Investigation on Strain Recovery During Microfabrication by ColloidalIsopressing

Zhuo Zhang*,w,z and Frederick F. Lange**

Materials Department, University of California, Santa Barbara, California 93106

During microfabrication of ceramics by the Colloidal Isopress-ing method, cracks were a major problem when features withhigh aspect ratios were molded into the surface. As differentialstrain recovery (different elastic expansion of the polymer moldmaterial relative to the consolidated powder compact) is onecause of stress that introduces cracking during pressure release,the strain recovery of the consolidated alumina body was inves-tigated. Spheres of different materials with different elasticmoduli were embedded within a pre-consolidated slurry and iso-pressed at 250 MPa. The strain recovery of the powder compactwas also measured via a uni-axial compression test. Resultsshowed that cracks did not form when the elastic moduli of theinclusions were greater than 3 GPa. Inclusions were made byconsolidating wax (low-modulus) and aluminum (high modulus)powders so that the elastic modulus of the composite was largeenough to avoid crack during pressure release. The wax wasremoved via a low-temperature heat treatment. This heat treat-ment also strengthened the powder compact so that the residualaluminum powder could be dissolved in a weak acid. Internalcavities could be formed in dense ceramics by this method.

I. Introduction

IT was previously demonstrated that micron-size surface fea-tures could be rapidly produced on alumina powder compacts

by the colloidal isopressing method.1,2 Colloidal Isopressing, anew shape-forming method, was first developed by Yu and La-nge,3 in which a pre-consolidated slurry is injected into an el-astomeric mold and isopressed to convert the slurry rapidly intoan elastic body that can be removed from the mold withoutshape distortion.

As reported previously,2 cracks were a major problem whenfeatures with high aspect ratios were molded into the surface ofa powder compact during Colloidal Isopressing. During iso-pressing, the fluid-like, pre-consolidated slurry is transformedinto an elastic body that stores strain energy during consolida-tion. This strain energy is released when the pressure is removedafter isopressing. Lange et al.4 found that when the pressure isreleased from 80 MPa, A12O3 powder compacts exhibit lineargrowth of between 2% and 3% due to the non-Hookian elasticproperties of powder compacts as compared to solid, elasticbodies that exhibit a linear, Hookian response. When the pres-sure is released, the PDMS mold used for shape forming alsoreleases its strain energy, but it will expand with a Hookian re-

sponse, relative to the non-Hookian response of the powderbody. The differential strain recovered between the PDMSmoldand the consolidated powder compact will result in stresses.Cracks will develop in the consolidated body if tensile stressesdevelop within the body during differential strain recovery, andif the tensile stress is larger than the strength of the moldedpowder compact.

Previously reported stresses within the powder compact wereconcerned with producing micron-size surface features made byColloidal Isopressing.2 In this work, the enquiry is extended toproduce three-dimensional features within the consolidatedbody, namely, for the example pursued here, an internal, spher-ical cavity. To obtain an internal, spherical cavity, a spherical-shaped body must be centered, surrounded by a pre-consolidat-ed slurry, isopressed as described elsewhere,1 and then removedfrom within the elastic, isopressed body by either dissolving,melting (lost wax), or pyrolysis. However, the differential strainrecovery between the spherical inclusion and the isopressed,consolidated body during the removal of the applied iso-pres-sure can be substantial and can possibly result in residual tensilestresses that might fracture the consolidated body. Therefore, itwas essential to understand the relationship between strain re-covery, elastic modulus of the consolidated powder compact, thedifferential strain, and the possible fracture phenomena.

II. Background for State of Stress

Lange5 was one of the first to detail the criteria for crack ex-tension and arrest in residual, localized stress fields associatedwith second phase, spherical inclusions contained within a muchlarger, elastic body. He concluded that crack extension will notoccur unless the product of the squared root of the stress withinthe inclusion and the radius of the inclusion is greater than agiven value. Although Lange’s interest in this study concernedthe strain energy because of differential thermal expansion, thesame understanding applies for the differential strain recoveryproduced during the release of pressure after isopressing. For asingle, spherical inclusion of radiusR within an infinite matrix, auniform isostatic stress si arises within the inclusion and radial(sr), and tangential (st) stresses of siR

3/r3 and �siR3/2r3, re-

spectively, arise within the surrounding matrix when r � R,where r is the radial vector with an origin at the center of thespherical inclusion. The stress within the inclusion si depends onthe differential strain recovery of the inclusion and the matrixand is given by:

si ¼ De=k (1)

where De is the differential strain between the matrix and theinclusion, and k is given by the elastic constants (elastic modulus(E) and Poisson’s ratio (n)) of the two phases.

k ¼ 1þ nm2Em

þ 1� 2niEi

(2)

The subscripts m and i denote matrix and inclusion, respectively.

