**Authors: **Mojia Huang ChiSing Man

**Publish Date**: 2009/06/02

**Volume:** 209, **Issue:** 3-4, **Pages:** 311-323

## Abstract

Lode Z Tech Phys 3611–12 1926 introduced what we now call the Lode stress parameter μ S and the Lode plastic stretching or “strainrate” parameter μ D to verify the Lévy–Mises equation If the Lévy–Mises equation is valid the relation μ D = μ S should hold But Lode’s test results as confirmed by Taylor and Quinney Phil Trans R Soc Lond Ser A 230323–362 1931 and others show systematic deviation from the equality μ D = μ S Herein for isotropic FCC polycrystals under triaxial loading the Taylor–Bishop–Hill TBH theory is used to determine the Taylor factor overlineMq the yield deviatoric stress S and the functional dependence of the plastic stretching ratio qp on the yield deviatoric stress ratio p The function qp leads to a μ D versus μ S plot that manifests qualitatively the same deviation from the line μ D = μ S as the experimental results of Lode and others We introduce a yield function with which we can reproduce all the macroscopic predictions we derived from the TBH theory including the function qp and the relation between μ D and μ S The yield function introduced is even in the yield deviatoric stress S and is a sixth degree polynomial in the components of SThis project was supported by the Natural Science Foundation of China 10562004 10662004 by the Jiangxi Project to Nurture Academic and Technical Leaders in Targeted Areas by the Research Fund for the Doctoral Program of Higher Education 20070403003 and by the Natural Science Foundation of Jiangxi of China 2008GZW0005

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