Pressure Sensitive Nonassociative Plasticity Model for DRA Composites

[+] Author and Article Information
Xin Lei

Department of Engineering Science and Mechanics, 212 EES Building, Penn State University, University Park, PA 16802; Modine Manufacturing Company, Rancine, WI 53403-2552

Cliff J. Lissenden1

Department of Engineering Science and Mechanics, Penn State University, University Park, PA 16802lissenden@psu.edu


Corresponding author.

J. Eng. Mater. Technol 129(2), 255-264 (Sep 13, 2006) (10 pages) doi:10.1115/1.2400273 History: Received December 02, 2005; Revised September 13, 2006

Discontinuously reinforced aluminum (DRA) is currently used where design considerations include specific stiffness, tailorable coefficient of thermal expansion, or wear resistance. Plastic deformation plays a role in failures due to low cycle fatigue or simple ductile overload. DRA is known to exhibit pressure dependent yielding. Plastic deformation in metals is widely regarded to be incompressible, or very nearly so. A continuum plasticity model is developed that includes a Drucker–Prager pressure dependent yield function, plastic incompressibility via a nonassociative Prandtl–Reuss flow rule, and a generalized Armstrong–Frederick kinematic hardening law. The model is implemented using a return mapping algorithm with backward Euler integration for stability and the Newton method to determine the plastic multiplier. Material parameters are characterized from uniaxial tension and uniaxial compression experimental results. Model predictions are compared to experimental results for a nonproportional compression–shear load path. The tangent stiffness tensor is nonsymmetric because the flow rule is not associated with the yield function, which means that the commonly used algorithms that require symmetric matrices cannot be used with this material model. Model correlations with tension and compression loadings are excellent. Model predictions of shear and nonproportional compression–shear loadings are reasonably good. The nonassociative flow rule could not be validated by comparison of the plastic strain rate direction with the yield function and the flow potential due to scatter in the experimental results. The model is capable of predicting the material response obtained in the experiments, but additional validation is necessary for the condition of high hydrostatic pressure.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Cross section of extruded 6092/SiC/17.5-T6 bar

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Figure 2

Initial yield locus for 6092/SiC/17.5p-T6 based on 40×10−6m∕m offset definition (15)

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Figure 3

Flow chart for stress updating algorithm

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Figure 4

Fit of material hardening parameters to experimental data

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Figure 5

Model correlation with characterization data

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Figure 6

Model prediction compared to torsion test results

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Figure 7

Model input for three nonproportional compression–shear load cycles

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Figure 8

Comparison of model prediction (line) with experimental results (solid circles): (a) axial response; and (b) shear response

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Figure 9

Predicted yield loci (Eq. 5) for k=220MPa and a=0, 0.078, and 0.156

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Figure 10

Deviation of the direction of the plastic strain rate vector with respect to the outward normal of the yield function, f=0: (a) k=220MPa, a=0.078 used to characterize the model; and (b) k=211MPa, a=0.67 that fit the 40×10−6m∕m offset initial yield locus.

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Figure 11

Predicted and experimentally determined directions of the plastic strain rate vector with respect to the yield locus, f=0, and g=constant (k=211MPa, a=0.67).



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