residual stress evolution with compressive plastic deformation in 6061al–15 vol.% sicw composites...

$: Residual stress evolution with compressive plastic deformation in 6061Al–15 vol.% SiCw composites as studied by neutron diffraction$
Materials Science and Engineering A 403 (2005) 260–268

Residual stress evolution with compressive plastic deformation in6061Al–15 vol.% SiCw composites as studied by neutron diffraction

Ricardo Fernandeza,1, Giovanni Brunob,c, Gaspar Gonzalez-Doncela,∗a Department of Physical Metallurgy, Centro Nacional de Investigaciones Metal´urgicas (CENIM),

C.S.I.C., Av. de Gregorio del Amo 8, E-28040 Madrid, Spainb Institut Laue-Langevin, ILL, Rue Jules Horowitz, BP 156F-38042 Grenoble Cedex 9, France

c Manchester Materials Science Centre, Grosvenor Street, Manchester M1 7HS, UK

Received in revised form 28 April 2005; accepted 4 May 2005

Abstract

The evolution of the residual stress (RS) with compressive plastic deformation of several discontinuously reinforced 6061Al–15 vol.% SiCw

metal–matrix composites (MMCs) has been investigated. The composites were obtained by a powder metallurgical route and heat treated toa fully hardened, T6 condition. The RS was determined from neutron diffraction. The results show that deformation relaxes the hydrostaticc ydrostaticcc lastic strain.T rtion andm ggests alsot©

K

1

(icraieTe[

L

thisffect

n on

opicto anmis-stic

andre

cen-eenand

n the-o not

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omponent of the macroscopic RS (M-RS) progressively until a minimum is reached, around 2–5% plastic strain. Similarly, the homponent of the microscopic RS (m-RS) relaxes rapidly with deformation. Relaxation continues with further strain and at≈15% this m-RSomponent disappears. The deviatoric components of both the M-RS and the m-RS, however, remain unaltered with increasing phe increase of the full width at the half maximum (FWHM) of the Al diffraction peaks with strain reveals the increased lattice distoicroscopic RS gradient around the reinforcing particles. The linear correlation found between the FWHM of the two phases su

he activation of a lattice distortion transfer mechanism from the Al phase to the SiC phase.2005 Elsevier B.V. All rights reserved.

eywords:Metal–matrix composites; Residual stress; Neutron diffraction; Plastic deformation

. Introduction

Discontinuously reinforced metal–matrix compositesMMCs), in particular aluminum alloys reinforced by sil-con carbide, have better mechanical properties than theorresponding metallic matrices[1,2]. Among the factorsesponsible for this improvement, the residual stress (RS)rising from several sources plays a crucial role. Of particular

mportance is the microscopic RS originated on the differ-nt thermal expansion of the matrix and the reinforcement.his stress account, for example, for the strength differentialffect observed between uniaxial tensile and compressive test

3,4]. Despite the well-known correlation between RS and the

∗ Corresponding author. Tel.: +34 915538900; fax: +34 915347425.E-mail address:[email protected] (G. Gonzalez-Doncel).

1 Present address: Thin Film R&D Department INDO, SA, 08902’Hospitalet de Llobregat, Barcelona, Spain.

mechanical behavior, it is not yet well understood howstress evolves with plastic deformation and how it can aservice life performance of structural components[5]. Somefew studies analyzing the influence of plastic deformatiothe RS state in MMCs have been conducted[5–8]. Followingthe separation of the RS into macroscopic and microscRS (M-RS and m-RS) and the separation of the m-RS inelastic mismatch term and a thermo-plastic contribution (fit stress)[6], it has been shown that a small amount of pladeformation (≈1%) is sufficient to reduce the misfit stressthat thermal and plastic stresses are of the same natu[7].The deformation processes employed in these studiester mostly on bending tests. The effect of plasticity has balso studied at the front of crack front of notched samplesin the vicinity of a cold expanded hole[9] with the aim ofunderstanding the effect of changes in the misfit stress ofatigue crack propagation in MMCs[8]. Whereas the conclusions resulting from these studies are relevant, they d

921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2005.05.006

R. Fernandez et al. / Materials Science and Engineering A 403 (2005) 260–268 261

analyze the effect of accumulative (increasing) plasticity onthe RS of these materials.

