An experimental and numerical study of a planar blanking process

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1 Journal of Materials Processing Technology 87 (1999) 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 Eindho en Uni ersity of Technology, Faculty of Mechanical Engineering, P.O. Box 513, 5600 MB Eindho en, 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 a blanking 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 displacement and strain fields, load penetration curves are also determined for both clearances. The experimental results are in good agreement with numerical simulations, the latter of which are carried out using a plane-strain finite-element model based on an operator split arbitrary Lagrange Euler (OS-ALE) method 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 process since the beginning of this century. Blanking experiments with either planar [1,2] or axisymmetric [3 8] configurations have lead to general guidelines concerning process parameters such as punch and die radius, velocity, and clearance. Although some studies involve analytical models [9 11], the blanking process is not fully comprehended. Therefore, every new blanking product necessitates many trial-and-error experiments before qualifications are met. As requirements concerning cycle time and product dimensions become more severe, an appropriate model and understanding of the blanking process becomes increasingly important. Since the process is too complex for analytical models, the finite-element method has been used to simulate the blanking process with varying success [12 14]. One of the problems that is encountered in the numerical approach is the description of fracture. Both the fracture model and its implementation are still the subject of discussion. Even if a fracture model has been established, much experimental research is still required to quantify the necessary input parameters. * Corresponding author. Fax: ; ad@wfw.wtb.tue.nl There are many different formulations to describe fracture, since the fracture behavior for a specific material is influenced by process-dependent features, such as: the distribution and intensity of the applied loads, the geometry, the deformation history, and the hydrostatic pressure [15]. To limit the number of experiments, it seems appropriate to study the deformation and fracture behavior in loading situations strongly related to the industrial blanking process. In this study, the possibilities of in situ observation of the deformation behavior in a planar blanking process is investigated. Local deformations are monitored, and subsequently compared with numerical predictions. Although this study focuses on the deformation behavior, the methods developed will also be employed for characterization of fracture in future research. The present investigation is directed mainly towards the development and evaluation of an experimental set-up that will enable the study of the local deformations during the blanking process. Section 2 describes this experimental set-up, i.e. the planar blanking apparatus, the material used, and the experimental technique. The numerical method, which uses an elasto-plastic Von Mises model and an operator split arbitrary Lagrange Euler (OS-ALE) method, is described in Section 3. The experimental and numerical results obtained are discussed and compared in Section /99/$ - see front matter 1999 Elsevier Science S.A. All rights reserved. PII S (98)

2 Y.W. Stegeman et al. / Journal of Materials Processing Technology 87 (1999) Fig. 1. Blanking apparatus. 4. Finally, some concluding remarks are made in Section Experimental set-up As mentioned earlier, much research on the blanking process was concentrated on the influence of process parameters, such as the punch and die radius, the clearance, and the velocity [1 9]. In these studies, only the load penetration curves have been measured in situ. The deformation could only be visualized at distinct stages of the punching process, at which the experiment was stopped and the sample removed from the set-up. The experimental techniques used for the determination of the deformation include scribed lines, hardness measurements and micro-photographs. In the present study, not only the load penetration curve, but also the deformation is recorded in situ. For in situ determination of the displacement field, a planar configuration is required. Two clearances (2 and 10% of the specimen thickness) are used in order to determine whether this in situ technique can demonstrate the differences between the two configurations. This section describes the apparatus and material used for the planar blanking tests, as well as the experimental technique employed for monitoring the displacement and strain fields Blanking apparatus The planar blanking experiments have been carried out using an apparatus, shown in Fig. 1, that was built into a universal testing machine (Zwick 1484). The upper 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 align the upper body and the center body (D). Bolts (E) keep the upper and center body together when the upper body is pulled up in order to change the specimens. During the experiment, the testing machine pushes the upper body down, causing the springs (F) to exert a force on the center body. The pressure plate (G), attached to this center body, in turn exerts a pressure of approximately 5 MPa on the specimen (H). Mount (I) is used for the initial positioning of this specimen. The edges of the die (J) are 10 mm apart and have radii of 11 m. Two punches (K), each with a punch radius of 7 m, are used successively to obtain clearances of 2 and 10% of the specimen thickness. The horizontal motion of the punch is restricted by the pressure plate, whilst the vertical movement is controled by the testing machine. The punch load can be measured directly by a piezo force transducer (L) (35 kn, Kistler 9021 A) that is mounted between the punch and the upper body. Also, the (strain gauge Wheatstone bridge) force transducer of the testing machine can be used to measure the punch load, the spring forces being taken into account. The blanking velocity is controlled by the testing machine, which, however, is not able to maintain a constant velocity due to the finite stiffness of the system. The punch displacement is therefore measured by a separate displacement transducer Material Process parameters are, where possible, kept similar to the parameters in industrial blanking processes. Accordingly, the material selected for this study, a 13% Cr steel, is common in these processes (Table 1).

