Materials Science and Engineering A 427 (2006) 282–288

Nanoscale study of cyclic deformation behaviour andmechanism of annealing twin

Jun Ma ∗State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871, PR China

Received 4 March 2006; received in revised form 24 April 2006; accepted 24 April 2006

Abstract

Atomic force microscopy (AFM) and orientation imaging microscope (OIM) have been used to study the cyclic deformation of annealing twin.It found the existence of intrinsic deformation mechanism basing on the findings on the nanoscale. The slips on the planes intersecting and parallelto twin boundaries (TBs) lead to the formation of the unique chevron shapes “∧” and “∨” (consisting of the slopes on two sides of the TB) inthe areas of twin’s two opposite TBs, which makes a regular zigzag shape “/ \ /” or “\ / \”. The tilting angle of the slope increased with cyclenumber increasing in the initial stage, but some decreased due to deformation hardening whereas others continued increasing after certain cycles.The tilting angle of slope changes on the different sites along a long TB.©

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2006 Elsevier B.V. All rights reserved.

eywords: Copper; Deformation; Twin

. Introduction

Twin widely exists in all kinds of materials and has closeelation with many material problems. It affects many materialroperties such as mechanical and electrical properties [1–4],tc. In most practical circumstance, the material is used underyclic stress condition caused by physical contact, vibration,hermal, and electromagnetical factors, etc. Moreover, TBs haveeen shown to be the preferred sites for crack nucleation inyclic deformation [5–10]. Thus, studying the cyclic defor-ation behaviour of twin is helpful to assess the stability ofaterial properties and understand many twin-related problems.sing AFM with the precise measurement of surface profilen nanoscale, together with OIM measuring crystal orientation,report that there is an intrinsic deformation mechanism of

nnealing twin.

. Experimental procedure

Pure copper samples encapsulated in an atmosphere ofure argon were annealed for 50 h at 1000 ◦C in the furnace,

sions are: sample X: 3.75 mm × 2.1 mm × 6.0 mm; sampleY: 3.5 mm × 2.1 mm × 6.0 mm. The sample was then ground,mechanically polished and electropolished. The grain boundary(including the twin boundary) was etched in the electropolishingprocess and can be clearly seen under optical microscope.

The sample was observed and optical micrograghs were takenon Leica optical microscope. Crystal orientation was measuredon orientation image microscope (OIM) in JEOL 840A-OPALSEM whose working voltage is 20 kV, and the configurationof sample surface was measured with atom force microscope(AFM)—Digital Instruments Dimension TM 3100 scanningprobe microscope. The cycling test was conducted on an ESHServo-Hydraulic testing machine served with hydraulic loadingsystem in the air at ambient temperature. The sample was cycledby triangle wave tensile load under stress control with the fre-quency 2 Hz, and the minimum and maximum loads are 19.0and 70.0 MPa for sample X, 13.6 and 42.0 MPa for sample Y,respectively. The crystal orientation is described by pole figureobtained by using OIM. The slip plane and TB are determinedon the pole figure by trace analysis. The angles are measuredfrom the pole figure.

hen furnace cooled to room temperature. The gauge dimen-

∗ Tel.: +86 10 62754147x18; fax: +86 10 62751615.E-mail address: jma2@pku.edu.cn.

The AFM measurement was conducted in the air at theambient temperature. In Fig. 1, the square corresponds to a100 �m × 100 �m AFM scanning area (Area 10 includes sev-eral AFM scanning areas). The section profile in this article isan average profile of many cross-section profiles.

921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2006.04.098

J. Ma / Materials Science and Engineering A 427 (2006) 282–288 283

Fig. 1. Optical micrograph of twins and adjacent grains of sample X (22,000 cycles). Grains and twins are denoted by B1, −B1, B2–B13, and TB areas (dottedsquare) measured by AFM are numbered.

