Materials Letters 98 (2013) 82–85

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Materials Letters

0167-57

http://d

n Corr

E-m

journal homepage: www.elsevier.com/locate/matlet

Effect of prior deformation on internal friction in a Fe–Ni basedaustenitic alloy

Zhongwen Li, Xiaofeng Hu, Mingjiu Zhao, Lijian Rong n

Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, China

a r t i c l e i n f o

Article history:

Received 19 December 2012

Accepted 1 February 2013Available online 8 February 2013

Keywords:

Fe–Ni based alloy

Microstructure

Viscoelasticity

Internal friction

Prior deformation

7X/$ - see front matter & 2013 Elsevier B.V.

x.doi.org/10.1016/j.matlet.2013.02.002

esponding author. Tel./fax: þ86 024 2397197

ail address: ljrong@imr.ac.cn (L. Rong).

a b s t r a c t

Effect of prior deformation on strain amplitude-dependent internal friction has been studied in a Fe–Ni

based austenitic alloy subjected to solution and peak-aged treatment. The internal friction initially

shows increase and then decreases with pre-strain increase in solution-treated alloy. Nevertheless, it is

interesting to find that the internal friction shows continued increase with prior deformation degree in

peak-aged alloy. Results could be explained using the breakaway model of dislocation in both state

alloys. The discrepancy of internal friction behavior, correlated to dislocation arrangement observation,

is discussed in terms of slip mode transition from wavy slip to planar slip with introduction of coherent

precipitation particles.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Extensive researches have been performed on the effect ofprior deformation on internal friction (IF). It was usually foundthat subtle plastic deformation would cause an increase in IF.Nevertheless, the IF would then decrease with further priordeformation, and was even independent of strain amplitude [1].At large amount of prior deformation, similar decrease of IF hasbeen found in single crystal copper [2], polycrystalline copper [3]and Fe–Mn shape memory alloy [4,5]. The relevance of IF todeformation is a direct result of dislocation oscillation as thedominant source of IF. It is believed that the investigation of IFcan detect useful information about plastic deformation bydetermining the contributions from dislocation [6].

For alloys containing secondary phases, Zhang et al. [7] did anexcellent review in which the effects of secondary phases on IFwere summarized. However, the research of the effect of priordeformation on IF in alloys with secondary phases was notmentioned. Until now, there are few reports on it. In this paper,the effect of prior deformation on IF is reported in Fe–Ni basedalloy with solution and peak-aged state. Particular attention ispaid to detect IF behavior in peak-aged alloy.

2. Materials and methods

A Fe–Ni based austenitic alloy was obtained by melting thefollowing nominal compositions in a vacuum induction furnace:30Ni–15Cr–1.3Mo–2.0Ti–0.26Al–0.2Si–0.002B–Fe balance (wt%).

All rights reserved.

9.

After homogenization, bars were produced by forging and rollingthe ingots with intermediate softening annealing treatment. Barswere then solution treated at 1253 K for 1 h and water quenchedto produce a supersaturated solid solution structure of equiaxedgrains (referred to as ST). Some solution-treated bars were furthersubjected to peak-aged treatment at 1013 K for 8 h (referred to asPA). The ordered fcc g0 (Ni3Al) phase was uniformly dispersed ingrains, and coherent with austenite matrix in PA alloy. The detailsof the microstructure are provided in reference [8].

The gauge section size of tensile-strained samples was designedaccording to calculation by DEFORM software to fulfill the dimen-sion of 60�10�1 mm3 for IF measurement after individualdeformation. The samples were cut from bars, subjected tomechanical polishing, and then electro-polished to remove surfacestress layer. Prior tensile deformation was performed on a Dcs-10Ttensile machine at room temperature to induce uniform pre-strainbefore necking. IF measurement samples were cut from the parallelsection. Measurement was carried out on a TA Q800 DynamicMechanical Analyzer with dual cantilever at a frequency of 1 Hzand temperature of 298 K and the strain amplitude was in therange of elastic deformation. Five samples of each state alloy weremeasured and statistic IF data deviation at strain amplitude of1.5�10�5 was within 1.39%. In the above-mentioned prior defor-mation, several specimens were strained to failure to studydeformation microstructures. Microstructures at 5% strain andfailure were observed on Philips-Tecnai20 TEM.