3 268 Y.W. Stegeman et al. / Journal of Materials Processing Technology 87 (1999) Table 1 Material properties of X30Cr13 Young s modulus Poisson s ratio Yield strength GPa MPa Specimens of 48 mm length and 1 mm thickness are milled to a width of 10 mm (Fig. 2). This milling provides a rough surface, which gives enough contrast for the correlation technique described in Section 2.3. To a first approximation, the material used is regarded as isotropic, with isotropic hardening. For the occurrence of plastic deformation, the Von Mises yield criterion is used, which states that the deformation rate remains elastic if 3 2 tr( d d 2 ) in which d is the deviatoric stress tensor and is the actual yield stress. During plastic deformation, the equivalent Von Mises stress 3 2 tr( d d ) equals the yield stress. This yield stress increases with increasing effective plastic strain, as shown in Fig. 3. The relationship between the yield stress and the effective plastic strain is obtained by carrying out 20 tensile tests at low velocity, such that the strain rate has no influence on the yield stress. Each tensile specimen has been subjected to a different amount of rolling in order to obtain different initial plastic deformations. The yield stress effective plastic strain relationship is determined by fitting a master curve through the maxima of the stress strain curves of these tensile tests: = (1 e /0.15 ) (MPa) 2.3. Correlation technique During the blanking process, a CCD camera records a set of successive images (Fig. 4) of the sample surface shown in Fig. 2. In order to quantify the displacement of material points at this surface, the contrast correlation technique [16,17] is used. This digital image processing technique does not require markers on the specimen surface, which is advantageous, because the high deformations, in combination with the small area Fig. 3. Strain-hardening behavior. observed, make the use of markers nearly impossible. Instead of locating markers in successive images, the contrast correlation technique uses the contrast information (i.e. the gray level of each camera pixel) in the images to construct the displacement field. To determine the displacement of a material point, a window (A W ) is defined around the pixel coordinates of this point (Fig. 5). As described below, the contrast correlation technique uses the contrast distribution in this window to retrieve its location in the successive image. As long as the deformation within the window is homogeneous, the displacement of the center of the window equals the displacement of the associated material point. As shown in Fig. 5, however, the window is allowed to deform linearly between the first image A and the next image B, which suffices if the deformations in this area are small. This constraint on the deformations is met by restricting the punch displacement between successive images, which limits both the deformation and displacement of the window. Additionally, a search area B S can be defined, as a time-saving measure. This sub-set B S of image B has the size of the window A W increased by the maximum expected displacement. By storing the contrast information of an image in a matrix format, the problem can be defined in mathematical terms. In this formulation the sub-set B W,of the search area matrix B S, that is the best match of the given matrix A W has to be located. For this purpose, a correlation factor, which indicates how well two subsets match, is maximized in two steps by the following Fig. 2. Dimensions of a deformed sample (mm).