Journal

J. Am. Ceram. Soc., 89 [7] 2348–2351 (2006)

DOI: 10.1111/j.1551-2916.2006.01034.x

r 2006 The American Ceramic Society

2348

J. Roedel—contributing editor

Based in part on the dissertation submitted by Z. Zhang for the Ph.D. degree inmaterials, University of California, Santa Barbara, CA 2005. Supported by the ArmyResearch Office under grant� DAAD19-02-1-0380�.

*Member, American Ceramic Society.**Fellow, American Ceramic Society.wAuthor to whom correspondence should be addressed. e-mail: zhuozh@engineering.

ucsb.eduzPresent address: Applied Materials, Santa Clara, CA.

Manuscript No. 21285. Received December 23, 2005; approved February 25, 2006.

The recovery strain of the elastic inclusion placed within thepowder compact is determined only by its elastic modulus andgiven by :

ei ¼DVV¼ �sa

Bi(3)

where sa is the applied isostatic pressure, and Bi, the bulk mod-ulus of the inclusion, which depends on the elastic modulus (Ei)and Poisson’s ratio (ni) of the inclusion, and is given by

Bi ¼Ei

3 1� 2nið Þ (4)

The modulus of the powder compact matrix required to cal-culate the stresses in the powder is not simply related to theelastic modulus and Poisson’s ratio, Em and nm, of the particlesthat make up the powder. Although it is generally agreed thatthe stress–strain behavior of a powder compact should be Hertz-ian and not linear, there is no general agreement of how to relatethe modulus of the powder compact to the many properties ofthe compact including its volume fraction, the connectivity ofthe particles (i.e., how they distribute the applied stress), theparticle size, size distribution, and particle shape.

If the recovery strain of the inclusion network is larger thanthe recovery strain of the matrix, (DV/Vi4DV/Vm), the inclu-sion will be placed in compression during unloading, and a ten-sile stress will arise in the surrounding powder matrix, tangentialto the spherical inclusion. If the tensile stress in the powdercompact is sufficiently large, it will cause crack extension in theradial direction, relative to the spherical inclusion. Indeed, asshown below, our observations show that one or more largecracks occur after isopressing when the consolidated body con-tains an inclusion with a low bulk modulus.

On the other hand, if the bulk modulus of the spherical in-clusion is larger than that of the powder compact, the inclusionwill recover less strain than the powder compact. In this case, itcan be shown that the largest tensile stress within the powdercompact is a radial stress, and will arise at the interface betweenthe inclusion and powder compact. In this case, when the pres-sure is removed after isopressing, a crack will extend around theinterface between the inclusion and powder compact, withoutdamaging the powder compact as reported below.

When elastic, spherical bodies are included within the powdercompact, avoiding cracks during unloading is only one part ofthe problem in creating internal cavities. The second problem isto remove the internal body. If pyrolysis is used to remove theinternal inclusion, the powder compact and internal inclusionmust be heated. Experience has shown that the differential ther-mal expansion between the inclusion and the powder compact isanother cause for tensile stress and cracks. Therefore, the inclu-sion not only needs to have a relatively high elastic modulus butalso its thermal expansion coefficient should be either similar orless than the powder compact. If, on the other hand, the internalinclusion can melt at a low temperature, the differential thermalexpansion may not be a problem.

In this work, the strain recovery of consolidated Al2O3 pow-der compacts will be reported and compared with different strainrecovery of different internal inclusions to show that when themodulus of the inclusion is lower than that of the powder com-pact, the powder compact will fail when the pressure is removedafter isopressing. In, addition a method of avoiding crackingduring pressure release and a scheme to remove the internal in-clusions after isopressing has also been devised.

III. Experimental Procedure

(1) Strain Recovery Measurement

Because the powder continuously consolidates, namely, increas-es its volume fraction, when load is applied in a pressure filtra-

tion device, the stress–strain relation for a powder compactcannot be obtained during loading. Namely, although the pow-der compact stores strain during loading, densification duringloading due to particle rearrangement produces a non-recover-able strain. For this reason, once the powder compact is fullyloaded, the recovery strain must be measured during unloading.

