Analytical description of an asymmetric yield function (Yoon2014) by considering anisotropic hardening under non-associated flow rule

2021 ◽  
pp. 102978
Author(s):  
Qi Hu ◽  
Jeong Whan Yoon
Keyword(s):  
Analytical Description ◽  
Yield Function ◽  
Flow Rule ◽  
Anisotropic Hardening ◽  
Associated Flow Rule

A non-quadratic pressure-sensitive constitutive model under non-associated flow rule with anisotropic hardening: Modeling and validation

2020 ◽  
Vol 135 ◽  
pp. 102808 ◽  
Author(s):  
Yong Hou ◽  
Junying Min ◽  
Thomas B. Stoughton ◽  
Jianping Lin ◽  
John E. Carsley ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Flow Rule ◽  
Anisotropic Hardening ◽  
Pressure Sensitive ◽  
Associated Flow Rule

An Anisotropic Hardening Rule With Non-Associated Flow Rule for Pressure-Sensitive Materials

2009 ◽  
Author(s):  
K. S. Choi ◽  
J. Pan
Keyword(s):  
Cyclic Loading ◽  
Plastic Strain ◽  
Hysteresis Loops ◽  
Flow Rule ◽  
Loading Conditions ◽  
Anisotropic Hardening ◽  
Strength Differential ◽  
Hardening Rule ◽  
Pressure Sensitive ◽  
Associated Flow Rule

In this paper, cyclic plastic behaviors of pressure-sensitive materials based on an anisotropic hardening rule with two non-associated flow rules are examined. The Drucker-Prager pressure-sensitive yield function and the Mises plastic potential function are adopted to explore the cyclic plastic behaviors of pressure-sensitive materials or strength-differential materials. The constitutive relations are formulated for the initial loading and unloading/reloading processes based on the anisotropic hardening rule of Choi and Pan [1]. Non-associated flow rules are employed to derive closed-form stress-plastic strain relations under uniaxial cyclic loading conditions. The stress-plastic strain curves based on a conventional non-associated flow rule do not close, and show a significant ratcheting under uniaxial cyclic loading conditions. A new non-conventional non-associated flow rule is then formulated based on observed nearly closed hysteresis loops of pressure-sensitive materials. The stress-plastic strain curves based on the non-conventional non-associated flow rule show closed hysteresis loops under uniaxial cyclic loading conditions. The results indicate that the anisotropic hardening rule with the non-conventional non-associated flow rule describes well the strength-differential effect and the asymmetric closed hysteresis loops as observed in the uniaxial cyclic loading tests of pressure-sensitive materials.

Prediction of Central Bursting in Drawing and Extrusion of Metals

2004 ◽  
Vol 127 (3) ◽  
pp. 698-702 ◽  
Author(s):  
A. R. Ragab ◽  
S. N. Samy ◽  
Ch. A. R. Saleh
Keyword(s):  
Volume Fraction ◽  
Yield Function ◽  
Void Volume Fraction ◽  
Void Volume ◽  
Process Conditions ◽  
Flow Rule ◽  
Mean Stress ◽  
Band Formation ◽  
Void Shape ◽  
Associated Flow Rule

In this work central bursting in drawing and extrusion of metals is investigated. The analysis is based on a modified stress distribution within the die zone due to Shield (Shield, R. T., 1955, J. Mech. Phys. Solids, 3, pp. 246–258) together with Gurson–Tvergaard’s yield function (Tvergaard, V., 1981, Int. J. Fract., 17, pp. 389–407) and its associated flow rule for voided solids. The effects of hardening and evolution of void shape on void growth are considered. Various fracture criteria are employed to predict the process conditions at which central bursting occurs. The first criterion is due to Avitzur (Avitzur, B., 1968, ASME J. Eng. Ind., 90, pp. 79–91 and Avitzur, B., and Choi, J. C., 1986, ASME J. Eng. Ind., 108, pp. 317–321), the second and simplest criterion is based on vanishing mean stress while a suggested third criterion depends on the current value of the void volume fraction. Two other criteria which are basically due to Thomason’s internal necking condition (Thomason, P. F., 1990, Ductile Fracture of Metals, Pergamon, Oxford) as well as McClintock’s shear band formation criterion are applied (McClintock, F. A., Kaplan, S. M., and Berg, C. S., 1966, Int. J. Fract. Mech., 2, p. 614, and McClintock, F. A., 1968, in Ductility, ASM, Metals, Park, OH). The critical process conditions are predicted and compared with the available experimental data. Comparison showed that predictions based on the vanishing mean stress and the current void volume fraction criteria are closer to experiments than those based on Thomason’s internal necking and McClintock criteria.

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