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Materials Science and Engineering A 473 (2008) 49–57

The development of residual stresses in Ti6Al4V-Al3Timetal-intermetallic laminate (MIL) composites

Tiezheng Li a,b, Eugene Al Olevsky b, Marc Andre Meyers a,∗a Department of Mechanical and Aerospace Engineering, Materials Science and Engineering Program,

University of California, San Diego, La Jolla, CA 92093-0411, USAb Department of Mechanical Engineering, San Diego State University, San Diego, CA 92182-1323, USA

Received 11 January 2007; received in revised form 12 March 2007; accepted 15 March 2007

bstract

Residual stresses in the metal (Ti6Al4V)-intermetallic (Al3Ti) laminate composite are generated when cooled from the processing temperature∼700 ◦C) to ambient temperature, because of the difference in thermal expansion coefficients between Ti6Al4V and Al3Ti. Two stress releaseechanisms, creep and crack propagation, are proposed to explain the development of residual stress during cooling process. Both analytical

alculations and finite element simulations are performed. In the analytical modeling, a critical stress criterion is proposed in order to determine the

nitiation of crack propagation. In the finite element simulation, the J-integral is used as a criterion for crack evolution; it enables the establishmentf the distribution of the residual stress as a function of temperature. The results of both analytical modeling and finite element simulation showood agreement with the experimental results obtained through X-ray diffraction. 2007 Published by Elsevier B.V.

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eywords: Residual stress; Creep; Crack propagation; Laminate composites; F

. Introduction

Metal-intermetallic composites have become increasinglyttractive in recent years because of their low density, hightiffness, and high strength [1,2]. However, these desirable prop-rties are often accompanied by a high level of residual stressesenerated during the cooling phase from high temperature fab-ication. Since the composite ceramic or intermetallic matricesypically have limited plasticity at temperatures below one-halff their absolute melting temperature, residual stresses gener-ted cannot be relieved by plastic deformation. As a result, theelection of a reinforcement-matrix combination must carefullyonsider the coefficients of thermal expansion (CTE) of eachomponent to avoid the introduction of damage during cool-ng in processing and from thermal cycling experienced duringervice. The stresses are schematically presented in Fig. 1 for

he Ti6Al4V-Al3Ti system, with the intermetallic under tension,n undesirable situation. Therefore, it is essential that exist-ng residual stresses can be correctly anticipated and managed

∗ Corresponding author. Tel.: +1 619 534 4719; fax: +1 619 534 5698.E-mail address: mameyers@mae.ucsd.edu (M.A. Meyers).

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921-5093/$ – see front matter © 2007 Published by Elsevier B.V.oi:10.1016/j.msea.2007.03.069

lement simulation; Thermal expansion

uring heat treatment, processing and use. Under uniform tem-erature change, stresses induced in a composite depend on theollowing factors:

. Reinforcement volume fraction and morphology (i.e., par-ticle, fiber or plate size, shape, orientation distribution, andcontinuity).

. Matrix crystallographic texture and porosity.

. Possible voids or lack of adhesion at matrix-reinforcementinterfaces.

. The development of cracks.

Generally speaking, the residual stress is determined primar-ly by the elastic constants, relative concentration and the thermalxpansion coefficients of the matrix and reinforcement materi-ls. While realizing that material microstructural properties haven effect on both strength and thermal strain, depending on theagnitude of the residual stress, the thermal expansion or con-

raction can be (a) a reversible phenomenon when the materialsndergo elastic deformation, or (b) an irreversible process, if theaterials experience plastic yielding, microcracking, interface

ecohesion or creep.

50 T. Li et al. / Materials Science and Engineering A 473 (2008) 49–57

sasconstacacat

2

8gcactctdtc

fidsa

CTwft

Fc

3

3

(9sut

σ

wα

t

c

d(r

Fig. 1. Schematics of residual stress in Ti6Al4V-Al3Ti MIL composites.

Residual stresses and cracking due to differential CTE rea-ons are well-known problems for ceramic composite materials,nd numerous studies have been carried out on the residualtress in composites [3–31]. However, very few [3,12,28] includerack propagation. The present study investigates the evolutionf residual stress in a Ti6Al4V-Al3Ti metal-intermetallic lami-ate (MIL) composite using both analytical and finite elementimulation methods. The MIL composites used in this inves-igation were processed in open air and mechanical propertiesnd damage evolution have been evaluated [32,33]. The pro-essing method has been described in detail [34–40]. In thenalytical model, two stress release mechanisms, creep andrack propagation, are introduced. The same mechanisms arelso implemented in the finite element simulation to investigatehe residual stress evolution as well as distribution.

