Research Papers

On the Parameter Identification of Polynomial Anisotropic Yield Functions

[+] Author and Article Information
Wei Tong

Department of Mechanical Engineering,
Lyle School of Engineering,
Southern Methodist University,
Dallas, TX 75275-0337
e-mail: wtong@smu.edu

Manuscript received December 30, 2014; final manuscript received December 30, 2015; published online March 8, 2016. Assoc. Editor: Brad L. Kinsey.

J. Manuf. Sci. Eng 138(7), 071002 (Mar 08, 2016) (8 pages) Paper No: MANU-14-1720; doi: 10.1115/1.4032565 History: Received December 30, 2014; Revised December 30, 2015

Nonquadratic anisotropic yield functions have been developed in recent years for many lightweight automotive sheet metals. Realization of the improved performance of these advanced anisotropic yield functions depends in part on a careful calibration of their material constants via simple mechanical tests. This paper describes a novel approach on the parameter identification of plane–stress polynomial anisotropic yield functions by recasting them in a special form in terms of two principal stresses and one loading orientation angle. Independent mechanical tests for the parameter identification can thus be classified according to the plane stress state and the in-plane loading orientation, respectively. Parameter identification options have been examined in detail for a fourth-order homogeneous polynomial anisotropic yield function using the proposed approach. Some new insights have been gained on the permissible types and the number of independent mechanical test measurements per type that are needed for fully calibrating the material constants of the fourth-order yield function. The use of equal biaxial plastic strain ratio instead of equal biaxial yield stress makes the experimental calibration of the yield function more feasible as only simple in-plane uniaxial tension and out-of-plane compression tests of sheet metal samples are required.

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Grahic Jump Location
Fig. 1

Comparison of experimental data and the fourth-order yield function with various sets of calibrated parameters on the loading orientation dependence of R-values

Grahic Jump Location
Fig. 2

Comparison of experimental data and the fourth-order yield function with various sets of calibrated parameters on the loading orientation dependence of uniaxial yield stresses

Grahic Jump Location
Fig. 3

Projections on the biaxial plane of the calibrated fourth-order yield surface Case (d) with various τxy values

Grahic Jump Location
Fig. 4

Comparison of the projections on the biaxial plane of the fourth-order yield surface for various calibrated cases with τxy = 0




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