An experimental and numerical study of a planar blanking ... · An experimental and numerical study of a planar blanking process ... not only the load–penetration curve, but

Journal of Materials Processing Technology 87 (1999) 266–276

An experimental and numerical study of a planar blanking process

Y.W. Stegeman, A.M. Goijaerts *, D. Brokken, W.A.M. Brekelmans, L.E. Govaert,F.P.T. Baaijens

Eindho6en Uni6ersity of Technology, Faculty of Mechanical Engineering, P.O. Box 513, 5600 MB Eindho6en, Netherlands

Received 24 September 1997

Abstract

Aiming at a validated model of the blanking process, an in situ study of the displacement and strain fields is carried out in ablanking experiment using a digital image correlation technique. Specimens of 13% Cr steel, 1 mm thick, are blanked at low speed,using a planar configuration with two different clearances (2 and 10% of the specimen thickness). In addition to the displacementand strain fields, load–penetration curves are also determined for both clearances. The experimental results are in good agreementwith numerical simulations, the latter of which are carried out using a plane-strain finite-element model based on an operator splitarbitrary Lagrange Euler (OS-ALE) method. © 1999 Elsevier Science S.A. All rights reserved.

Keywords: Sheet metal; Planar blanking; Contrast correlation technique; Deformation field

1. Introduction

Research has been carried out on the blanking pro-cess since the beginning of this century. Blanking exper-iments with either planar [1,2] or axisymmetric [3–8]configurations have lead to general guidelines concern-ing process parameters such as punch and die radius,velocity, and clearance. Although some studies involveanalytical models [9–11], the blanking process is notfully comprehended. Therefore, every new blankingproduct necessitates many trial-and-error experimentsbefore qualifications are met. As requirements concern-ing cycle time and product dimensions become moresevere, an appropriate model and understanding of theblanking process becomes increasingly important.

Since the process is too complex for analytical mod-els, the finite-element method has been used to simulatethe blanking process with varying success [12–14]. Oneof the problems that is encountered in the numericalapproach is the description of fracture. Both the frac-ture model and its implementation are still the subjectof discussion. Even if a fracture model has been estab-lished, much experimental research is still required toquantify the necessary input parameters.

There are many different formulations to describefracture, since the fracture behavior for a specific mate-rial is influenced by process-dependent features, suchas: the distribution and intensity of the applied loads,the geometry, the deformation history, and the hydro-static pressure [15]. To limit the number of experiments,it seems appropriate to study the deformation andfracture behavior in loading situations strongly relatedto the industrial blanking process. In this study, thepossibilities of in situ observation of the deformationbehavior in a planar blanking process is investigated.Local deformations are monitored, and subsequentlycompared with numerical predictions. Although thisstudy focuses on the deformation behavior, the meth-ods developed will also be employed for characteriza-tion of fracture in future research.

The present investigation is directed mainly towardsthe development and evaluation of an experimentalset-up that will enable the study of the local deforma-tions during the blanking process. Section 2 describesthis experimental set-up, i.e. the planar blanking ap-paratus, the material used, and the experimental tech-nique. The numerical method, which uses anelasto-plastic Von Mises model and an operator splitarbitrary Lagrange Euler (OS-ALE) method, is de-scribed in Section 3. The experimental and numericalresults obtained are discussed and compared in Section

* Corresponding author. Fax: +31 40 2447355; e-mail:[email protected]

0924-0136/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved.

PII S0924-0136(98)00362-8

Y.W. Stegeman et al. / Journal of Materials Processing Technology 87 (1999) 266–276 267

Fig. 1. Blanking apparatus.

4. Finally, some concluding remarks are made in Sec-tion 5.

2. Experimental set-up

As mentioned earlier, much research on the blankingprocess was concentrated on the influence of processparameters, such as the punch and die radius, theclearance, and the velocity [1–9]. In these studies, onlythe load–penetration curves have been measured insitu. The deformation could only be visualized at dis-tinct stages of the punching process, at which theexperiment was stopped and the sample removed fromthe set-up. The experimental techniques used for thedetermination of the deformation include scribed lines,hardness measurements and micro-photographs. In thepresent study, not only the load–penetration curve, butalso the deformation is recorded in situ. For in situdetermination of the displacement field, a planarconfiguration is required. Two clearances (2 and 10% ofthe specimen thickness) are used in order to determinewhether this in situ technique can demonstrate thedifferences between the two configurations. This sectiondescribes the apparatus and material used for the pla-nar blanking tests, as well as the experimental tech-nique employed for monitoring the displacement andstrain fields.

