Non-associated flow rule with symmetric stiffness modulus for isotropic-kinematic hardening and its application for earing in circular cup drawing

AbstractUnder a standard derivation, the stiffness modulus for the non-associated flow rule is asymmetric since its plastic potential (for the plastic strain increment under the normality rule) differs from the plastic yield stress function (to define the elastic range). A new formulation was developed in this work, which leads to the symmetric stiffness modulus for the non-associated flow rule, under the framework of the combined isotropic-kinematic hardening law for generalization purposes. As for its application, the non-quadratic Yld2000-2d (Barlat et al., 2003) function (and Hill’s (1948) function for comparison) was utilized to validate the formulation for earing in circular cup drawing of AA2090-T3 and AA5042 sheets, which successfully represented 6 and 8 ears, respectively

Modeling the plastic deformation of crystals with thin precipitates

AbstractPrecipitates, present in most commercial alloys, can have a strong influence on strength and hardening behavior of a single crystal. The effect of thin precipitates on the anisotropy of initial slip resistance and hardening behavior of crystals is modeled in this article. For the convenience of the computational derivation and implementation, the material formulation is given in the unrotated intermediate configuration mapped by the plastic part of the deformation gradient. Material descriptions for the considered two phased aggregates consisting in lattice hardening as well as isotropic hardening and kinematic hardening are suggested. The corresponding elastic–plastic rate-independent algorithmic treatment is derived and numerical simulations of various loading cases are presented to discuss and assess the performance of the suggested model and its rate-independent algorithmic treatment

PARAMETER IDENTIFICATION OF ADVANCED PLASTIC POTENTIALS AND IMPACT ON PLASTIC ANISOTROPY PREDICTION

In the work presented in this paper, several strain rate potentials are examined in order to analyze their ability to model the initial stress and strain anisotropy of several orthotropic sheet materials. Classical quadratic and more advanced non-quadratic strain rate potentials are investigated in the case of FCC and BCC polycrystals. Different identifications procedures are proposed, which are taking into account the crystallographic texture and/or a set of mechanical test data in the determination of the material parameters.International audienceIn the work presented in this paper, several strain rate potentials are examined in order to analyze their ability to model the initial stress and strain anisotropy of several orthotropic sheet materials. Classical quadratic and more advanced non-quadratic strain rate potentials are investigated in the case of FCC and BCC polycrystals. Different identifications procedures are proposed, which are taking into account the crystallographic texture and/or a set of mechanical test data in the determination of the material parameters

Parameter identification of advanced plastic potentials and impact on plastic anisotropy prediction

In the work presented in this paper, several strain rate potentials are examined in order to analyze their ability to model the initial stress and strain anisotropy of several orthotropic sheet materials. Classical quadratic and more advanced non-quadratic strain rate potentials are investigated in the case of FCC and BCC polycrystals. Different identifications procedures are proposed, which are taking into account the crystallographic texture and/or a set of mechanical test data in the determination of the material parameters

Direct design method based on ideal forming theory for hydroforming and flanging processes

Conventional practices to predict preform shapes in hydroformimg and flanging processes are based on FEM analysis and/or experiment, which require many trials. In an effort to effectively improve the design procedure by overcoming the indirect nature of the conventional design tools, a direct design method based on the ideal forming theory has been previously developed as a newly added design tool in the design procedure. Here, the direct design method based on the ideal forming theory was applied to the preform design for hydroforming and flanging operations. In order to account for anisotropy, the anisotropic strain rate potential which simultaneously accounts for the anisotropy of yield stress as well as the anisotropy of plastic strain ratio was used as a part of the constitutive equation

Ideal sheet forming with frictional constraints

The ideal forming theory, previously developed as a direct design method to guide iterative design practices based on analytic methods, does not properly account for frictional effects prevalent in real forming. A method for introducing the effects of the Coulomb friction in the ideal sheet forming theory was developed in this work by modifying the extremum work criterion. For numerical implementation, a rigid-plastic finite element method was used based on triangular membrane elements. Computational results were compared with experiments given in NUMISHEET'93 using a planar anisotropic strain rate potential proposed by Barlat et al. and the Coulomb friction model

Crash simulations considering sheet forming effects based on ideal forming theory and hybrid membrane/shell method

In order to achieve reliable but cost-effective crash simulations of stamped parts, sheet forming process effects were incorporated in simulations using the ideal forming theory mixed with the 3D hybrid membrane/shell method, while the subsequent crash simulations were carried out using a dynamic explicit finite element code. Example solutions performed for forming and crash simulations of I- and S-shaped rails verified that the proposed approach is cost-effective without sacrificing accuracy. The method required a significantly small amount of additional computation time, less than 3% for the specific examples, to incorporate sheet forming effects to crash simulations. As for the constitutive equation, the combined isotropic-kinematic hardening law and the non-quadratic anisotropic yield stress potential as well as its conjugate strain-rate potential were used to describe the anisotropy of AA6111-T4 aluminum alloy sheets

Design optimization of extruded preform for hydroforming processes based on ideal forming design theory

The conventional practice to predict preform shapes in hydroformimg processes based on finite-element analysis and/or experiment is an iterative procedure and requires many trials. In this paper, a computationally efficient direct design method, which effectively improves the design procedure, was introduced. The direct design method based on ideal forming theory, which was successfully applied for the design of flat blanks for stamping processes, was extended for the design of non-flat preform for tube hydroforming processes. A preform optimization methodology for non-flat blank solutions was proposed based on the penalty constraint method for the cross-sectional shape and length of a tube. The hybrid membrane/shell method was employed to capture thickness effect while maintaining membrane formulation in the ideal forming theory. Several classes of examples were analyzed to verify the current formulation