Experimental Mechanics (2012) 52:669–678DOI 10.1007/s11340-011-9532-x

Multi-Axial Deformation Setup for MicroscopicTesting of Sheet Metal to Fracture

C.C. Tasan · J.P.M. Hoefnagels ·E.C.A. Dekkers · M.G.D. Geers

Received: 27 September 2010 / Accepted: 20 July 2011 / Published online: 20 August 2011© The Author(s) 2011. This article is published with open access at Springerlink.com

Abstract While the industrial interest in sheet metalwith improved specific-properties led to the design ofnew alloys with complex microstructures, predictingtheir safe forming limits and understanding their micro-structural deformation mechanisms remain as signifi-cant challenges largely due to the inadequacy of theexisting experimental tools. The investigation of thestrain-path dependent failure mechanisms requiresminiaturized testing equipment, which can be placedin a scanning electron microscope for in situ experi-ments. So far, such tests could only be carried out fora single strain path (uniaxial tension). In this work,in order to fill this gap, a miniaturized Marciniak testsetup is designed, built and tested. With this setupreal-time, multi-axial tests of industrial sheet metalcan be carried out to the point of fracture within a

C.C. Tasan (SEM member)Materials Innovation Institute (M2i), Delft, The Netherlands

C.C. TasanMax Planck Institute for Iron Research,Dusseldorf, Germanye-mail: C.Tasan@mpie.de

J.P.M. Hoefnagels (B, SEM member) · M.G.D. GeersDepartment of Mechanical Engineering, Mechanics ofMaterials, Eindhoven University of Technology,Eindhoven, The Netherlandse-mail: J.P.M.Hoefnagels@tue.nl

M.G.D. Geerse-mail: M.G.D.Geers@tue.nl

E.C.A. DekkersGTD, Eindhoven University of Technology,Eindhoven, The Netherlandse-mail: E.C.A.Dekkers@tue.nl

scanning electron microscope. Proof-of-principle ex-periments demonstrate that a realm of informationcan be obtained, crucial for the understanding of themechanical behavior of new alloys.

Keywords Strain path · Marciniak test ·In situ testing · Biaxial tension · Sheet metal

Introduction

There is a growing scientific and industrial interest inthe development of sheet metal with improved specific-properties, governed primarily by the weight-reductionmotivations in the automotive industry [1]. Whereas re-lated metallurgical research has lead to new alloys withcomplex microstructures (e.g. transformation inducedplasticity steels, twinning induced plasticity steels, dual-phase (DP) steels, magnesium alloys, aluminium alloys,etc.), it also triggered two main challenges regarding theproper character of the mechanical behavior of thesealloys:

(i) Experimental or numerical determination of theforming and fracture limits (e.g. tensile instability,ductile fracture, shear fracture) of these new al-loys in different stress and strain states,

(ii) Understanding the underlying micromechanismsthat dictate the observed global material behaviorand its accompanying failure mechanisms.

Although the literature has seen an extensive amountof research on both aspects separately, the connectionbetween them is only rarely established, e.g., to link thestrain path dependent forming limits to the underlyingmicrostructural deformation mechanisms [2, 3]. The

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major cause of this gap in the literature is the limitationsof the commonly available experimental methodolo-gies, i.e. macro-scale mechanical deformation tests formeasuring forming limits and post-mortem fractogra-phy analyses for revealing microstructural-deformationmechanisms. Although these techniques have providedclear insight in the behavior of metal microstructuresover the past century, thorough understanding of thedeformation mechanisms in the complex microstruc-tures of the aforementioned new alloys requires real-time analysis of microstructural deformation mecha-nisms. Therefore, recent studies employ miniaturizedtensile testing equipment inside scanning electron mi-croscopes, e.g., to investigate the influence of temper-ing [4] or segregation-induced banding [5] in DP steels.These studies clearly demonstrate the benefits of real-time microstructural analysis. In fact, a mechanical-microscopical approach makes it possible to addressboth challenges stated above simultaneously, by high-resolution real-time imaging enabling the investigationof the underlying deformation mechanisms and subse-quent micrographic digital image correlation to enabledetermination of deformation limits even locally.