4 Y.W. Stegeman et al. / Journal of Materials Processing Technology 87 (1999) Fig. 4. Example of images recorded during the blanking process. method. In the first step, it is assumed that the window does not deform. A Fast Fourier Transformations method can be used to determine the correlation factor between sub-set A W and every possible sub-set B W of the search area B S. The sub-set B W that gives the maximum correlation factor defines the position of the window in image B and therefore the displacement of the material point between the two images at pixel level. Starting from these displacements, in the second step a Newton Raphson method of partial differential corrections is used to determine the sub-pixel displacements. To achieve this, gray levels are interpolated between pixels, for which a bicubic spline interpolation is used [16]. The mentioned iterative algorithm, which allows linear deformation of the window, is described in detail by Sutton et al. [17]. In this study, images of pixels with 256 gray levels are used, with windows and search areas of and pixels, respectively. It proved to be beneficial to smooth the images prior to the Fourier transforms by G (x, y)= 10 n 1 G(x, y)+ i, j G(x+i, y+j) i, j { 1, 0, 1} where G(x, y) and G (x, y) represent the old and new gray level values at a point with array integers (x, y). The accuracy of the measured total displacement (undeformed stage until fracture) is observed to be in the order of 0.3 pixel, corresponding to approximately 1 m (magnification 3 m per pixel). The recorded blanking experiments, using both clearances, are carried out at a velocity of 10 mm min 1, whilst images are stored every 0.04 s. The material points are chosen to form a grid, which facilitates the application of the second-order method to calculate the two-dimensional deformation gradient tensor from the displacements, developed by Geers et al. [18]. Using the right polar decomposition of this tensor, the logarithmic strain field can be determined. Due to the coarseness of the grid, the error in the strain is about 0.1 in regions of high strain gradients (near to the radii). 3. Numerical model To a first approximation, the blanking process is simulated using a two-dimensional, plane-strain model, although the authors are well aware that the deformation behavior at the surface is three dimensional. A quasi-static analysis is carried out on a model geometry that matches the experimental set-up, i.e. a 11 m die radius, a 7 m punch radius, and a clearance of 20 or 100 m. The specimen is modeled with an isotropic elasto-plastic material, using the material properties as specified in Section 2.2. The plastic material behavior is described by the Von Mises yield condition, isotropic hardening, and the Prandtl Reuss representation of the flow rule [19]. The strain-hardening behavior is entered as a table with yield stress effective plastic strain points. Strain-rate dependence is not implemented in the model. Since the problem is symmetric, only half of the specimen is modeled, as shown in Fig. 6. Along the left boundary (specimen center), the symmetry condition is prescribed. The other boundaries are either free surfaces or in interaction with a contacting body. If contact exists, friction is described by a Von Mises model with coefficient 0.1( f 0.1 / 3), in which f is the tangential stress applied and is the yield stress [19]. The punch (body 1) is in motion and penetrates the specimen, resulting in constantly changing boundary conditions. Therefore the solutions are not trivial and an advanced finite-element procedure is used to obtain the displacement fields as well as the punch load. An arbitrary Lagrange Euler (ALE) approach is used, because the punching process involves large deformations [20,21]. In this approach, the reference system is not necessarily fixed in space (Euler) or attached to the material (Lagrange). The relationships between the nodal points and the material points are subject to change, although there is always a one-to-one mapping. As in the Lagrangian formulation, surface movement and deformation-history-dependent state variables can be taken into account, whilst avoiding the numerical

5 270 Y.W. Stegeman et al. / Journal of Materials Processing Technology 87 (1999) Fig. 5. Window and search area for one of the selected material points. difficulties of element distortion. The OS-ALE method separates the calculation of material displacements and mesh adaptation. The material displacement increment is solved with the commercially available finite-element code MARC, using an updated Lagrange formulation. In order to avoid mesh distortion, the nodal points are shifted after each increment: however, the mesh topology is preserved. A discontinuous Galerkin method is used to update the state variables [14]. Since mesh distortion cannot be completely avoided, total re-meshing, which does change the topology, is carried out every five OS-ALE steps. As shown in Fig. 6, quadrilateral elements (with four nodes) are used, which become smaller as either the die or punch radius is approached. Near to the radii, the element proportions need to be of order 1 m, resulting in up to 7500 elements in the whole mesh. Except for the symmetry condition, the specimen is only subjected to forces and displacements imposed by the other bodies. On the pressure plate (body 3), modeled as a linear elastic body with a very high stiffness, a distributed load is prescribed, representing the spring forces. The punch (rigid body 1) moves with a fixed displacement of m per computational increment, whilst the die (rigid body 2) is fixed in space. The transversal movements of all bodies are confined. Convergence of the calculation is reached if the relative change in increment displacement becomes less than 1%. Fig. 6. Two dimensional, plane strain mesh for blanking. 4. Discussion of the results With the experimental technique described previously, displacement and strain fields are determined in a planar blanking process with clearances of 20 and 100 m. As is common in studies concerning blanking, the punch load penetration curve is measured also for both clearances and different velocities. In this section, all of the experimentally obtained results are described and compared with the numerical predictions Punch load penetration cur es The load penetration curves can be measured by means of both the piezo force transducer and the force transducer of the testing machine. In the latter case, the results should be corrected for the spring forces. For this purpose, experiments with the test device are carried out without a specimen. During these experiments, the force transducer of the testing machine records a (spring) force that is linear with punch displacement and independent of the velocity. Consequently, the punch load can be obtained by subtracting this spring force from the total load. At medium velocities, it was experienced that, after adjustment, both force transducers give the same punch load penetration curves, confirming that the adjustment is correct. Since the piezo crystal (normally used for high speed processes) underestimates the punch load at very low velocities, the force measured by the testing machine force transducer is used here. The velocities investigated vary between and 200 mm min 1, which is the maximum velocity of the testing machine. Only the load penetration curves at velocities of 0.1 and 100 mm min 1 are presented, but experiments at other speeds show similar results. Fig. 7 shows that the punch load increases with the velocity. A velocity increase of three decades, causes a considerable punch load increase to over 1000 N. At low velocities, the punch load reaches a minimum and becomes independent of the velocity. With clearances of 20 and 100 m, this minimum punch load is reached at a velocity of 0.02 and 0.10 mm min 1, respectively, indicating that strain rate, rather than velocity, is dominating this behavior.

