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Journal of Materials Processing Technology 210 (2010) 396–407

Contents lists available at ScienceDirect

Journal of Materials Processing Technology

journa l homepage: www.e lsev ier .com/ locate / jmatprotec

etermination of optimal cutting edge geometry on a stamped orthotropicircular electrical steel sheet

itoslav Bratus a,∗, Franc Koselb, Marko Kovaca

Hidria Institute for Materials and Technologies d.o.o., Spodnja Kanomlja 23, 5281 Spodnja Idrija, SloveniaUniversity of Ljubljana, Faculty of Mechanical Engineering, Askerceva 6, 1000 Ljubljana, Slovenia

r t i c l e i n f o

rticle history:eceived 9 March 2009eceived in revised form7 September 2009ccepted 30 September 2009

a b s t r a c t

Today engineers involved in the stamping process used for high-volume production of rotor and statorlaminations are faced with a great challenge to achieve extremely narrow dimensional and geometricaltolerance on their products. Because materials are produced by different suppliers, adjustments of tech-nological parameters to the emerging differences are required to maintain the high quality of products.An upgraded engineering method was developed in which electrical steel sheet of semi-finish grade wasnot treated traditionally, but as a 3D body with orthotropic material behaviour. The round profile of the

eywords:tamping processrthotropytress–strain responseutting edge profileccuracy

cutting edge was studied from the experimental and numerical point of view. If the completely roundpunch was used, the profile of the cutting edge appeared as a non-round shape. With additional FEManalyses a new profile of punch was designed as a non-round shape to be able to provide much bettercircularity. FEM simulation showed that 10 times lower profile deviations were found on the workpieceshaped by the new cutting element profile.

© 2009 Elsevier B.V. All rights reserved.

echanical properties

. Introduction

Technological competitiveness is one of the key factors forrogress and a most powerful driving force that makes compa-ies successful today. Limited resources of raw materials, pressuren the product’s price and shorter time to market are some of thehallenges not only imposed on new technological processes butlso on conventional technologies that have been well known forecades. For all these reasons, special attention is given to a com-any’s ability to achieve the tightest dimensional and geometricalolerances.

Stamping technology as a conventional process is generally rec-gnized as an industrial process for high-volume production. Maitit al. (2000) presented some industrial sectors, where stamping islaced as a core technology to produce semi-manufactured prod-cts. Among others, it is used for processing electrical steel sheet,here laminations for rotor and stator components – key elements

f electric drives – are produced. Jocic (2008) collected the typ-cal mechanical properties of many different metallic materialsogether, where electrical steel sheet is specified as a high qual-ty, alloyed cold rolled steel with special physical properties. It has

∗ Corresponding author. Tel.: +386 5 375 6377/31 375 401; fax: +386 5 375 6472.E-mail addresses: vito.bratus@hidria.com (V. Bratus), franc.kosel@fs.uni-lj.si

F. Kosel), marko.kovac@hidria.com (M. Kovac).

924-0136/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2009.09.029

a significantly higher level of yield stress as well as tensile strengthin comparison to cold rolled steel – typical mechanical propertiesreported by Backley (2000). On the other hand, the elongation ismuch lower and high quality materials for cutting elements arerequired to process this material.

The approach of mechanical engineering to stamping technol-ogy in lamination businesses and to materials involved in thistechnology has been unchanged for some decades. It has beentreated as a typical plane or 2D process, since the processed steelsheet as a workpiece has one dimension (thickness) much smallerthan the other two (width and length). Some of the non-linearmechanical phenomena directly related to mechanical propertiesof the workpiece and generally treated as undesirable, have so farbeen neglected. Unfortunately, experience has shown that theirinfluence on the end product’s quality, especially through displace-ment state, could in some cases lead to inaccuracies so that thestamped product does not meet its specifications. Taking into con-sideration the requirements for ever narrower dimensional andgeometrical tolerances, it is crucial for future engineering work tounderstand the influence of imperfections in the electrical steelsheet. All these facts lead to an obvious conclusion: a 2D-approach

to the stamping process is not sufficient any more. A step forward to3D-modelling is needed, where a real phenomenon such as materialorthotropy on the workpiece is considered.

The purpose of this study was to develop an accurate, real mate-rial and real geometric 3D model of thin electrical steel sheet for

rocess

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V. Bratus et al. / Journal of Materials P

inite Element Method (FEM) analysis of the lamination stamp-ng process. An orthotropy of the workpiece is incorporated as the

ain source of its geometrical imperfection. A backward comput-ng method will be developed in order to redefine the stampingool geometry. In this way a perfectly round cutting edge on theorkpiece will be able to take shape.

.1. Competitive and market driven approach to laminationtamping process

Modern trends dictated by automotive industry require a fullyontrolled and stable stamping process. According to Schey (1987),eneral parameters affecting the overall quality of stamping prod-cts can be divided into three major groups: stamping tools with allheir specifics in design, stamping machines, and mechanical prop-rties of workpiece. However, a study of fully processed electricalteel sheet demonstrated by Brownlee and Smythe (1970) pointedut that geometry and dimension of stamping products to a largextent depend on mechanical properties of electrical steel sheet.