The purpose of this research is, therefore, to study the evo-lution of the RS state in 6061Al–15 vol.% SiCw compositeswith accumulative compressive plastic deformation and tounderstand the mechanisms that govern RS relaxation.

2. Materials and experiment

The materials studied were three 6061Al–15 vol.% SiCwcomposites, labeled C38, C45, and E219, and the unrein-forced 6061Al alloy, labeled E220, prepared by powder met-allurgy (PM) involving hot extrusion[10–12]. Letters C andE of material’s code denote conical and flat extrusion dies,respectively. This characteristic of materials preparation didnot affect the RS state of the composites[13]. The evolution ofRS with deformation was studied in a T6 condition obtainedafter solution treatment at≈520◦C followed by waterquenching and annealing at 146◦C (see[10–12]for details).

The micro-structure was studied by scanning electron andoptical microscopy (SEM and OM) and the texture of the Aland SiC phases by X-ray diffraction. The detailed analysis ofthis study is reported elsewhere[11]; only a brief descriptionwill be given here.

The RS was studied by neutron diffraction (ND) usingt archL .7A e of3 tryo erea d theh gtha thee sts,w hasei meh er toa ureda

om-p ferents hinea edo pidh hp o oft weres tion.

3

ianf es

the ω geometry (the sample is tilted within the scatteringplane), was utilized. The lattice parameter of the 3 1 1 planesof both the Al and SiC phases was determined[14] by apply-ing Bragg equation. Then, the lattice strains at different tiltangles, fromψ = 0◦ (axial direction, parallel to the extrusionaxis) toψ =±90◦ (radial direction) could be calculated (see[4,12] for more details). The axial and radial RS componentscould finally be obtained from the residual strain data usingthe generalized Hooke’s law, which for the case of cylindricalsymmetry it reads:

σax = E

(1 − 2ν)(1 + ν)[(1 − ν)εax + 2νεrad] (1a)

σrad = σhoop = E

(1 − 2ν)(1 + ν)[εrad + νεax] (1b)

whereE and ν are the Young modulus and Poisson ratio,respectively. The radial and hoop terms of the strain andstress tensors coincide because the measurements have beenperformed at the center of the samples. An analysis of thefull width at the half maximum (FWHM) of both the Al andSiC peaks (FWHMAl and FWHMSiC, respectively) was alsoconducted. The calculation of the RS from Eqs.(1a)and(1b)was done using plane-specific diffraction elastic constants asevaluated by means of a Kroner model[15]:

E = 69 GPa; ν = 0.35;

T aluesf

ationf

4

sid-u orks[ iCpt 1Alma thee reso ein-f 19;( , thec om-p thani ilarm

di-ta atrixa r thep SiC

he REST diffractometer at Studsvik Neutron Reseaboratory, Sweden. The neutron wavelength was 1A.ppropriate slits were selected to produce a gauge volummm× 3 mm× 3 mm. Because of the cylindrical symmef the extrusion process, the principal directions wssumed to be the axial (extrusion axis), the radial, anoop, mutually perpendicular. Samples of 13 mm lennd 6.5 mm diameter (with the sample axis parallel toxtrusion direction), also suitable for compression teere used. Reference samples for the aluminum p

ncluded the 6061Al alloy and 6061Al powder. The saeat treatment given to the alloy was given to the powdchieve the T6 condition. Loose SiC powder was meass a reference of this phase.

Samples for ND measurements underwent ex situ cression tests. These tests were conducted up to diftrain levels in a conventional screw driven testing mact a strain rate of 10−4 s−1. Particular interest was focusn the initial regions of plastic deformation, where a raardening rate is observed[4]. Determination of RS at higlastic strain values, however, was also conducted in tw

he composites under study. Specifically, strain valueselected around 1, 2, 5, and 15% compressive deforma

. Residual stress determination

The diffraction peaks were fitted with simple Gaussunctions. The sin2ψ method (withψ the angle between thample axis direction and the scattering vector,Q), using

311−Al 311−Al

E311−SiC = 387 GPa; ν311−SiC = 0.19

hese elastic constants are very similar to macroscopic vor both Al and SiC.

