Materials Science and Engineering A 501 (2009) 1–5

Contents lists available at ScienceDirect

Materials Science and Engineering A

journa l homepage: www.e lsev ier .com/ locate /msea

AFM and OIM study of cyclic deformation behaviors of polycrystalline copper

Jun MaDepartment of Materials Science and Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA

a r t i c l e i n f o

Article history:Received 17 February 2008Received in revised form 18 June 2008Accepted 7 October 2008

a b s t r a c t

Using the atomic force microscope (AFM) and orientation imaging microscopy (OIM), slip deformation ofpolycrystalline copper under cyclic loading was studied. It was found that under cyclic load the operatingslip systems of coarse grains in polycrystalline copper are consistent with the Schmids law of single crystal.The micro-strain of the sample surface was compared with its corresponding macro-strain (of the wholesample), and the loading effect on the deformation was analyzed.

Keywords:Atomic force microscope (AFM)Orientation image microscopy (OIM)PolycrystallineS

© 2008 Elsevier B.V. All rights reserved.

1

s�mrsltbotuwc

otawpoc

2

2

acAmgHt

2

CwLOpI

0d

lip

. Introduction

When a single crystal is loaded by an applied force, the sheartress acting on the slip plane along the slip direction is [1]:= � cos � cos �, where � and �, are the angles the slip plane nor-al and the slip direction oriented with respect to the loading axis

espectively. When � reaches a critical value (the critical resolvedhear stress �crss) a slip system starts to operate. This is the Schmidsaw. Taylor [2] found that if the shear stress is resolved parallelo all the four possible slip planes in each of the three possi-le directions of slip in an fcc crystal, the operative slip is thatne of the 12 possible for which the shear stress is greatest inhe single crystal. One purpose of this paper is to test whethernder the cyclic load the operating slip systems in polycrystallineith coarse grains are consistent with the Schmids law of single

rystal.Classical research studies using optical metallography have

bserved slip in grains. Nowadays, technology is available to studyhe surface profiles of materials after cyclic deformation by usingtomic force microscope (AFM), and to study crystal orientationith orientation imaging microscopy (OIM), as described in thisaper. This provides new information needed to be analyzed inrder to describe detailed study of slips of cyclic deformed poly-

rystalline copper.

E-mail address: jma15@jhu.edu.

ATmtlmar

921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2008.10.007

. Experimental procedure

.1. Materials

Pure copper samples encapsulated in an atmosphere of purergon were annealed for 50 h at 1000 ◦C in the furnace, then furnaceooled to room temperature. The gauge dimensions were: sample: 3.5 mm × 2.1 mm × 6.0 mm; sample B: 3.75 mm × 2.1 mm × 6.0m; sample C: 3.8 mm × 2.1 mm × 6.0 mm. The samples were

round, mechanically polished, then electropolished in 50% (v/v)3PO4 for 1 min, and dipped in 10% (v/v) H3PO4 for 10 s to remove

he surface layer produced by electropolish.

.2. Mechanical testing and characterization

The samples were examined using Leica optical microscope.rystal orientation was measured on OIM in JEOL 840A-OPAL SEMith working voltage of 20KV. OIM was equipped with the software

ink Opal Revision 3.0 (OPAL MAN 3.0). The sample tilted 70◦ inIM, and the working distance is 17 mm. The configuration of sam-le surfaces of samples A and B was measured with AFM—Digital

nstruments Dimension TM 3100 Scanning Probe Microscope. TheFM measurement was conducted in air at ambient temperature.he cycling test was conducted on an ESH Servo-Hydraulic testingachine served with hydraulic loading system in air at ambient

emperature. The samples were cycled by triangle wave tensileoad under stress control with frequency of 2 Hz. The minimum and

aximum load were 13.6 MPa and 42.0 MPa for sample A, 19.0 MPand 70.0 MPa for sample B, 17.9 MPa and 100.0 MPa for sample C,espectively. The cycle number of sample A was 1000 and 800,000,

2 J. Ma / Materials Science and Engineering A 501 (2009) 1–5

Fifi

srpom

Ttanb

3

3

FsmihiBBoScissiAi

3

dftsd

Table 1The orientations of B3, B6, B11 are the same. P1, P2, P3, and P4 represent the fourdifferent {1 1 1} planes. F1, F2, and F3 are the Schmid factors corresponding to the

�1, �2, and �3 values, respectively. ‘a, b, c, d, e, and f’ represent the different⟨

1 1̄ 0⟩

directions.