. Experimental measurements

As processed MIL composite blocks [41–43] of0 mm × 18 mm × 8 mm were ground from 220 to 4000rit, before final polishing by 0.05 �m Al2O3, and were thenharacterized by optical microscopy. Photomicrographs weressembled in montages (e.g., Fig. 2). It is observed that mostracks in the Al3Ti layers are perpendicular to the interface. Inhe 35% MIL composites, 72% of the cracks are perpendicularracks, thus the discussion in the following sections focuses onhe development of perpendicular cracks in the MIL compositesuring cooling. Li et al. [33] provide a detailed discussion ofhe crack morphology and distribution in the as processed MILomposites analyzed herein.

The X-ray diffraction was preceded by a detailed procedureor specimen surface preparation which started with grindingn 250 and 400 grit SiC. This was followed by polishing usingiamond paste (6–10 �m) and alumina (1 �m). The surface wasubsequently etched with a 10% HF for 2–5 s in order to removeny strain in the surface due to sample preparation.

The X-ray diffraction was carried out by Harvey [44] using

u K� radiation with a Rigaku Rotaflex rotating anode device.itanium peaks were chosen. Care was taken not to take a peakhich coincided with an Al3Ti peak. Spectra were collected

rom 2θ between 20◦ and 135◦. Additional considerations led tohe selection of peaks between 121.5◦ and 124.5◦.

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ig. 2. Montage of part of the cross-section of as-processed 35% Ti6Al4V MILomposite showing cracks (marked by arrows).

. Analytical modeling

.1. Residual stress in MIL composites: elastic analysis

When the Ti6Al4V-Al3Ti MIL composite cools down, Al3TiCTE: 13 × 10−6 ◦C−1) shrinks more than Ti6Al4V (CTE:.5 × 10−6 ◦C−1) because of its higher CTE. This mismatch oftrain puts the Ti6Al4V layer under compression and Al3Ti layernder tension. For a composite with an infinite number of layers,he residual stress [45] is:

Ti = ETi · (1 − c) · (αTi − αAl3Ti)�T

[1 + (ζ − 1) · c] · (1 − υTi)(1)

here ζ = ((1 − υAl3Ti)/(1 − υTi)) · (ETi/EAl3Ti), αTi andAl3Ti are the CTE of Ti6Al4V and Al3Ti, respectively and c,

he volume fraction of Ti6Al4V, is defined as:

= dTi · W

dTi · W + dAl3Ti · W= dTi

dTi + dAl3Ti(2)

Ti and dAl3Ti are the thickness of the Ti6Al4V and Al3Ti layersFig. 1), respectively, and W is the width of the specimen. Theesidual stresses as a function of temperature for different vol-me fractions of Ti6Al4V are plotted in Fig. 3, in comparison

ith experimental measurements (also shown in Table 1). The

xperimental values were obtained by K.S. Harvey through X-ay measurements. Fig. 3 shows that the residual stress increasess the temperature decreases from the processing temperature of

T. Li et al. / Materials Science and Engineering A 473 (2008) 49–57 51

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ig. 3. Calculated residual stress as a function of temperature from the differencen CTE for different volume fractions of Ti6Al4V; experimental measurementsn lower left-hand corner.

1000 K. The slow cooling in Table 1 refers to the slow coolingate after processing as compared to the normal cooling rate. Its observed that the level of residual stresses decreases with theolume fraction of Ti6Al4V and the calculated residual stressesre much higher than the measured ones.

.2. Residual stress release mechanism I: creep

As seen in Table 1, the experimentally measured residualtresses for slow cooling rate are lower than in the normal coolingate. This suggests that some time-dependent stress relaxationechanism is active in the cooling process. The experimental

ooling curve, shown in Fig. 4, was linearized to facilitate thealculation.

