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TECHNICAL PAPERS

Anisotropic Nonlinear Kinematic Hardening Rule Parameters From Reversed Proportional Axial-Torsional Cycling

[+] Author and Article Information
J. C. Moosbrugger

Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5725

J. Eng. Mater. Technol 122(1), 18-28 (Jul 14, 1999) (11 pages) doi:10.1115/1.482760 History: Received October 05, 1998; Revised July 14, 1999
Copyright © 2000 by ASME
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References

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Figures

Grahic Jump Location
Schematic illustrating expected behavior of the axial-torsional subspace hardening moduli for conformances to the anisotropic, superposed A-F kinematic hardening rules: h1 versus (s1a−s1 sgn (n1)) or d1 and h3 versus (s3a−s3 sgn (n1)) or d3. The inset indicates the ideal proportional loading response. Quantities taken from such plots for the determination of A-F rule parameters are also indicated.
Grahic Jump Location
Experimental hardening moduli curves for a proportional cycle obtained under total strain control at ea=0.0045j1+0.0039j3,|ea|=6.0(10−3): (a) full scale and (b) expanded scale at low values of h1,h3 showing the linear region used to determine cM1,cM3,ΔaM1 and ΔaM3
Grahic Jump Location
Comparison of experimental response and correlation using M=2 model with isotropic A-F rules (M=2 isotropic model) at ea=0.0045j1+0.0039j3,|ea|=6.0(10−3): (a) axial, s1 versus e1 response, (b) normalized shear, s3 versus e3 response and (c) stress subspace, s1 versus s3 response
Grahic Jump Location
Comparison of experimental hardening moduli plots and experimental correlations using M=2 model with isotropic A-F rules (M=2 isotropic model) at ea=0.0045j1+0.0039j3,|ea|=6.0(10−3): (a) full scale and (b) expanded scale at low values of h1,h3
Grahic Jump Location
Comparison of experimental response with correlations using M=2 model with anisotropic A-F rules, (M=2 anisotropic model) and M=3 modal with anisotropic A-F rules (M=3 anisotropic model) at ea=0.0045j1+0.0039j3,|ea|=6.0(10−3): (a) axial, s1 versus e1 response, (b) normalized shear, e3 versus s3 response and (c) stress subspace, s1 versus s3 response
Grahic Jump Location
Comparison of experimental hardening moduli plots and experimental correlations using M=2 model with anisotropic A-F rules (M=2 anisotropic model) and M=3 model with anisotropic A-F rules (M=3 anisotropic model) at ea=0.0045j1+0.0039j3,|ea|=6.0(10−3): (a) full scale and (b) expanded scale at low values of h1,h3
Grahic Jump Location
Experimental hardening moduli curves for a proportional cycle obtained under total strain control at ea=0.0060j1+0.0052j3,|ea|=7.9(10−3): (a) full scale and (b) expanded scale at low values of h1,h3 showing the linear region used to determine cM1,cM3,ΔaM1 and ΔaM3
Grahic Jump Location
Comparison of experimental response and correlation using M=3 model with isotropic A-F rules (M=3 isotropic model) at ea=0.0060j1+0.0052j3,|ea|=7.9(10−3): (a) axial, s1 versus e1 response, (b) normalized shear, s3 versus e3 response and (c) stress subspace, s1 versus s3 response
Grahic Jump Location
Comparison of experimental hardening moduli plots and experimental correlations using M=3 model with isotropic A-F rules (M=2 isotropic model) at ea=0.0060j1+0.0052j3,|ea|=7.9(10−3): (a) full scale and (b) expanded scale at low values of h1,h3
Grahic Jump Location
Comparison of experimental response with correlations using M=2 model with anisotropic A-F rules (M=2 anisotropic model) and M=3 model with anisotropic A-F rules (M=3 anisotropic model) at ea=0.0060j1+0.0052j3,|ea|=7.9(10−3): (a) axial, s1 versus e1 response, (b) normalized shear, s3 versus e3 response and (c) stress subspace, s1 versus s3 response
Grahic Jump Location
Comparison of experimental hardening moduli plots and experimental correlations using M=2 model with anisotropic A-F rules (M=2 anisotropic model) and M=3 model with anisotropic A-F rules (M=3 anisotropic model) at ea=0.0060j1+0.0052j3,|ea|=7.9(10−3): (a) full scale and (b) expanded scale at low values of h1,h3
Grahic Jump Location
Evolution of cM1 and cM3 with cycle number for initial 25 proportional cycles at ea=0.0060j1+0.0052j3,|ea|=7.9(10−3)
Grahic Jump Location
cM1 and cM3 versus cycle number for 25 proportional cycles at ea=0.0060j1+0.0052j3,|ea|=7.9(10−3) following 25 cycles with strain components 90 degrees out of phase

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