� �1 �2 �3 F1 F2 F3

B1P1 86◦ b 40◦ e 22◦ f 82◦ 0.05 0.06 0.01P2 25◦ a 74◦ d 66◦ f 82◦ 0.25 0.37 0.13P3 70◦ c 61◦ d 66◦ e 22◦ 0.17 0.14 0.32P4* 51◦ a 74◦ b 40◦ c 61◦ 0.17 0.48*,** 0.31

B2P1* 48◦ a 42◦ b 70◦ d 66◦ 0.50*,** 0.23 0.27P2 32◦ b 70◦ c 61◦ f 80◦ 0.29 0.41 0.15P3 70◦ c 61◦ d 66◦ e 22◦ 0.17 0.14 0.32P4 80◦ a 41◦ e 22◦ f 80◦ 0.13 0.16 0.03

B3 (B6, B11)P1* 53◦ a 76◦ b 57◦ c 40◦ 0.15 0.33 0.46*,**P2 62◦ a 76◦ e 34◦ f 54◦ 0.11 0.39 0.28P3 40◦ b 57◦ d 87◦ f 54◦ 0.42 0.04 0.45P4 68◦ c 40◦ d 87◦ e 34◦ 0.29 0.02 0.31

B4P1* 67◦ a 32◦ b 85◦ c 40◦ 0.33*,** 0.03 0.30P2 5◦ b 85◦ d 87◦ f 88◦ 0.09 0.05 0.03P3 77◦ a 32◦ e 34◦ f 88◦ 0.19 0.19 0.01P4 68◦ c 40◦ d 87◦ e 34◦ 0.29 0.02 0.31

B8P1 42◦ c 86◦ f 54◦ a 57◦ 0.05 0.44 0.40P2 69◦ c 86◦ d 33◦ b 41◦ 0.02 0.30 0.27P3* 51◦ a 57◦ e 78◦ b 41◦ 0.34 0.13 0.47*,**P4 61◦ f 54◦ d 33◦ e 78◦ 0.28 0.41 0.10

B12P1* 19◦ a 72◦ b 86◦ c 76◦ 0.29* 0.07 0.23P2 62◦ c 76◦ e 34◦ f 54◦ 0.11 0.39** 0.28P3 66◦ a 72◦ d 26◦ f 52◦ 0.13 0.37 0.25P4 90◦ b 86◦ d 26◦ e 34◦ 0 0 0

P0(

wmsu5ptwFsoatwlstms

s

ig. 1. Optical micrograph of slip bands in grains of sample C after 1000 cycles. Insets the optical micrograph of grains of sample A after 800,000 cycles. Arrows indicatene slip lines.

ample B was 1000, 5000 and 22,000, and sample C was 1000,espectively. The crystal orientations were determined from theole figures of OIM measurement. The slip planes were determinedn the pole figure by trace analysis, and the angles �0 and �0 wereeasured from OIM pole figure.The samples’ surface was etched in the electropolishing process.

he etching extent was quite different. Grain boundary (includingwin boundary) was etched and can be clearly seen in samples And B under optical microscope, but the surface of sample C wasot etched and the grain boundary cannot be seen. However, grainoundaries in sample C can be clearly seen after cyclic deformation.

. Results and discussion

.1. Slip systems and Schmid factor

A low stress range (�� = 28.4 MPa) was applied to sample A.ew obvious slip bands can be seen in most grains or twins, andlip occurred in only a few areas. As observed under the opticalicroscope, the slip was still very fine after 800,000 cycles (Fig. 1,

nset). Obvious slip bands formed in sample B (Fig. 2), and moreeavy slip bands were produced in sample C (Fig. 1) due to increas-

ng load. As shown in Table 1, except one case for a “narrow” twin12, all operating slip systems in indicated grains/twins in samplesare on the slip plane which has the maximum Schmid factor. Theperating slip systems of samples A and C also have the maximumchmid factor. This indicates that the operating slip systems underyclic load were consistent with the Schmids law and Taylor’s find-ng [2]. Although the test material is polycrystalline copper, its grainize is large, up to several hundreds of microns. It is reasonable touppose that the large grain size enables the system to response asf a set of independent single crystals of independent orientations.s shown in Fig. 3, the Schmid factor of most operating slip systems

s the big value, close to the largest value of Schmid factor, 0.5.

