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Numerical investigations on sheet metal blanking with high speed deformation H. Marouani a,*, A. Ben Ismailb, E. Hugc, M. Rachikb aLaboratoire Gnie Mcanique, ENIM, Avenue Ibn Eljazar, 5000 Monastir, Tunisia bLaboratoire Roberval, FRE 2833UTC, CNRS, BP 20529, 60205 Compigne cedex, France cLaboratoire CRISMAT, UMR 6508 CNRS, ENSICAEN, 6 Bd. du Marchal Juin, 14050 Caen, France a r t i c l ei n f o Article history: Received 21 March 2008 Accepted 28 February 2009 Available online 9 March 2009 Keywords: Damage Sheet metal blanking Rate dependent plasticity Numerical simulation a b s t r a c t The ferromagnetic sheet metal blanking is widely used for the manufacturing of rotating electrical machines. However, the optimization of the designed machines depends on full understanding of the shearing process. The material mechanical state and magnetic properties near the cut edge depend on various parameters like geometric confi guration (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 been proposed to assess the infl uence 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 to improve 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 fi t the con- stitutive model parameters to the experimental data. Classical tensile tests and video-tensile tests are combined to establish the sheet metal constitutive law. The identifi ed model is, then, used for numerical simulations (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 work the numerical results obtained are compared to the measurement. The comparisons relate to the punch force and the punch penetration at fracture that are affected by the clearance and the strain rate. ? 2009 Elsevier Ltd. All rights reserved. 1. Introduction The blanking of ferromagnetic sheet is widely used for the de- sign of rotating electrical machines. Soft ferromagnetic materials such as FeSi alloys are massively used to make stator and rotor for motor core. Their magnetic properties are deeply reduced dur- ing the processing 1,2. Consequently, without the post processing heat treatment, the reliability of the designed machines depends on the quality of the blanked parts and thus on the blanking pro- cess parameters 35. For these reasons, the predictive models for the simulation of blanking process can be very helpful for the rotating electrical machine design 6,7. It can be used to establish correlation between the material mechanical state resulting from the straining process and the loss of the magnetic properties. In- deed, with the previously mentioned correlation, the material mechanical state like residual stress, damage, etc., can be deter- mined from the magnetic measurements 8. For instance, the magnetic Barkhausen emission was successfully used for the resid- ual stress evaluation 9,10 and for the diagnosis of component fatigue 11. Some studies of the blanking process have been suggested to as- sess the infl uence of the process parameters. For the experimental aspects, the investigations were devoted to the infl uence of the punch die clearance 12, the friction effect 13 and the tool blade radius 14. For the numerical ones, the main researches have focused on the modelling of the blanking process. The models pro- posed range from quite simple simulation based on idealized assumptions 15 to some sophisticated approaches that take into account the large strain and the material separation involved in the process. Taupin et al. 16 introduced the use of a ductile fracture criterion to simulate the material separation by deleting the mesh elements. A numerical procedure based on an Arbitrary Lagrangian Eulerian (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 is handled with the help of discrete crack propagation. Recently, some authors have used the coupled damage model to predict the shape of the cut edge of the blanked parts 1922. The previ- ously cited works were not exhaustive since several researches are carried out in this fi eld contributing to a best understanding of the shearing process. Today, the new industrial challenge consists in studying the high speed punching impact on the material behaviour, then to correctly integrate this aspect on the numerical blanking 0261-3069/$ - 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) 35663571 Contents lists available at ScienceDirect Materials and Design journal homepage: investigations. Stegman et al. 23 concluded that for low speed, the material response is not affected by the strain rate. But the strain rate effect signifi cantly increases with speed. However, to the authors best knowledge, little attention was paid to the strain rate effect. In this paper, the numerical and experimental investigations are combined to study the high speed blanking of a ferromagnetic sheet. The simulations are performed using Abaqus software. A particular 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 of the studied sheet, the identifi cation of the sheet metal constitutive law and the various blanking tests carried out. Section 