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Synchrotron X-ray diffraction measurements of internal stressesduring loading of steel-based metal matrix composites reinforced

with TiB2particles

D.H. Bacon, L. Edwards 1, J.E. Moffatt, M.E. Fitzpatrick

Materials Engineering, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK

Received 3 February 2011; accepted 7 February 2011Available online 5 March 2011

Abstract

High-energy synchrotron X-ray diffraction was used to measure the internal strain evolution in the matrix and reinforcement ofsteel-based metal matrix composites reinforced with particulate titanium diboride (TiB2). Two systems were studied: a 316L matrix with25% TiB2 by volume and a W1.4418 matrix with 10% reinforcement. In situ loading experiments were performed, where the materialswere loaded uniaxially in the X-ray beam. The results show the strain partitioning between the phases in the elastic regime, and theevolution of the strain partitioning once plasticity occurs. The results are compared with results from Eshelby modelling, and very goodagreement is seen between the measured and modelled response for elastic loading of the material. Heat treatment of the 316-basedmaterial did not affect the elastic internal strain response.2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Synchrotron radiation; Metal matrix composites (MMCs); Particulate-reinforced composites; Internal stresses

1. Introduction

Metal matrix composites (MMCs) are an importantclass of engineering material, by virtue of their enhancedspecific properties and their ability to be tailored to suitmany different applications. There has been significantresearch into aluminium-based MMCs, because ofthe inherently low density of the aluminium matrix.Steel-based systems are less common, because steel alreadyhas a high elastic modulus. However, there is scope to useceramic reinforcement in steels to increase the elastic mod-ulus further and to improve wear resistance. In addition,the high toughness of steel means that the reduction intoughness which is associated with MMCs as comparedto the unreinforced alloys is less critical than in some alu-

minium-based systems. Furthermore, ceramic reinforce-ments such as TiB2 have a lower density than iron, sotheir addition gives the additional benefit of reducing thedensity of the final material, as well as increasing its stiff-ness. As a result, steel-based MMCs are of increasing inter-est for many aerospace and automotive applications due tothe initial high strength and toughness of the unreinforcedmatrix.

There have been numerous investigations of the internalstrains in aluminium alloys reinforced with a variety ofceramic particulate [17], and most of these studies haveused neutron diffraction. However, little or no work hasbeen conducted on the internal strains of steel-based com-posite systems. In the present work, steel composite sys-tems reinforced with titanium diboride were studied.Boron is strongly neutron-absorbing, and therefore high-energy synchrotron X-ray diffraction was applied forstudying the internal strains in the material.

The load bearing capacity of an MMC is dictated by theload transfer occurring between the compliant, soft matrix

1359-6454/$36.00 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

doi:10.1016/j.actamat.2011.02.012

Corresponding author. Tel.: +44 1908 653100; fax: +44 1908 653858.E-mail address:[email protected](M.E. Fitzpatrick).

1 Present address: Australian Nuclear Science and Technology Organi-sation, PMB1, Menai, NSW 2234, Australia.

www.elsevier.com/locate/actamat

Available online at www.sciencedirect.com

Acta Materialia 59 (2011) 33733383
http://dx.doi.org/10.1016/j.actamat.2011.02.012mailto:[email protected]://dx.doi.org/10.1016/j.actamat.2011.02.012http://dx.doi.org/10.1016/j.actamat.2011.02.012mailto:[email protected]://dx.doi.org/10.1016/j.actamat.2011.02.012

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to the stiff, hard reinforcement [8]. The load partitioningratio between matrix and reinforcement remains constantas long as both phases are deforming elastically. Uponplastic deformation of the matrix, the partitioning ratiochanges and the reinforcement phase carries a greater pro-portion of the load. Thus, the composite becomes more

efficient, as a greater proportion of the load is being carriedby the stiffer reinforcing phase. However, with the increas-ing levels of stress placed on the reinforcement (as thematrix continues to plastically deform), that phase mayfracture or debond from the matrix, thus reducing the loadcarried by the reinforcement and the overall load bearingcharacteristics of the composite, which often leads to mac-roscopic failure. Experimental measurements of the loadpartitioning between phases of an MMC can thus give awealth of information on the micromechanical evolutionof composites during deformation.

