内容简介：: Numerical investigations on sheet metal blanking with high speed deformationH. Marouania,*, A. Ben Ismailb, E. Hugc, M. RachikbaLaboratoire Gnie Mcanique, ENIM, Avenue Ibn Eljazar, 5000 Monastir, TunisiabLaboratoire Roberval, FRE 2833UTC, CNRS, BP 20529, 60205 Compigne cedex, FrancecLaboratoire CRISMAT, UMR 6508 CNRS, ENSICAEN, 6 Bd. du Marchal Juin, 14050 Caen, Francea r t i c l ei n f oArticle history:Received 21 March 2008Accepted 28 February 2009Available online 9 March 2009Keywords:DamageSheet metal blankingRate dependent plasticityNumerical simulationa b s t r a c tThe ferromagnetic sheet metal blanking is widely used for the manufacturing of rotating electricalmachines. However, the optimization of the designed machines depends on full understanding of theshearing process. The material mechanical state and magnetic properties near the cut edge depend onvarious parameters like geometric configuration (shape of the tools, punch blade radius), clearance, fric-tional contact at the interfaces and the punch speed. Several studies of the blanking process have beenproposed to assess the influence of these parameters, but only a few are concerned with the punch veloc-ity. In this paper we use a rate dependent constitutive model for the blanking process investigation toimprove the accuracy of the predictions. A 0.65 mm thickness sheet of a non-oriented full-process FeSi(3 wt.%) steel is used. The material testing and the characterization are carried out in order to fit the con-stitutive model parameters to the experimental data. Classical tensile tests and video-tensile tests arecombined to establish the sheet metal constitutive law. The identified model is, then, used for numericalsimulations (which are performed using ABAQUS/Explicit software) of various blanking tests: the clear-ance is ranging from 3.8% to 23%, punch velocity of 23 mm/s and 123 mm/s. In order to validate this workthe numerical results obtained are compared to the measurement. The comparisons relate to the punchforce and the punch penetration at fracture that are affected by the clearance and the strain rate.? 2009 Elsevier Ltd. All rights reserved.1. IntroductionThe blanking of ferromagnetic sheet is widely used for the de-sign of rotating electrical machines. Soft ferromagnetic materialssuch as FeSi alloys are massively used to make stator and rotorfor motor core. Their magnetic properties are deeply reduced dur-ing the processing 1,2. Consequently, without the post processingheat treatment, the reliability of the designed machines dependson the quality of the blanked parts and thus on the blanking pro-cess parameters 35. For these reasons, the predictive modelsfor the simulation of blanking process can be very helpful for therotating electrical machine design 6,7. It can be used to establishcorrelation between the material mechanical state resulting fromthe straining process and the loss of the magnetic properties. In-deed, with the previously mentioned correlation, the materialmechanical state like residual stress, damage, etc., can be deter-mined from the magnetic measurements 8. For instance, themagnetic Barkhausen emission was successfully used for the resid-ual stress evaluation 9,10 and for the diagnosis of componentfatigue 11.Some studies of the blanking process have been suggested to as-sess the influence of the process parameters. For the experimentalaspects, the investigations were devoted to the influence of thepunch die clearance 12, the friction effect 13 and the toolblade radius 14. For the numerical ones, the main researches havefocused on the modelling of the blanking process. The models pro-posed range from quite simple simulation based on idealizedassumptions 15 to some sophisticated approaches that take intoaccount the large strain and the material separation involved in theprocess. Taupin et al. 16 introduced the use of a ductile fracturecriterion to simulate the material separation by deleting the meshelements. A numerical procedure based on an Arbitrary LagrangianEulerian (ALE) formulation combined with re-meshing was pro-posed by Brokken et al. 17 and widely applied for further analy-ses as discussed by Goijaerts et al. 18. The ductile fracture ishandled with the help of discrete crack propagation. Recently,some authors have used the coupled damage model to predictthe shape of the cut edge of the blanked parts 1922. The previ-ously cited works were not exhaustive since several researches arecarried out in this field contributing to a best understanding of theshearing process.Today, the new industrial challenge consists in studyingthe high speed punching impact on the material behaviour, thento correctly integrate this aspect on the numerical blanking0261-3069/$ - see front matter ? 