On the other hand, commonly used sheet metalforming processes almost always impose complex strainpaths to the sheet being formed, making it unreal-istic to analyze the strain path dependent behaviorand failure of the sheet through tests along a singlestrain path only (i.e. the standard uniaxial tension test).Realistically, a full understanding of this path depen-dency requires in situ examination of the deformation-induced microstructure evolution in all relevant strainpaths. However, this was so far not possible due tothe absence of a setup that allows in situ multi-axial

testing of sheet metal up to the point of failure. Thispaper presents a miniaturized Marciniak test setup thatis dedicated for this purpose. In the following sections,first the choice for the Marciniak deformation conceptis motivated through a critical comparison betweenpossible candidates. Next, the challenges related to theminiaturization of the Marciniak setup to enable real-time in situ scanning electron microscope (SEM) visu-alization are explained, and the resulting final designis presented. The paper is finalized with results fromproof-of-principle experiments.

Critical Comparison of Potential TestingMethodologies for Miniaturized Multi-Axial Loading

Several multi-axial testings setups have been developedto study deformation of sheet metal, e.g. bulge pressuretests [6, 7], hemi-spherical punch (i.e. Nakazima) tests[2, 8], cruciform tests [9–11], flat punch (i.e. Marciniak)tests [12, 13], multiaxial compression tests [14, 15], elec-tromagnetic forming tests [16, 17] (Fig. 1). Each ofthese techniques have specific strengths and weak-nesses regarding the degree of the control of the stressstate, the quality of information provided, practicality,etc. The minimum requirement for any methodologyfor real-time mechanical-microstructural characteriza-tion of multi-axial deformation in a miniaturized con-figuration, is to:

– avoid constraining the physical deformation andfailure mechanisms of the sheet being tested toallow characterization of “true” microstructuralmechanisms,

Fig. 1 Commonly usedmethodologies for applyingmulti-axial loading,illustrated here for the case ofbiaxial tension testing:(a) bulge test, (b) Nakazimatest, (c) cruciform test,(d) Marciniak test,(e) compression test, and(f) electro-magnetic test Bulge Test Hemisphere Punch Test Cruciform Test

Flat Punch Test CompressionTest Electromagnetic Testing

)c()b()a(

)f()e()d(

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0 0.1 0.2 0.3 0.40

100

200

300

400

500

600

True Strain (%)

Tru

e S

tres

s (M

Pa)

Fig. 2 Material properties for the finite element simulations areobtained from the shown tensile test data of deep-drawing steel

– operate safely within the vacuum chamber of aSEM to allow for in situ visualization and localstrain mapping,

– produce the required level of load and displace-ment to reach sheet metal failure.

In this section, these methods are comparativelyanalyzed for their potential as a miniaturized setup.Where required, results from finite element simulationsare presented. Note that all simulations mentioned inthis work are modeled with an isotropic elasto-plasticmaterial model of high-quality deep-drawing steel, forwhich the elastic and plastic material properties aredetermined from tensile tests (Fig. 2). The sheet is mod-eled using solid axisymmetric elements, a four nodequadrilateral element with bilinear interpolation, whilethe punch and the two clamps are modeled as rigidbodies. For friction the coulomb model is used, and thecoefficients of friction are varied between 0 and 1.

Commonly used methodologies such as the com-pression test and the hemi-sphere punch test exertthe required force through direct contact with the testpiece. This makes the observed material behavior heav-ily dependent on the degree of friction, the level ofinfluence of which is difficult to assess in small-scaletests. For instance, finite element simulations show thatthe location of fracture in the hemi-sphere punch testis directly related to the level of friction between the

Fig. 3 Finite elementsimulations of thehemi-sphere punch testsdemonstrate the challenges inminiaturization: (a) frictionstrongly influences the stressdistribution and failure, suchthat increasing friction causesthe highest stresses to occuraway from the top of thepunch, as shown here for theequivalent Von Mises stressdistribution. (b) Minia-turization of the punchdecreases Von Mises stressand plastic strainhomogeneity along thethickness direction. Note thatthe punch, which has beenomitted from the graphs forclarity, comes in from left toright. Only half of the sheet issimulated

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punch and the sheet metal being pressed (Fig. 3(a)).Similar concerns hold for the compression test, forwhich a direct view of observation in SEM is also notpossible. For the hemi-sphere punch test the imposedstrain path is further complicated due to the existenceof a bending component, which increases with theminiaturization of the punch (Fig. 3(b)). As a result ofthese complications, characterization of the microstruc-

tural mechanisms using the hemi-sphere punch test andthe compression test is not trivially possible.