3, deals with the numerical procedure used for the blanking simulation. The adopted fi nite element model is briefl y 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, the numerical results from the model proposed are compared with the measurements for a validation purpose. First, tensile tests are carried out to check the validity of the rate dependent model. Sec- ond, the blanking tests are simulated, then the numerical results obtained are compared with the measurements. The comparisons relate to the punch force and the punch penetration at fracture, which are infl uenced by the clearance and the strain rate. 2. Experimental aspects 2.1. Material characterization 2.1.1. Microstructural observations The material investigated in the framework of this study is a 0.65 mm thickness sheet of a non-oriented full-process FeSi (3 wt.%) steel. The SEM observations reveal an isotropic grain structure in the thickness (see Table 1). 2.1.2. Quasi-static behaviour Various tensile tests are performed with a strain rate of 10?5s?1. This value is classically used to describe the quasi-static material behaviour. They are made along the rolling direction (RD), the 45? and the transversal direction (TD). The general behaviour consists of an initial yield drop (rmin e andrmax e ), followed by a Lders 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 conventional Ludwik law. The quasi static yield stress is as follows: ?r0?ep k?epn 1 k = 770 MPa and n = 0.26 are the identifi ed material parameters. 2.1.3. High strain behaviour The 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 are interested in identifying a strain rate behaviour law. Several approaches are proposed to defi ne the viscoplastic behaviour of materials. For the strain rate dependent plasticity, the overstress model is commonly used. In such a model, the rate of effective plastic strain is related to the difference between the current stress and the yielding stress. It should be noted that in the case of rate dependent plasticity, the yielding condition can be 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 rate is given by: _? ep_?ep 0 rj j ?r?ep ?1 m 2 ?epis the equivalent plastic strain and_?epis the equivalent plastic strain rate._?ep 0is the reference strain rate used to measure the quasi static yield stress. m is the rate sensitivity parameter (m 0). As the blanking process is not time dependent, the strain rate dependency is taken into account with the help of rate dependent yield. 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?r is defi ned as: ?r?ep;_?ep ?r0?ep _? ep _? ep 0 !m 3 ?r0?ep is the quasi static yield stress at the quasi static strain rate_?ep 0. We notice that the quasi static yield stress?r0?ep is obtained for plastic straining at the reference strain rate_?ep 0. 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 important to guarantee constant strain rate during the test. Hence, the true stressstrain curves are measured with the help of an INSTRON machine equipped with a CCD camera and a data acquisition sys- tem that regulates the prescribed displacement so that a constant strain rate is maintained in the specimen centre. The technique used for these video controlled tests is based on the procedure developed by Gsell and Jonas 25. It consists in printing four dark markers on the specimen surface before its extension. The in plane strain components are then measured thanks to the real time mon- itoring of the markers displacements. A schematic description of the used apparatus is given in Fig. 1 but the reader can refer to 26 for recent extensions of the video control test. Table 1 Nominal composition of used material. Fe (%)Si (%)Mn (%)C (%) 96.52.410.1 Table 2 Material characteristics for Fe(3 wt.%)Si. RD45?TDAverage rmax e MPa312322317317 rmin e MPa301311295302 rm(MPa)422444428433 A (%)40404240 Fig. 1. Schematic description of the video control tensile test. H. Marouani et al./Materials and Design 30 (2009) 356635713567 The set-up described by Fig. 1 is used to perform tensile tests at different strain rates ranging from 10?5s?1to 5 10?3s?1. The ref- erence strain rate _?ep 0 is taken at 10?5s?1. It was shown that the variations of the mechanical properties for the strain rate less than 10?5s?1remain very small. The so obtained experimental data are used to fi t the strain rate sensitivity parameter m in Eq. (3) with the help of a linear regression modelled by a least squares function (Eqs. (4)(6). Log ?r?ep;_?ep ?r0?ep ! m ? Log _? ep _? ep 0 ! 4 m nPn i1xiyi ? Pn i1xi Pn j1yj nPn i1x 2 i ? Pn i1x? 2 5 R2 nPn i1xiyi ? Pn i1xi Pn j1yj? 2 nPn i1x 2 i ? Pn i1x 2? ? nPn i1y 2 i ? Pn i1y 2? 6 With n is the number of data points, x Log _?ep _?ep 0 ? ? ; y Log ?r?ep;_?ep ?r0?ep ? and R is the correlation coeffi cient. The result obtained for the investigated material shows a signif- icant strain rate sensitivity (m = 0.0085) (see Fig. 2). 