Research Papers

Polycrystal Plasticity Based Predictions of Strain Localization in Metal Forming

[+] Author and Article Information
Joel V. Bernier1

Engineering Technologies Division, Lawrence Livermore National Laboratory, B141 R1054, L-227, Livermore, CA 94551bernier2@llnl.gov

Nathan R. Barton

Engineering Technologies Division, Lawrence Livermore National Laboratory, B141 R1024, L-227, Livermore, CA 94551barton22@llnl.gov

Jaroslaw Knap

Materials Science and Technology Division,  Lawrence Livermore National Laboratory, B242 R1212, L-367, Livermore, CA 94551knap2@llnl.gov


Corresponding Author.

J. Eng. Mater. Technol 130(2), 021020 (Mar 27, 2008) (5 pages) doi:10.1115/1.2884331 History: Received August 20, 2007; Revised January 23, 2008; Published March 27, 2008

In this study, a multiscale material model is employed to simulate two metal forming processes: 2D plane strain compression and a 3D biaxial bulge test. A generalized Taylor-type polycrystal model is employed to describe the fine scale viscoplastic response of the material, while the coarse scale response is computed using a multiphysics finite element code. The coupling between the local responses of the textured polycrystal and the continuum level is achieved via an adaptive sampling framework, which is shown to greatly reduce the total number of fine scale evaluations required to achieve a specified error tolerance. The anisotropy represented at the fine scale is sufficient to observe strain localization in both forming processes. For the case of idealized plane strain compression, a fairly diffuse yet distinct patterning of plastic strain localization develops in a manner consistent with experimental observations. The application of friction constraints to the compression surfaces—as is present in channel die compression tests—dramatically strengthens and redistributes the localization patterns. The simulated biaxial bulge test also demonstrates strain localization that is in agreement with the locations of diffuse necks in experimental observations. The tests are conducted using a federated multiple-program multiple-data simulation, which allows for load balancing between the coarse and fine scale calculations. Such a simulation framework is capable of efficiently embedding physically robust, but computationally expensive material models in component scale simulations appropriate to design decisions.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

A schematic of MPMD parallelism showing the RMI pattern during the material model evaluation. Each box indicates a separate instance of a given executable program.

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Figure 2

Pole figures calculated from the idealized rolling texture.

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Figure 3

Effective plastic strain rates for idealized plane strain compression. (a) shows the sample after 15% engineering strain. The range of effective plastic strain rates is approximately [0.6,1.4]. The strain rate is intensified on bands inclined to the compression axis by ≈45deg. (b) shows the same sample after 33% engineering strain using the same color map as in (a). The range of values is approximately [0.02,2.9]. The bands have both intensified and multiplied (from 3 to 5) while maintaining roughly the same angle of inclination.

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Figure 4

Effective plastic strain rates for plane strain compression using contact with elastic dies and Coulomb friction on compression surfaces. (a) shows results from an isotropic material model after 15% engineering strain. The range of rates is [0.7,2.9]. (b) shows results from the Taylor FSM and ASF. The isotropic material parameters were chosen parameters chosen to match effective stress/strain curve obtained from the Taylor model. The range of rates is [0.07,8.1]. The color map is equivalent to what is used in Fig. 3.

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Figure 5

Quarter-symmetry mesh of the biaxial bulge test workpiece deformed under a pressure of 6.4MPa. The false color depicts the effective plastic strain rate. The original ODF-relative RD nominally falls in the near-side cut plane, and the strongest localization of plastic strain occurs along this cut plane.

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Figure 6

(a) shows the evolution of the minimum, mean and maximum rates of plastic strain over the interior region of the workpiece (radius⩽100mm). (b) shows the ratio of the maximum plastic strain rate to the mean value over the same region. The onset of localization occurs at a bulge pressure of ≈45MPa.




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