Errors have been calculated according to error propagormulae[16].

. Results

The micro-structure, the texture, and the initial real stress of the materials are described in previous w

4,11,12]. In summary, the extrusion process of the Al/Sowder blends leads to a〈1 1 1〉 + 〈1 0 0〉 fiber texture (with

he fiber axis parallel to the extrusion axis) of the 606atrix, typical in extruded aluminum alloys[11,17], and toslight trend of the short SiC fibers to be aligned with

xtrusion axis.Fig. 1describes, through inverse pole figuf the extrusion axis direction, the texture of: (a) the unr

orced alloy; (b) the aluminum matrix of the composite E2c) the SiC whiskers of this composite. As can be seenomposite matrix and the alloy develop similar texture conents. The texture is more accentuated in the alloy

n the composites. All composites have, roughly, a simicro-structure and texture.The initial total RS state of the materials in the T6 con

ion is fully described in Table 1 of[12]. It is very similar inll composites. In summary, the RS is tensile in the mnd compressive in the reinforcement, and accounts foresence of m-RS with length scale of the order of the

262 R. Fernandez et al. / Materials Science and Engineering A 403 (2005) 260–268

Fig. 1. Inverse pole figures of the extrusion axis showing the texture of theunreinforced alloy and of both phases (Al and SiC) of one of the composites(E219). The〈1 1 1〉 + 〈1 0 0〉 fiber texture of the unreinforced alloy is strongerthan that of the Al phase of the composite.The SiC tends to be aligned withthe extrusion axis.

inter-particle distance[18]. This m-RS term is caused by thedifferent coefficient of thermal expansion, CTE, of aluminumand of silicon carbide[19]. Also, the absolute total axial RS(atψ = 0◦) is higher than the radial one (atψ =±90◦), i.e. adeviatoric RS state is developed.

Although smaller than in the composites, also a tensileRS with a deviatoric character builds up in the 6061Al alloy

Fig. 2. True stress–true strain compressive curves of the unreinforced alloy(E220) and of the three composites (C38, C45, and E219). The better behav-ior of the composites than that of the unreinforced alloy is apparent.

[12]. This RS is macroscopic and is caused by the severetemperature gradient brought about by the quenching priorto the annealing for the T6 condition. A tensile M-RS result-ing from material’s quenching has been obtained in severalinvestigations[20–22].

To separate m-RS and M-RS terms appropriate stress equi-librium condition has been applied[7],

σMac,i = (1 − fr)σAlTot,i + frσ

SiCTot,i (2)

whereσPhaseTot,i = σMac,i + σPhase

mic,i , sub-indexes Tot, Mac, andmic refer to total, macroscopic, and microscopic RS, respec-tively, sub-indexi the axial and radial (hoop) component,and fr is the volume fraction of the reinforcement. Thebars stand for the fact that average stress values over thegauge volume are determined. This is a large region if com-pared to the micro-structural scale of these composites. Themagnitude of the hydrostatic and deviatoric stress termscould be readily calculated using:σhd = (σax + 2σrad)/3 (withσrad=σhoop �= σax) andσd =σax− σrad.

As it has been already summarized in previous works[4,12], the M-RS in the undeformed condition is mostlyhydrostatic, and higher in the alloy than in the composites inagreement with the higher CTE of the former[23]. A certaindeviatoric character is present because of sample shape; theboundary conditions along the axial and the radial directionsa res-s taticb torict witht

nicalr risont ingr up to0 met-r rvedi ter-

re different. The m-RS is tensile in the matrix and compive in the reinforcement, and is also strongly hydrosecause the SiC is mostly randomly oriented. The devia

erm is due to the population of short SiC fibers alignedhe extrusion axis (≈30%[12]).

