A Simple Analogous Model for the Determination of Cyclic Plasticity Parameters of Thin Wires to Model Wire Drawing

[+] Author and Article Information
T. Schenk1

 Netherlands Institute for Metals Research, Mekelweg 2, NL-2628 CD Delft, Netherlandstschenk@nimr.nl

T. Seifert, H. Brehm

 Fraunhofer Institute for Mechanics of Materials IWM, Wöhlerstrasse, 9-13, D-79106 Freiburg, Germany


Author to whom correspondence should be addressed.

J. Eng. Mater. Technol 129(3), 488-495 (Feb 11, 2007) (8 pages) doi:10.1115/1.2744436 History: Received July 17, 2006; Revised February 11, 2007

Cyclic stress-strain measurements have to be performed in order to determine the cyclic plasticity parameters of material models describing the Bauschinger effect. For thin wires, the performance of tensile tests is often not possible due to necking of the specimen on exceeding the yield stress, whereas compression tests are uncritical. This paper presents an approach to determine the cyclic plasticity parameters by performance of compression tests for wires before and after drawing. Here, a simple analogous model is used instead of finite-element (FE) simulations. This approach has been applied for two different integration time steps in order to evaluate their influence on the fit and the accuracy of the integration. It is shown that good accuracy can be obtained for the cyclic plasticity parameters. For FE simulations using larger integration time steps, large deviations have been noted. However, there the analogous model could also be adopted in order to find appropriate model parameters. In general, it is the intention of this paper to show that searching an analogous model can be a very time- and cost-saving task.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Experimental data of the compression tests for the virgin and the drawn wire. Experiments have been performed using the following strain rates: (F) and (S) correspond to a constant technical strain rate of 0.21s−1 and 0.044s−1 for the virgin wire and 0.27s−1 and 0.056s−1 for the drawn wire.

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Figure 2

Photograph of the experimental setup, from (9)

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Figure 3

Structural model of the drawing process. The wire is drawn from an initial diameter r1 to a smaller diameter r2. The drawing angle is given by α. Coulomb’s law of friction has been applied using a friction coefficient μ. Due to symmetry, axially symmetric, simulations have been performed.

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Figure 4

Sketch of the analogous model. The wire drawing process is approximated by a simple tension. By analogy to the real drawing process, the total strain and the strain rate are given by 0.6 and 36s−1, respectively.

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Figure 5

Fit of the experimental data using a very small integration time step. The fits agree very well with the experimental data by applying the analogous model. The deviation is about 3%.

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Figure 6

Comparison of the curves obtained after drawing using the fitted parameters in combination with the analogous model and FE simulations using small time steps. There is a deviation of about 2% between the analogous model and the FE simulations.

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Figure 7

Comparison of the curves obtained after the drawing using the fitted parameters in combination with the analogous model and FE simulations. There is a deviation of about 10–15% between the analogous model and the FE simulations.

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Figure 8

Distribution of the isotropic hardening R (denoted as SDV11, left picture) and the plastic deformation in the longitudinal direction ε22vp (SDV13, right picture)

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Figure 9

Results of the fits using the adapted analogous model with the rescaled values of (R1,α1,ε1). For reasons of clarity, only the fits of the drawn wire are shown since only these curves are affected by the analogous model.

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Figure 10

Comparison of the model curves obtained after the drawing using the fitted parameters in combination with the rescaled analogous model and FE simulations. The deviation of the model curve to the FE simulations is negligible. Hence, the rescaled analogous model is appropriate to model the experimental data.




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