3. Results and discussions

Fig. 1 represents strain-amplitude dependent IF behavior of STand PA alloy with different prior deformation. In ST alloy, the IF,

Fig. 1. (a) and (b) Variations of IF with strain amplitude of ST and PA alloy, respectively. (c) Variations of IF with pre-strain at strain amplitude of 1.5�10�4 in (a) and (b).

Fig. 2. The relationship of ln(dhe) versus 1/e in (a) ST and (b) PA alloys.

Table 1C1 and C2 values of experimental alloy after different prior deformation.

Pre-strain (%) ST PA

C1 (10�6) C2 (10�4) C1 (10�6) C2 (10�4)

0 4.35 2.45 2.96 2.38

5 7.96 2.43 3.23 2.40

18 2.57 2.47 5.03 2.37

Z. Li et al. / Materials Letters 98 (2013) 82–85 83

compared to undeformed samples, increases at 5% pre-strain andthen exhibits drastic decrease at further deformation of 18% asshown in Fig. 1a. Though IF in PA alloy increases at 5% pre-strain,which is similar to ST alloy, the IF behavior does not correspond tothe decreasing trend but shows increase at 18% pre-strain (Fig. 1b).Based on the results of strain-amplitude dependence of IF underdifferent prior deformation, variation of IF with pre-strain can beobtained and the typical IF at strain amplitude of 1.5�10�4 isillustrated in Fig. 1c. It can be found in ST alloy, IF increases rapidly toa maximum at 5% pre-strain and then decreases steeply with furtherincrease of pre-strain. Nevertheless, the IF always increases with pre-strain in PA alloy. This observation of the continuous enhancement inIF with pre-strain increase is new and has not been reported before.

Several dislocation mechanisms can explain strain amplitude-dependent IF, such as relaxation mode, drag mode and dislocationbreakaway model [9]. The G–L model, proposing quantitatively IFvalue based on the breakaway model, is used to discuss IF behavior[10]. The dislocation can overcome the pinning of weak point defects(solute atoms) under applied stress. Two IF mechanisms, bowing outand breakaway, occur in dislocation oscillation between weak pin-ning points and between strong pinning points (dislocation tanglesand precipitation particles), respectively. The energy loss originatingfrom bowing out is strain-amplitude independence of IF, di. It is notdiscussed here due to less di. The energy loss from breakaway isstrain-amplitude dependence of IF, dh. The dh shows marked depen-dence on strain amplitude beyond critical strain, ecr, which isachieved by drawing tangent of di and dh. The dh is expressed by

dh ¼C1

e exp�C2

e

� �ð1Þ

C1 ¼4Oð1�nÞ

p3

LL3N

LcC2, C2 ¼

KbZLc

where e is the strain amplitude, O is an orientation factor, n isPoisson’s ratio, K is a factor depending on the anisotropy of the elasticconstants and the orientation, b is the Burgers vector, Z is Cottrell’smisfit parameter, LN is the average distance between strong pinningpoints, L is the movable dislocation density, and Lc is the averagedistance between weak pinning points [10].

In order to verify if dh is accurate to breakaway model, Eq. (1)can be alternated to

lnðdheÞ ¼ lnC1�C2

eð2Þ

It is considered that ln(dhe) versus 1/e should be a straight line,whose slope and intercept are –C2 and –ln C1, respectively.

