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Title: Earing Prediction in Cup Drawing Based on Non-Associated Flow Rule

Abstract

An anisotropic constitutive model based on Non-Associated Flow Rule (Non-AFR), which incorporates plane stress yield functions (Hill's quadratic function and Yld2000-2d by Barlat et al.), was implemented to finite element codes (ABAQUS, LS-DYNA 3D) by using User Material options. By using Non-AFR, Yld2000-2d is capable of predicting more than four ears which is possible only with Yld2004 by Barlat et al. when used with an Associated Flow Rule. A short review of the Non-Associated Flow Rule was provided. Simulation of the cup drawing process for a rigid container sheet alloy using mini-die geometry was performed to show the cup height profile (earing profile) obtained from Non-AFR. The simulation results were compared with experimental earing profile data and it was shown that the simulations using Yld2000-2d and the Non-AFR led to the excellent prediction of the earing profile.

Authors:
;  [1];  [2]
  1. Alcoa Technical Center, 100 Technical Dr., Alcoa Center, PA 15069-0001 (United States)
  2. GM Research Center, Warren, MI 48090-9055 (United States)
Publication Date:
OSTI Identifier:
21061743
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 908; Journal Issue: 1; Conference: NUMIFORM 2007: 9. international conference on numerical methods in industrial forming processes, Porto (Portugal), 17-21 Jun 2007; Other Information: DOI: 10.1063/1.2740890; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 36 MATERIALS SCIENCE; A CODES; ALLOYS; ANISOTROPY; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; DRAWING; ENGINEERING; FINITE ELEMENT METHOD; L CODES; N CODES; REVIEWS; SHEETS; STRESSES; THREE-DIMENSIONAL CALCULATIONS; Y CODES

Citation Formats

Yoon, J. W., Dick, R. E., and Stoughton, T. B. Earing Prediction in Cup Drawing Based on Non-Associated Flow Rule. United States: N. p., 2007. Web. doi:10.1063/1.2740890.
Yoon, J. W., Dick, R. E., & Stoughton, T. B. Earing Prediction in Cup Drawing Based on Non-Associated Flow Rule. United States. doi:10.1063/1.2740890.
Yoon, J. W., Dick, R. E., and Stoughton, T. B. Thu . "Earing Prediction in Cup Drawing Based on Non-Associated Flow Rule". United States. doi:10.1063/1.2740890.
@article{osti_21061743,
title = {Earing Prediction in Cup Drawing Based on Non-Associated Flow Rule},
author = {Yoon, J. W. and Dick, R. E. and Stoughton, T. B.},
abstractNote = {An anisotropic constitutive model based on Non-Associated Flow Rule (Non-AFR), which incorporates plane stress yield functions (Hill's quadratic function and Yld2000-2d by Barlat et al.), was implemented to finite element codes (ABAQUS, LS-DYNA 3D) by using User Material options. By using Non-AFR, Yld2000-2d is capable of predicting more than four ears which is possible only with Yld2004 by Barlat et al. when used with an Associated Flow Rule. A short review of the Non-Associated Flow Rule was provided. Simulation of the cup drawing process for a rigid container sheet alloy using mini-die geometry was performed to show the cup height profile (earing profile) obtained from Non-AFR. The simulation results were compared with experimental earing profile data and it was shown that the simulations using Yld2000-2d and the Non-AFR led to the excellent prediction of the earing profile.},
doi = {10.1063/1.2740890},
journal = {AIP Conference Proceedings},
number = 1,
volume = 908,
place = {United States},
year = {Thu May 17 00:00:00 EDT 2007},
month = {Thu May 17 00:00:00 EDT 2007}
}
  • Planar anisotropy and cup-drawing behavior were investigated for high-strength steel sheets containing different volume fractions of martensite. Macrotexture analysis using XRD was conducted to capture the effect of crystallographic orientation on the planar anisotropy of high-strength steel sheets. A phenomenological yield function, Yld96, which accounts for the anisotropy of yield stress and r-values, was implemented into ABAQUS using the user subroutine UMAT. Cup drawing of high-strength steel sheets was simulated using the FEM code. The profiles of earing and thickness strain were compared with the experimentally measured results.
  • Sample evaporation and its effect on analytical error were studied. Several factors influencing evaporative loss have been identified and measured: environmental, instrumental, and operational factors, and the chemical and physical properties of the sample and its container. Such losses from several different types of sample cups have been measured, either chemically or gravimetrically, and compared with those calculated by using a model that allows evaporative loss from a cup of known geometry to be predicted under various environmental conditions. Some steps are discussed that may be taken to minimize evaporative loss, and an example is given to demonstrate that analyticalmore » error from this source can be decreased to a routine 1--2 percent or less by selecting a particular cup design.« less
  • In this report (prepared in collaboration with Prof. Jeong Whan Yoon, Deakin University, Melbourne, Australia) a research effort was made to develop a non associated flow rule for zirconium. Since Zr is a hexagonally close packed (hcp) material, it is impossible to describe its plastic response under arbitrary loading conditions with any associated flow rule (e.g. von Mises). As a result of strong tension compression asymmetry of the yield stress and anisotropy, zirconium displays plastic behavior that requires a more sophisticated approach. Consequently, a new general asymmetric yield function has been developed which accommodates mathematically the four directional anisotropies alongmore » 0 degrees, 45 degrees, 90 degrees, and biaxial, under tension and compression. Stress anisotropy has been completely decoupled from the r value by using non associated flow plasticity, where yield function and plastic potential have been treated separately to take care of stress and r value directionalities, respectively. This theoretical development has been verified using Zr alloys at room temperature as an example as these materials have very strong SD (Strength Differential) effect. The proposed yield function reasonably well models the evolution of yield surfaces for a zirconium clock rolled plate during in plane and through thickness compression. It has been found that this function can predict both tension and compression asymmetry mathematically without any numerical tolerance and shows the significant improvement compared to any reported functions. Finally, in the end of the report, a program of further research is outlined aimed at constructing tensorial relationships for the temperature and fluence dependent creep surfaces for Zr, Zircaloy 2, and Zircaloy 4.« less