The general market rule stays unchanged: the best and the mosttable quality keeps the highest price. Small-scale companies todayo not have a strong purchase negotiation power when faced withxcellent market positioned steel mills, so they are forced to buyaw material as cheap as possible. This kind of strategy required inrder to survive, unfortunately, causes strong suffering from a sideffect as well: the purchased material has wide deviations from thelaimed mechanical, physical and chemical properties. In this casehe only solution for competitiveness is the following: adaptationf the company’s production process to different quality levels ofncoming electrical steel sheet. This can be done by investigatingome selected material properties and transferring their influenceirectly to the parameters of the stamping process and to the designf the stamping tool. So far traditional approaches to this problemnown as trial and error methods have usually been taken as theost convenient and reliable. However, considering today’s “time

o profit” criterion, which is becoming globally the only measure foruccess, this approach does not meet the requirements any more.

Previous experimental studies published by Bratus (2002) havehown that electrical steel sheet could be treated as orthotropicaterial with an additional distribution of internal stresses.ccording to Keeler (2002), a final geometry of the workpiecelso depends on additional residual stress state. Both orthotropynd internal stresses finally contribute to the fact that the prefer-ble round profile of the product is deformed resulting in a new,on-round profile of the cutting edge on the product. In the

amination production, wherever narrower dimensional and geo-etrical tolerances up to 0.050 mm are required, this phenomenon

s undesirable. Many cases have shown that for this specific reasontamped products with round geometry have not met their speci-cations. However, a FEM method can help redefine the stampingool geometry, always targeting centres of stable technological win-ows. By this approach, the first step in direct process stabilityontrol has been done, following a good example of its success-ul introduction into wire bending process as reported by Kuzman2007). Similarly, Bonte et al. (2008) showed the solving of opti-

isation problems methodology which has a big potential in thendustrial metal forming processes.

. Experimental: tests and results

Electrical steel sheet of semi-finish grade M660-50D waselected. Three important sets of data relevant for FEM analysisere obtained by experimental work. The first set was focused on

tress–strain response of the processed material in different direc-ions of the Cartesian coordinate system. These data were needed

ing Technology 210 (2010) 396–407 397

to select the right 3D material model out of the numerous options inFEM software. Additionally, the failure criterion used in FEM analy-sis was estimated with these results. The second set of data referredto the stamping process, where the profile of cutting edge was mea-sured. The third set of data refers to the real geometry of the cuttingelements. The results were taken into consideration when the 3Dgeometric model was designed.

2.1. Stress–strain response of electrical steel sheet

Based on the characteristics of FEM software used in this study,experimental results in the form of tensile and shear stress–strainresponse in all three dimensions of the Cartesian coordinate sys-tem are required to build a reliable material model. Due to theinconvenient geometry of electrical steel sheet, the tensile testin Z-direction was not performed. However, an additional ten-sile stress–strain response in XY-plane of the Cartesian coordinatesystem was defined. As demonstrated by Meinders (2000) thisapproach is commonly used to optimize 2D deep drawing pre-shape processed material. In order to get accurate and useful resultsout of FEM analysis, a high priority was put on this segment ofexperimental work.

Stage No. 1 sample was represented by a steel sheet already slitto appropriate strip width to be run on the experimental stampingtool. Its overall dimensions together with the fundamental orien-tation of the Cartesian coordinate system are shown in Fig. 1a aswell as orientation of additional direction in XY-plane – designationMid(X–Y). It was assumed that stage No. 1 sample with its geometrywas big enough to retain all preferable and non-preferable effectsof the final rolling process in the steel mill. Thus, orthotropy, inter-nal stresses and others effects were all supposedly contained in thissample.

A tensile test was selected as the most convenient and simpletest to define tensile stress–strain response in X,Y and Mid(X–Y)-direction. Stage No. 2 sample (see Fig. 1b, where samples inX-direction are shown) was shaped by an additional cutting toolinto a typical tensile test specimen representing stage No. 3specimen—Fig. 1c. Its shape and dimensions conformed to ISO 6892(1998). A tensile test procedure was applied on five specimens inX-direction followed by five specimens processed to be tested in Yand Mid(X–Y)-direction. The average tensile stress–strain responsein all three directions is shown in Fig. 2. The stress–strain curvesin all charts represent engineering stress–strain response, if notmentioned differently.

A completely different approach was needed to determine shearstress–strain response of electrical steel sheet in XY-, YZ- andXZ-plane of the Cartesian coordinate system. Since the stampingprocess is recognized as a typical maximum shear strain process,testing procedures for material shear response were investigatedon the basis of the standard test method for shear properties ofcomposite material by V-Notched Beam Method (2005). This test,known also as Iosipescu test, was designed to produce shear prop-erties of material involved.