Steady-state creep was described by the power-law equation:

˙s = AbμD

kT

(σ

μ

)n

(3)

here εs is the steady-state strain rate, μ the shear modulus, D

he diffusion coefficient, b the Burgers vector, T the temperature,Boltzmann’s constant, and σ is the stress. A and n are material-ependent parameters. Table 2 shows the creep parameters usedor Ti6Al4V [46] and Al3Ti (adapted from Ref. [47]).

able 1omparison of calculated residual stresses at ambient temperature by various

tress release mechanisms with experimental measurements (marked in bold)

olume fraction of Ti6Al4V (%) 14 20 35easured, high cooling rate(MPa)

65.01 32.38 8.29

easured, slow cooling rate(MPa)

30.79 25.24 10.59

alculated from difference inCTE (MPa)

345 327 282

alculated, with creep inTi6Al4V only (MPa)

280 260 208

alculated, with creep in bothTi6Al4V and Al3Ti (MPa)

257 240 195

alculated, with creep and crackpropagation in Al3Ti (MPa)

86.16 69.33 46.63

E simulation (MPa) 89.53 77.86 60.73

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3p

toTic

TC

nAμ

ig. 4. Experimental and linearized cooling curve (normal cooling rate) of MILrom processing temperature.

The procedure used in incorporating creep into the residualtress is given below. The cooling is divided into discrete inter-als. As the temperature decreases from Ti to Ti−1, the initialesidual stress, σi i, is obtained from Eq. (1). The residual stresss released during this period of time through the creep effect,nd the reduction in residual stress is obtained from:

σi = ETi · εs i · (ti − ti−1) (4)

The residual stress (including creep influence) is the reduc-ion of the change of stress from the initial residual stress, σi i:

r i = σi i − �σi (5)

The calculation is continued as the temperature decreases tooom temperature. Residual stresses including the influence ofreep in Ti6Al4V, and in both Ti6Al4V and Al3Ti, are com-ared with the experimental measurements for different volumeractions of Ti6Al4V, in Fig. 5. The inclusion of creep effec-ively reduces the level of residual stress, especially at higheremperatures. However, when the temperature decreases below40 K, the residual stresses begin to build up again, consistentith the fact that creep is not effective at lower temperatures. As

xpected, creep in Ti6Al4V is more pronounced than in Al3Ti.

.3. Residual stress release mechanism II: crackropagation

Previous research [32,33] indicates that a significant concen-ration of cracks is present in as processed MIL composites. They

ccur mostly in Al3Ti layers and perpendicular to the interface.his was attributed to the development of residual stresses dur-

ng the cooling process. A detailed statistical analysis of theseracks is given by Li et al. [33]. As the brittle Al3Ti layers

able 2reep parameters for Ti6Al4V and Al3Ti

Ti6Al4V Al3Ti

4.55 3b (nm) 8.82 × 10−5 4.89 × 10−5

(GPa) 43.8 92.3

52 T. Li et al. / Materials Science and Engineering A 473 (2008) 49–57

FTt

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[dt

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Fm

iw

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E

wYorF

ig. 5. Calculated residual stresses including creep in Ti6Al4V, and in bothi6Al4V and Al3Ti; the experimental measurements for different volume frac-

ions of Ti6Al4V are in lower left-hand corner.

ndergo increasing tensile stresses, microdefects begin to bectivated and cracks develop. These microcracks have a nega-ive effect on the material properties and help to release the levelf residual stresses. It was observed that these cracks do notenetrate into the Ti6Al4V layers, and therefore their length iseometrically connected to the thickness of the Al3Ti layers.

Two models, a simple spring model and the Salganik model48], are used to quantify the effect the crack propagation on theevelopment of residual stress. Fig. 6 shows the schematics ofhe spring and Salganik models.

In the spring model, the initial crack is assumed to be per-endicular to the interface, and its length equals the thickness ofhe Al3Ti layer (2a = dAl3Ti). The elliptical region (with majorxis 4a) denotes the approximate volume of material in whichhe stored elastic strain energy is released; this unloaded regions assumed to have an elastic modulus equal to zero. This is aeasonable assumption and the same as the one used by Griffith49]. The effective Young’s modulus of Al3Ti, Ee

Al3Ti, depends

n the separation between two cracks, s, and is a function of theormalized distance, s/a. The relationship between the effectiveoung’s modulus of Al3Ti and the theoretical Young’s modulusf Al3Ti can be expressed, to a first approximation, by consider-

btiY

Fig. 6. Schematic representation of (a) s

ig. 7. The effect of cracking on Young’s modulus by Salganik and Springodels.

ng springs in series, one with Young’s modulus EAl3Ti and oneith E0 = 0, corresponding to the unloaded region. This gives:

EeAl3Ti

EAl3Ti= 1 − 4

s/a(6)

Salganik [48] developed a more realistic model. The cracksre also assumed to be perpendicular to the interface, but theirength is smaller than the thickness of the Al3Ti layer. The effectf microcracks on Young’s modulus, Ee

2, of Al3Ti, predicted byhe Salganik model is

e2 = E2

(1 + ((16 · (10 − 3υ2) · (1 − υ22))/

(45 · (2 − υ2) · N(a, (s/a)) · a3)

(7)

here Ee2 is the effective Young’s modulus of Al3Ti, E2 the

oung’s modulus of the uncracked Al3Ti, υ2 the Poisson’s ratiof Al3Ti, N(a,(s/a)) the number of cracks per unit volume, a theadius of a mean crack, and s is the distance between two cracks.ig. 7 shows the effect of cracks on the Young’s modulus with

oth spring and Salganik models as a function of normalized dis-ance, s/a. It is seen that the spring model is more conservativen predicting the crack influence on the elastic modulus. Theoung’s modulus in the spring model decreases to zero when

pring model; (b) Salganik model.

and Engineering A 473 (2008) 49–57 53

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T. Li et al. / Materials Science

he spacing is less than 4a ((s/a) < 4), by virtue of the assump-ion that the ellipsis with major axis 4a is unloaded. On thether hand, the Salganik model is more realistic for smaller s/aalues.

.4. Combining creep and crack propagation mechanisms

As the specimen is cooled, the Al3Ti layer is under increasingensile stress. Due to the brittleness of intermetallics, existingaws in Al3Ti will start to propagate when the stress exceeds aritical value. The residual stress, σr, is a function of crack size,rack density and temperature:

r = σr

(a,

s

a, T

)(8)

The critical stress, σ∗c , is a function of the effective fracture

oughness of Al3Ti, which is a combination of the intrinsic frac-ure toughness of Al3Ti and the extrinsic fracture toughness,etermined by the residual stress in Al3Ti layer, crack size andrack density:

∗c = Keffective√

πa(9)

effective = Kintrinsic + Kextrinsic

(a,

s

a, σr

)(10)

As the existing cracks start to propagate, the residual stress iseleased, affecting the effective toughness and the critical stress.he cracks will continue to grow until the residual stress ismaller than the critical stress. As the temperature decreases,he residual stress competes with the critical stress to determinehe propagation of the cracks. This process continues until theemperature reaches room temperature or until the crack sizeeaches the width of the Al3Ti layer, dAl3Ti.

It is assumed that the initial crack size is 25% of the thicknessf the Al3Ti layer and that the MIL composites are infinitelyong. The results obtained by an iterative calculation are shownn Fig. 8.

It is observed in Fig. 8(a) that the residual stresses with dif-erent concentrations of Ti6Al4V all increase steadily beforehe critical stresses in Al3Ti are exceeded, during which time,he creep in Ti6Al4V and Al3Ti is the dominant mechanism ineleasing the residual stresses. After that, crack growth dom-nates the residual stress release process, as demonstrated byhe steady decrease in residual stress in Ti6Al4V. The sharpestecrease in residual stress is observed in 14% MIL, followedy 20 and 35% MIL. This is attributed to the higher residualtress level and larger initial crack size in 14% MIL composites,nd implies that the effective fracture toughness in 14% MIL isore negatively affected by crack growth, at the corresponding

ritical stress.Fig. 8(b) shows the evolution of crack length in the MIL

omposites during cooling. The cracks remain stable at higheremperature as the residual stress accumulates, and when the

ritical stress level is reached, the cracks begin to propagate.he larger slope (in magnitude) of crack length evolution in the4% Ti6Al4V composite corresponds to a higher growth forcertain temperature gradient. The crack length is eventually

e

s

ig. 8. Analytical model for Ti6Al4V-Al3Ti MIL composites as a function ofemperature including both creep and crack propagation: (a) residual stress; (b)rack length.

onstrained by the size of the Al3Ti layers, and the crack stopsrowing at the interface.

. Finite element simulation of residual stressistribution

The analytical modeling of residual stress evolution discussedbove assumes an infinite length of Ti6Al4V and intermetallicayers, and the results reflect the average stress level in Ti6Al4V.n reality, the MIL composites have finite size with boundaryonditions, and the distribution of residual stress in Ti6Al4V isneven. Finite element simulation provides us a powerful toolo simulate not only the magnitude but also the distribution ofesidual stress during cooling. The commercially available finitelement software, ABAQUS, was used to conduct the residualtress simulation during the cooling in 3D formulation. Becausef the symmetry, only one eighth of the specimen was simulatednd is shown.