The compressive tests revealed the improved mechaesponse of the composites in the T6 condition in compao that of the alloy (Fig. 2). The pronounced strain-hardenate of the composites in the early stages of deformation,.05 strain, accounts for a rapid multiplication rate of geoically necessary dislocations (GNDs). This is not obsen the E220 alloy in which the dislocation-precipitate in


action (cutting mechanism) should predominate, leading toa limited strain-hardening rate. At high values of strain, thecomposites and the alloy behave similarly. This is becausethe multiplication of statistical dislocations dominates thehardening process similarly in the alloy and the compos-ites [24]. The slight differences in the stress–strain curvesof the composites is attributed to the differences in the orien-tation/distribution and to the inter-particle spacing of the SiC.

The evolution of the M-RS and m-RS components withcompressive plastic deformation is shown inFigs. 3 and 4,respectively. A rapid drop of the hydrostatic M-RS occurswith small plastic strain in all materials investigated (Fig. 3).The relaxation of RS with plastic deformation is consistentwith previous investigation on the effect of plasticity on theRS state of MMCs[7]. The M-RS reaches a minimum around2–5% of deformation. However, it increases again with fur-ther plasticity. A RS value close to that in the undeformedcondition is reached at 15% of deformation in compositesC38 and C45. On the other hand, the deviatoric term remainsessentially constant in the complete range of deformation.

Similarly to the M-RS, the axial and radial componentsof the m-RS evolve in parallel, such that the deviatoric termremains constant with plastic deformation (Fig. 4). Thisresult is consistent with the observation that the stress–strain

curves in tension and compression run nearly parallel, sep-arated by a certain stress value, i.e. the strength differentialeffect SDE[4]. The hydrostatic m-RS relaxes progressivelywith plastic pre-deformation. Relaxation occurs rapidlyduring the initial stages of plastic deformation, <2%, andslowly at high levels of strain.

The radial component of the m-RS reverts its sign(becomes compressive in the matrix and tensile in thereinforcement) at about 2% of plastic deformation (Fig. 4).Sign reversal of the m-RS with strain has been reportedin a cold expanded hole (expanded 4% by a split-sleevetechnique) at a distance up to some 5 mm from the edgeof the hole in a 2124Al–17 vol.% SiCp plate [9]. Sincedeformation was imposed by the split-sleeve technique (itdepends on the distance from the edge of the hole and on thestrain hardening behavior of the material), it is not evidentfrom[9] the amount of plastic deformation needed to achievesign reversal of the RS. The present work indicates that signreversal occurs with only≈2% strain. This effect has beenattributed to a mechanism of load transfer from the matrixto the reinforcement[9,25].

Although the instrumental contribution could not be sep-arated in the analysis of the FWHM, it can be assumed tobe the same at the diffraction angles for the Al and SiC

Ff

ig. 3. Macroscopic RS of each composite and of the unreinforced alloy. Thunction of compressive pre-strain.

e axial, radial, deviatoric, and hydrostatic stress components are represented as a


Fig. 4. Evolution of the axial, radial, deviatoric, and hydrostatic components of the m-RS in both phases of the three composite materials with compressivepre-strain.

phases (they are relatively near). Therefore, a deconvolutionof the different sources of peak broadening was not needed.In this way, the variation of the FWHM can be attributed onlyto micro-structural changes with plastic pre-strain (latticemicro-strains or type-III RS, m-RS-III[17]). The evolutionof FWHMAl and FWHMSiC with plastic strain is summa-rized in the plots ofFig. 5. As can be seen, the FWHMincreases with increasing plastic deformation in all materi-

als. The increase of FWHMAl is more evident than that ofFWHMSiC.

5. Discussion

Once the different components of the RS are known, it isworth comparing the evolution of the hydrostatic and devia-


Fig. 5. Evolution of the FWHMAl and FWHMSiC with plastic deformation.

toric M-RS and m-RS of the composites with accumulativeplastic strain. This is shown in the plots ofFig. 6a and b forthe C38, and C45 composites, respectively.