2.1. Blanking apparatus

The planar blanking experiments have been carriedout using an apparatus, shown in Fig. 1, that was builtinto a universal testing machine (Zwick 1484). Theupper body (A) is connected to the moving part of the

testing machine, whilst the lower body (B) is fixed.Roller bearings (C) at both sides of the apparatus alignthe upper body and the center body (D). Bolts (E) keepthe upper and center body together when the upperbody is pulled up in order to change the specimens.During the experiment, the testing machine pushes theupper body down, causing the springs (F) to exert aforce on the center body. The pressure plate (G), at-tached to this center body, in turn exerts a pressure ofapproximately 5 MPa on the specimen (H). Mount (I)is used for the initial positioning of this specimen. Theedges of the die (J) are 10 mm apart and have radii of11 mm. Two punches (K), each with a punch radius of7 mm, are used successively to obtain clearances of 2and 10% of the specimen thickness. The horizontalmotion of the punch is restricted by the pressure plate,whilst the vertical movement is controled by the testingmachine. The punch load can be measured directly by apiezo force transducer (L) (35 kN, Kistler 9021 A) thatis mounted between the punch and the upper body.Also, the (strain gauge Wheatstone bridge) force trans-ducer of the testing machine can be used to measure thepunch load, the spring forces being taken into account.The blanking velocity is controlled by the testing ma-chine, which, however, is not able to maintain a con-stant velocity due to the finite stiffness of the system.The punch displacement is therefore measured by aseparate displacement transducer.

2.2. Material

Process parameters are, where possible, kept similarto the parameters in industrial blanking processes. Ac-cordingly, the material selected for this study, a 13% Crsteel, is common in these processes (Table 1).

Y.W. Stegeman et al. / Journal of Materials Processing Technology 87 (1999) 266–276268

Table 1Material properties of X30Cr13

0.185 GPaYoung’s modulus0.28Poisson’s ratio368 MPaYield strength

Fig. 3. Strain-hardening behavior.

Specimens of 48 mm length and 1 mm thickness aremilled to a width of 10 mm (Fig. 2). This millingprovides a rough surface, which gives enough contrastfor the correlation technique described in Section 2.3.

To a first approximation, the material used is re-garded as isotropic, with isotropic hardening. For theoccurrence of plastic deformation, the Von Mises yieldcriterion is used, which states that the deformation rateremains elastic if

32tr(sd · sd)Bs 6

2

in which sd is the deviatoric stress tensor and s6 is theactual yield stress. During plastic deformation, theequivalent Von Mises stress'3

2tr(sd ·sd)

equals the yield stress. This yield stress increases withincreasing effective plastic strain, as shown in Fig. 3.

The relationship between the yield stress and theeffective plastic strain is obtained by carrying out 20tensile tests at low velocity, such that the strain rate hasno influence on the yield stress. Each tensile specimenhas been subjected to a different amount of rolling inorder to obtain different initial plastic deformations.The yield stress–effective plastic strain relationship isdetermined by fitting a master curve through the max-ima of the stress–strain curves of these tensile tests:

s6=443.28+291.21(1−e−e/0.15)+124.67 e

+173.24e (MPa)

2.3. Correlation technique

During the blanking process, a CCD camera recordsa set of successive images (Fig. 4) of the sample surfaceshown in Fig. 2. In order to quantify the displacementof material points at this surface, the contrast correla-tion technique [16,17] is used. This digital image pro-cessing technique does not require markers on thespecimen surface, which is advantageous, because thehigh deformations, in combination with the small area

observed, make the use of markers nearly impossible.Instead of locating markers in successive images, thecontrast correlation technique uses the contrast infor-mation (i.e. the gray level of each camera pixel) in theimages to construct the displacement field.