.1. Finite element simulation of residual stress with creep

ffect

A 3-D 17 layer body was created to model the real MILample size, in which three faces of the sample were con-

54 T. Li et al. / Materials Science and Engineering A 473 (2008) 49–57

fisaaFaaeaaarFll

Fm

Fi

so

4a

sTTtttt

Fig. 9. FE model for MIL composites: initial stage.

ned in X1, X2 and X3 global directions as shown by theymmetric boundary conditions. The initial condition assumesn initial temperature of 1023 K, and creep in both Ti6Al4Vnd Al3Ti was considered. The meshed model is shown inig. 9. Eight-node brick elements are used in the simulation,nd the results (for σ11) including creep in both Ti6Al4Vnd Al3Ti are shown in Fig. 10. While most Ti6Al4V lay-rs experience relative constant stress levels, there exist areasround the boundaries where the residual stress level is notice-bly lower. The residual stress in Ti6Al4V was calculated byveraging the stresses in different Ti6Al4V layers, and the

esults are compared with the analytical solutions in Fig. 11.E results predict a similar trend in the residual stress evo-

ution. However, in FE simulation, creep is effective for aonger period of time during cooling and, as a result, a smaller

ig. 10. FE simulation of residual stresses including creep in both phases:agnitude and distribution at room temperature.

gw

Fp

ig. 11. FE results of residual stress during cooling, in comparison with analyt-cal modeling and experimental results.

tress than that in the analytical modeling in Ti6Al4V layers isbserved.

.2. Finite element simulation of residual stress with creepnd crack propagation

The detailed crack morphology and distribution were mea-ured and are recorded in the two proceeding papers [32,33].his served as a basis for their introduction into the simulation.he Salganik model was employed to adjust the material proper-

ies during crack propagation. The initial crack sizes are assumedo be 25% of the thickness of Al3Ti layers, and located in the cen-er of the layers. The initial condition is shown in Fig. 12 (noticehe existing microcracks in Al3Ti visible as mesh distortions).

The J-integral, which represents the energy required to propa-ate a crack, was calculated around the crack tips and comparedith the critical value to determine whether the cracks would

ig. 12. FE simulation at processing temperature (∼1000 K), including crackropagation; existing flaws visible through mesh distortion.

and Engineering A 473 (2008) 49–57 55

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J

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H

wtr

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F

Fa

T. Li et al. / Materials Science

urther propagate. The J-integral is calculated in ABAQUS as:

=∫

Aλ(s)n · H · q dA (11)

here λ(s) is a virtual crack advance in the plane of a three-imensional fracture; dA is a surface element along a vanishingmall tubular surface enclosing the crack tip; n is the outwardormal to dA; and q is the local direction of virtual crack exten-ion. H is given by:

= WI − σ · ∂u

∂x(12)

here for elasto-viscoplastic material behavior, W is defined ashe elastic strain energy density plus the plastic dissipation, thusepresenting the strain energy in an “equivalent elastic material.”

Although, in theory the J-integral is path independent, expe-ience has shown that the first contour calculated in ABAQUS isf significantly lower accuracy. Therefore at least 10 J-integralsround the crack tip were used for each crack. If the J-integralxceeds the critical value, crack length is extended and the elasticodulus is reduced according to the Salganik model; otherwise,

he crack remains stable. Since ABAQUS does not have theapability to simulate crack propagation in 3D automatically,he simulation was interrupted periodically, and comparison andhe necessary adjustments were made manually.

Fig. 13 shows the magnitude and distribution of residualtresses, σ11, at room temperature. It shows a dramatic decreasen the stress levels around cracks, in both Ti6Al4V and Al3Ti lay-rs. It is also observed that from the start of cooling, there existsn elliptical area of stress relaxation in Al3Ti, which by and largeonfirms the spring model. This relaxation area even extends

nto the neighboring Ti6Al4V layers and thus contributes to theelease of stress levels in Ti6Al4V.

Fig. 14 shows the evolution of residual stress and crackength with creep and crack propagation by FE simulation.

ig. 13. FE simulation at room temperature including crack propagation.