A slurry was prepared and pre-consolidated as described else-where.1 The pre-consolidated body was fluidized within a sealed,plastic bag to prevent drying by placing it on a tube vibrator(The Cleveland Vibrator Company Inc., Cleveland, OH) andthen injected into a cylindrical chamber of a pressure filtrationdevice with a diameter of 24.955 mm. The arrangement of thedevice was identical to that used for pressure filtration experi-ments described elsewhere.4 To insure that no air bubbles weretrapped within the die cavity, the whole device was placed on avibrator to reduce the viscosity of the shear-rate thinning, pre-consolidated slurry. A pressure of 45 MPa was applied with anInstron 1123 testing machine (Instron Corp., Los Alamitos,CA); this pressure was held for 5 min and then released at a rateof 0.1 in./min to mimic the condition of isopressing. Two piecesof laser tape were attached onto the plunger and the retainingring so that the displacement of the plunger could be recordedduring unloading using a laser extensometer (Electronic Instru-ment Research, Irwin, PA). The consolidated specimen was thenre-loaded to 45 MPa at 0.1 in./min. After unloading and waitingfor approximately 15 min to achieve a sufficient relaxation pe-riod, a lower load was reapplied and the relaxation displacementwas again measured. The thickness of the consolidated body wasmeasured after the experiment was terminated and the relaxa-tion strain was determined by dividing the displacement by thethickness of the consolidated body. The pressure exerted on thespecimen was calculated by dividing the applied load plus theweight of the plunger by the cross-sectional area of the plunger.

(2) Introducing Spherical Inclusions within the PowderCompact

One-quarter and one-eighth inch diameter spheres of materialsincluding high-density polyethylene (HDPE), polypropylene(PP), polystyrene (PS), acrylic (PMMA) (United States PlasticCorp., Lima, Ohio), and aluminum (Bal-tec., Los Angeles, CA)were placed in the center of different pre-consolidated aluminabodies before isopressing at 250 MPa for 2 min. The elasticmoduli and Poisson’s ratios of the spherical inclusions usedin these experiments are listed in Table I; the bulk moduli arecalculated using Eq. (4).

IV. Results

Similar to data reported by Lange et al.,4 strain recovery wasobserved to be time- dependent as shown in Fig. 1, which weredata obtained upon unloading at 0.1 in./min from 45 MPa. Asshown in Fig. 1, a larger percentage (90%) of the strain wasquickly recovered inB50 s, whereas the total recovery time wasB15 min.

Figure 2 illustrates the strain recovered after 15 min as afunction of the applied stress. As shown, the effective modulusof the powder compact can be obtained from the slope of thestress–strain curve, assuming a linear behavior, which is approx-imately 2.22 GPa.

Table I. Elastic Moduli of Different Materials

Materials Aluminum PMMA PS PP HDPE

Elastic modulus (GPa)6 70 3.4 3–3.4 0.9 0.7Poisson’s ratio 0.347 0.35–0.48 0.339 0.427 0.427

Bulk modulus (GPa) 72.9 3.78 3.33 1.88 1.46

PMMA, acrylic; PS, polystyrene; PP, polypropylene; HDPE, high-density

polyethylene.

July 2006 Communications of the American Ceramic Society 2349

Cracks were observed after pressure release for consolidatedbodies containing spheres made of materials with bulk modulusless than 2 GPa, for example, HDPE and PP, whether their sizewas either 1/4 1/8 in. diameter, as shown in the picture below thestress–strain curve in Fig. 2. More cracks were observed withinclusions of decreasing elastic modulus. Cracks were not ob-served for those bodies with spheres made of materials withelastic moduli larger than 3 GPa, for example, those made of PS,PMMA, and aluminum. This is because all of these inclusionsexpanded less than the alumina powder matrix.

Although inclusions made of materials with elastic moduligreater than 3 GPa did not introduce cracks during the releaseof pressure after isopressing, after drying and heating to 5001Cto either pyrolyze the polymer inclusions or strengthen the bodyfor further removing the aluminum inclusion in acid, crackswere formed due to differential thermal expansion.

V. Discussion

As shown in Fig. 2, the experimental results are qualitativelyconsistent with the theory. When the modulus of the inclusionwas larger than 3 GPa, which is larger than the apparent mod-ulus of the alumina powder compact, the inclusion will recoverless strain than the powder compact. For these cases, the tan-gential stress in the powder compact is compressive, whereas,when the modulus of the inclusion was less than that of the

alumina compact, a tangential tensile stress will arise in thepowder matrix, which can cause crack extension in the powdercompact.

As shown above, although it was observed that cracks did notform when the iso-pressure was released if the material used toform the internal cavity had a modulus � 3 GPa, the materialwithin the cavity could not be removed because the body had tobe heated and heating produced cracks due to differential ther-mal expansion. With regard to removing the inclusion, a waxwould be an ideal material because many waxes melt at tem-peratures less than 1001C, which would avoid cracking becauseof differential thermal expansion, namely, the wax would meltand redistribute within the powder compact. Unfortunately, theelastic modulus of wax, of many different varieties, is generallyr0.5 GPa, and would produce cracking during pressure release,as observed in the experiments not reported above.