The specimen with specific shape and geometry was neededto carry out this test properly. Stage No. 4 sample with overalldimensions corresponding to Fig. 1d was produced from stage No.1 sample. Additionally, the V-notch was cut out by wire erosion tothe final shape of stage No. 5 specimen (see Fig. 1e) correspond-ing to ASTM D-5379 standard. However, its thickness was far from2.5 mm, which is recommended by standard as the minimum valueto get reliable results. Therefore, the specimen was strengthened

and stabilized by increasing local thickness. Additional four tabsin the gripping region were bonded to both faces of the specimenaway from the tested region. The stage No. 5 specimen ready to betested for shear strain response in XY-plane is presented in Fig. 3.Note that only two front support tabs are shown.

398 V. Bratus et al. / Journal of Materials Processing Technology 210 (2010) 396–407

F r over( No. 5

est

Fs

ig. 1. Schematic presentation of all types of samples used in experiments with theib) Stage No. 2 samples. (c) Stage No. 3 specimen. (d) Stage No. 4 samples. (e) Stage

Moreover, a special fixture was needed to perform this test prop-rly. The suggested fixture design defined by standard is relativelyimple, unfortunately a lot of undesirable factors could influencehe result of the measurement. For this reason a special fixture

ig. 2. Results of experimental tensile test in X,Y and Mid(X–Y)-direction withchematic presentation of specimens orientation in Cartesian coordinate system.

all dimensions and positions in Cartesian coordinate system. (a) Stage No. 1 sample.specimen. (f) Stage No. 6 samples. (g) Stage No. 7 sample.

with additional clamping mechanism as demonstrated by Melinand Neumeister (2006) was used in the following experiments. Thestage No. 5 specimen was inserted into the fixture with a V-notchlocated along the line of action. The two halves of the fixture werecompressed by the testing machine while the load was indicated.A schematic drawing of the basic setup for Iosipescu test is shownin Fig. 4a. The final experimental setup with additional clamping

mechanism is clearly shown in Fig. 4b. Because of extremely incon-venient geometry of the specimen–one dimension (thickness) ismuch smaller than the other two (width and length), the shearstrain response could not be measured by strain gages. Therefore,

Fig. 3. Specimen with supporting tabs for local strengthening and stabilizing.

V. Bratus et al. / Journal of Materials Processing Technology 210 (2010) 396–407 399

F ng meM een oo

Dtdt1Ima

i

Fs

ig. 4. (a) Schematic drawing of Iosipecsu test setup (without additional clampieasurement of angle deformation out of DSP (alignment pin of V shape is clearly s

n the bottom side)

igital Speckle Photography (DSP) was used in this study. The sys-em follows a speckle image (spray paint) applied to the surfaceuring deformation with a CCD camera. With an image correla-ion algorithm, deformed and undeformed subimages of typically5 × 15 pixels were compared to determine displacements fields.

n-plane strain fields are obtained by differentiating the displace-ents with accuracy below 0.1% in strain. Presentation of measured

ngle deformation results is demonstrated in Fig. 4c.The measurement results as average values out of five spec-

mens are shown in shear stress–strain response in Fig. 5. For

ig. 5. Presentation of Iosipescu test result for XY- and YX-plane together with thehear strain response of electrical steel sheet in YZ- and XZ-plane.

chanism). (b) Final experimental setup with clamped stage No. 5 specimen. (c)n the bottom side) deformation out of DSP (alignment pin of V shape is clearly seen

validation purposes only, five additional specimens were tested inYX-plane.

The experimental results corresponded very well to the theory:shear stress �xy is equal to �yx in the entire range of the curve. Someminor deviations are noted only in the strain range over 0.15. Intesting the shear stress–strain response of electrical steel sheet inXY-plane, the strain measurements near to breakage point wereslightly influenced by the geometry of the fixture. The specimenwas blocked by an alignment pin (clearly seen on Fig. 4c) so thetest did not end with a final breakage. More importantly, the trendof shear strain response in XY-plane was experimentally achievedin spite of the fact that ultimate shear strain was not defined.

A special fixture used for Iosipescu test was needed again toperform the final experiment of material testing. In fact, it was theimitation of the stamping process. The overall sample dimensionsexcept material thickness were defined according to dimensionallimitations of the fixture. The strips (Fig. 1f) were cut out of steelsheet stage No. 1 sample in the first step, then additionally short-ened to the final length of 78 mm. Stage No. 7 samples (Fig. 1g)were finally produced in order to experimentally define the shearstress–strain response of electrical steel sheet in XZ- and YZ-plane.This test with assistance of a special fixture was designed for thefirst time to quantify material datasheet of selected electrical steelsheet for FEM analysis of the stamping process. However, inconve-nient geometry of stage No. 7 sample required another modificationof the clamping system. Additional four tabs (see Fig. 6) produced

from special hardened tool steel were required to guarantee shearforce acting only along the line of action. Clearance of 0.02 mm wascreated between the upper two and bottom two tabs in order toeliminate potential influence of friction force on the test results.This specific clearance corresponds to the clearance between the

