations should be maxim&d. The resolved shear stress condition of the second criterion predicts the slip direction of the emerging slip system. Since in the hexagonal close-packed system the slip directions in the prism and pyramidal slip planes for the l/3< 1120> dislocations are the corresponding < 1120> directions [7], the resolved shear stress need not to be considered in order to determine the slip direction in contradiction with the cubic materials, where more than one slip directions are equally favourable in the same slip plane and thus resolved shear stress has to be taken into account. In [6,8] it is stated that for the geometric condition of the second criterion only the cos p term has to be considered and its maximisation predicts the slip plane of the emerging slip system. The third slip criterion takes into account the Burgers vector of the residual dislocation left in the GB after an incoming matrix dislocation has crossed the GB. The most probable emerging slip system is predicted from the minimisation of the residual Burgers vector. The third and the second criteria might result in different solutions, since the system that exhibits the maximum resolved shear stress does not TABLE 1 Results from the Application of the Slip Criteriaon the GB of Figure 2 Slip System

T

P (de&

M

lkd (nm)

(1i00)[1120]

1.912

0.5

0.999

0.991

0.04

(1010)[1210]

1.388

4.5

0.997

0.388

0.49

(01 io)[2iio]

0.524

17.5

0.954

0.574

0.26

4

(1 ioi)[ll20]

1.763

32.5

0.843

0.836

0.04

5

(liol)[ll2o]

2.062

35.5

0.814

0.807

0.04

6

(loii)[iZlo]

1.391

33.5

0.834

0.324

0.49

7

(loil)[lZlo]

1.385

24.5

0.910

0.354

0.49

8

(olil)[2iio]

0.670 I

9

coil l)r2iioi

64 I

0.378

-0

0.438 I

72.5

0.264 I

0.301

I

0.26 I

0.181

I

0.26

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SLIP TRANSFER

1886

always give the minimum residual Burgers vector [6,9]. The system that will finally operate in our experiment rninimisationof the residual Burgers vector, as it will be clear from the results that istheonethatresultsithe are depicted below. The occurrence of residual dislocations resulting from this slip transfer across the GB of Figure 2 was examined. Calculationscan be greatly facilitated if Frank’s &space coordinate system for hexagonal materials is used [lo]. In this system the Miller-Bravais vectors can be considered as [ 11lo] projections of the corresponding 4-vectors. The Frank’scoordinates system is four-dimensionally cubic and thus all calculations can be performed as if the material was cubic. In Frank’s coordinates the direction [uvtw] corresponds to the Cartesian 4-vector [u,v,t,Aw], and the normal to the plane (bkil) is (h,k,i,l/h),, where A = (2/3)“’ (c/a). All 4-vectors are expressed in units of the magnitude of the unit 4-vector e, given by )e 1= (312)“’)al. Therefore, no approximation of the c/a ratio is necessary, as it was previously. The rotation matrix R4 canbe readily formulated in this system using the methodology of Pond et al. [ 111.For greater accuracy, the exact rotation relationship between the two crystals, i.e. the experimental rotation matrix, can be used. For the low-angle GB studied here, using methods developed for the characterisation of GBs by TEM [12-151, the rotation relation&ripbetween the two grains was found to be 11.6’ around the [ 14,52,-66,531 axis of grain G 1. Thus, the experimental rotation matrix using the Frank notation is: 0.987

- 0.065

0.078

0.127

0.081

0.991

- 0.072

- 0.079

- 0.068

0.074

0.994

- 0.048

-0.124

0.091

0.033

0.988

1 R4

=

4

Figure 3. A second low-angle GB in defoEed Ti where slip transfer ocmrs. Grain G2 is the same one of the previous bicrystal. The micrograph is taken with the 1101 and 1011 reflections of grains G2 and G3 respectively. For these di&cting conditions, the Amy 2C of dislocations is in extinction Notice the dislocation-like cmtmst in the k§ion of the active slip planea with the boundary plane, depicted by two small arrows.

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The residual Burgers vector b, can be calculated from the following expression: b,=

- Rd. l/3 <1120>,,

113 <1120>,,

All possible emerging slip systems were examined and the results are depicted in Table 1. From these results the following conclusions can be drawn: i) the combination of the geometric condition of the second criterion together with the third criterion predicts the (lTOO)[l120], as the most probable emerging slip system, a result that is in accordance with the experimentally observed slip system; ii) the first criterion failed to predict the experimental emerging slip system and proves to be insuEcient in our case. Residual dislocations resulting from this slip transfer process possess very small Burgers vector that exhibits very low contrast. That explains why these residual dislocations were not observable in our experiments. A similar situation is observed in the low-angle boundary of Figure 3. Dislocations gliding on the slip system (lTOO)[ lT20] of grain G3 (Array 3) are crossing the GB and continue their motion on the (lTOO)[l 1201 slip system of grain G2 (Array 2C). Thus, slip is transferred exactly in the same manner as in the GB between grains Gl and G2. Applying the g - b = 0 criterion, it is found that dislocations in both sides of the interface possess a l/3 [ 11201 Burgers vector. The existence of residual dislocations left in the GB was also examined. Here, the rotation relationship between grains G2 and G3 was found to be 8.2” around the [32,40,-72,-461 axis of grain G3. Following the procedure described above we find an experimental rotation matrix:

R4

-

0.994

0.051

- 0.045

0.085

- 0.041

0.995

0.047

- 0.082

0.047

-0.045

0.998

-0.002

- 0.088

0.078

0.010

0.993

4

The results of the application of the slip criteria on all possible emerging slip systems are listed in Table 2. TABLE 2 Results from the Application of the Slip Criteria on the GB of Figure 3

5

(1101)[1120]

2.089

38

0.788

0.786

0.03

6

(ioii)[l21io]

0.777

36.5

0.804

0.456

0.52

7

(loil)[l21lo]

0.636

81

0.156

0.089

0.52

8

(olfl)[2iio]

1.313

37.5

0.793

0.341

0.32

9

(oil 1)[2iio]

1.196

21

0.934

0.401

0.32

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As mentioned before, the combination of the second and the third criterion predicts again the (liOO)[ 11ZO], as the most probable emerging slip system in accordance with the experimental data. Since the same slip system is favoured in both examples, it would be not far from true to assume that this slip system exhibits the maxim um resolved shear stress. An interesting aspect of this case is the dislocation-like contrast that is observed in the intersection of the (liO0) slip planes with the boundary plane (Fig. 3). This contrast probably arises from the interaction of the incoming and the outgoing dislocations with the existing GB dislocations. Conclusions A mechanism

of slip transmission across low-angle GBs of deformed Ti, at room temperature, is observed. This slip transfer process was verified from two slip criteria: 1) the angle between the intersections of the boundary plane and the slip planes of the incoming and the outgoing dislocations should be a minimum and 2) the Burgers vector of the residual dislocations left in the GB after a matrix dislocation crosses the interface should be minimised. The criteria predicted the emerging slip system in exact accordance with the experimental data. Hexagonal metals have a speciIic slip direction on slip planes for dislocations with specific Burgers vectors, thus resolved shear stress considerations are not necessary for the determination of the slip direction of the emerging slip system, as they are in cubic materials where more than one slip directions on the same slip plane are equally possible. Indirectly, it could be assumed that the slip system which is favoured Corn the two slip criteria exhibits also the maximum resolved shear stress. Residual GB dislocations resulting from this process possess very small Burgers vectors with very low contrast and were not observed in tbis experiment. Acknowlednement This work has been supported by the Greek General Secretariat for Research and Technology References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

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