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.matdes.2009.02.028* Corresponding author. Tel.: +216 73 500 244; fax: +216 73 500 514.E-mail address: h.marouani (H. Marouani).Materials and Design 30 (2009) 35663571Contents lists available at ScienceDirectMaterials and Designjournal homepage: /locate/matdesinvestigations. Stegman et al. 23 concluded that for low speed,the material response is not affected by the strain rate. But thestrain rate effect significantly increases with speed. However, tothe authors best knowledge, little attention was paid to the strainrate effect.In this paper, the numerical and experimental investigations arecombined to study the high speed blanking of a ferromagneticsheet. The simulations are performed using Abaqus software. Aparticular attention is paid to the strain rate contribution to the in-volved phenomena during the shearing process. Section 2 is de-voted to the experimental aspects including the description ofthe studied sheet, the identification of the sheet metal constitutivelaw and the various blanking tests carried out. Section 3, deals withthe numerical procedure used for the blanking simulation. Theadopted finite element model is briefly described but the sheet me-tal constitutive model used for the numerical simulation is ex-plained in more details as it is a key point. In Section 4, thenumerical results from the model proposed are compared withthe measurements for a validation purpose. First, tensile tests arecarried out to check the validity of the rate dependent model. Sec-ond, the blanking tests are simulated, then the numerical resultsobtained are compared with the measurements. The comparisonsrelate to the punch force and the punch penetration at fracture,which are influenced by the clearance and the strain rate.2. Experimental aspects2.1. Material characterization2.1.1. Microstructural observationsThe material investigated in the framework of this study is a0.65 mm thickness sheet of a non-oriented full-process FeSi(3 wt.%) steel. The SEM observations reveal an isotropic grainstructure in the thickness (see Table 1).2.1.2. Quasi-static behaviourVarious tensile tests are performed with a strain rate of10?5s?1. This value is classically used to describe the quasi-staticmaterial behaviour. They are made along the rolling direction (RD),the 45? and the transversal direction (TD). The general behaviourconsists of an initial yield drop (rmineandrmaxe), followed by aLders strain plateau and classically encountered in bcc steels.The material behaviour can be assumed to be mechanically isotro-pic (in particular the ultimate stressrmand the fracture strain A)despite the weak scattering of its properties in the sheet plane.The average mechanical properties are listed in Table 2.The material work hardening is described by a conventionalLudwik law. The quasi static yield stress is as follows:?r0?ep k?epn1k = 770 MPa and n = 0.26 are the identified material parameters.2.1.3. High strain behaviourThe industrial punch velocity is very high in the blanking pro-cess. The investigations on this process using a quasi-static mate-rial behaviour are then not adequate. That is why, we areinterested in identifying a strain rate behaviour law.Several approaches are proposed to define the viscoplasticbehaviour of materials. For the strain rate dependent plasticity,the overstress model is commonly used. In such a model, the rateof effective plastic strain is related to the difference between thecurrent stress and the yielding stress. It should be noted that inthe case of rate dependent plasticity, the yielding condition canbe surpassed. To illustrate this approach, we recall the model pro-posed by Peirce et al. 24. For one dimension rate dependent plas-ticity and isotropic work hardening, the effective plastic strain rateis given by:_?ep_?ep0rj j?r?ep?1m2?epis the equivalent plastic strain and_?epis the equivalent