3. Results and discussion

3.1. The observation after cyclic deformation

Only single slip lines can be seen on samples X and Y butnot on most grains of sample Y. No slip lines parallel to TBtrace but intersecting it are seen on sample X, whereas both sliplines parallel to and intersecting TB trace are found on sam-

ple Y. Single slip lines can be seen in B1, B3, B4, B6, B11(Fig. 1), in −B1, B2, B8 under high magnification of opticalmicroscope, and in B12 from AFM micrograph. Crystal orien-tation is the same for B1 and −B1; B7 and B9; B3, B5, B6, B10and B11. On all the operating slip planes determined from traceanalysis, the 〈1 1 0〉 direction making the smallest angle withthe tensile direction has the maximum Schmid factor among all12 slip systems except for that of B12. This result is consis-

284 J. Ma / Materials Science and Engineering A 427 (2006) 282–288

Fig. 2. (a and b) AFM three-dimensional profile of the “∧” and “∨” shapes. (c) Geometry relations of sample surface, TB and slip planes (“∧” shape). The sectionline ac perpendicular to TB trace ab. T, TB plane; S and S′, sample surfaces before and after deformation, respectively; K, plane perpendicular to S and passing ab; Mand N, slip planes with normals 1, 1′ and slip directions 2, 2′, respectively. (d) U ( ) and Q (�) values. For face-center cubic copper, on a slip plane intersecting TB,there are two slip directions intersecting TB denoted by “a” and “b”, and the strains ε produced in B1 along slip directions “a” and “b” are denoted by B1a and B1b,respectively, and so on. Crystal orientation is the same for B1 and −B1; B3, B6 and B11. Q: A, (−)B1a/B2a; B, (−)B1a/B2b; C, (−)B1b/B2a; D, (−)B1b/B2b; E,B3a(6a)/B4a; F, B3a(6a)/B4b; G, B3b(6b)/B4a; H, B3b(6b)/B4b; I, B3a(11a)/B12a; J, B3a(11a)/B12b; K, B3b(11b)/B12a; L, B3b(11b)/B12b. (e) The deformationmodel of twin and adjacent grains. OP and RQ, cross-section of TB. A and G, points on TB trace; C, D, H and E, points on sample surface before deformation.

tent with single crystal deformation, which may results from thebig grain size. The “∧” and “∨” shapes which are caused bythe two sides of a TB protruding outwards and moving inwardsrespectively, are formed in the areas of twin’s two opposite TBs,respectively (Fig. 2(a and b)), which produces the shear com-ponent γ normal to horizontal surface (sample surface beforedeformation),

γR = tan θR = YR

XR, similarly γL = tan θL = YL

XL(1)

γ is on plane K perpendicular to sample surface and passing TBtrace (Fig. 2(c)).

3.2. Analysis of strain propagating across TB

Only single slip lines intersecting TB are observed for sampleX, so suppose single slips on planes M and N (actually on manyplanes parallel to M and N) produce shear strains ε12 and ε′1′2′along the slip directions, respectively. From the strain compati-bility and second order tensors transform under a change of the

J. Ma / Materials Science and Engineering A 427 (2006) 282–288 285

coordinate system [11]:

ε′1′2′ = cos(1′∧1) cos(2′∧2)ε12 (slip propagates from grain to twin);

ε12 = cos(1′∧1) cos(2′∧2)ε′1′2′ (slip propagates from twin to grain)(2)

(1′∧1) is the angle between two normals of slip planes and (2′∧2)is the angle between two slip directions.

Suppose U = ∣∣cos(1′∧1) cos(2′∧2)∣∣, Q = ε′1′2′/ε12 or ε12/

ε′1′2′ , Q < 1. Thus,

U = Q (3)

The strain components γR and γL are produced by ε12 andε′1′2′ , respectively. ε12(ε′1′2′ ) is similarly got from second ordertensors transform and the γ value of AFM measurement,

γ = ε cosω cosψ (4)

ω is the angle between the normal to slip plane and the normal toplane K, and ψ is the angle between the directions of ε12(ε′1′2′ )and γR (γL). To check whether strain compatibility is satisfied,calculations are made for U and Q values to see if they meetEq. (3). For almost all cases, Q �= U (Fig. 2(d)). This indicatesif only single slip intersecting TB occurred, the strain in thegrain cannot be compatible with that in the adjacent twin, andvice versa. Therefore, the strain component γ measured fromthe surface was not produced by single slip but by multiple slip.