In this present work synchrotron X-ray diffraction hasbeen used to measure the internal lattice strains of both

matrix and reinforcement phases within an MMC sub-jected to uniaxial tensile loading to failure. This enablesthe load transfer to be assessed for both elastic and plasticdeformation of the matrix. The measured results are com-pared to the expected load transfer between the phases pre-dicted by the Eshelby equivalent inclusion method. Asecondary goal was to investigate the effects of differingheat treatments on the load partitioning of the composite.

2. Experimental procedure

2.1. Materials

Two materials were studied: a 316L stainless steel rein-forced with 25% of titanium diboride (TiB2) particles,and a W1.4418 martensitic stainless steel reinforced with10% TiB2. The reinforcement particles had a nominaldiameter of 5 lm. The material was manufactured byAerospace Metal Composites Ltd. (Farnborough, UK)by a mechanical alloying, powder metallurgy route. Thematerial was studied as-hot isostatic pressed (HIPed), with-out any secondary processing. Fig. 1 shows an opticalmicrograph of the 316L composite. It can be seen thatthe reinforcement has been well distributed, and there arefew areas of reinforcing particle clusters or large areas ofunreinforced matrix.

The as-received billet was heat treated for 3 h at1040 C, followed by a cold water quench. In this statethe material has an ultimate tensile strength (UTS) of1100 MPa and an elastic modulus of242 GPa. The bil-let was then cut in half and the material was then given atempering treatment, of either 1 h at 480 C followed byan air cool or 4 h at 550 C followed by an air cool.

The W1.4118 composite was also treated at 1040 C andthen tempered at 550 C. This material has a UTS of1280 MPa and an elastic modulus of220 MPa.

Dog-bone-shaped, flat tensile test specimens were

fabricated by electric discharge machining from the three

tempered blocks, with a gauge length measuring1525 mm3 and broader ends for gripping the samples.Uniaxial tensile tests were performed at room temperatureusing a loading rig in situ on the X-ray diffractometer. Aclip-gauge extensometer was attached to the specimens tomeasure the macroscopic strain, and the stress was calcu-lated from the recorded loads. The loading was conductedin strain control (using strain measurements from the

extensometer) at a strain rate of 2 10

5

s

1

.

2.2. Strain measurements

Synchrotron X-ray diffraction measurements were per-formed on the ID11 beamline at the European SynchrotronRadiation Facility (ESRF) (Grenoble, France). The X-raydiffraction experimental setup is shown inFig. 2. The spec-imen was irradiated by a parallel beam of 50 keV photons(corresponding to a wavelength of k 0.245 A

0

), withapproximate dimensions 0.10.1 mm2, positioned in thecentre of the gauge section along a direction parallel tothe sample thickness. A reference powder sample (LaB6)

was affixed to the specimen to monitor any drift in the dif-fraction peaks as a result of changes in the beam energyprofile. LaB6 was chosen because its diffraction rings donot overlap with those of the Fe or TiB2.

The diffraction pattern from the sample was recordedusing a 16-bit CCD camera with a 1242 1152 pixels sen-sor. The camera was positioned1 m from the specimen atan angle of 2h= 8 from the incident beam. This distanceallows for high strain resolution, recording diffraction ringsbetween 5.5and 10. However, only a segment of the dif-fraction rings was captured, and therefore it was onlypossible to measure one strain direction at a time

(Fig. 3a). Each test was therefore performed twice: once

Fig. 1. Optical micrographs of the 316L-based MMC.

3374 D.H. Bacon et al. / Acta Materialia 59 (2011) 33733383

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with a sample loaded to failure with the detector orientedto measure the longitudinal strains and once with a sample

loaded to failure with the detector oriented to measure thetransverse strains. Good reproducibility was foundbetween the tests, as shown inFig. 4. It was assumed thatthe two transverse strain components, which arise fromPoisson effects, would be identical.

Each CCD image was then caked, where an angularsum of the intensity data is effected to produce a mean dif-fraction pattern from the segment of the diffraction ringsrecorded in the CCD image. Owing to the high resolutionof the CCD, very sharp diffraction peaks can be obtained(Fig. 3b).