.2. Cyclic deformation behavior

As indicated by the previous paper [3], the micro-strain pro-

uced by the slip bands on the surfaces of samples A and B variedrom the magnitude orders of 10−3 to 10−2. This article discusseshe comparison of the micro-strain of sample surface with its corre-pondent macro-strain (of the whole sample) and the larger surfaceeformation produced by the larger load in the other work.

ccttP

n* represents the operating slip plane. A asterisk (*) with the Schmid factor such as.48* represents the Schmid factor of the operating slip system, a double asterisks**) with the Schmid factor represents the maximum Schmid factor in slip systems.

Cyclic stress–strain curve of annealed polycrystalline copperas reported in Ref. [4], which can be used to approximately esti-ate the stress/strain relationship, i.e. the strain produced by the

aturation stress amplitude in the present experiments. The sat-ration stress amplitudes for samples A, B and C were 28.4 MPa,1.0 MPa and 82.1 MPa, respectively. Thus, it was estimated that thelastic saturation strains were about 10−6 to 10−5 for sample A, 10−5

o 10−4 for sample B, 10−4 for sample C, respectively. These strainsere macro-strains in contrast to the micro-strains (e.g. � = y/x in

ig. 2, inset) on the sample surface formed by the slip bands. Theurface micro-strains of one grain of sample A produced by the slipn slip plane were 3.88 × 10−2 and 4.84 × 10−2 after 1000 cyclesnd 800,000 cycles, respectively [3], which were much larger thanhe macro-strain value, 10−6 to 10−5. In sample B, the micro-strainsere the magnitude orders, 10−3 to 10−2 [3]. Those were also far

arger than the macro-strain 10−5 to 10−4. However, there wereome areas which displayed relatively ‘flat’ profiles correspondingo very small shear strain between the slip bands. Therefore, the

icro-strain in some local areas in the samples was found to beignificantly larger than the macro-strain of the whole sample.

Persistent slip bands (PSBs) were observed more frequently iningle crystals oriented for single glide than in multiple-slip singlerystals or in polycrystals [5–10]. The formation of PSBs in poly-

rystals was relatively complex. Some researchers [5,11] found thathe formation of PSBs was confined mainly to the areas adjacento twin boundaries whereas grain interiors were almost entirelySB free for low-amplitude fatigue. Cottrell and Hull [12] and Hull

J. Ma / Materials Science and Engineering A 501 (2009) 1–5 3

F ) [15]p rograD

[ctbsoaACban

btTa1

[c

gtasiacsts

ig. 2. Optical micrograph of twins and adjacent grains of sample B (22,000 cyclesicture. Slip lines on B2 and B8 can be seen on the high magnification of optical micash line x corresponds to the section line of sample surface before deformation.

13] studied PSBs in copper polycrystals fatigued in push–pull atonstant stress amplitude and found that PSBs along the slip planeraces consisting of extrusions and intrusions in comparable num-ers. Secondary slip can prevent PSB formation. Wang et al. [14]howed TEM results and reported that a labyrinth structure insteadf ladder-like PSB structure formed when the secondary slip oper-ted. In the present experiments, no PSBs were produced in samples, B and C, which is consistent with the Ref. [14]. In samples B and, the primary slip bands intersect twin boundaries. Secondary slipands cannot be seen but it is inferred to be parallel to twin bound-ry plane [15]. The secondary slip may be the reason that PSBs didot form.

Cretegny and Saxena [16] reported that the height of the slip

ands was found to vary between 30 and 900 nm, which is largerhan the height varying from 160 to 570 nm in the present work.he reason may be that the macroscopic strain for sample B isbout 10−5 to 10−4 which is far below that for samples tested at.61 × 10−3 strain amplitude in the work of Cretegny and Saxena

atRab

. Grains and twins are denoted by B1, B2,. . ., B13. Slip on B12 can be seen on AFMph. Inset is the example of section figure of the sample B surface after 5000 cycles.