Contact related problems are not an issue for bulgetests, electromagnetic forming tests or cruciform tests.However, for the former two cases, operation withinSEM is not possible, due to the required fluid pres-sure (that is released upon sheet metal fracture) andstrong magnetic field, respectively. The cruciform test,

Fig. 4 Finite elementsimulations of thecruciform samples with(a) original thickness,(b) homogeneously-reducedthickness and(c) bowl-shaped profile.(d) Experiments carried outusing a home-built biaxialdeformation setup showingthat the thickness reducedcruciforms fail in their center

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on the other hand, is an interesting candidate for minia-turization, and upon initial consideration there seemsto be no direct influence of boundary conditions onthe region of interest (i.e. center of the cruciform).However, finite element simulations carried out withthe same material model used in Fig. 3 revealed thatreaching high levels of deformation in the center ofthe cruciform is not possible, unless the thickness inthe center is significantly reduced to a bowl-profilewith the central thickness approximately ∼20% of thatof the as-received sheet (Fig. 4(a–c)). It was reportedearlier that such a thickness reduced geometry maybe manufactured by electro-discharge machining orelectro-chemical machining, ensuring that the failure isforced to occur at the center (Fig. 4(b)) [11]. Unfortu-nately, it is well-known that industrial sheet metals havea non-homogeneous microstructure distribution alongthe thickness direction. Removing layers from top andbottom of the sheet render the probed microstructurenot representative anymore for the as-received sheetmetal. Furthermore, it is questionable whether the realmaterial failure behavior is properly probed, since thecenter of the bowl, with the smallest thickness, is forcedto fracture first (Note that in case of a bowl with a flatbase, the fracture always occurs at the edge of the flatbase, see Fig. 4(b)). Due to these reasons, the cruci-form test is also regarded as unsuited for investigatinglarge deformation induced macro and microstructuralphenomena in sheet metal.

Finally, in the Marciniak test, the load is transferredfrom a flat punch to the specimen via a so-called

‘washer’ plate, which has an opening window in themiddle under the region of interest. Hence, there areno friction effects in this gauge region of the speci-men. Both the specimen and the washer are drawnsimultaneously, the latter at a larger velocity due to theopening in the center. This creates the main differencefrom a typical deep drawing experiment, as the re-sulting relative velocity between the specimen and thewasher in the Marciniak test creates friction forces onthe specimen in the opposite direction of those thatoccur in a normal deep-drawing experiment without awasher (Fig. 5).

This reversed friction force in the Marciniak testlimits the level of deformation of the regions wherethere is contact between the washer and the sheet and,as shown by the finite element simulation in Fig. 6,allows the largest deformation and failure to occur atthe center, where there is no contact, making the testfundamentally different from a standard punch test. Asa result of the absence of contact a true in-plane defor-mation occurs and inhomogeneous material deforma-tion is not artificially enforced. Accordingly, this testis perfectly suitable for characterizing microstructuralmechanisms and, therefore, regained a lot of interestrecently [18–21]. Furthermore, the Marciniak tests canbe carried out safely in SEM since there is no influenceon the working principles of electron microscopy. Allthese considerations qualify the Marciniak test as themost suitable candidate for a in situ miniaturized multi-axial deformation test, however, the challenge lies inminiaturization of the Marciniak setup.