To determine the displacement of a material point, awindow (AW) is defined around the pixel coordinates ofthis point (Fig. 5). As described below, the contrastcorrelation technique uses the contrast distribution inthis window to retrieve its location in the successiveimage. As long as the deformation within the window ishomogeneous, the displacement of the center of thewindow equals the displacement of the associated mate-rial point. As shown in Fig. 5, however, the window isallowed to deform linearly between the first image Aand the next image B, which suffices if the deformationsin this area are small. This constraint on the deforma-tions is met by restricting the punch displacement be-tween successive images, which limits both thedeformation and displacement of the window. Addi-tionally, a search area BS can be defined, as a time-sav-ing measure. This sub-set BS of image B has the size ofthe window AW increased by the maximum expecteddisplacement.

By storing the contrast information of an image in amatrix format, the problem can be defined in mathe-matical terms. In this formulation the sub-set BW, ofthe search area matrix BS, that is the best match of thegiven matrix AW has to be located. For this purpose, acorrelation factor, which indicates how well two sub-sets match, is maximized in two steps by the following

Fig. 2. Dimensions of a deformed sample (mm).


Fig. 4. Example of images recorded during the blanking process.

method. In the first step, it is assumed that the windowdoes not deform. A Fast Fourier Transformationsmethod can be used to determine the correlation factorbetween sub-set AW and every possible sub-set BW ofthe search area BS. The sub-set BW that gives themaximum correlation factor defines the position of thewindow in image B and therefore the displacement ofthe material point between the two images at pixellevel. Starting from these displacements, in the secondstep a Newton–Raphson method of partial differentialcorrections is used to determine the sub-pixel displace-ments. To achieve this, gray levels are interpolatedbetween pixels, for which a bicubic spline interpolationis used [16]. The mentioned iterative algorithm, whichallows linear deformation of the window, is described indetail by Sutton et al. [17].

In this study, images of 400×400 pixels with 256gray levels are used, with windows and search areas of21×21 and 43×43 pixels, respectively. It proved to bebeneficial to smooth the images prior to the Fouriertransforms by

G %(x, y)=110

�G(x, y)+%i, j G(x+ i, y+ j)

ni, j�{−1, 0, 1}

where G(x, y) and G %(x, y) represent the old and newgray level values at a point with array integers (x, y).The accuracy of the measured total displacement (unde-formed stage until fracture) is observed to be in theorder of 0.3 pixel, corresponding to approximately 1mm (magnification93 mm per pixel). The recordedblanking experiments, using both clearances, are carriedout at a velocity of 10 mm min−1, whilst images arestored every 0.04 s. The material points are chosen toform a grid, which facilitates the application of thesecond-order method to calculate the two-dimensionaldeformation gradient tensor from the displacements,developed by Geers et al. [18]. Using the right polardecomposition of this tensor, the logarithmic strainfield can be determined. Due to the coarseness of thegrid, the error in the strain is about 0.1 in regions ofhigh strain gradients (near to the radii).

3. Numerical model

To a first approximation, the blanking process issimulated using a two-dimensional, plane-strain model,although the authors are well aware that the deforma-tion behavior at the surface is three dimensional. Aquasi-static analysis is carried out on a model geometrythat matches the experimental set-up, i.e. a 11 mm dieradius, a 7 mm punch radius, and a clearance of 20 or100 mm. The specimen is modeled with an isotropicelasto-plastic material, using the material properties asspecified in Section 2.2. The plastic material behavior isdescribed by the Von Mises yield condition, isotropichardening, and the Prandtl–Reuss representation of theflow rule [19]. The strain-hardening behavior is enteredas a table with yield stress–effective plastic strainpoints. Strain-rate dependence is not implemented inthe model. Since the problem is symmetric, only half ofthe specimen is modeled, as shown in Fig. 6. Along theleft boundary (specimen center), the symmetry condi-tion is prescribed. The other boundaries are either freesurfaces or in interaction with a contacting body. Ifcontact exists, friction is described by a Von Misesmodel with coefficient 0.1(tf50.1s6/3), in which tf isthe tangential stress applied and s6 is the yield stress[19]. The punch (body 1) is in motion and penetratesthe specimen, resulting in constantly changingboundary conditions. Therefore the solutions are nottrivial and an advanced finite-element procedure is usedto obtain the displacement fields as well as the punchload.