16]. Both heights are much lower than those observed in singlerystals, which were on average between 3 and 4 �m high [17–20].

Boettner et al. [21] carried out four-point bending tests on large-rained specimens of copper. Deformation was more intense nearwin boundaries than within the grains. Material was extruded toheight of 4 �m above the surface in contrast to a 1.5 �m extru-

ion (for slip bands within the grains). Boettner et al. found limitedntrusions which had not been indicated relating to twin bound-ries. The extent of intrusion formation was limited and did notorrespond to the quantity of material extruded. Except that theimilarity of the formation of the extrusion at twin boundaries,he present results are different from these findings. The intru-ion shape ‘∨’ (Fig. 4(a)) and the extrusion shape ‘∧’ (Fig. 4(b))

dopts its formation of a pair, associating with the two oppositewin boundaries of the twin. A crack formed in an extrusion inef. [21]. However, in the present experiments, no crack formedt the ‘∧’ or ‘∨’ shape or other positions. The materials used inoth sets of experiments are similar: OFHC polycrystalline copper,

4 J. Ma / Materials Science and Eng

Fig. 3. The values of Schmid factor for different grains (twins). ‘A1 and A2’ representgBrc

airfcpu

Fot

awRrwtwH2w

pbtrouessgttr

rains of sample A; ‘B1, B2, B3, B4, B12, and B8’ represent grains (twins) of sample, ‘C1, C2, C3, C4, C5, and C6’ represent grains (twins) of sample C. The ‘star’ symbolepresents an exception example of the twin B12 whose operating slip system is notonsistent with the Schmids law.

nnealed at 1050 ◦C for 48 h in Ref. [21] and at 1000 ◦C for 50 hn the present work. The presence or absence of cracks probably

elates to difference in the plastic strain applied. In Ref. [21], theour-point bending tests under fully reversed strain conditions wereonducted at surface strains ranging from 10−3 to 2 × 10−3. In theresent experiments, a cyclic tensile test with positive �min wassed. The saturation stress amplitude �� for sample B was 51 MPa,

ig. 4. The intrusion ‘∨’ shape (a) and the extrusion ‘∧’ shape (b) formed on the twopposite twin boundary areas of a twin (22,000 cycles). The black arrows indicatehe slip bands.

te1igcsItli

4

2

3

A

af

R

ineering A 501 (2009) 1–5

s estimated above, the macroscopic saturation strains of sample Bas about the order 10−5 to 10−4, which is far less than the strains inef. [21]. This may be the reason that the fatigue lifetimes of mate-ial in the previous bending tests varied from 103 to 107 cycles [21]hereas no crack even formed after 2.2 × 103 cycles in the present

est. The extrusions at a twin boundary reached a height of 4 �mhich is larger than the height of the ‘∧’ shape in the present work.owever, an extrusion at twin boundary in Ref. [21] was found to be�m, which is close to the height of some ‘∧’ shapes in the presentork.

For annealed material under stress control, the strain amplituderoduced by the stress amplitude is the largest in the first cycle [22],ut such strain cyclically hardens the specimen and the strain con-inuously decreases during the initial period of cycling, and finallyeaches a saturation value after some hundreds of cycles dependingn the material and the stress amplitude. For polycrystalline coppernder load control, the saturation strains of specimens with differ-nt loads range from a scope rather than the close value when theaturation is achieved [4]. In Ref. [4], for the curve of the saturationtress amplitude of 52 MPa, in the first 1000 cycles, the strain valueradually decreased due to hardening. With the cycles increasingo 5000 cycles, the responding strain continually decreased due tohe hardening. From 5000 to 22,000 cycles, the responding straineduced to the saturation strain value. The saturation stress ampli-ude of sample B was 51.0 MPa. The slope (Fig. 4) growth of thextrusion (‘∧’) and intrusion (‘∨’) shapes was largest in the first000 cycles. From 1000 to 5000 cycles, due to the material harden-ng in the first 1000 cycles, the slope still grew but the amount ofrowth was less than in its first 1000 cycles. From 5000 to 22,000ycles, some slopes still increased but the amount of growth wasmall; other slopes remained almost unchanged or even decreased.n the case of slope decreasing, the displacement (due to deforma-ion) of the sample surface in areas away from twin boundary wasarger than that in twin boundary area because the hardening wasncreasing with the position close to twin boundary.