plasticstrain rate._?ep0is the reference strain rate used to measure the quasistatic yield stress. m is the rate sensitivity parameter (m 0).As the blanking process is not time dependent, the strain ratedependency is taken into account with the help of rate dependentyield. When the strain and the strain rate dependencies are as-sumed to be separable and isotropic work hardening is considered,the strain rate dependent yield stress?ris defined as:?r?ep;_?ep ?r0?ep_?ep_?ep0 !m3?r0?ep is the quasi static yield stress at the quasi static strain rate_?ep0.We notice that the quasi static yield stress?r0?ep is obtained forplastic straining at the reference strain rate_?ep0. In addition, for high-er strain rates, the yield stress increases while it decreases for low-er rates.For the investigation of the strain rate sensitivity, it is importantto guarantee constant strain rate during the test. Hence, the truestressstrain curves are measured with the help of an INSTRONmachine equipped with a CCD camera and a data acquisition sys-tem that regulates the prescribed displacement so that a constantstrain rate is maintained in the specimen centre. The techniqueused for these video controlled tests is based on the proceduredeveloped by Gsell and Jonas 25. It consists in printing four darkmarkers on the specimen surface before its extension. The in planestrain components are then measured thanks to the real time mon-itoring of the markers displacements. A schematic description ofthe used apparatus is given in Fig. 1 but the reader can refer to26 for recent extensions of the video control test.Table 1Nominal composition of used material.Fe (%)Si (%)Mn (%)C (%)96.52.410.1Table 2Material characteristics for Fe(3 wt.%)Si.RD45?TDAveragermaxeMPa312322317317rmineMPa301311295302rm(MPa)422444428433A (%)40404240Fig. 1. Schematic description of the video control tensile test.H. Marouani et al./Materials and Design 30 (2009) 356635713567The set-up described by Fig. 1 is used to perform tensile tests atdifferent strain rates ranging from 10?5s?1to 5 10?3s?1. The ref-erence strain rate_?ep0is taken at 10?5s?1. It was shown that thevariations of the mechanical properties for the strain rate less than10?5s?1remain very small. The so obtained experimental data areused to fit the strain rate sensitivity parameter m in Eq. (3) with thehelp of a linear regression modelled by a least squares function(Eqs. (4)(6).Log?r?ep;_?ep?r0?ep ! m ? Log_?ep_?ep0 !4m nPni1xiyi ?Pni1xiPnj1yjnPni1x2i ? Pni1x?25R2nPni1xiyi ?Pni1xiPnj1yj?2nPni1x2i ? Pni1x2? ? nPni1y2i ? Pni1y2?6With n is the number of data points, x Log_?ep_?ep0? ?; y Log?r?ep;_?ep?r0?ep?and R is the correlation coefficient.The result obtained for the investigated material shows a signif-icant strain rate sensitivity (m = 0.0085) (see Fig. 2).2.2. Blanking testsVarious blanking tests are carried out using one of CETIMsmechanical presses (200t, 80 SPM). The tools are equipped witha piezoelectric sensor and a signal acquisition and processing sys-tem to measure the punch force during the blanking operation. Theblanking test configuration and the geometric relevant parametersare given in Fig. 3.In this experimental study, we mainly investigate two parame-ters, namely the clearance and the punch velocity. For the clear-ance effect study, the die radii rdis kept constant and the punchradius rpis adjusted to obtain the appropriate clearance rangingfrom 3.8% to 23%. To complete this description, a sharp punchand die with 0.02 mm blade radius are used. As the punch dis-placement is controlled by means of a crank-connecting rod sys-tem, the punch linear velocity during the blanking is variable. Italso depends on the crankshaft angular velocity and the distancebetween the blanked sheet and the bottom dead centre. By varyingthese two parameters, the punch linear velocity at impact canrange from 23 mm/s to 123 mm/s for the considered blanking test(Table 3).3. Numerical aspectsThe numerical simulation of the sheet metal blanking processhas been the object of several researches. Different approachesare proposed to simulate the shearing process and to handle theductile fracture. For this purpose, uncoupled and coupled damagemodel are combined with mesh adaptivity and other ingredientsof the finite element method. In the following sections, we brieflydescribe the finite element model with more extensive discussionof the sheet metal constitutive model since it is the key point ofthis work.3.1. Finite element modelAs the blanking process leads to the material separation, a par-ticular attention must be paid to the finite element model, espe-cially the load stepping algorithm and the mesh adaptivity thatensure a reliable solution for high strain level. Because of the highnon linearities associated with the shearing process, the classicaliterative NewtonRaphson method is not adapted as it can involveFig. 