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the slope of B3 increased from 0.05◦ to 1.37◦, 0◦ to 0.15◦, and0.23◦ to 0.78◦, respectively. For “∧” shape in Areas 6, 7, 9 onTB B4/B6, the slope of B4 increased from 1.10◦ to 1.19◦, 0.63◦to 1.59◦, and 0.02◦ to 1.06◦; the slope of B6 decreased from1.57◦ to 1.23◦, 1.63◦ to 0.98◦, and 1.51◦ to 0.60◦, respectively.From 1000 to 22,000 cycles, for “∧” shape in Areas 15, 16 onTB B11/B12, the slope of B11 increased from 1.18◦ to 1.79◦,1.22◦ to 1.66◦; whereas the slope of B12 decreased from 0.46◦to 0◦, 0.76◦ to 0.58◦, respectively. Thus, the slope angle can besignificantly different on different sites along long TB trace. Thereason is that the extent of slip bands intersecting TB developsdifferently at different sites under cyclic loading; those slipsinteract with the slips on the planes parallel to TB, and theirco-effect results in the height difference “AB” between sites “A”and “G” on TB trace (Fig. 2(e)). The height difference makesangle difference,∠ADC >∠GHE. The operating slips on planesintersecting and parallel to TB do not take effect independently,they influence and interact to each other, thus the final formedprofile is not simply adding two profiles produced by single slipon planes intersecting TB and on planes parallel to TB. However,the growth or reduction tendency for θ of different sites is similar,which indicates that the slope shape stems from the result of slipon the planes parallel to TB plane. Therefore, the slope angle isjointly contributed by slips on the planes intersecting and parallelto TB. Slopes of “∧” and “∨” shapes forming in B7, B9, B10 andsome grains (twins) of sample Y indicates that slips occurred int

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.3. The cyclic deformation model of annealing twin

The section profile of a twin and two adjacent grains exhibits“/ \ /” or “\ / \” shape with the “∧” and “∨” shapes in the areasf two opposite TBs and TB trace lying on the top of “∧” profiler at the bottom of “∨” profile (Fig. 2(a, b and e)). Consideringtwin under the external force F which can be resolved into twoomponents F⊥ and F‖ perpendicular to and parallel with TBlane respectively, equilibrium demands that,

F⊥ = 0,∑

F‖ = 0, i.e.

⊥OP = −F⊥RQ,−F‖OP = −F‖RQ (5)

hose forces acting on the two TBs are equal in magnitudeut opposite in direction. So F‖OP and −F‖RQ produce sheartresses τTB and −τTB on two TB planes, and moreover, slopesormed at two sides of TB and the displacement (from horizontalurface) caused by slope near TB is larger than that away fromB, which indicates that shear strain was produced and glideccurred between the slip planes parallel to TB plane. The “∧”hape formed by shear stress acting on TB is as if pulling a cardsrom a deck of cards brings its two sides of cards out to form a∧” shape. It is also supported by the evidence that one slope of“∧” shape formed with observation of single slip lines parallel

o TB trace on sample Y. Thus, it is inferred that secondary slipccurred on the slip planes parallel to TB plane on both sides ofB to form the “∧” and “∨” shapes. From 5000 to 22,000 cycles,

or “∨” shape in Areas 3, 4, 5 lying on TB B3/B4 (TB between3 and B4, and so on), the slope of B4 decreased from 3.85◦ to.56◦, 3.42◦ to 2.38◦, and 1.32◦ to 0.92◦, respectively; whereas

hem though no slip line can been seen.