400 V. Bratus et al. / Journal of Materials Processing Technology 210 (2010) 396–407

ensu

ppffiNwcsAawtearsemsT7ave

wps

2

n

Fig. 6. Additional internal clamping system to

unch and the die relevant for the next experiment, which waserformed as a conventional stamping process. Two spacers, oneor the upper two tabs and one for the bottom tabs, were used tonally prepare an additional internal clamping system with stageo. 7 sample in between. As soon as the test started, both spacersere removed. Again, due to the thin sample, the shear response

ould not be measured by a strain gage. Therefore the DSP was usedince the conventional method could not be effective in this case.complete setup of stage No. 7 sample (Fig. 6) was installed intospecial fixture on the same place as before stage No. 5 sampleith supporting tabs having been positioned (Fig. 4a). Elements of

he additional clamping mechanism (Fig. 4b) were not used in thisxperiment. Five samples were tested in XZ- and YZ-plane, the aver-ge shear stress–strain responses are given in Fig. 5. The end pointselate to the final breakage of samples. Thus, the maximum sheartrain is defined in the reference direction. The shear response oflectrical steel sheet is similar in both directions. However, someinor deviations should be pointed out. Initial slope of the shear

tress–strain response of YZ-plane sample is lower than the others.his could be attributed to the partly unavoidable slip of stage No.sample in the internal clamping system (Fig. 6). Introduction of

lternative claming system was not an option due to highly incon-enient geometry of sample as well as bigger uncontrollable sideffect on the experimental results.

The result of DSP is presented in Fig. 7. The stage No. 7 sampleith a thickness 0.5 mm is positioned vertically and is loaded byure shear load. A black horizontal line, clearly seen on the leftide, represents the clearance of 0.02 mm.

.2. Stamping round profiles out of electrical steel sheet

A high number of experiments in the stamping process wereeeded for a reliable comparison of experimental results with FEM

Fig. 7. Shear strain result from DSP under loading condition.

re shear test of steel sheet in YZ- or XZ-plane.

analysis. The electrical steel sheet used in this experiment hadexactly the same overall dimensions as stage No. 1 sample. Based onthe width and thickness dimension of the strip, the most suitableprogressive stamping tool was selected from regular production.Some small technical adjustments were needed in order to stamponly round profiles without any additional cuts nearby. With thisapproach, potential influences on dimension and geometry mea-surements were eliminated.

The profile of cutting edge on stage No. 1 sample was producedby the action of the punch on the workpiece, the bottom supportwas provided by the die side. Two pieces were produced (Fig. 8aand b) and the profile of the cutting edge was measured by opticalmeasuring device 3D MarVision MS 442 with an accuracy of ±1 �m.Based on orientation of the Cartesian coordinate system shown inFig. 8a, the dimension B was measured in 360 points all around theprofile of the cutting edge. Due to the fact that the cutting edge pro-file 2B is specified with smaller geometrical tolerance than profile2B1 on the stamped-out part, our study focused on the profile ofcutting edge 2B only.

In order to simplify visualization of the profile of cutting edgeB, a cylindrical coordinate system was introduced. So in continua-tion, whenever the geometry of cutting elements or profiles of thecutting edge as a result of experiments or FEM analysis is shown,the cylindrical coordinate system was used. The link between bothcoordinate systems is clearly shown in Fig. 8a. Four samples weremeasured and analysed. Referring to the assumption of electricalsteel sheet as orthotropic material, already confirmed by prelimi-nary studies and used also in FEM analysis, the real profile of cuttingedge B in the cylindrical coordinate system is calculated from:

B(ϕ) =14

∑4i=1[Bi(ϕ) + Bi(180 − ϕ) + Bi(180 + ϕ) + Bi(360 − ϕ)]

4,

0 ≤ ϕ ≤ 360. (1)

The average value B = B(ϕ) is given in a radar chart in Fig. 9. Somepotential errors that are part of the measuring protocol were min-imized by Eq. (1). This step is needed to obtain the accuracy of themethod on a high level. The imperfection of geometrical tolerancelike circularity was prioritized over the absolute dimension B.

The analysis of results shows that the maximum difference ondimension B and 2B was 0.0058 mm and 0.0116 mm, respectively.The results shown in Fig. 9 also correspond to conclusions from reg-ular stamping production, where inspection in 0◦ and 90◦ directionsis daily provided: B value in 90◦ is always bigger than B value in 0◦

direction.

2.3. Measurements of the cutting elements geometry

The importance of this measuring procedure is associated withdirect correlation between the results of the experiment and FEManalysis. If the geometric model of FEM analysis is not as closeas possible to the real geometry used in the experiment, good

V. Bratus et al. / Journal of Materials Processing Technology 210 (2010) 396–407 401

F ple ws

cBrt

twsa

mwhewbatrarwp

ig. 8. (a) Schematic presentation of real profile of cutting edge 2B on stage No. 1 samystem. (b) Profile 2B1 on stamped-out part.

orrelation of the profile of the cutting edge could not be expected.earing in mind the level of maximum difference on 2B dimensioneached in the experimental stamping test in the range of 0.01 mm,he importance of this step is recognized as a key issue for success.