An arbitrary Lagrange–Euler (ALE) approach isused, because the punching process involves large de-formations [20,21]. In this approach, the reference sys-tem is not necessarily fixed in space (Euler) or attachedto the material (Lagrange). The relationships betweenthe nodal points and the material points are subject tochange, although there is always a one-to-one mapping.As in the Lagrangian formulation, surface movementand deformation-history-dependent state variables canbe taken into account, whilst avoiding the numerical


Fig. 5. Window and search area for one of the selected material points.

difficulties of element distortion. The OS-ALE methodseparates the calculation of material displacements andmesh adaptation. The material displacement incrementis solved with the commercially available finite-elementcode MARC, using an updated Lagrange formulation.In order to avoid mesh distortion, the nodal points areshifted after each increment: however, the mesh topol-ogy is preserved. A discontinuous Galerkin method isused to update the state variables [14]. Since meshdistortion cannot be completely avoided, total re-mesh-ing, which does change the topology, is carried outevery five OS-ALE steps.

As shown in Fig. 6, quadrilateral elements (with fournodes) are used, which become smaller as either the dieor punch radius is approached. Near to the radii, theelement proportions need to be of order 1mm, resultingin up to 7500 elements in the whole mesh. Except forthe symmetry condition, the specimen is only subjectedto forces and displacements imposed by the other bod-ies. On the pressure plate (body 3), modeled as a linearelastic body with a very high stiffness, a distributedload is prescribed, representing the spring forces. Thepunch (rigid body 1) moves with a fixed displacementof 1.25–2.5 mm per computational increment, whilst thedie (rigid body 2) is fixed in space. The transversalmovements of all bodies are confined. Convergence ofthe calculation is reached if the relative change inincrement displacement becomes less than 1%.

4. Discussion of the results

With the experimental technique described previ-ously, displacement and strain fields are determined in aplanar blanking process with clearances of 20 and 100mm. As is common in studies concerning blanking, thepunch load–penetration curve is measured also forboth clearances and different velocities. In this section,all of the experimentally obtained results are describedand compared with the numerical predictions.

4.1. Punch load—penetration cur6es

The load–penetration curves can be measured bymeans of both the piezo force transducer and the forcetransducer of the testing machine. In the latter case, theresults should be corrected for the spring forces. Forthis purpose, experiments with the test device are car-ried out without a specimen. During these experiments,the force transducer of the testing machine records a(spring) force that is linear with punch displacementand independent of the velocity. Consequently, thepunch load can be obtained by subtracting this springforce from the total load. At medium velocities, it wasexperienced that, after adjustment, both force transduc-ers give the same punch load–penetration curves, confi-rming that the adjustment is correct. Since the piezocrystal (normally used for high speed processes) under-estimates the punch load at very low velocities, theforce measured by the testing machine force transduceris used here. The velocities investigated vary between0.002 and 200 mm min−1, which is the maximumvelocity of the testing machine. Only the load–penetra-tion curves at velocities of 0.1 and 100 mm min−1 arepresented, but experiments at other speeds show similarresults. Fig. 7 shows that the punch load increases withthe velocity. A velocity increase of three decades, causesa considerable punch load increase to over 1000 N. Atlow velocities, the punch load reaches a minimum andbecomes independent of the velocity. With clearances of20 and 100 mm, this minimum punch load is reached ata velocity of 0.02 and 0.10 mm min−1, respectively,indicating that strain rate, rather than velocity, is dom-inating this behavior.Fig. 6. Two dimensional, plane strain mesh for blanking.


Fig. 7. Influence of velocity and clearance on the load-penetration characteristic.

