An Associated and Nonassociated Flow Rule Comparison for AISI 439-430TI Forming: Modeling and Experimental Analysis

Abstract

The plastic anisotropy behavior of ferritic stainless steel (FSS) sheets was analyzed and modeled under associated and nonassociated flow rule approaches. Three orthotropic flow functions, known as quadratic Hill48 and nonquadratic (Yld2000-2d and BBC2005), were developed and employed under an associated and nonassociated flow rule hypothesis. For the NAFR based on the initial anisotropy, the mechanical behavior was described by the nonexponential model functions of Yld2000-2d and BBC2005 to predict the directional dependence of mechanical parameters. It provided a considerable advantage in terms of flexibility and good agreement with the experiment. According to the results, the polynomial fit functions of the transverse versus longitudinal true plastic strain curve were used to describe the designated properties corresponding to a selected level of strain. To describe the evolution of anisotropic hardening and potential plastic hardening, seven different loading conditions were considered. The proposed evolutionary non-AFR Yld2000-2d and BBC2005 criteria showed good accuracy in predicting the evolution of hardening yield and Lankford coefficients depending on the plastic deformation.

Keywords:
Yield function; Anisotropic behaviour; Constitutive model; Nonassociated flow rule; Sheet metal forming; Evolution of plastic anisotropy

Graphical abstract