TratopesttrsAcisctfirei

bs

ig. 14. Evolution of (a) residual stress and (b) crack length by FE simulationnd comparison with analytical solutions.

he residual stress obtained by FE simulation (Fig. 14(a)) atoom temperature is comparable with the analytical solutionsnd the experimental measurements. However, the evolution ofhe residual stress itself is very different. The effect of creepn the residual stress obtained by FE simulation is much morerominent than that in the analytical solutions, as the creep veryffectively prevents the residual stress accumulation in the earlytage. In the later stage of the cooling process, however, unlikehe analytical solution, the FE simulation predicts a sudden erup-ion and the cracks keep growing in an unstable fashion untileaching the interfaces, while the residual stress experiences aharp decrease. One explanation is that at that temperature, thel3Ti has become sufficiently brittle and has little resistance to

rack growth; therefore, FE prediction simulates what happensn reality. The other explanation is that the nature of this FEimulation restricted the minimum size of the crack incrementonfined by the finite size of the element, which may not capturehe changes within that minimum increment. In that sense, thenite element simulation provides a more accurate solution foresidual stress evolution and distribution by taking into consid-ration the finite size of MIL composites. On the other hand, its less accurate by increasing crack size in a finite fashion.

Table 1 shows the comparison of residual stresses obtainedy analytical modeling, FE simulation and experimental mea-urements. The analytical modeling and FE simulation results

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6 T. Li et al. / Materials Science a

re comparable with the experimental measurements, althoughhe predictions are still higher than the measurements. One rea-on for the deviation is that the measurement was conductedn small samples, and the results are average values. There-ore, the measured values may only reflect the local averagetress level, which, when measured in the boundary area (asbserved in Figs. 10 and 13), are lower than the rest of the sam-le. Another reason is that the residual stress may be releaseduring specimen preparation, such as cutting and polishing, andherefore, the measured values are lower than the real ones exist-ng in the specimens after just being processed. The resultsere also checked with a previous study [50], in which stress

elaxation mechanisms were not taken into consideration. Thenalytical modeling and FE simulation thus may provide a moreccurate residual stress, especially as the finite element simu-ation provides not only the stress evolution but also the stressistribution.

. Conclusions

The development of residual stresses in a metal (Ti6Al4V)-ntermetallic (Al3Ti) laminate composite made by reactionynthesis at ∼1000 K followed by cooling to ambient tem-erature was investigated. The residual stresses experimentallyeasured by X-ray diffraction are much lower than the predic-

ions from differences in thermal expansion coefficients alone.he residual stresses in Ti6Al4V-Al3Ti MIL composites werealculated analytically and by FE simulation, and two stresselease mechanisms, creep and crack propagation, were includedn the analysis. The following conclusions were drawn:

. In the analytical modeling, the stress release mechanismswere implemented by an iterative calculation. Creep is thedominant stress release mechanism at high temperature,while below 740 K, when the residual stress reaches the crit-ical value, crack growth becomes the primary mechanism toreduce the stress level. The analytical prediction was suc-cessfully compared with the experimental measurements.

. Finite element simulation was conducted, including bothcreep and crack propagation. FE simulation confirmed theanalytical calculation of the stress level on average, anddemonstrated the presence of an uneven stress distribution,especially at the boundaries. FE simulation predicts an unsta-ble crack growth, as the cracks keep growing until reachingthe interfaces; the corresponding residual stress experiencesa sharp decrease. The FE results were in good agreement withthe analytical solutions and the experimental measurements.

. The difference of stress level between predictions by ana-lytical modeling and FE simulation with experimentalmeasurements has two explanations: (a) experimental mea-surements were conducted on small samples, which onlyreflect the local average stress level, and thus may underesti-mate the real stress level, especially when the measurement

was conducted around the boundary; (b) during specimenpreparation, the residual stress level can be reduced throughprocesses like cutting and polishing. Thus, the calculatedresults provide a better assessment of the residual stresses.

[[[

gineering A 473 (2008) 49–57

cknowledgements

K.S. Harvey conducted the residual stress measurements.iscussions with Prof. K.S. Vecchio are gratefully acknowl-

dged. Dr. Jiang provided the specimens for our research. Helpnd discussion with Dr. J. Ma and Buyang Cao are greatly appre-iated. This research was sponsored by DARPA through contracto. DAAD 19-00-1-0511.

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