The general geometry of the punch and die developed throughhis study is not traditional, actually it is a very rare case. The punch,hich is optimally prepared for the stamping process, is generally

haped as a cylindrical body with a sharp cutting edge or radius Rp1t the bottom (Fig. 10a).

However, the real geometry, represented in Fig. 10b, is muchore complicated. It is formed through severe friction mechanismhile the punch is penetrating into electrical steel sheet up to H2eight. After a few million stamping cycles the sharpness of cuttinglement becomes blunted and a new radius Rp is formed. Additionalear of the punch is observed also on H2 height of the cylindrical

ody – the new punch profile is shaped by radius R. When the burrs the consequence of wear process approaches maximum height,he re-sharpening operation is needed. LR height of the punch isemoved by grinding operation to get the cutting edge as sharp

s possible once again. By this procedure the Rp is removed butadius R on the cylindrical body still remains. The punch profileith radius R at H1 length on cylindrical body represents the finalunch geometry being modelled in FEM analysis.

Fig. 9. Real (measured) profile of cutting

ith orientation of Cartesian coordinate system and link to the cylindrical coordinate

The punch geometry could be described by parameters fromFig. 10b. The measurements are shown in Table 1. In addition,radius Rmin and inside diameter d on the die side (see Fig. 14) arepresented in the same table. All of them except R were measuredwith an optical measuring device 3D MarVisoin MS 442. Taking intoconsideration the punch geometry (Fig. 10b), the dimension R wascalculated as

R = 12(D − D1)

H12 +(

D − D1

2

). (2)

Dimensions d, D and D1 were measured in 360 points all aroundthe profile. Since the standard deviations are more than 10 timeslower than 0.01 mm, the average values were considered. To con-clude, Table 1 was the basis for creating the geometric model in FEManalysis, which could then be directly correlated to experimentalresults.

3. Numerical analysis

FEM simulations are increasingly used for investigating andoptimizing the stamping process. Industrial and numerical aspectsof processing thin steel sheet material were discussed by Span andKuzman (1993), where similarities to processing electrical steel

edge B = B(ϕ) on stage No. 1 sample.

402 V. Bratus et al. / Journal of Materials Processing Technology 210 (2010) 396–407

b) Rea

ssmrprddtMci(popms

timmhAtBiocitt

3

at

(�xx

TG

Fig. 10. (a) Traditional geometry of the punch. (

heet material could be found. Several other researchers empha-ized different aspects of the stamping process. They showed thatechanical characteristics of the stamping process and geomet-

ical aspects of the sheared edge are mainly affected by differentarameters. Hambli et al. (2003) reported about experimentalesults of a blanking process where was basically impossible toefine an universal optimal clearance value between the punch andie. Influence of geometry and mechanical properties of the cut-ing elements were investigated by Klingenberg and Singh (2003).

echanical properties of workpiece such as hardness, ductility andoating type, lubrication type and stroke rate were found as verymportant parameters in the research presented by Biglari et al.2004) and Hambli et al. (2003). In addition, Brokken et al. (2000)resented a FEM model of the metal blanking process, focusingn prediction of the shape of the cutting edge of the blankingrocess. Hambli (2002) investigated material parameters whichainly have influence on burr height. Cherouat et al. (2006) demon-

trated the use of elastoplastic model with damage occurrence on

he stamping process, where steel sheet of a thickness 2.5 mm wasnvestigated under different wear conditions of the cutting ele-

ents. Contrary to that, the blanking operation of very thin sheetetals (membranes) was investigated by Shim et al. (2004). Burr

eight prediction on steel sheet up to 0.8 mm thickness reported byl-Momani and Rawabdeh (2008) showed a high potential of using

he explicit integration FEM code in steel metal blanking processes.ased on the reported cases of using FEM models, the FEM explicit

ntegration code LS Dyna was selected for numerical simulation inur study. Whenever a selected failure criterion in any of elementsreating the body of electrical sheet steel is reached, this elements excluded. Moreover, this specific FEM software allows users toreat the workpiece material as an orthotropic body, which is nothe case in previously mentioned studies.

f =√

F(�yy − �zz)2 + G(�zz − �xx)2 + H

.1. Selection of material model

One of the key points of our study is to implement orthotropys real material phenomena into the electrical steel sheet. Addi-ionally, the stamping process is a typical operation of processing

able 1eometry of punch and die – parameters.

Parameter Ф D/2 Ф D1/2 H1 H2 R

Value (mm) 47.540 47.494 1.200 1.350 0

l geometry of the punch used for FEM analysis.

material in the plastic range of its stress–strain curve. These twofactors clearly need to be taken into consideration.