. Conclusions

1. The operating slip systems in the cyclic deformed polycrystallinewith the coarse grains are consistent with the Schmids law ofsingle crystal, namely, the operating slip system is the one hasthe largest value of Schmid factor.

. The micro-strain of the sample surface could be much larger thanthe macro-strain of the whole sample. No persistent slip bandsformed for the saturation stress amplitude �� of 51 MPa and82.1 MPa.

. Though being somewhat similar, the extrusion and intrusionin twin boundary area have the different characteristics frommacroscopic extrusion and intrusion under cyclic deformation.

cknowledgment

I thank S. Dipple for help with AFM experiment and D. Price forssistance with cyclic test. I am grateful to the British Departmentor Education and Skills for financial support of this work.

eferences

[1] S. Suresh, Fatigue of Materials, Cambridge University Press, Cambridge, 1991.[2] G.I. Taylor, J. Inst. Metals 62 (1938) 307.[3] J. Ma, Mater. Sci. Eng. A 457 (2007) 63.

[4] J.C. Figueroa, S.P. Bhat, R. De La Veaux, S. Murzenski, C. Laird, Acta Metall. 29

(1981) 1667.[5] H. Mughrabi, R. Wang, in: N. Hansen, A. Horsewell, T. Leffers, H. Lilholt (Eds.),

Proceedings of the Second RisØ International Symposium on Metallurgy andMaterial Science, RisØ National Laboratory, RisØ, Roskilde, 1981, p. 87.

[6] A.T. Winter, O.B. Pedersen, K.V. Rasmussen, Acta Metall. 29 (1981) 731.

d Eng

[[

[[[[

[[

J. Ma / Materials Science an

[7] A. Ackermann, L.P. Kubin, J. Lepinoux, H. Mughrabi, Acta Metall. 32 (1984) 715.[8] N.Y. Jin, A.T. Winter, Acta Metall. 32 (1984) 1173.[9] Z.S. Basinski, S.J. Basinski, Acta Metall. 33 (1985) 1319.10] L. Llanes, C. Laird, Mater. Sci. Eng. 157 (1992) 21.11] P. Neumann, A. Tönnessen, in: P.O. Kettunen, T.K. Lepistö, M.E. Lehtonen (Eds.),

Proceedings of the Eighth International Conference on the Strength of Metalsand Alloys, vol. 1, Tampere, Finland, Pergamon, Oxford, 1988, p. 743.

12] A.H. Cottrell, D. Hull, Proc. R. Soc. A 242 (1957) 211.13] D. Hull, J. Inst. Metals 86 (1957–58) 425.14] Z. Wang, B. Gong, Z. Wang, Acta Mater. 45 (1997) 1379.15] J. Ma, Mater. Sci. Eng. A 427 (2006) 282.

[[[[[

ineering A 501 (2009) 1–5 5

16] L. Cretegny, A. Saxena, Acta Mater. 49 (2001) 3755.17] H. Mughrabi, R. Wang, K. Differt, U. Essmann, in: J. Lankford, D.L. Davidson, W.L.

Morris, R.P. Wei (Eds.), Fatigue Mechanisms: Advances in Quantitative Mea-surements of Physical Damage, ASTM STP 81, American Society for Testing andMaterials, USA, 1983, p. 5.

18] A. Hunsche, P. Neumann, Acta Metall. 34 (1986) 207.19] J. Polák, T. Lepistö, P. Kettunen, Mater. Sci. Eng. 74 (1985) 85.20] Z.S. Basinski, S.J. Basinski, Acta Metall. 33 (1985) 1307.21] R.C. Boettner, A.J. McEvily, Y.C. Liu, Phil. Mag. 10 (1964) 95.22] C. Laird, in: R.W. Cahn, P. Haasen (Eds.), Physical Metallurgy, vol. III, North-

Holland, New York, 1996, p. 2294.