6 Y.W. Stegeman et al. / Journal of Materials Processing Technology 87 (1999) 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, are compared with experimental results at the velocity of 0.02 mm min 1, since the material model is determined at such a low speed that strain rate has no influence. As shown in Fig. 8, the punch loads are slightly over-estimated by the numerical simulation, which could be caused by the constitutive model, as well as the boundary conditions. The influence of a change in clearance is well predicted. In the numerical as well as in the experimental results, an increase in clearance causes a decrease in the punch load. Experimentally, an increase in clearance is also found to cause decrease of the work done after fracture and increase of the punch penetration at maximum load Correlation technique As described in Section 2.3, digital images of the specimen surface are recorded during the blanking process. This information can be compared with the numerically-predicted contour, as is done in Fig. 9. Especially, the roll-over is of interest, since this zone is determined only by the first part of the blanking process [13] and the final product quality is partly defined by the amount of roll-over. Fig. 9 shows that the roll-over is predicted correctly by the numerical method (solid contour line). Furthermore, the recorded images enable the determination of the displacements of the material points. The material points are defined in a grid of ten rows between 0.05 and 0.5 mm from the upper side of the specimen. Each row consists of 15 points, of which the central 13 points have a mutual distance apart of 20 m. Initially, the central point of each row is situated exactly below the punch edge. In Figs. 9 12, the (maximum) punch displacement is 0.23 mm. Between the undeformed stage and this stage, 35 images are recorded. For the sake of clarity, only the displacements of the material points on three of the ten rows are given in Fig. 10. The dotted lines connect the final positions of the material points in the set-up with 20 m clearance, and the solid lines those with 100 m clearance. Initially, 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 material points in the configurations with clearances of 20 and 100 m, are marked by gray crosses and black circles, respectively. Between the left part of Fig. 10, which shows the experimentally-determined displacements, and its right part, which presents the numerically-predicted displacements, a significant difference can be noticed. In the experimental results, all material points shift, at least initially, to the left (towards the center of the punch). The numerical method, however, predicts a shift to the right (away from the punch) for almost all of the material points. This disagreement might be caused by an incorrect modeling of the boundary conditions (especially friction). Despite this pronounced difference, several features can be observed in both the experimental and the numerical results. All displacement fields show that the shear gradient increases as the punch edge is approached. The deformation zone near to the third row (middle of the specimen) is therefore

7 272 Y.W. Stegeman et al. / Journal of Materials Processing Technology 87 (1999) Fig. 8. Comparison of experimental and numerical load-penetration curves. broader than that near to the upper row. Although the experimentally-observed deformation zone is wider than that predicted numerically, this tendency is still visible. As can be expected, the deformation is shown to be more localized in the case of the smaller clearance. In this case, the material points of the lower two Fig. 9. Defined grid of material points. rows, which are located to the right of the punch edge, move more to the right than in the case of the larger clearance. It appears that the narrow clearance prevents the material in the shear zone from moving down, causing it to move away from the punch in the horizontal direction. In the numerical simulation, this behavior is also present, although less obvious, when using the larger clearance. Between each pair of successive images, the local 2D deformation gradient tensor F is calculated [18] from the relative change in position of all of the 150 points shown in Fig. 9. Once the right polar decomposition of the deformation gradient tensor (F=R U) is determined, the incremental logarithmic strain, according to: = xx xy n =R log(u) R C xy yy can be calculated. The total logarithmic strain can be obtained easily by adding the increments. With this method, the strain fields are not only determined from the experimentally-obtained displacement field, but also from the numerically-obtained displacement field, using an identical grid of 150 points. It can be questioned whether the fundamentally three-dimensional deformation in the experiment may be compared with the two-dimensional plane-strain numerical model. Therefore it is examined as to what extent the experimental deformation differs from planestrain deformation. Assuming volume invariance ( zz = xx yy ), the plane-strain condition ( zz =0) becomes xx = yy. As is demonstrated in Fig. 11, this is not really the case at the specimen surface. As expected, zz is positive beneath the punch, where the