Fig. 5 Sheet displacementand friction directions in(a) deep drawing and(b) the Marciniak test

(a)

(b)

specimen

washer

punch

friction

displacement

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Fig. 6 Finite elementsimulation of the Marciniaktests reveal that the highestlevel of deformation occurs atthe center of the testedspecimen, if the experimentalparameters shown in thefigure (punch radius (rp),punch edge radius (rpe),washer hole radius (rwh), dieedge radius (rde), distancefrom die to punch (ddp)) andfriction (i.e. between thepunch and the washer (μpw)and between the washer andthe sheet (μws)) areoptimized. Note that thematerial model is the same asin the previous figures, andthat the punch comes frombelow

rde

rpe

ddp rp

rwh

0.4

0.3

0.2

0.1

0.0

µws

µpw

Eq

. Pla

stic

Str

ain

samplewasher

Challenges in the Design of a Miniaturized MarciniakTest Setup

It was observed in preliminary macro-scale Marciniaktests that unwanted failure modes (see Fig. 7, andalso [21]) may be triggered under certain experimentalsettings (e.g. too small punch radius, too small punchcorner radius, too small or too large washer openingradius, too large friction, etc.), all affecting the relativedrawing velocity of the washer compared to the testedsheet. Of specific concern for miniaturization is a deepdrawing type of failure (Fig. 7(b)), which occurs when

the reverse friction effect is insufficient, thereby causinga stress concentration, σe, at the corner of the flatpunch, that exceeds the stress level, σc, at the contact-less region at the specimen center. In order to evaluatethe sensitivity of the stress ratio σe/σc to miniaturiza-tion of the setup and to provide specifications for theminiaturized Marciniak setup, finite element simula-tions of the Marciniak test are carried out, with a rangeof different geometries (0 < rwh < 16 mm; 0 < rpe <

25 mm; 0 < rp < 30 mm) and friction settings (i.e. μpw

and μws between 0 and 1) (Fig. 6). These simulationsincorporate the same material model, finite elements

b)a) c)

Fig. 7 Different failure modes in the Marciniak test investigated on IF steel (for rp = 50 mm, rpe = 10 mm): (a) washer hole initiatedfailure (washer hole too large) (b) deep drawing failure (i.e. the reverse friction effect not sufficiently strong) and (c) successful failuretriggering a random crack in the center region

Exp Mech (2012) 52:669–678 675

and material parameters (Fig. 2) as the hemi-spherepunch test explained above, but with a flat punch andan additional washer sheet with an opening in the cen-ter, both of which are modeled with the same materialproperties.

The simulation results revealed that rpe should beabove ∼5 mm and that the friction between the punchand the washer should be as low as possible (μpw < 0.2)to keep σe/σc to a minimum, while the friction betweenthe washer and the specimen should be maximized(μws > 0.8). Furthermore, the washer hole radius, rwh,also has a strong influence on the stress ratio, and hasto be chosen <∼13 mm (to avoid “cutting” the testedsheet at the corner (Fig. 7(a)) yet larger than ∼5 mm(to avoid deep drawing failure at the cup (Fig. 7(b))).

The most important choice from a miniaturizationperspective is the size of the punch, rp, since it directlyaffects the mode of failure, as well as the requiredforce and total stroke to reach failure. In general,an increase in the punch size ensures failure at thespecimen center, however, it also quickly increases therequired force level to reach failure. As the designis limited by the available small SEM sample cham-ber volume, the punch size should be kept at a min-imum to have a force specification that can still berealized, while having a low enough ratio of σe/σc.Finite element simulations show that for rp <∼ 20 mmthe stress ratio rises significantly, which should beavoided in the miniaturized setup. Determining designspecifications for the required force level and totalstroke is not trivially possible through finite elementsimulations due to the complexity of the deformationin the Marciniak test concept. Therefore, preliminarymacro-scale Marciniak experiments were carried outwith two steels at different extremes of formability,a 1 mm thick advanced high strength steel DP steel(σUTS = 600 MPa) and a 0.7 mm thick high formabilitydeep-drawing steel (Fig. 2), to determine force andstroke specifications that would allow testing of sheetmetal with a wide range of properties.