The punch loads predicted by the numerical model,which does not include strain-rate dependence, arecompared with experimental results at the velocity of0.02 mm min−1, since the material model is determinedat such a low speed that strain rate has no influence. Asshown in Fig. 8, the punch loads are slightly over-esti-mated by the numerical simulation, which could becaused by the constitutive model, as well as theboundary conditions. The influence of a change inclearance is well predicted. In the numerical as well asin the experimental results, an increase in clearancecauses a decrease in the punch load. Experimentally, anincrease in clearance is also found to cause decrease ofthe work done after fracture and increase of the punchpenetration at maximum load.

4.2. Correlation technique

As described in Section 2.3, digital images of thespecimen surface are recorded during the blanking pro-cess. This information can be compared with the nu-merically-predicted contour, as is done in Fig. 9.Especially, the roll-over is of interest, since this zone isdetermined only by the first part of the blanking pro-cess [13] and the final product quality is partly definedby the amount of roll-over. Fig. 9 shows that theroll-over is predicted correctly by the numerical method(solid contour line). Furthermore, the recorded imagesenable the determination of the displacements of thematerial points.

The material points are defined in a grid of ten rowsbetween 0.05 and 0.5 mm from the upper side of thespecimen. Each row consists of 15 points, of which the

central 13 points have a mutual distance apart of 20mm. Initially, the central point of each row is situatedexactly below the punch edge. In Figs. 9–12, the (max-imum) punch displacement is 0.23 mm. Between theundeformed stage and this stage, 35 images arerecorded.

For the sake of clarity, only the displacements of thematerial points on three of the ten rows are given inFig. 10. The dotted lines connect the final positions ofthe material points in the set-up with 20 mm clearance,and the solid lines those with 100 mm clearance. Ini-tially, these lines are positioned at a distance of 0.05,0.30 and 0.50 mm from the upper side of the specimen.The positions (in the subsequent images) of the materialpoints in the configurations with clearances of 20 and100 mm, are marked by gray crosses and black circles,respectively. Between the left part of Fig. 10, whichshows the experimentally-determined displacements,and its right part, which presents the numerically-pre-dicted displacements, a significant difference can benoticed.

In the experimental results, all material points shift,at least initially, to the left (towards the center of thepunch). The numerical method, however, predicts ashift to the right (away from the punch) for almost allof the material points. This disagreement might becaused by an incorrect modeling of the boundary con-ditions (especially friction). Despite this pronounceddifference, several features can be observed in both theexperimental and the numerical results. All displace-ment fields show that the shear gradient increases as thepunch edge is approached. The deformation zone nearto the third row (middle of the specimen) is therefore


Fig. 8. Comparison of experimental and numerical load-penetration curves.

broader than that near to the upper row. Although theexperimentally-observed deformation zone is widerthan that predicted numerically, this tendency is stillvisible. As can be expected, the deformation is shownto be more localized in the case of the smaller clear-ance. In this case, the material points of the lower two

rows, which are located to the right of the punch edge,move more to the right than in the case of the largerclearance. It appears that the narrow clearance preventsthe material in the shear zone from moving down,causing it to move away from the punch in the horizon-tal direction. In the numerical simulation, this behavioris also present, although less obvious, when using thelarger clearance.

Between each pair of successive images, the local 2Ddeformation gradient tensor F is calculated [18] fromthe relative change in position of all of the 150 pointsshown in Fig. 9. Once the right polar decomposition ofthe deformation gradient tensor (F=R ·U) is deter-mined, the incremental logarithmic strain, according to:

De=�Dexx

Dexy

Dexy

Deyy

n=R · log(U) ·RC

can be calculated. The total logarithmic strain can beobtained easily by adding the increments. With thismethod, the strain fields are not only determined fromthe experimentally-obtained displacement field, but alsofrom the numerically-obtained displacement field, usingan identical grid of 150 points.

It can be questioned whether the fundamentallythree-dimensional deformation in the experiment maybe compared with the two-dimensional plane-strain nu-merical model. Therefore it is examined as to whatextent the experimental deformation differs from plane-strain deformation. Assuming volume invariance (ezz=−exx−eyy), the plane-strain condition (ezz=0)becomes exx= −eyy. As is demonstrated in Fig. 11, thisis not really the case at the specimen surface. Asexpected, ezz is positive beneath the punch, where theFig. 9. Defined grid of material points.


