• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.2113-2122
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• 1994

The 3-D FEM analysis for simulating the stamping operation of planar anisotropic sheet metals with arbitrarily-shaped tools is introduced. An implicit, incremental, updated Lagrangian formulation with a rigid-viscoplastic constitutive equation is employed. Contact and friction are considered through the mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of tool surfaces. The consistent full set of governing relations, comprising equilibrium equation and mesh-normal geometric constraints, is appropriately linearized. The linear triangular elements are used for depicting the formed sheet, based on membrane approximation. Barlat's non-quadratic anisotropic yield criterion(strain-rate potential) is employed, whose in-plane anisotropic properties are taken into account with anisotropic coefficients and non-quadratic function parameter. The planar anisotropic finite element formulation is tested with the numerical simulations of the stamping of an automotive hood inner panel and the drawing of a hemispherical punch. The in-plane anisotropic effects on the formability of both mild steel and aluminum alloy sheet metals are examined.

• Journal of Mechanical Science and Technology
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• v.15 no.10
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• pp.1349-1355
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• 2001

As most fractures of ductile materials in metal forming processes occurred due to the results of evolution of internal damage - void nucleation, growth and coalescence. In this paper, an approximate yield criterion for voided (porous) anisotropic ductile materials is developed. The proposed approximate yield function is based on Gurson's yield function in conjunction with the Hosford's non-quadratic anisotropic yield criterion in order to consider the characteristic of anisotropic properties of matrix material. The associated flow rules are presented and the laws governing void growth with strain are derided. Using the proposed model void growth of an anisotropic sheet under biaxial tensile loading and its effect on sheet metal formability are investigated. The yield surface of voided anisotropic sheet and void growth with strain are predicted and compared with the experimental results.

• Transactions of Materials Processing
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• v.31 no.4
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• pp.214-228
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• 2022

The yield criterion, or called yield function, plays an important role in the study of plastic working of a sheet because it governs the plastic deformation properties of the sheet during plastic forming process. In this paper, we propose a novel anisotropic yield function useful for describing the plastic behavior of various anisotropic sheets. The proposed yield function includes the anisotropic version of the second stress invariant J₂ and the third stress invariant J₃. The anisotropic yield function newly proposed in this study is as follows. F(J₂)+ αG(J₃)+ βH (J₂ × J₃) = k^m The proposed yield function well explains the anisotropic plastic behavior of various sheets by introducing the parameters α and β, and also exhibits both symmetrical and asymmetrical yield surfaces. The parameters included in the proposed model are determined through an optimization algorithm from uniaxial and biaxial experimental data under proportional loading path. In this study, the validity of the proposed anisotropic yield function was verified by comparing the yield surface shape, normalized uniaxial yield stress value, and Lankford's anisotropic coefficient R-value derived with the experimental results. Application for the proposed anisotropic yield function to aluminum sheet shows symmetrical yielding behavior and to pure titanium sheet shows asymmetric yielding behavior, it was shown that the yield curve and yield behavior of various types of sheet materials can be predicted reasonably by using the proposed new yield anisotropic function.

• Structural Engineering and Mechanics
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• v.57 no.6
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• pp.1015-1038
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• 2016

In the current research an advanced criterion with non-associated flow rule (non-AFR) for depicting the behavior of anisotropic sheet metals is presented to consider the strength differential effects (SDEs) for these materials. Owing to the fact that Lou et al. (2013) yield function is dependent on structure of an anisotropic material (BCC, FCC and HCP), an advanced yield function with inspiring of Yoon et al. (2014) yield function is proposed which is dependent upon anisotropic structures. Furthermore, to compute Lankford coefficients, a new pressure sensitive plastic potential function which would be dependent to anisotropic structure is presented and coupled with the proposed yield function with employing a non-AFR in a novel criterion which is called here 'dvanced criterion'. Totally eighteen experimental data are required to calibrate the criterion contained of directional tensile and compressive yield stresses for the yield function and directional Lankford coefficients for the plastic potential function. To verify the criterion, three anisotropic sheet metals with different structures are taken as case studies such as Al 2008-T4 (a BCC material), Al 2090-T3 (a FCC material) and AZ31 (a HCP material).

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1994.03a
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• pp.118-128
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• 1994

The planar anisotropic FEM analysis for predicting the earing profiles and draw-in amounts in the deep-drawing processes is introduced. An implicit, incremental, updated Lagrangian formulation with a rigid-viscoplastic constitutive equation is employed. Contact and friction are considered through the mesh-based unit vectors and the normal contact pressure. the consistent full set of governing relations, comprising equilibrium and geometric constraint equations, is appropriately linearized. Barlat's strain-rate potential is employed, whose in-plane anisotropic properties are taken into account with anisotropic coefficients and potential parameter. The linear triangular membrane elements are used for depicting the formed sheet. with the numerical simulations of deep drawing processes of flat-top cylindrical cup for the 2090-T3 aluminum effects on the earing behavior are examined. Earing predictions made for the 2090-T3 aluminum alloy sheet show good agreement with experiments, although some discrepancies were observed in the directional trend of cup height and thickness strains.