Experiments with the critical punch radius of rp =20 mm on the DP steel sample and the washer revealedthat a maximum force of 100 kN is sufficient to reachfailure, and the failure indeed occurred in the specimencenter (Fig. 7(c)). In order to take into a factor of safetyand the possibility to test even higher strength sheetmaterial when needed, a maximum force specificationof 150 kN is set for the miniaturized Marciniak setup.Experiments with a slightly larger punch of rp = 25 mmof the deep drawing steel sample and the washer re-vealed that a maximum stroke of 15 mm is required toreach failure. This value is taken as the specification forthe total stroke of the miniaturized Marciniak setup.

Design of the Miniaturized Marciniak Test Setup

To manufacture a Marciniak apparatus with a 15 mmstroke and a load range of 150 kN, a hydraulic presswould be the most logical way for the small workingvolume available. However, this is obviously not pos-sible in the vacuum environment of a SEM chamber.An alternative idea consists in using a spindle with anut, driving the nut with an electric motor. Yet, theamount of friction consumes too much torque, makingit impossible to select a gearbox-motor combinationwithin the maximum working volume. Even going to16 small spindle-nut combinations around the sampledoes not match up the design specifications within theworking volume of the SEM.

Therefore, an alternative solution is pursued, con-sisting in the use of a long strong string between twothick plates (Fig. 8). The sample and the washer areclamped in the top plate, and a punch is fixed in thebottom plate. During a test, the top plate is drawntowards the bottom plate, pulling the sample onto thestationary punch.

With this concept, the force on the string is amplifiedby a factor of 72 towards the sample in the final setup,because the string is wrapped around 36 pulleys in thetop plate and 36 pulleys in the bottom plate, mountedaround the sample (Fig. 9). In fact not one string, butthree separate strings are used, driving three equallysized segments with (2 × 12) rolls around the sam-ple, in order to provide a linear vertical displacementwithout rotation between bottom and top plate (andthus between top plate and punch). The three stringsare reeled on a winch with a 22 mm brushless motorcombined with a harmonic drive gearbox (component6 in Fig. 9). The force can be accurately measured

Fig. 8 A schematic drawing of the miniaturized Marciniak testconcept: specimen (yellow); top plate (brown); bottom plate(dark green); punch (light green); long string (red; only one of thethree strings is shown); pulleys (blue); and winch (grey)

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Fig. 9 The components of the miniaturized Marciniak apparatus:the sample and washer (depicted in yellow) are clamped withthe clamping ring (1) to the top plate (2), and are deformed bythe punch (3) which is mounted on the bottom plate (4). Thepunch force is supplied by pulling three cables (depicted in red)over 72 pulleys (5) (i.e. 36 pulleys in the top plate and 36 in thebottom plate, all journalled in needle bearings for low friction),and the excess cable is reeled in using a winch mechanism (6). Thepunch displacement is measured using a contactless Eddy currentsensor (7); the punch force is measured using strain gauges on thebottom plate (not shown). A picture of the finalized setup is alsoshown below

with strain gauges placed on the bottom plate, due tothe relatively high bending strains on the lower centralpart of the elastically deforming bottom plate. The dis-placement is measured at the two sides with contactlessEddy current displacement sensors (component 7 inFig. 9). Depending on the sheet metal to be tested,the force level, stroke and stress ratio can be modifiedby the use of different punches that are manufacturedwithin the specifications determined with the numericalanalysis explained above. For the experiments that arepresented here two punches are used, the first onehaving rp = 20 mm and rpe = 12.5 mm and the secondhaving rp = 25 mm and rpe = 12.5 mm.