Fig. 10. Experimentally (left) and numerically (right) obtained displacements of the material points.

material is compressed in the vertical direction. Thetensile stresses in the roll-over zone lead to a negativeezz. The strain fields for the experimental set-up with 20mm clearance are shown. The strain fields for the set-upwith 100 mm clearance are comparable.

It is stated that the influence of the three-dimensionaleffect on the equivalent strain

eeq='2

3(exx

2 +eyy2 +2 ·exy

2 )

is small, since this equivalent strain consists of about90% of shear strain. It is therefore useful to comparethe experimentally- and numerically-obtained equiva-lent strain fields. Fig. 12 shows the equivalent logarith-mic strain at a punch displacement of 0.23 mm for bothof the clearances. The features observed in Fig. 10concerning the width of the shear zone are also visiblein the equivalent strain field. However, the differencebetween the experimental and numerical results con-cerning the horizontal displacements is no longervisible.

5. Concluding remarks

In the present investigation, the deformation in aplanar blanking process was monitored up to fractureby means of the contrast correlation technique. Thismethod proved to be suitable for in situ observation ofthe blanking process. Moreover, the plane-strain nu-merical model used also proved to give qualitative good

results, although the experimentally-observed deforma-tion is not perfectly plane strain. A change in clearanceinfluences the experimental and numerical techniquessimilarly. Nevertheless, there are still some quantitativedifferences observed between the experimental data andthe numerical results. For instance, the predicted punchload is 500 N (96%) too high, while the total equiva-lent strain is over-predicted by 10%. However, by somestandards, these results would be regarded as successful.

The differences could, among others, be caused bythe material model and/or the boundary conditionsapplied in the simulation. The material model assumesisotropy and isotropic hardening. If this is not correct,the yield stress–plastic strain relationship, obtained inuniaxial deformation, will not be valid in shear. In thiscase, the numerical results will not be reliable, sinceshear is observed to be the dominating deformationmode in the blanking process. Another important as-pect of the material model is the neglect of the depen-dence of strain rate and hydrostatic pressure. Thematerial behavior, however, is clearly dependent on thestrain rate, as illustrated in Fig. 7, and this featureshould be taken into account if greater velocities areconsidered. Disregarding the influence of hydrostaticpressure is probably not advisable also, since thesehydrostatic stresses are very high: at a punch displace-ment of 0.23 mm, the numerical method predicts apressure of 500 MPa.

As mentioned in Section 4.2, the boundary condi-tions also require more attention. Friction has beendescribed by the Von Mises model, although this model


Fig

.11

.St

rain

field

sfr

omm

ater

ial

poin

tdi

spla

cem

ents

inan

expe

rim

enta

lse

t-up

wit

ha

clea

ranc

eof

20mm

.N

ote

the

diff

eren

tsc

ales

.


Fig. 12. Total equivalent strain fields from material point displacements.

does not capture all of the characteristics involved.For instance, the predicted tangential force is totallyindependent of the normal pressure. For simulation ofindustrial forming processes such as blanking, develop-ment of a sufficiently realistic friction model is re-quired.

In conclusion, it can be stated that the contrastcorrelation technique is very well suited for experimen-tal investigation of the blanking process. The numeri-cal plane-strain deformation proved to be an adequatefirst approximation of the actual deformation at thesurface. For a quantitative description, however, thenumerical method still requires some adjustments. Infuture research, the numerical and experimentalmethod will be combined to obtain a reliable fracturemodel, as well as the necessary parameters, to eventu-ally describe fracture in the blanking process.

Acknowledgements

We would like to thank Kees Donkers of PhilipsCFT for supplying the blanking apparatus. Jan Postof Philips DAP/LTM is gratefully acknowledged forsupplying the material and the material model.

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An experimental and numerical study of a planar blanking ... · An experimental and numerical study of a planar blanking process ... not only the load–penetration curve, but