8 Y.W. Stegeman et al. / Journal of Materials Processing Technology 87 (1999) Fig. 10. Experimentally (left) and numerically (right) obtained displacements of the material points. material is compressed in the vertical direction. The tensile stresses in the roll-over zone lead to a negative zz. The strain fields for the experimental set-up with 20 m clearance are shown. The strain fields for the set-up with 100 m clearance are comparable. It is stated that the influence of the three-dimensional effect on the equivalent strain eq = 2 3 ( 2 xx+ 2 yy +2 2 xy ) is small, since this equivalent strain consists of about 90% of shear strain. It is therefore useful to compare the experimentally- and numerically-obtained equivalent strain fields. Fig. 12 shows the equivalent logarithmic strain at a punch displacement of 0.23 mm for both of the clearances. The features observed in Fig. 10 concerning the width of the shear zone are also visible in the equivalent strain field. However, the difference between the experimental and numerical results concerning the horizontal displacements is no longer visible. 5. Concluding remarks In the present investigation, the deformation in a planar blanking process was monitored up to fracture by means of the contrast correlation technique. This method proved to be suitable for in situ observation of the blanking process. Moreover, the plane-strain numerical model used also proved to give qualitative good results, although the experimentally-observed deformation is not perfectly plane strain. A change in clearance influences the experimental and numerical techniques similarly. Nevertheless, there are still some quantitative differences observed between the experimental data and the numerical results. For instance, the predicted punch load is 500 N ( 6%) too high, while the total equivalent strain is over-predicted by 10%. However, by some standards, these results would be regarded as successful. The differences could, among others, be caused by the material model and/or the boundary conditions applied in the simulation. The material model assumes isotropy and isotropic hardening. If this is not correct, the yield stress plastic strain relationship, obtained in uniaxial deformation, will not be valid in shear. In this case, the numerical results will not be reliable, since shear is observed to be the dominating deformation mode in the blanking process. Another important aspect of the material model is the neglect of the dependence of strain rate and hydrostatic pressure. The material behavior, however, is clearly dependent on the strain rate, as illustrated in Fig. 7, and this feature should be taken into account if greater velocities are considered. Disregarding the influence of hydrostatic pressure is probably not advisable also, since these hydrostatic stresses are very high: at a punch displacement of 0.23 mm, the numerical method predicts a pressure of 500 MPa. As mentioned in Section 4.2, the boundary conditions also require more attention. Friction has been described by the Von Mises model, although this model

9 274 Y.W. Stegeman et al. / Journal of Materials Processing Technology 87 (1999) Fig. 11. Strain fields from material point displacements in an experimental set-up with a clearance of 20 m. Note the different scales.

10 Y.W. Stegeman et al. / Journal of Materials Processing Technology 87 (1999) 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 totally independent of the normal pressure. For simulation of industrial forming processes such as blanking, development of a sufficiently realistic friction model is required. In conclusion, it can be stated that the contrast correlation technique is very well suited for experimental investigation of the blanking process. The numerical plane-strain deformation proved to be an adequate first approximation of the actual deformation at the surface. For a quantitative description, however, the numerical method still requires some adjustments. In future research, the numerical and experimental method will be combined to obtain a reliable fracture model, as well as the necessary parameters, to eventually describe fracture in the blanking process. Acknowledgements We would like to thank Kees Donkers of Philips CFT for supplying the blanking apparatus. Jan Post of Philips DAP/LTM is gratefully acknowledged for supplying the material and the material model. References [1] T.M. Chang, H.W. Swift, Shearing of metal bars, J. Inst. Met. 78 (1950) [2] A.G. Atkins, Surfaces produced by guillotining, Phil. Mag. 43 (1981) [3] T.M. Chang, Shearing of metal blanks, J. Inst. Met. 78 (1951) [4] F.W. Timmerbeil, Effect of blanking edge wear on the blanking process of sheet, Werkstattstech. Maschinenbau 46 (1956) in German.

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