.4. The decrease of slope angle

The height of most “∧” and “∨” shapes ranges from hundredsf nanometers to 2–3 �m. The typical developing tendency oflope angle θ for “∧” and “∨” shapes is shown in Fig. 3(a and), respectively. It indicates that the angle increment was theargest in the first 1000 cycles, because the harden process didot proceed too much in the initial stage. From 1000 to 5000ycles, most slope angles continued increasing, but the growthate greatly reduced due to hardening. However, from 5000 to2,000 cycles, although some angles still increased, other anglesecreased. The changing tendency of other areas is similar withhose in Fig. 3. Sample Y shows some similarities, its largestngle increment with 0.50–0.69◦ occurred in the first 1000ycles, whereas it slightly increased to 0.63–0.91◦ after 800,000ycles due to hardening indicated by Vickers hardness numberncreasing from 52 (before cycling) to 57.7. Besides reduced θalues mentioned in preceding paragraph, other reduced valuesre as follows, for “∧” shape: from 5000 to 22,000 cycles, θ for2 in Area 1 (2.15◦↘1.69◦), for B6 in Area 8 (1.71◦↘1.16◦).or “∨” shape, θ for B3 in Area 17 from 1000 to 22,000 cycles1.11◦↘0.54◦); from 5000 to 22,000 cycles, θ for B2 in Area

(1.87◦↘1.40◦). Peralta et al. [12] suggested that the regionround a TB may suffer a higher level of hardening than the restf the material far from grain boundaries (or TBs) due to doublelip. In this work, TB lying at the top of “∧” or bottom of “∨”hapes indicates that the displacement of an area close to TB isarger than that of the area away from TB. Therefore, in the firstcycles, the area close to TB becomes harder than the area away

286 J. Ma / Materials Science and Engineering A 427 (2006) 282–288

Fig. 3. Typical curve of slope angle θ varying with cycles. (a) For the “∧” shape. �, B2 in Area 1; , B1 in Area 1; , B4 in Area 6; , B6 in Area 6; , B7 inArea 13; , B8 in Area 13. (b) For the ”∨” shape. �, B2 in Area 2; , −B1 in Area 2; , B8 in Area 14; , B9 in Area14; , B3 in Area 4; , B4 in Area 4.

from TB because its larger displacement is produced by muchslip than that of the area away from the TB. As a result, in thenext m cycle process, less slip could occur in the area near TBthan away from TB, so the displacement growth of the area nearTB could be less than that in the area away from TB, ee′ < dd′(Fig. 4(a), take the example of “∧” shape, similarly in case of“∨” shape). It leads to θ′ < θ, the angle of slope decreased aftern + m cycles.

3.5. The comparison of narrow twin and general twin

The twins and adjacent grains display similar “∧” and “∨”shapes which constitute the “/ \ /” or “\ / \” shape (Fig. 4(b)).But for the large twin B4, the “∧” and “∨” shapes only lieon TB area, in the middle of twin B4 (Area 10), the slopegradually disappears. This also indicates that the “∧” and “∨”shapes are the characteristics relating to TB. Most θ values lieapproximately between 0.50◦ and 1.80◦, and the maximum θ

value is 3.85◦. But for sample Y, θ values range from 0.50◦ to0.91◦, which indicates that the angle decreases with the loadreducing.

On the two sides of twin B5, the left side sheared upwardsfrom the surface and the right side sheared downwards(Fig. 4(c)), the tilt of B5 surface “dc” indicates that the obviousshear strain occurred. From 1000 to 22,000 cycles, slope “ae”increased from 0.28◦ to 0.58◦, however, slope “bg” decreased

from 1.90◦ to 1.69◦, and slope “dc” (1.03◦) remained almostunchanged. This suggests that the small slope value (0.28◦) cor-responds to less displacement produced by slips, so it did notharden much after 1000 cycles. But the relatively larger θ value(>1◦) corresponds to larger displacement produced by slips inTB area, so it had hardened during the first 1000 cycles. Theprofile displays a “/ \ /” shape. Those results are consistentwith the above-mentioned twins. However, as a narrow twin(width 12.1 �m), the profile of B4 has some difference withthat of wider twins. ‘dc’ is the common slope of both “∧”and “∨” shapes, but for wider twin, the “\” slopes of “∧”and “∨” shapes are not overlapped and their slope angles aredifferent.