On the other hand, it was hypothesized that if an inclusion wasa composite material consisting of wax and a much stiffer ma-terial, e.g., aluminum powder, the composite could be formulat-ed with a modulus 43 GPa, to avoid cracking during pressurerelease, and yet could be removed by melting the wax, and treat-ing with an acid to remove the residual aluminum powder.

Therefore, inclusions made of wax and aluminum powderswere produced. To make cavities inside an alumina powdercompact, a composite disk consisting of mixtures of Paraffinwax, Parowax (Amoco Oil Company, Chicago, IL), and alumi-num powder (Johnson Matthey Electronics, Ward Hill, MA)were produced with different ratios of the two phases. Parowaxwas first melted in a glass beaker on a hot plate with a temper-ature above 751C, and then mixed with the aluminum powder.Different composites were produced with different ratios of waxto aluminum powder and dry pressed into pellets (6.3 mm di-ameter). The elastic modulus of Paraffin wax is reported to be110–267 MPa.10 The pellets were placed in the center of the pre-consolidated alumina body prior to isopressing and then thewhole system was isopressed to 250 MPa for 2 min, dried in a701C oven, and then pre-heated to 5001C at 0.51C/min for 2 hand cooled to room temperature at 0.51C/min. This heat treat-ment removed the wax and strengthened the powder compactwithout removing porosity.

It was observed that cracks were neither produced upon pres-sure release after isopressing nor during the heat treatment to5001C for the powder compacts for composite inclusions con-taining � 10 vol% of aluminum, namely bodies containingcomposite inclusions made with 0.1, 0.2, 0.4, 0.6, and 0.8 vol%aluminum survived without any cracks after isopressing, drying,and heat treatment. Using a very simple linear law of mixtures,the elastic modulus of pellet containing 0.1 vol% aluminum wasestimated to be 7.5 GPa, which is greater than the 3 GPa ob-served above to prevent cracking during pressure release. Asreported above, when the inclusion was solid aluminum, nocracking occurred after pressure release, but cracking occurredwhen the consolidated body was heated to strengthen the pow-der compact to enable acid leaching of the aluminum. Thus,when the inclusion was made of a mixture of wax and aluminumpowder, the elastic modulus could be adjusted to be sufficientlylarge to prevent cracking during pressure release, and the bodycould be heated to melt the wax without cracking due to differ-ential thermal expansion. The residual aluminum powder couldbe dissolved by diluted acid, leaving a cavity with the sameshape as the inclusion.

VI. Conclusions

Differential strain recovery is the reason for cracks upon un-loading after isopressing. The elastic modulus of consolidatedalumina body was measured and the stress–strain behavior wasnon-linear. It was demonstrated that inclusions with elasticmodulus � 3 GPa would not produce cracks during releaseof the isostatic pressure. Inclusions made from a mixture of waxand aluminum could avoid cracking after isopressing, and also

0

0.005

0.01

0.015

0.02

0.025

0 200 400 600 800 1000

Rec

over

y st

rain

Time (s)

Fig. 1. Time-dependent strain recovery upon unloading of 45 MPapressure.

Fig. 2. Total strain recovered after a 15 min relaxation time plotted as afunction of applied pressure. Cracks occurred for specimens with inclu-sions made of high-density polyethylene, polypropylene , whereas therewere no cracks for those with inclusions made of polystyrene , acrylic,and Al.

2350 Communications of the American Ceramic Society Vol. 89, No. 7

avoid cracking during a heat treatment needed to strengthen thepowder compact to remove the aluminum powder by acid leach-ing. This provides a possible approach to fabricating ceramicbodies containing internal, 3-D cavities by Colloidal Isopressing.

References

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4F. F. Lange and K. T. Miller, ‘‘Pressure Filtration—Consolidation Kineticsand Mechanics,’’ Am. Ceram. Soc. Bull., 66 [10] 1498–504 (1987).

5F. F. Lange, ‘‘Criteria for Crack Extension and Arrest in Residual, LocalizedStress Fields Associated with Second Phase Particles’’; pp. 599–609 in FractureMechanics of Ceramics, Vol. 2., Edited by R. C. Bradt, D. P. H. Hasselman, andF. F. Lange. Plenum Press, New York, 1974.

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Use,’’ J. Oral Rehabil., 24 [7] 517–21 (1997). &

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