The hydrostatic m-RS decreases monotonically towardstotal relaxation. On the other hand, the hydrostatic M-RSterm first decreases rapidly, but surprisingly it increaseswith further deformation after some 2–5% plastic strain.Upon homogeneous deformation in compression, the misfitbetween internal and external regions should be “washed out”and the M-RS should go to zero. The increase in M-RS must,therefore, be attributed to some kind of non-homogeneousdeformation occurring during composite deformation at largestrains. In fact, barreling was observed in the highly deformedsamples. This leads to a higher plastic deformation in thecenter of the sample than in regions close to the platens. Thisplasticity gradient may have helped to the re-generation ofthe M-RS, when large plastic deformation accumulated.

The relaxation of the hydrostatic m-RS agrees with pre-vious experimental work which have shown that plasticityreduces the misfit between the matrix and the reinforce-ment and, hence, the m-RS[5–7,26–28]. It is interesting tonote that this is also valid for non-homogeneous deforma-tion (large level of plastic compression) because the lengthscale of variation of m-RS and M-RS are very different. Itis worth mentioning that simple mechanistic models on theinfluence of plastic deformation on the residual stress state ofM en-

Fig. 6. Evolution of the deviatoric (axial) and hydrostatic components of themacroscopic residual stress in the unreinforced alloy and in the compositesC38 and C45 with compressive pre-strain.

erate a m-RS which would be compressive in the aluminummatrix in the axial direction (and tensile in the radial one).On the other hand, the opposite would be expected after uni-axial compressive plastic flow[5,6]. Previous experimentshave shown results in full agreement with our observations.Further work is, therefore, needed to understand in detail thespecific micro-mechanisms that lead to the relief of the m-RSwith plasticity.

The deviatoric component of both the M-RS and m-RSseems to stay constant within the error bar. In particular,the m-RS behavior reveals the strong influence of thenon-isotropic nature of materials micro-structure. This RSis associated to the micro-structural parameters linked tothe reinforcing SiC (orientation and distribution) and to thetexture of the matrix material, whereas the M-RS is mostlyassociated to sample geometry. The fact that the m-RS turnstotally deviatoric with compressive plastic deformationaccounts for the relevance of the activity of geometricallynecessary dislocations. GNDs are particularly active at theends of the short SiC whiskers[29]. Since a part of the rein-forcement population is aligned with the extrusion axis, thesymmetry of the GNDs distribution after deformation should
MCs predicts that uniaxial tensile plastic flow would g


Fig. 7. Evolution of the normalized compressive flow stress and FWHM ofthe Al and SiC phases (composite C38) with plastic pre-strain. The goodcorrelation between the increasing flow stress with strain (hardening rate)and the increase of the FWHMAl and FWHMSiC is evident.

be similar and the axial m-RS state should remain withstrain.

The direct connection of the increasing FWHM with plas-tic deformation becomes evident from the plot ofFig. 7. Inthis plot, the compressive stress–strain curve of the compositeC38 and the FWHM of the two phases at the different levelsof plastic strain are shown. The data have been normalizedbetween 0 and 1 to render all variables dimensionless accord-ing to,

Yn(ε) = Y (ε) − Ymin

Ymax − Ymin

whereYn(ε) andY(ε) denote the normalized and measuredvalue (flow stress and FWHM) as a function of the true plas-tic strain,ε and sub-indexes min, and max denote minimumand maximum values, respectively. The rate at which theFWHMAl increases with plastic strain follows very closelythe rate at which the flow stress increases with strain (hard-ening rate). This result is in good agreement with severalinvestigations[30] and reveals the increasing lattice distor-tion due to the increasing dislocation density,ρ, with plasticdeformation.

Specifically, the edge character of the dislocations gener-ates a “pressure”,P, at a given distance (x,y) of the dislocationcore (in a coordinate system in which the dislocation liesa lipp ivenb

P

wH e thed e isl oad-e withit

Fig. 8. Correlation between FWHMAl and FWHMSiC at the different levelsof increasing plastic deformation for all the three composites investigated.A linear correlation is obtained for all data.

A change of the RS distribution around the SiC rein-forcement with plastic deformation, as calculated by Duttaet al. [25] by means of finite element models (FEM), canalso result in broadening of the diffraction peaks. Regions ofcompressive and tensile hydrostatic stress alternate aroundthe fibres and their tips, thus creating a highly inhomoge-neous RS field and broadening of the diffraction peaks. Othermicro-structural factors, such as grain size variations, couldalso affect peak broadening, but these factors do not changesignificantly with plastic pre-strain and, therefore, do not con-tribute to the increase of the FWHM.