The diffraction peaks were then fitted using a Gaussianprofile. The internal strain for each reflection was then cal-

culated using:

ed d0

d01

whered0is the unstressedlattice parameter. Although anattempt was made to determine d0from powder samples ofthe matrix and reinforcement materials, the difficulty ofpositioning the powder container reproducibly at the sameposition as the test samples meant that there were geome-try-based shifts in the peak positions which renderedobtaining d0 values by this method impossible for thisexperimental setup. Hence the d0 values were set as the

measured lattice parameters before loading of the sample,which allows for monitoring of the stress evolution fromthe applied load but neglects any pre-existing thermalresidual stress in the material. It is probable that thereare thermal misfit stresses in the material which are tensilein the matrix and compressive in the reinforcement, owingto the difference in coefficient of thermal expansion be-tween the phases.

3. Modelling the phase stresses

The partitioning of an applied stress between the matrixand reinforcement phases can be calculated by using a

model such as Eshelbys equivalent inclusion approach[810].

The measured strain and the principal stress calcu-lated from it r are composed of three components. This

discussion will focus on the analysis of the measured (andmodelled) stresses. There is a macrostress component rma-cro, which is the same in both phases and which in thiscase arises from the applied loading. Secondly, there isan elastic stiffness mismatch contribution hri

mE, which

expresses the extent of load transfer of the macrostressfrom the relatively compliant matrix to the stiffer rein-forcement. Thirdly, there is a shape misfit contribution:stress-free shape misfits (i.e. misfits that are independentof any applied load) between matrix and reinforcementcan occur in a number of ways, such as plastic deforma-

tion of the matrix, phase transformations and thermalexpansion misfits caused by changes in temperature. Inthese experiments it has not been possible to determinethe shape misfits as in previous studies [2,5,11] because,as described earlier, no absolute stress-free reference lat-tice spacing was obtained.

The elastic mismatch contribution expresses the redistri-bution of the macroscopic load arising from the mismatchin elastic constants: it is therefore directly related to themacroscopic term, and can be written as[8]:

hrimE

i r Birmacror 2

whereBiis a tensor which depends on the mean reinforce-ment particle shape (primarily the aspect ratio) and volumefraction, and on the elastic constants of the two phases.The components ofB may be calculated from theory usinga model such as Eshelbys equivalent homogeneous inclu-sion approach[9], and in this study the calculations wereperformed using a program developed by Clyne et al.[8,12].

It was assumed that the reinforcing particles are spheri-cal; this is a reasonable assumption, given that the particleshave a low aspect ratio, and as the billet was not subjectedto any secondary processing operations after fabricationthere is no reason to expect any preferred alignment.

Fig. 2. Schematic representation of the experimental setup on ID11, ESRF.

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The coefficientsB that were used are shown in Table 1for particles with an aspect ratio (AR) = 1 (spheres); forcomparison, values are also provided for aspect ratios of1.5 and 2.0, representing ellipsoidal particles with a pre-ferred alignment. InTable 1, the coefficientsBst,mand Bst,p

describe the dependence of the mean phase elastic mis-

match stresses in the matrix and particles respectively inthe s direction to the component of the macrostress inthe t direction. For example, B13,p r

macro3 r is the stress

transferred to the particles in the 1-direction due to themacrostress component in direction 3. The volume

fractions listed in the table, namely, 10%, 17% and 25%,

Fig. 3. (a) CCD image of the diffraction spectrum from the 316/25% TiB2composite, for measurement of the longitudinal strains. (b) Diffraction spectrumproduced following caking of the CCD image.


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Fig. 5. Loading response of the 316L/25% TiB2 material: (a) longitudinal response, 480C heat treatment; (b) transverse response, 480 C heat treatment;(c) longitudinal response, 550 C heat treatment.


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matrix, which will increase the mismatch with the elasticreinforcement. The yield point of the iron is higher in thisMMC compared to that in the 316L MMC as the basematrix has a higher strength as well as a slightly higherelastic modulus (200 vs. 190 GPa). There is also very littleplastic flow before the onset of failure of the material,

which is indicated by the rapid unloading of the matrixabove 1100 MPa.

The transverse strain response is different from that forthe 25%-reinforced MMC, as the particles maintain a neg-ative strain throughout loading. This is a consequence ofseveral factors: the material has a much higher yield stressthan the 316L, although its strain-to-failure is higher(Fig. 7); therefore the matrix carries a higher elastic strainbefore the onset of plasticity, meaning that the overall Pois-son strain mismatch in the reinforcement is much largerbefore plasticity occurs. Furthermore, the smaller volumefraction carries a proportionately higher strain when plas-ticity does occur (the final strain in the reinforcement at

failure is greater than that in the 25% TiB2 material) andthe internal Poisson strain in the reinforcement balancesthe Poisson loading of the plastic matrix.