2. Identification of the strain rate sensitivity parameter m.Fig. 3. Axisymmetric blanking test configuration.Table 3Blanking tests.Clearance (%)Punch speed (mm/s)23477987971141233.8jjjjjjj7.7jjjjjjj11.5jjjj15.4jjjj19.2jjjj3568H. Marouani et al./Materials and Design 30 (2009) 35663571convergence problems. In this work, we focus on the non iterativeexplicit approach. The displacement solution is introduced withthe help of the central finite difference integration scheme.Another aspect of the finite element simulation of the blankingprocess is the large distortion of the elements that occurs duringthe calculation and leads to strain localization, element degrada-tion and important errors that make the solution unreliable.Among the several mesh adaptivity methods, the ALE (ArbitraryLagrangian Eulerian) formulation seems to be the most convenientfor blanking simulation since this process involves large inelasticdeformations. The ALE method consists in two fundamental stages:creating a new mesh (mesh smoothing) and remapping the solu-tion variable from the old mesh to the new one (advection). In thiswork, the adaptive meshing procedure of Abaqus Explicit softwareis used:? The mesh smoothing is performed by means of a simple volumesmoothing method that relocates a node by computing a volumeweighed average of the element centres in the elements sur-rounding the node.? As the finite difference explicit scheme is conditionally stable,and as the stability requirement limits the amount of motionwithin a time increment, an operator split is used to decouplethe Lagrangian motion from the mesh motion. The advectionis performed by means of a second order method that isdescribed in Abaqus Explicit users manual.3.2. Sheet metal constitutive modelAmong several existing sheet metal forming processes, theblanking process stands apart since plastic straining is followedby ductile fracture and material separation. This involves someadditional difficulties, particularly when dealing with the numeri-cal simulation of this process. Therefore, we must take into consid-eration the sheet constitutive model. In previous works 20, wesuccessfully used the GursonTvergaardNeedleman model tohandle the ductile fracture. Yet, in this work, this model is associ-ated with a rate dependent plasticity to take into account the effectof the punch velocity. In addition, the strain localization and themesh dependency are limited with the help of the strain ratedependency.Starting from the classical plasticity model, the yielding func-tion is extended to porous metal plasticity as follows 27,28:Ureq?r 2q1f?cosh?q23rm?r?1 q3f?2? 07reqffiffiffiffiffiffiffiffiffiffiffiffiffiffi32r0ijr0ijqis the Von Mises equivalent stress,r0is the Cauchystress deviator,?ris the yielding stress,rmis the hydrostatic stressand q1,q2, q3are adjustable material parameters. The three stages ofthe ductile fracture (void initiation, void growth and void coales-cence) and the rapid loss of the capacity of the material are mod-elled using the variable f*that is related to the damage variable f(void volume fraction) as follows:f?ff ? fcfc?fF?fcfF?fcf ? fcfc? f ? fF?fFf ? fF8:8fcis the critical void volume fraction and fFis the void volume frac-tion at failure?fF 1=q1whenq3 q219The evolution of the void volume fraction comes from the growth ofthe existing void and the nucleation of new void:_f _fgr_fnucl10The void growth_fgris related to the compressibility of the sur-rounding material. It depends on the volumetric part of plasticstrain rate_epkk:_fgr 1 ? f_epkk11The void nucleation is described by a normal distribution around amean value 29:_fnuclfNSffiffiffiffiffiffi2ppexp ?12?ep?eNS?2#_?ep12fNis the volume fraction of the nucleating void,eNis the mean strainfor void nucleation and S is the standard deviation. The