3.6. Twin lying in another twin

Twin B13 lies in twin B12 and it moved downwards from B12surface after loading (Fig. 4(d)): HL = 362 nm (1000 cycles),438 nm (22,000 cycles); HR = 124 nm (1000 cycles), 86 nm(22,000 cycles), HL (HR) is the height difference between left(right) TB B12/B13 trace and the left (right) surface of B12(before deformation, due to electropolishing, left and right TBB12/B13 traces protruded 96 and 80 nm from their surroundingsurface, respectively, and right TB trace is lower than left TBtrace by 21 nm). Therefore, meanwhile the displacement down-wards from their surrounding surface increased 76 nm for left

J. Ma / Materials Science and Engineering A 427 (2006) 282–288 287

Fig. 4. The section profiles. (a) θ angle decreases with increasing cycles (“∧” shape). ab, section line of sample surface before deformation; ac and ac′, section linesof TB plane after n and n + m cycles, respectively. cd and c′d′, section lines of the slopes formed after n and n + m cycles, respectively. (b) Deformed twin and adjacentgrains. (c) B4 and narrow twin B5. de and cb, steps produced on TBs by electropolish; dc, section line of B5 surface. (d) Twin B13 lies in twin B12. HL (HR) is theheight difference between the left (right) TB trace of B13 and the left (right) surface of B12, and HTB is the height difference between left and right TB traces. LS,left surface; RS, right surface.

TB trace and decreased 38 nm for right TB trace. Moreover,the downward slope on the left hand of left TB trace increasedfrom 1.24◦ to 1.43◦. Those indicate that left TB trace moveddownwards from 1000 to 22,000 cycles. However, the distancebetween it and right TB trace remained almost unchanged,HTB = 352 nm (1000 cycles), 355 nm (22,000 cycles). Thus,right TB trace also moved downwards to maintain their dis-tance unchanged. The distance decreasing between right TBtrace and the right surface indicates that the right surface alsomoved downwards. Fig. 4(d) is got from the bottom of Area 18lying in the area near TB B12/B3 where the downward slope(dotted line) of “∨” shape should have formed, which leads totwin B13 and the right surface to sink downwards. However,right TB trace being higher than left TB trace indicates thatthe shear stress direction is downward on left TB and upwardon right TB, which should have produced “∧” shape (dashedline) to lift up twin B13 and the right surface. In fact, the oper-ating slip systems to form those two profiles (dotted line anddashed line) interact to each other, which make the eventu-

ally formed profile (Fig. 4(d)) is not simply one profile plusthe other.

4. Conclusion

(1) The unique chevron shapes “∧” and “∨” (consisting of theslopes on two sides of the TB) formed in the areas of twin’stwo opposite TBs, respectively. The twin and two adjacentgrains make a regular zigzag shape “/ \ /” or “\ / \” which isproduced by the slips on the planes intersecting and parallelto TB.

(2) The tilting angle of the slope increased with cycle numberincreasing in the initial stage, but some decreased due todeformation hardening whereas others continued increasingafter certain cycles.

(3) The tilting angle of slope changes on the different sites alonga long TB. The slope disappears in the middle of the widetwin. For narrow twin, the “\” slopes of “∧” and “∨” shapesare overlapped.

288 J. Ma / Materials Science and Engineering A 427 (2006) 282–288

(4) In case of a twin lying in another twin, the profile was deter-mined jointly by those two twin’s movement.

Acknowledgements

I thank S. Dipple for help with AFM experiment and D. Pricefor assistance with cyclic test. I am grateful to the British Depart-ment for Education and Skills for financial support of this work.

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