4.2. Internal stresses

The measured longitudinal and transverse strains can beused to calculate the axialr1stress and transverse r2stressin each phase of the composite. Assuming that the twotransverse strain components are equal,e2=e3:

r1 2le1ke12e2 3

r2 r3 2le2 ke1 2e2 4

where k and lare Lames constants, calculated as:

k mE

1m1 2m 5

l E

21m 6

Fig. 6. Internal strains in the W1.4418/10% TiB2composite: (a) longitudinal strains; (b) transverse strains.


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whereEis the Youngs modulus and mis the Poissons ratioof each phase of the material. For the TiB2, E= 565 GPaand m= 0.11; for both of the steels m= 0.3, and E= 190and 200 GPa, respectively, for the 316L and W1.4418matrices.

For the steel, the individual peaks show different strainresponses, which is indicative of the elastic anisotropy ofthe lattice: the (1 1 1) direction is the stiffest austenitic

direction and the (2 0 0) is the least stiff. Hence, if the bulkmaterial elastic modulus is used in the calculation of stress,there will be an error introduced in the calculated strainsfor each reflection. In order to account for this, the stressesderived from the response of the austenite peaks werecalculated from the component strains using plane-specific elastic constants calculated using a Kroner-basedmodel [14]. This gave values of E111= 246 GPa andE200= 147 GPa, with corresponding Poisson ratio valuesof 0.24 and 0.32.

4.2.1. 316L/25% TiB2, 480 C temper

The calculated internal stresses for the 316-based MMCare shown inFig. 8. The two heat treatments showed sim-ilar responses in the internal stresses. As strain values fromtwo separate tests were used in calculation of the stresses,the longitudinal and transverse strain responses were fittedusing a Matlab smoothing routine, and the resulting datafit was used in the calculation of the stress response. Thisallowed for calculation of a smooth stress/load responseand overcame the problem that longitudinal and transversestrains will not have been determined at precisely the sameload in each test. In the plots selected points only are dis-played for overall clarity.

Fig. 8a shows the calculated longitudinal stresses and

Fig. 8b the transverse stresses. It can be seen clearly that,

for the longitudinal stresses, there is transfer of load fromthe matrix to the reinforcement during the elastic regimebelow around 600 MPa. The two titanium diboride reflec-tions show very similar behaviour, as do the steel reflec-tions in the elastic region: note that the good agreementbetween the Fe(1 1 1) and Fe(2 0 0) response indicates that

the approach of using plane-specific elastic constants isappropriate. With reference toTable 1, it can be seen that,for uniaxial loading, an applied macrostress of 400 MPawould be expected to partition to give 518 MPa in the rein-forcing particles: for 25% volume fraction and a particleaspect ratio of 1, B11,p= 0.296, so from Eq. (2) the elasticmisfit stresshri

mE

p 0:296400 MPa 118 MPa, giving atotal stress of 400 + 118 = 510 MPa. Likewise, for thematrix, B11,m=0.099, giving an elastic misfit of40 MPa and a total stress of 360 MPa in the steel matrix.The measurements show that, at 400 MPa, there are stres-ses of around 350 MPa in the matrix and 570 MPa in thereinforcement; these results are summarized in Table 2.

Hence there is excellent agreement for the matrix stresses,and acceptable agreement for the reinforcement. The differ-ence may be a consequence of small errors in the conver-sion from strain to stress or may reflect some preferredalignment of the particles within the material, although thisis unlikely, given that the test samples were extracted fromthe test billet following HIPing without any secondary pro-cessing having been applied.

Once the matrix becomes plastic, there is no increase instress in the steel, and the reinforcement bears an increas-ing proportion of the applied stress. It is notable that thereis actually some unloading of the Fe(1 1 1) grain family as

plasticity increases.The transverse stresses are relatively low, and although

Eshelby modelling can be used to predict the bulkresponse, the response of individual reflections will not nec-essarily be in good agreement, as the response of a partic-ular plane in the Poisson direction is dependent on whichplane is aligned with the load axis[15]. Following the onsetof plasticity, there is a tensile stress generated in the rein-forcement, whilst the different matrix reflections showopposing behaviour.

