Keywords: shearing, blanking, sheet metal, finite element method, element elimination method.

Shearing processes such as blanking, piercing, notching, trimming etc. are extensively used in industry. It is a highly non-linear process and involves complex mechanisms such as crack initiation and propagation, and deliberate fracture of the material for obtaining the desired geometry. In industry, the traditional trial-and-error method, which is costly and time-consuming, is commonly used during design of shearing process and necessary dies. The finite element method (FEM), as an alternative tool, can be used for these purposes.

The parameters that are affecting the blanking process, such as tool clearance, friction, sheet thickness, punch-die size, and blanking layout on the sheet are analysed by using the FEM [1,2]. Many commercial FEA programs contain crack initiation and propagation simulation options, which may be used in cutting and shearing simulations. However, these procedures are complicated and not effective and most packages do not provide ready-to-use shearing analysis procedures.

Workability depends on the local conditions of stress, strain, strain rate, temperature and also on material factors, such as the resistance of a metal to failure. However, the desired material failure occurs during shearing sheet metals. Shear strain energy, effective plastic strain, Freudenthal, Cockroft-Latham, Brozzo and Oyane are the alternative failure criteria [3]. These criteria can be utilized to determine the material failure by using different techniques such as element elimination and node separation methods [4].

A commercial FEA package, MARC [5] is used in this study. An elastic-plastic updated Lagrangian approach is applied. To model material failure during the shearing process, a subroutine has been developed and integrated with the MARC software [6]. This subroutine predicts failure by using the shear strain energy density or effective plastic strain failure criteria and applies the element elimination method. The maximum stress and strain values, which are determined from simple tension test of the workpiece material, are input to the program [6]. One of the failure criteria is selected during the analysis. The main software MARC computes stress and strain values at integration points of each element. These values are compared with the maximum stress or the maximum strain value depending on the selected failure criterion in the particular subroutine. If the failure criterion is satisfied, the current element is eliminated from the mesh. The eliminated element does not contribute to the stiffness matrix and internal force calculation. When all the elements along a shear surface have been eliminated, the modelling of the shearing process is successfully completed.

As a case study, blanking of a circular workpiece with a diameter of 40 mm from a sheet metal with a thickness of 2 mm, has been analysed by using the MARC software together with the developed subroutine. The material is deep drawing quality steel with an elastic modulus of 210 GPa, a yield strength of 400 MPa, ultimate strength of 640 MPa and the Poisson's ratio of 0.3. The stress-strain relation for the material is given as . The coefficient of friction is taken as 0.2 for all contacting surfaces.

The workpiece is modelled using axisymmetric finite elements with four nodes in the analysis. Each element contains four integration points. The die and the punch are assumed to be rigid during the study. A finer mesh is used around the shear region. Equivalent von Mises stress and total equivalent plastic strain values at different punch displacements have been obtained. The rupture has been detected and displayed. The punch force variation with respect to punch displacement has also been analysed.

The finite element simulation of shearing process has been successfully achieved by using the element elimination method. A numerical example is given for blanking process and satisfactory results have been obtained. It can be concluded that the same approach can be applied to other shearing processes.

1

S.K. Maiti, A.A. Ambekar, U.P. Singh, P.P. Date, K. Narasimhan, "Assessment of Influence of Some Process Parameters on Sheet Metal Blanking", Journal of Materials Processing Technology, 102, 249-256, 2000. doi:10.1016/S0924-0136(99)00486-0

2

W. Thomas, T. Oenoki, T. Altan, "Process Simulation in Stamping - Recent Applications for Product and Process Design", Journal of Materials Processing Technology, 98, 232-243, 2000. doi:10.1016/S0924-0136(99)00204-6

3

S.E. Clift, P. Hartley, C.E.N. Sturgess, G.W. Rowe, "Fracture Prediction in Plastic Deformation Processes", International Journal of Mechanical Sciences, Vol.32, 1-17, 1990. doi:10.1016/0020-7403(90)90148-C

4

K. Komori, "Simulation of Shearing by Node Separation Method", Computers and Structures, 79, 197-207, 2001. doi:10.1016/S0045-7949(00)00118-8

5

MARC User's Guide, Volume A-Theory and User Information, MARC Analysis Research Corporation, 1996.

6

S. Isbir, "Finite Element Analysis of Trimming Process", M. Sc. Thesis, Department of Mechanical Engineering, Middle East Technical University, Ankara, Turkey, 2002.

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