Fig. 2 represents the relationship between ln(dhe) and 1/e in STand PA alloys. It is found that ln(dhe) and 1/e are in accord withpredicted linear relationship at high strain-amplitude beyond ecr,and thus the IF mechanism of ST and PA alloys is consistent with thebreakaway model. Additionally, the values of C1 and C2 are obtainedas listed in Table 1. A notable feature is that the value of C2 appearsto be independent of pre-strain not only in ST alloy but also in PAalloy since all lines have the same slope for each state alloy. Thus,the value of dh is determined by C1 at a given stain amplitude.

Fig. 3. TEM images of specimens subjected to (a) failure and (b) 5% pre-strain in PA alloy, and (c) failure in ST alloy.

Fig. 4. Schematic illustrations of dislocation oscillation resulting in dh when g0

particle is intact, partly sheared and completely sheared.

Z. Li et al. / Materials Letters 98 (2013) 82–8584

In ST alloy, small deformation creates new dislocations, so thatdislocation multiplication prevails. Therefore, the increase ofdislocation density leads to an increase in C1 and IF. At higherdeformation, the initial increase in IF associated with the increaseof dislocation density is offset when the average network length,LN, is reduced by dislocation tangles, which leads to the decreaseof C1 at higher pre-strain. The IF behavior of ST alloy in thisinvestigation is in good agreement with previous reports [1].

Ageing in ST alloy causes a change of obstacles impedingdislocation oscillation by the formation of g0 particle, which is astrong pinning point, and the less IF in PA alloy than that in ST alloywithout deformation can be explained. The result is in accordancewith Wang’s report in aged Cu–Al–Mn alloy [11]. Since lower IFshows that dislocation escapes from the atmospheres of pinningobstacles more difficultly, it can be assumed that the stress for theactivation of dislocation source increases after PA [12]. Therefore,the increase of IF caused by dislocation density at 5% pre-strain isalso much less pronounced, as compared with ST alloy.

To understand why IF of PA alloy increases with pre-strain, thecomparison of TEM microstructure between ST alloy and PA alloywas performed. During macro-plastic deformation, slip is initiallyplanar in PA alloy because dislocations shear g0 particles andthereby enforce continued slip on the first slip plane which is

active [13]. Thus following dislocations overcome obstacles ofonly minor strength on the activated slip plane until the particleshave been totally sheared [14]. This can be illustrated in Fig. 3aand b showing that the distribution of dislocation is moreuniform, and additionally g0 particles are sheared by dislocationon slip plane in localized region, a typical slip planarity mode.Nevertheless, a wavy slip mode was observed in ST alloy, in whichdislocation distribution is uneven and most dislocations areclustered in high density regions adjacent to areas which arealmost dislocation free, as shown in Fig. 3c.

In general, movable dislocation density can be basically con-sidered to maintain invariable with deformation increase to acertain extent [15], which cannot make contribution to IF anylonger. In ST alloy, dislocations oscillation occurs in glide zonemainly between tangles which can act as obstacles against motionfor IF source [16]. In PA alloy the LN variation is significantlyaffected by macro-deformation. One can regard dislocation tanglesand dislocation shearing precipitation particle as competing pro-cesses in PA alloy. The macro-deformation resulting in IF increaseis depicted in the schematic in Fig. 4. The g0 particles strongly pindislocation without plastic deformation. With prior deformationincrease, the sheared g0 particle becomes increasingly weak andeven loses the pinning effect for dislocation oscillation on the softslip plane. Though serious dislocation tangles are inevitable, onlystrong pinning effect loss for a large amount of g0 particles cancause the increase of LN and C1. This is the reason that IF in PA alloystill increases up to 18% pre-strain.

4. Conclusions

The IF shows continued increase with prior deformation in PAalloy containing precipitation particles, while a peak value isobtained in ST alloy. The discrepancy of IF behavior can beexplained by a planar slip of dislocation in PA alloy, otherwisethe wavy slip in ST alloy.

Acknowledgment

The authors are grateful to the National Natural Foundation ofChina (No. U1230118).

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