Proof-of-Principle Experiments

The capabilities of the miniaturized Marciniak appara-tus are demonstrated by in situ testing of two industrialalloys: an aluminium 6016 alloy and a DP600 alloy.The use of the larger punch (rp = 25 mm) is mostsuitable experiments for the former whereas the useof the smaller punch (rp = 20 mm) is more suitablefor the DP steel. Experiments are carried out in threedifferent strain paths (i.e. uniaxial tension (Fig. 10(a),plane strain tension (Fig. 10(b)) and biaxial tension(Fig. 10(c)) through the use of specimens of differentgeometries, although for the DP600 steel we presentonly the results of the biaxial sample (Fig. 10(d)), forwhich the highest force level is required. The differencein the strain path is achieved by imposing different levelof deformation constraint in the minor axis as a result ofthe changes in specimen width or notch geometry. Forthe presented experiments the full sample (i.e. the biax-ial strain path sample) had the diameter of 94.5 mm, theplane strain sample had a reduced width of 20 mm witha small notch radius of 2 mm, and the uniaxial tensionsample had a reduced width of 20 mm with a largenotch radius of 40 mm. The washer material is chosenas the deep drawing steel for the aluminium samplesand an extra DP steel sheet for the DP steel samples.Note that the washer material needs to withstand therising force level, while deforming together with thetested material. Due to these requirements the bestcandidate for the washer material is typically the testedmaterial itself. Before mounting the sample and thewasher, the facing sides of the washer and the samplesare ground for enhanced friction, except for the centerof the sample. The bottom side of the washer, on theother hand, is polished to reduce the friction betweenthe washer and the punch. Alternating layers of teflonand vacuum grease is used to further reduce friction.

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(a) (b) (c) (d)

Fig. 10 Results of the proof-of-principle experiments for aluminium samples in (a) uniaxial tension, (b) plane strain tension and (c)biaxial tension strain paths and (d) the DP sample in biaxial tension strain path. Strain fields at the macro-level (using images from anoptical camera), strain fields at the micro-level (using images from in situ SEM testing), and captured damage nucleation mechanisms(shown with the red arrows before and after deformation) are also shown for each of these samples. The micron-bar at the bottom rightcorner represents the scale in all microscope images. For the scale of the optical camera images please refer to Fig. 9

In all the tests, the setup operated within the de-termined working principles, verifying the success ofthe original design concept. Furthermore, fracture isreached in the flat central region of the punch, evenfor the most difficult case of the biaxial tension path,proving that the choice for the critical experimentalparameters (i.e. rp, rpe, rwh, rde, ddp, μpw and μws) iseffective, and the miniaturization related challenges inthe Marciniak test have successfully been overcome.

Obtained results from these proof-of-principle ex-periments clearly underline the benefits of in situ test-ing: high resolution SEM images captured during de-formation allow (i) carrying out micrographic digitalimage correlation to measure strains at the microstruc-ture level, and (ii) studying deformation-induced mi-

crostructural mechanisms (e.g. damage evolution) fromthe obtained SEM image sequences (Fig. 10). For thetwo materials investigated here, for example, differentstrain partitioning behaviors (i.e. more pronouncedstrain partitioning in the DP steel due to the soft ferriticgrains and hard martensitic islands) and different dam-age mechanisms (i.e. martensite cracking or martensite-ferrite decohesion in DP steel vs. damage from inclu-sions in aluminium alloy) are clearly captured.

Conclusions

In this work a miniaturized test setup was designed,built and tested, that allows real-time, multi-axial

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testing of industrial sheet metal within a scanning elec-tron microscope. A prior numerical-experimental com-parison of the existing (macro-scale) multi-axial testingsetups revealed that the Marciniak test concept suitsperfectly to the requirements of miniaturized in situtesting (e.g. avoiding manipulation of material behav-ior, operating (safely) within a scanning electron micro-scope, etc.). Next, miniaturization induced challengesin the Marciniak concept were investigated throughfinite element simulations, which led to a number ofdesign guidelines to avoid unwanted failure modes forthe miniaturized setup. An original design concept wasdeveloped to meet the determined guidelines withinthe limited volume of a scanning electron microscope.Proof-of-principle experiments revealed that the de-veloped miniaturized Marciniak setup operates suc-cessfully within the design specifications, allowing arealm of information (e.g. high resolution SEM imagesof different stages of deformation, strain field at mi-crostructure level, etc.) to be obtained.

Acknowledgements This research was carried out under theproject number MC2.05205 in the framework of the ResearchProgram of the Materials innovation institute M2i (www.m2i.nl),the former Netherlands Institute for Metals Research. The au-thors would like to thank Gerard Quaak, Carel ten Horn, andRick Peters for their contribution.

Open Access This article is distributed under the terms of theCreative Commons Attribution Noncommercial License whichpermits any noncommercial use, distribution, and reproductionin any medium, provided the original author(s) and source arecredited.

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