2.2. Blanking tests Various blanking tests are carried out using one of CETIMs mechanical presses (200t, 80 SPM). The tools are equipped with a piezoelectric sensor and a signal acquisition and processing sys- tem to measure the punch force during the blanking operation. The blanking test confi guration and the geometric relevant parameters are 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 punch radius rpis adjusted to obtain the appropriate clearance ranging from 3.8% to 23%. To complete this description, a sharp punch and 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. It also depends on the crankshaft angular velocity and the distance between the blanked sheet and the bottom dead centre. By varying these two parameters, the punch linear velocity at impact can range from 23 mm/s to 123 mm/s for the considered blanking test (Table 3). 3. Numerical aspects The numerical simulation of the sheet metal blanking process has been the object of several researches. Different approaches are proposed to simulate the shearing process and to handle the ductile fracture. For this purpose, uncoupled and coupled damage model are combined with mesh adaptivity and other ingredients of the fi nite element method. In the following sections, we briefl y describe the fi nite element model with more extensive discussion of the sheet metal constitutive model since it is the key point of this work. 3.1. Finite element model As the blanking process leads to the material separation, a par- ticular attention must be paid to the fi nite element model, espe- cially the load stepping algorithm and the mesh adaptivity that ensure a reliable solution for high strain level. Because of the high non linearities associated with the shearing process, the classical iterative NewtonRaphson method is not adapted as it can involve Fig. 2. Identifi cation of the strain rate sensitivity parameter m. Fig. 3. Axisymmetric blanking test confi guration. Table 3 Blanking tests. Clearance (%)Punch speed (mm/s) 2347798797114123 3.8jjjjjjj 7.7jjjjjjj 11.5jjjj 15.4jjjj 19.2jjjj 3568H. Marouani et al./Materials and Design 30 (2009) 35663571 convergence problems. In this work, we focus on the non iterative explicit approach. The displacement solution is introduced with the help of the central fi nite difference integration scheme. Another aspect of the fi nite element simulation of the blanking process is the large distortion of the elements that occurs during the 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 (Arbitrary Lagrangian Eulerian) formulation seems to be the most convenient for blanking simulation since this process involves large inelastic deformations. 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 this work, the adaptive meshing procedure of Abaqus Explicit software is used: ? The mesh smoothing is performed by means of a simple volume smoothing method that relocates a node by computing a volume weighed average of the element centres in the elements sur- rounding the node. ? As the fi nite difference explicit scheme is conditionally stable, and as the stability requirement limits the amount of motion within a time increment, an operator split is used to decouple the Lagrangian motion from the mesh motion. The advection is performed by means of a second order method that is described in Abaqus Explicit users manual. 3.2. Sheet metal constitutive model Among several existing sheet metal forming processes, the blanking process stands apart since plastic straining is followed by ductile fracture and material separation. This involves some additional diffi culties, 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, we successfully used the GursonTvergaardNeedleman model to handle the ductile fracture. Yet, in this work, this model is associ- ated with a rate dependent plasticity to take into account the effect of the punch velocity. In addition, the strain localization and the mesh dependency are limited with the help of the strain rate dependency. Starting from the classical plasticity model, the yielding func- tion is extended to porous metal plasticity as follows 27,28: U req ?r 2q1f?cosh?q2 3rm ?r ? ?1 q3f? 2 ? 07 req ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi 3 2r 0 ijr 0 ij q is the Von Mises equivalent stress,r0is the Cauchy stress deviator,?ris the yielding stress,rmis the hydrostatic stress and q1,q2, q3are adjustable material parameters. The three stages of the 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 ? fc fc ?fF?fc fF?fcf ? fc fc? f ? fF ? fFf ? fF 8 : 8 fcis the critical void volume fraction and fFis the void volume frac- tion at failure ? fF 1=q1whenq3 q2 1 9 The evolution of the void volume fraction comes from the growth of the existing void and the nucleation of new void: _ f _ fgr _ fnucl10 The void growth _ fgris related to the compressibility of the sur- rounding material. It depends on the volumetric part of plastic strain rate_ep kk: _ fgr 1 ? f_ep kk 11 The void nucleation is described by a normal distribution around a mean value 29: _ fnucl fN S ffiffi ffiffi ffiffi 2p pexp ? 1 2 ?ep?eN S ?2 # _? ep12 fNis the volume fraction of the nucleating void,eNis the mean strain for void nu