Broadening of the Al diffraction peaks is, hence, dueto the increasing lattice distortion and to the increasingm-RS gradient around the SiC particles, both caused bydislocation multiplication. However, since the SiC rein-forcement does not deform during testing, the origin ofthe FWHMSiC increase must be different. The fact thatthe normalized FWHMSiC and FWHMAl increase at asimilar rate (Fig. 7) suggests a linear correlation betweenFWHMAl and FWHMSiC for the different composites andat the different levels of plastic strain. This dependence isshown in the plot ofFig. 8 in which the average slope is�FWHMAl /�FWHMSiC = 6.32, which correlates reason-ably well with the ratio [E311-SiC(1− ν311-Al)]/[E311-Al(1−ν311-SiC)] = 4.5.

This good correlation and, yet, the small mismatchsa -RSg Alp -RSg ina d tot -typem�

A

long thez-axis andxandydenote the distance from the slane and the distance in the sip plane, respectively) gy,

= − Ebedge

6π(1 − ν)

y

x2 + y2 (3)

herebedgeis the edge component of the Burgers vector[31].ence, the corresponding m-RS-III is compressive abovislocation slip plane (in the region where the extra plan

ocated) and tensile below it. The net effect results in brning of the diffraction peaks. Peak width increases

ncreasingρ (Fig. 7), and according to Eq.(3), is propor-ional toE/(1− ν).

uggest that the increase in FWHMSiC is also due ton increasing distortion of the SiC lattice and to mradient in the particles induced by those of thehase. In other words, the increasing distortion and mradient of the Al lattice is transmitted to the SiC

similar manner as an external load is transferrehe particles (as predicted by Shear–Lag or Eshelbyechanisms). This would explain the inequality,�FWHMAl /FWHMSiC > [E311-SiC(1− ν311-Al)]/[E311-Al(1− ν311-SiC)].dditional contributions could be as follows:


(i) The occurrence of local damage at Al–SiC interfaceduring straining which lead to local debonding or deco-hesion at the Al–SiC interface or to SiCw breakup (see,for example, Ref.[32]) and, hence, to local m-RS-IIIrelaxation of the SiCw particles (but not of the Al phase).

(ii) Dislocation rearrangement in low energy configurations,leading to sub-grain or domain formation, as observedin Al–SiC system by transmission electron microscopyafter small plastic strain[33]. In this case, peak broaden-ing in the Al phase would occur not only by dislocationaccumulation, but also by sub-grain or domain forma-tion, according to the Scherrer’s formula.

These two additional sources of peak broadening arebelieved to be minor in our case because no debonding wasobserved, and the sub-grain size stays constant.

6. Conclusions

The evolution of the macroscopic and microscopicresidual stress, M-RS and m-RS, in powder metallurgy6061Al–15 vol.% SiCw composites with increasing compres-sive plastic deformation has been studied. Neutron diffractionhas been used for this investigation. The following are themain conclusions that can be drawn from this investigation.

d inevi-partisaperior6)and

ites

for-rlys anfor-

ionoricn at

( nottaticnot

for-cteddeds ofthe

( sesthee

straight line correlates well with the ratio of the term(1− ν)/E of the SiC and Al phase. This suggest thatplasticity in the matrix phase causes increasing latticedistortion (RS of type III) in both phases. The increasedinhomogenity of the m-RS also influences broadeningof the diffraction peaks.

Acknowledgements

The authors thank for Projects MAT 01-2085 from MCYTand 07N-0066-98 from CAM, Spain, and support from NFL(Studsvik) under Contract No. N01 HPRI-CT-1999-00061 inthe frame of ARI Program. The authors gratefully acknowl-edge for help from Mihail Butman, who performed the com-pression tests, and Ru Lin Peng and Bertil Trostell († ),scientific and technical responsible of REST diffractometerat NFL, Studsvik, respectively.

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residual stress evolution with compressive plastic deformation in 6061al–15 vol.% sicw composites...

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