predictionsobtained with the previously described constitutive model aremesh-dependent because of strain localization. To overcome thisdifficulty, several regularization techniques are available 30, how-ever, the strain rate dependency can be used for this purpose31,32. Indeed, taking into account that the strain rate dependencyintroduces a length scale in the constitutive model and thus limitsthe excessive strain localization and the mesh dependency.4. Results and discussionIn this section we present only some of the carried blankingtests. The conclusions and the remarks are the same for all thepunching configurations.The influence of the punch speed on the punch force versus thepunch penetration curve is illustrated in Fig. 4 (clearance of 7.7%).It clearly shows the punch penetration at fracture is quite sensitiveto the punch velocity. In fact, the maximum punch force is not af-fected by the punch velocity: a neglected difference exists betweenspeeds of 23 mm/s and 97 mm/s and beyond this value the maxi-mum punch force becomes constant.The measurements described previously are used to validatethe numerical results from the finite element model. The valida-tions are carried out at two different levels. The first is the identi-fication of the rate dependent constitutive model from the video-tensile test. The second level concerns the numerical simulationof the blanking tests and the assessment of the clearance and thepunch velocity influences. Various blanking tests are simulatedusing rate dependent and rate independent constitutive modelsand the results obtained are compared with the measurements.Fig. 4. The punch velocity effect.H. Marouani et al./Materials and Design 30 (2009) 356635713569The tensile test is simulated using a plane stress finite elementmodel with different prescribed strain rates. Considering the prob-lem symmetry, a quarter of the specimen is discretized with 60four nodded plan stress elements. The strain rate dependency is ta-ken into account using yield stress ratios. To illustrate the resultsobtained, Fig. 5 represents a comparison between the measure-ments and the numerical results.Fig. 5a shows that for the quasi-static behaviour (assimilated on10?5strain rate), the classical Ludwik law is sufficient to correctlydescribe the material behaviour. However, for a greater strain rate(Fig. 5b), a difference is denoted between the experimental and therate independent material behaviour simulation. The predictionsfrom the rate dependent model are in good agreement with themeasurements. Consequently, the material input data (work hard-ening and strain rate sensitivity parameters) are well fitted to themeasurements and can be used for the blanking numericalinvestigations.3003504004500.050.10.15p (MPa)MeasurementsRate independentRate dependent(a)3003504004500.050.10.15p (MPa)Rate independentMeasurementsRate dependent(b)Fig. 5. Validation of the rate dependent constitutive model on tensile test: (a)_e 10?5s?1; (b)_e 5 ? 10?3s?1.Fig. 6. Finite element model for the blanking test simulation.Table 4Material input data for FeSi steel.PlasticityDamageYieldingNucleationFailurek(MPa)nmq1q2q3SeNfNfc(%)fF(%)7500.2450.00851.50.04111201234567punch penetration (mm)punch force (KN)MeasurementsRate dependentRate independent(a)01234567punch force (KN)MeasurementsRate dependentRate independent(b)012345670punch force (KN)MeasurementsRate dependentRate independent(c)punch penetration (mm)0punch penetration (mm)0Fig. 7. Comparison between predictions and measurements for 123 mm/s punchvelocity and different clearances: (a) clearance 3.8%; (b) clearance 7.7%; (c)clearance 11.5%.3570H. Marouani et al./Materials and Design 30 (2009) 35663571The blanking tests described in Section 3.2 are simulated by asolid axisymmetric finite element model. This finite element modelis described in Fig. 6. The tools (punch, die and blank holder) aremodelled using rigid bodies.For the sheet constitutive model, the rate dependent plasticitymodel is compared to the rate independent one. Both models arecoupled with the GursonTvergaardNeedleman model for dam-age handling. The material input data for the examined FeSi steelare summarized in Table 4.To show the numerical model ability in assessing the influenceof clearance on the punch force, Fig. 7 reveals a comparison be-tween the measurements, the