4.2.2. W1.4418/10% TiB2Internal stress calculations for the W1.4418 material are

shown inFig. 9. Plane-specific elastic constants were againused in the determination of the Fe stresses, with values ofE110= 212 GPa and E200= 165 GPa. This material has ahigher yield strength than the 316-based material, ataround 1000 MPa (Fig. 7). This is reflected in the internalstress response, which is linear to a much higher appliedstress, although there is perhaps some evidence of deviationfrom linearity below 1000 MPa in the internal stresses. Thelongitudinal response in Fig. 9a again clearly shows thetransfer of load from the matrix to the reinforcement. Asa consequence of the lower volume fraction in this mate-rial, there is less load shedding from the matrix, but the

stress magnitude in the reinforcing particles is higher.

Fig. 7. Macroscopic stressstrain response of the two samples tested ofthe W1.4418-matrix composite.


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In comparison with the Eshelby modelling, there is verygood agreement, as shown inTable 3. By linearly fitting theelastic response, the experimentally determined stress at1000 MPa applied in the reinforcement is 1400 MPa, com-pared to a predicted response of 1380 MPa (Table 1),whilst for the matrix the predicted stress is 960 MPa andthe measured is around 980 MPa.

The transverse response is again more difficult to

interpret. However, the TiB2does show the expected com-

pressive stress, though the average response of the two ironpeaks is significantly more compressive than predicted.

5. Conclusions

The synchrotron X-ray diffraction technique has beenused to study the internal stress response of two steel-basedmetal matrix composites reinforced with titanium diboride

particles. Samples of the materials were loaded uniaxially

Fig. 8. (a) Longitudinal and (b) transverse stresses in the Fe and TiB 2phases of the 316/25% TiB2 composite in the 480 C temper.

Table 2Comparisons of measured internal stresses at and predicted internal stresses from the Eshelby model at 400 MPa for the 316-based MMC.

Longitudinal (MPa) Transverse (MPa)

Measured value Eshelby model Measured value Eshelby model

316L matrix 350 360 30 12TiB2 reinforcement 570 520 10 36


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in tension in situ in the X-ray beam. The resultsshow a trans-fer of load from the matrix to the reinforcement during theelastic regime, and additional load transfer once the matrixbecomes plastic. Heat treatment of the material alters thestrength but does not affect the elastic load transfer.

The elastic response of the composite has been predicted

using an Eshelby-based modelling approach. For the longi-

tudinal stress response, parallel to the loading axis, there isexcellent agreement between the experimentally determinedinternal phase stresses and those predicted using theEshelby approach. The agreement with the transverseresponse is relatively poor, although this is not unexpected.

The load transfer is consistent throughout elastic load-

ing, and following plasticity there is increasing load

Fig. 9. (a) Longitudinal and (b) transverse stresses in the Fe and TiB2 phases of the W1.4418/10% TiB2composite.

Table 3Comparisons of measured internal stresses at and predicted internal stresses from the Eshelby model at 1000 MPa for the W1.4418 matrix MMC.

Longitudinal (MPa) Transverse (MPa)

Measured value Eshelby model Measured value Eshelby model

W1.4418 matrix 980 960 95 14TiB2reinforcement 1400 1380 100 124

The transverse matrix stress is the average of the two diffraction peak values.


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transfer to the reinforcement and some unloading of cer-tain grain families within the matrix. This indicates thatthere is good interfacial cohesion between the matrix andthe reinforcement during loading of the material, and theresults show no evidence of particle decohesion or crackingduring tensile deformation.

Acknowledgements

We are grateful to AMC Ltd. for the supply of the mate-rials studied. We acknowledge the European SynchrotronRadiation Facility for the provision of beamtime and wewould like to thank Dr M. Moret for assistance in usingbeamline ID11; Professor Mark Daymond is thanked forhelp with the experimental execution, and Dr David Dyefor help with the Kroner modelling. D.H.B. was supportedby a Doctoral Training Award from the UK Engineeringand Physical Sciences Research Council. M.E.F. is sup-

ported by a grant through The Open University fromThe Lloyds Register Educational Trust, an independentcharity working to achieve advances in transportation, sci-ence, engineering and technology education, training andresearch worldwide for the benefit of all.

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http://www.msm.cam.ac.uk/mmc/publications/soft.htmlhttp://www.msm.cam.ac.uk/mmc/publications/soft.htmlhttp://www.msm.cam.ac.uk/mmc/publications/soft.htmlhttp://www.msm.cam.ac.uk/mmc/publications/soft.html

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