From several different options of testing and correlating theresults of FEM analysis to the experimental results, an anisotropic-elasto-plastic material model was chosen. Orthotropic behaviourof the electrical steel sheet 3D model in the plastic region wascompletely covered by this selection. Due to limitations of theselected FEM code reported by LS-Dyna Keyword User’s Manual(2007), it should be noted that the elastic range of the stress–straincurve in all directions (see the Cartesian coordinate system inFig. 1) was treated as isotropic. However, the definition of ele-ment exclusion was related to the plastic range of the referencedstress–strain curve only, and a minor influence of elastic isotropywill be neglected.

The anisotropic yield criterion was applied for the selectedmaterial model. As it is showed by Chen and Han (1988), Hill’squadratic potential function is a simple extension of Von Misesfunction, which can be expressed in terms of stress componentsin the Cartesian coordinate system as

− �yy)2 + 2L�2yz + 2M�2

zx + 2N�2xy − �ref(ε

p) = 0 (3)

where F, G, H, L, M and N are material constants determined bytesting the material in different directions. �ref is the referencedyield stress. In Section 2.1 the tensile stress–strain responses of thespecimen in X,Y and Mid(X–Y)-directions were performed as wellas shear stress–strain response in XY-, YZ- and ZX-plane. If Eq. (3)is written for all three tensile tests, Iosipescu test and imitation ofstamping process test for YZ- and ZX-plane, the material constantscan be obtained directly from experiments as follows:

L = 12

· �2ref

�2yz

, M = 12

· �2ref

�2xz

, N = 12

· �2ref

�2xy

(4)

F = �2ref2

(− 1

�2xx

+ 4 · 1

�2Mid(x–y)

+ 1

�2yy

)− N

G = �2ref

(1 + 4 · 1 − 1

)− N (5)

2 �2xx �2

Mid(x–y) �2yy

H = �2ref2

(1

�2xx

− 4 · 1

�2Mid(x–y)

+ 1

�2yy

)+ N.

p R Z1 LR Ф d/2 Rmin

.12 12.006 0.005 0.15 47.560 0.05

V. Bratus et al. / Journal of Materials Processing Technology 210 (2010) 396–407 403

Table 2Material constants.

ycTfcy

dfMcctitpe

3

eros

srsid

ε

εt

swIci

Fs

imental facts and FEM analysis results:

1. The profile of cutting edge 2B on stage No. 1 sample is shaped by

Material constant L M N F G H

Value 0.780 0.750 0.6947 0.335 0.526 0.474

Each �ij and �Mid(x−y) in Eqs. (4) and (5) represents the measuredield stress value when �ij is applied as the only nonzero stressomponent. The final values of material constants are shown inable 2. The reference yield stress function �ref(εp) was determinedrom the tensile stress–strain response in X-direction (related toorresponding yield stress �xx). Relation between true referencedield stress �ref and true plastic strain is shown in Fig. 11.

The damage in the material model was simulated through theiscrete failure of finite elements, when their state exceeds theailure criterion. As it is demonstrated by LS-Dyna Keyword User’s

anual (2007), this approach also enabled simpler tracking of therack propagation within the possibilities of FEM code. The failureriterion was basically determined by the nature of the deforma-ion. Stamping process causes strong shear deformations. Even thentroduction of an air gap (between punch and die) and radii ofhe punch and die does not contribute much to the change of therevailing loading type. Therefore the failure criterion at whichlements were excluded was maximum shear strain.

.1.1. Validation of material modelIn the next step, the material model was validated against the

xperimental results of the stress–strain response. The FEM mate-ial model for all 6 experiments, presented in Section 2.1, was basedn one and only true referenced yield stress function �ref(εp) ofelected electrical steel sheet (Fig. 11).

Figs. 12 and 13 show a comparison of results of tensile andhear tests with simulations. The form of engineering stress–strainesponse is applied in these charts. The relation between truetress–strain FEM results and engineering stress–strain responsess defined by expressions, for which practical application wasemonstrated by Ling (1996):

= ln(1 + εeng), � = �eng(1 + εeng). (6)

and � represent true strain and stress, εeng and �eng correspondo engineering strain and stress, respectively.

Only small discrepancies between the experimental results andimulations are observed. The maximal error is in the order of 3%,

hich is estimated to be small enough in FEM stamping simulation.

t is estimated that the main difference is caused by inability of thehosen material model to cope with some irregularities observedn the experiments.

ig. 11. True referenced yield stress function �ref(εp) of selected electrical steelheet.

Fig. 12. Validation of material model by experimental tensile test.

3.2. Design of geometric model

The real geometry of the cutting elements was measured pre-cisely (see Table 1) and transferred directly into the geometricmodel. Punch and die were modelled as non-deformable bodies.The electrical steel sheet as stage No. 1 sample was modelled as ahomogeneous orthotropic 3D body with overall dimensions equalto those in experiments. Due to orthotropy in the electrical steelsheet and symmetry of the cutting elements only 1/4 model wasused in FEM analysis—Fig. 14.