numerical results from the ratedependent plasticity and those from rate independent plasticity.The results are compared for one punch velocity (123 mm/s) andthree clearance value (3.8%, 7.7% and 11.5%). The numerical resultsfrom the strain rate dependent model are in good accord with themeasurements. Nevertheless, it should be noticed that for verynarrow clearance, the numerical solution displays oscillations.All the results presented above show that the rate dependentconstitutivemodelimprovesthepredictionaccuracy.Theimprovement involves the maximum force as well as the punchpenetration at fracture. Thus enhancing the prediction of the shapeof the cut edge.5. ConclusionIn this paper, both the experimental and the numerical investi-gations of the sheet metal blanking process are carried out. Theseinvestigations focus on the punch velocity (strain rate) and theclearance effect. The presented work leads to some improvementsof our previous works on the numerical simulation and the exper-imental investigation of the considered process. The most relevantkey finding concerns the influence of the strain rate. It is clear thatboth the maximum punch force and the shape of the cut edge areaffected by the strain rate (punch velocity). The maximum punchforce increases for the low speed until a limited value where it be-comes constant. Stegman et al. 23 explain it by the heat inversecontribution: High strain rate generate an adiabatic behaviourwhich leads to a softness material plasticity. Concerning thenumerical simulation, it is shown that with a rate dependent con-stitutive model, the punch penetration at fracture is well pre-dicted. Moreover, the strain localization and the resulting meshdependency are limited to some extent since the strain rate depen-dency introduces a length scale leading to a delayed plastic insta-bility. Finally, the prediction of the punch maximum force isimproved.AcknowledgementsFinancial and technical support for this research was providedby Le Conseil Rgional de Picardie” and CETIM. The authors grate-fully acknowledge the support.References1 Sinram K, Grafen A, Janzon K, Weber K. The influence of fine blanking on themagnetic properties of soft magnetic steel. IEEE Trans Magn 1988;24:83942.2 Hubert O, Hug E. Influence of plastic strain behaviour of non-oriented Fe3Siand application to manufacturing test by punching. Mater Sci Technol1995;11:4827.3 Hancock RG. Effect of stress relief annealing on the magnetic properties of cutlaminations and assembled cores produced from nonoriented electrical steel. JMagn Magn Mater 1979;19:658.4 Kim DH, Lee SB, Ko DC, Kim BM. Process design and forming analysis of apermalloy shielding can for instrument clusters. J Mater Process Technol2003;135:36674.5 Aggarwal S, Bhushan B, Katsube N. Three-dimensional finite element analysisof the magnetic tape slitting process. Mater Process Technol 2005;170:7188.6 Ossart F, Hug E, Hubert O, Buvat C, Billardon R. Effect of punching on electricalsteels: experimental and numerical coupled analysis. IEEE Trans Magn2000;36:313740.7 Choi JC, Kim C. A compact and practical CAD/CAM system for the blanking orpiercing of irregular shaped-sheet metal products for progressive working. JMater Process Technol 2001;110:3646.8 Kleber X, Vincent A. On the role of residual internal stresses and dislocationsonBarkhausennoiseinplasticallydeformedsteel.NDT&EInt2004;37:43945.9 Stewart DM, Stevens KJ, Kaiser AB. Magnetic Barkhausen noise analysis ofstress in steel. Curr Appl Phys 2004;4:30811.10 Moorthy V, Shaw BA, Hopkins P. Surface and subsurface stress evaluation incase-carburised steel using high and low frequency magnetic Barkhausenemission measurements. J Magn Magn Mater 2006;299:36275.11 Moorthy V, Shaw BA, Hopkins P. Magnetic Barkhausen emission technique fordetecting the overstressing during bending fatigue in case-carburised En36steel. NDT & E Int 2005;38:15966.12 Jana S, Ong NS. Effect of punch clearance in the high-speed blanking of thickmetals using an accelerator designed for a mechanical press. J Mech WorkTechnol 1998;19:5572.13 Thiruvarudchelvan S, Ong NS. Exploration of the piercing of round holes inmetal sheets in the presence of frictionally induced radial compressive stress. JMater Process Technol 1990;23:295310.14 Li M. An exp

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