• Transactions of Materials Processing
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• v.7 no.3
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• pp.233-245
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• 1998

A new approach has been proposed for the incremental analysis of the nonsteady state large deformation of planar anisotropic elastic-plastic sheet forming. A mathematical brief review of a constitutive law for the incremental deformation theory has been presented from flow theory using the minimum plastic work path for elastic-plastic material. Since the material embedded coordinate system(Lagrangian quantity) is used in the proposed theory the stress integration procedure is completely objective. A new return mapping algorithm has been also developed from the general midpoint rule so as to achieve numerically large strain increment by successive control of yield function residuals. Some numerical tests for the return mapping algorithm were performed using Barlat's six component anisotropic stress potential. Performance of the proposed algorithm was shown to be good and stable for a large strain increment, For planar anisotropic sheet forming updating algorithm of planar anisotropic axes has been newly proposed. In order to show the effectiveness and validity of the present formulation earing simulation for a cylindrical cup drawing and front fender stamping analysis are performed. From the results it has been shown that the present formulation can provide a good basis for analysis for analysis of elastic-plastic sheet metal forming processes.

• Journal of Mechanical Science and Technology
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• v.15 no.2
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• pp.210-216
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• 2001

This paper presents an analytical study that can predict the path-dependent forming limit of anisotropic sheet materials that experience various combinations of strain paths. To predict the forming limit diagrams(FLD), the proposed analytical procedure is performed within the framework of the Marciniak and Kuczynski(M-K) approach by using the Barlat and Lians non-quadratic anisotropic yield criterion and introducing the effect of the existence of a strain gradient over a stretching punch. The predicted path-dependent forming limit of an anisotropic sheet has been compared with the published experimental results. It has been found that the predicted path-dependent forming limits are in good agreement with the experimental data.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1994.10a
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• pp.44-54
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• 1994

A variational formulation and the associated finite elemet equations have been derived for general three-dimensional deformation of a planar anisotropic rigid-plastic sheet metal which obeys the strain-rate potential proposed by BARLAT et al [13]. By using the natural convected coordinate system, the effect of geometric change and the rotation of planar anisotropic axes are considered efficiently. In order to check the validity of present formulation, a cylindrical cup and a square cup deep drawing test was modeled. good agreement was found between the FE simulation and the experiment. The results have shown that the present formulation for planar anisotropic deformation can be efficiently applied to the analysis of sheet metal working processes for planar anisotropic nonferrous metals.

• Transactions of Materials Processing
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• v.31 no.6
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• pp.351-364
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• 2022

The yield criterion, or called yield function, plays an important role in the study of plastic working of a sheet because it governs the plastic deformation properties of the sheet during plastic forming process. In this paper, we propose a modified version of previous anisotropic yield function (Trans. Mater. Process., 31(4) 2022, pp. 214-228) based on J2 and J3 stress invariants. The proposed anisotropic yield model has the 6th-order of stress components. The modified version of the anisotropic yield function in this study is as follows. f(J₂⁰,J₃⁰) ≡ (J₂⁰)³ + α(J₃⁰)² + β(J₂⁰)^3/2 × (J₃⁰) = k⁶ The proposed anisotropic yield function well explains the anisotropic plastic behavior of various sheets such as aluminum, high strength steel, magnesium alloy sheets etc. by introducing the parameters α and β, and also exhibits both symmetrical and asymmetrical yield surfaces. The parameters included in the proposed model are determined through an optimization algorithm from uniaxial and biaxial experimental data under proportional loading path. In this study, the validity of the proposed anisotropic yield function was verified by comparing the yield surface shape, normalized uniaxial yield stress value, and Lankford's anisotropic coefficient R-value derived with the experimental results. Application for the proposed anisotropic yield function to AA6016-T4 aluminum and DP980 sheets shows symmetrical yielding behavior and to AZ31B magnesium shows asymmetric yielding behavior, it was shown that the yield locus and yielding behavior of various types of sheet materials can be predicted reasonably by using the proposed anisotropic yield function.

• Transactions of Materials Processing
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• v.14 no.4 s.76
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• pp.392-398
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• 2005

The deterioration of dimensional accuracy, caused by springback, is one of problems to always occur In sheet metal forming processes. As the demand for lighter and stronger metals increases, the development of improved forming processes settling the springback problem becomes more important. In this work, asymmetric springback phenomena are investigated, which occur in the shallow-drawing process with the anisotropic sheet metal and axisymmetric tools. The improvement possibility of dimensional accuracies, mainly, flatness, was examined by applying segmented blank holding forces as a method for springback control.