The boundary conditions on the inner boundaries of the pro-cessed material were symmetrical. The outer boundary conditionson electrical steel sheet were free to move in any direction. Theexact situation during the stamping process was mimicked by thisset of boundary conditions. The punch has prescribed displacementin Z-direction (stroke downwards to minimum depth H1 + 0.25 mmand stroke upwards). Mass damping was imposed on the electricalsteel sheet to minimize vibration after the product had been cut off.The link between the Cartesian and cylindrical coordinate systemsis clearly shown in Fig. 14.

The main criterion for suitability of the electrical steel sheetmesh generation was the correlation between some general exper-

the profile of the punch

Fig. 13. Validation of material model by experimental imitation of stamping processtest.

404 V. Bratus et al. / Journal of Materials Processing Technology 210 (2010) 396–407

d mar

2

34

mabawasv

dc

Fig. 14. Side and top view on the complete geometric model an

. The profile 2B1 on stamped-out part is shaped by the profile ofthe die

. 2B and 2B1 dimensions are never equal in stamping technology

. Failure criterion in electrical steel sheet never takes place at once,two stages are typically formed.

A high order of accuracy of FEM analysis results is one of theain conditions for successfully solving the problem. The main

ctivity of 2B profile forming is happening only in the air gapetween the punch and die. For the steel sheet of 0.5 mm thickness,n air gap of 0.02–0.025 mm is used. When the mesh dimensionsere defined, this fact had to be taken into consideration. However,minimal mesh dimension is pushed by numerical limitation of the

elected FEM code related to the mesh design to a still acceptablealue of 0.005 mm in radial direction.

Thus, a mesh of electrical steel sheet needs to be appropriatelyense only in the clearance region, anywhere else the mesh can beoarser.

ked 1/4 model with boundary conditions used in FEM analysis.

The final geometric model of electrical steel sheet is shownin radial cross-section in Fig. 15. It could reach almost 800,000elements, however, it corresponds to all the above listed facts ofthe stamping process. Some of the problems are avoided by non-vertical position of key region C. In addition, dimensions of mesh ineach region are shown in Table 3, where the cylindrical coordinatesystem is taken into consideration.

4. Results and discussion

The incoming data relevant to create a trustful FEM analysiswere acquired by complex experimental work. Each sample wasprepared carefully in several phases to get its stress–strain response

in different directions of the Cartesian coordinate systems. A step-by-step manufacturing process from stage No. 1 sample to the finalstage of the specimen or sample clearly indicates that potentialinternal stresses induced into electrical steel sheet by the previousrolling operation have been released. Thus, it is assumed that FEM

V. Bratus et al. / Journal of Materials Processing Technology 210 (2010) 396–407 405

ion wi

ai

1

2

i

TM

Fs

Fig. 15. Electrical steel sheet mesh generat

nalysis results of cutting edge B on stage No. 1 sample are directlynfluenced by two factors:

. geometry of the cutting elements—punch and die profile (Fig. 14,Table 1)

. orthotropy of work piece—electrical steel sheet, which has beenimplemented into the material model by importing differentstress–strain responses in referenced directions. Based on allacquired datasheets, the optimal referenced yield stress func-

0

tion � (εij) for electrical steel sheet of semi-finished grade hasbeen calculated.

The profile of cutting edge B as a result of FEM analysis is shapedn three stages:

able 3esh types and dimensions in different regions of electrical steel sheet.

Region A B

Mesh type Regular (orthogonal) WhirlingDimensions (r, ϕ, Z) [mm, ◦ , mm] 0.038 × 1 × 0.416 0.005 × 0

ig. 16. (a) Presentation of additionally shaped FEM profile of sheared edge in electricaheared edge.

th different regions in radial cross-section.

1. The punch is acting on processed material by increasing com-pressive stress, the highest shear strains are located near thesharp edge. When the failure criterion – shear strain at failure – isreached, the element in the mesh is excluded. The same situationhappens on the radius of the die side.

2. When the failure criterion in each layer of the electrical steelsheet is fulfilled, the stamped-out part is separated from stageNo. 1 sample. The punch still penetrates into the die side, the pro-file of cutting edge B is additionally shaped by radius R and by the

cylindrical part of the body. This approach to real geometry ofthe cutting punch is very rare in the literature. It is schematicallypresented in Fig. 16a. For reference only, a photo of the exper-imental profile of the sheared edge is shown in Fig. 16b. Thebending effect is clearly revealed on the experimental profile.

C D

mesh Mesh skewed by 25◦ Regular (orthogonal).05 × 1 × 0.02 0.005 × 0.5625 × 0.02 0.023 × 1 × 0.416

l steel sheet by radius R of the cutting punch. (b) Photo of experimental profile of

406 V. Bratus et al. / Journal of Materials Processing Technology 210 (2010) 396–407

d FEM

3

pcritFceto

tyer

Fig. 17. Correlation of experimental an

. When the punch is extracted from the electrical steel sheet com-pletely and a stationary state of material is obtained, the value Bof cutting edge on stage No. 1 sample is recorded.

Presentation of experimental results (Fig. 9) was slightly sim-lified for further analysis and discussion. The number of pointsreating the profile of cutting edge B on stage No. 1 sample waseduced. In experimental measurements, the profile was measuredn steps of 15◦, starting with rolling direction 0◦. In a final presenta-ion, the results of experimental work can be directly compared toEM analysis results – see radar chart in Fig. 17, where the cylindri-al coordinate system was used. Two additional profiles of cuttinglements are shown for reference only. The die profile has charac-eristically 0.02 mm bigger dimension than the cylindrical profilef the punch.

It is obvious that the profile of the cutting edge B is smaller thanhe profile of the punch. Both experimental results and FEM anal-sis are showing the same trend. These values could be quantifiedxactly from the chart in Fig. 17. A slightly smaller profile B wasecorded from experimental results. Taking into consideration the

Fig. 18. Effect on cutting edge profile of workpiec

analysis results B = B(ϕ) in radar chart.

average value of both profiles, the difference is 0.0023 mm. Sincethe stress–strain responses imported into the material model ofFEM analysis represent only the influence of orthotropy, some devi-ations were expected anyway. However, looking from the productpoint of view, this result is very promising: absolute tolerance ina similar range of profiles is up to 0.04 mm. The difference is only5.8%. Based on this fact the following conclusion could be made:The material and geometric models of FEM analysis developed in thisstudy are capable to predict the profile of the round cutting edge within5.8% deviation from the real dimension. Internal stresses and all otheruncontrollable influences are having only a minor effect on the finalprofile of the cutting edge of similar range. Curves oscillation in Fig. 17should be directly related to the influence of electrical steel sheetorthotropy. Both profiles are having the same range of amplitude– 0.005 mm. The maximum values are positioned exactly at the

same angles: 60◦, 120◦, 240◦ and 300◦. The minimum values on theFEM analysis results are located at 0◦ and 180◦, while the exper-imental results are slightly dislocated for their minimum valuesto 15◦, 165◦, 195◦ and 345◦. The difference between these valuesand experimental result at 0◦ or 180◦ is only 0.00018 mm, which

e based on the punch profile design change.

rocess

cfTsqiersc

pctotptaapT

5

ltmmr

aam

bvtr

tmmtt

wiMprpo

V. Bratus et al. / Journal of Materials P

ould be simply explained as measuring error. Both profiles areollowing the same trend. The second conclusion could be made:he material and geometric models of FEM analysis developed in thistudy are capable of predicting the oscillation of the profile as a conse-uence of electrical steel sheet orthotropy. This achievement is verymportant for the engineer involved in creating the profile of cuttinglements. Since the geometrical tolerances on the profiles of similarange are getting smaller and smaller (up to 0.025 mm), FEM analy-is results shown here are capable of offering an additional, crucialompetitive point for middle and small range stamping companies.

In Fig. 18 the potential of FEM analysis is presented. The result –rofile of the cutting edge – of the punch with a completely roundylindrical profile is presented by the line with squares. This ishe result of experimental work under Section 2.2. If the profilef cutting edge is mirrored over its average value and added tohe original round profile of the punch, the new non-round punchrofile is formed. Taking into consideration also radius R (Fig. 14)ogether with the newly calculated non-round profile, a new FEMnalysis was done. The result is shown in Fig. 18 as the line with tri-ngles. It is obvious that the redesigned punch profile gives a newrofile of the cutting edge, where the oscillation is 10 times smaller.he new one is in the range of 0.00053 mm.

. Conclusions

This investigation was related to the stamping process whereamination products of very narrow geometrical and dimensionalolerances are produced. When different suppliers of processed

aterial have to be used, the production process is not stable any-ore. This paper showed a way how the competitiveness could be

eached even in this situation based on real material datasheets.Electrical steel sheet was dealt with in a non-conventional way:

3D body was designed in FEM code LS Dyna and orthotrophy asnegative effect of processed material was incorporated into theaterial model.A virtual simulation of the cutting edge profile was developed

y FEM analysis. Anisotropic-elasto-plastic material models werealidated by experiments needed to describe orthotropy of elec-rical steel sheet in the sense of different stress–strain response ineferenced directions.

Experimental work was focused first on getting the data on elec-rical steel sheet to build a reliable material model and second, on

imicking the geometry of cutting elements directly on the geo-etric model of FEM analysis. The imitation of the stamping process

est as an upgraded version of Isosiposcu test was used for the firstime to define shear material response on electrical steel sheet.

FEM analysis results on the profile of the cutting edge agreeith the experiment in a high order of accuracy. It is shown that

nternal stresses have had no influence on oscillation of the profile.

oreover, based on FEM analysis developed in this study the new

rofile of cutting elements could be designed easily. The simulationesult showed that practically no deviations appeared on the finalrofile of the cutting edge. This approach confirms the possibilityf predicting the stamping process results by FEM analysis (virtual

ing Technology 210 (2010) 396–407 407

world) and not following the traditional system of “learning bydoing” as a solution not good enough in today’s highly competitiveworld.

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