• 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.

• 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 the Korean Society of Mechanical Engineers A
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• v.22 no.2
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• pp.444-450
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• 1998

In the present investigation, it is attempted to derive a yield function and associated flow rules of loose metal powders to predict plastic deformation and density change during compaction. The loose metal powders yield by shear stress as well as hydrostatic stress and the yield strength is much smaller in tension than compression. Therefore, a yield function for the powders is expressed as a shifted ellipse toward the negative direction in the hydrostatic stress axis in the space defined by the two stresses. Each of parameters A, B and .delta. used in the yield function is expressed as a function of relative density and it is determined by uniaxial strain and hydrostatic compressions using Cu powder. Flow rules obtained by imposing the normality rule to the yield function are applied to the analyses of unidirectional, bidirectional and hydrostatic compressions, resulting in an excellent agreement with experiments. The yield function is further examined by checking volume changes in plane stain, uniaxial strain and shear deformations.

• 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).

• Transactions of the Korean Society of Automotive Engineers
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• v.18 no.2
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• pp.56-60
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• 2010

Since the forming process involves the strain rate effect, a yield function considering the strain rate is indispensible to predict the accurate final blank shape in the forming simulation. One of the most widely used in the forming analysis is the Hill48 quadratic yield function due to its simplicity and low computing cost. In this paper, static and dynamic uni-axial tensile tests according to the loading direction have been carried out in order to measure the yield stress and the r-value. Based on the measured results, the Hill48 yield loci have been constructed, and their performance to describe the plastic anisotropy has been quantitatively evaluated. The Hill48 quadratic yield function has been modified using convex combination in order to achieve accurate approximation of anisotropy at the rolling and transverse direction.

• Journal of the Korean Institute of Telematics and Electronics
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• v.22 no.5
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• pp.102-109
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• 1985

A new yield maximization procedure by investigating method of the multidimensional Monte Carlo integration is presented. And then maximum yield is obtained by the new modified weight selection algorithm applied to objective function of MOSFET NAND GATE Also this yield maximization procedure can be applied to nonconvex objective function.

• Structural Engineering and Mechanics
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• v.58 no.4
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• pp.677-687
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• 2016

On the basis of the energy approach it is reported a development of the yield function and the constitutive equations for the orthotropic material with consideration of the crystal lattice constants and parameters of the crystallographic texture for the general stress state. For practical use in sheet metal forming analysis it is considered different loading scenarios: plane stress and plane strain states. Using the proposed yield function, the influence of single ideal components on the shape of yield surface was analyzed. The six texture components investigated here were cube, Goss, copper, brass, S and rotated cube, as these components are typically observed in rolled sheets from FCC alloys.

• Structural Engineering and Mechanics
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• v.6 no.4
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• pp.395-409
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• 1998

This paper concerns the development and implementation of an orthotropic, stress resultant elasto-plastic finite element model for the collapse load analysis of reinforced concrete plates. The model implements yield line plasticity theory for reinforced concrete. The behaviour of the yield functions are studied, and modifications introduced to ensure a robust finite element model of cases involving bending and twisting stress resultants ($M_x$, $M_y$, $M_{xy}$). Onset of plasticity is always governed by the general yield-line-model (YLM), but in some cases a switch to the stress resultant form of the von Mises function is used to ensure the proper evolution of plastic strains. Case studies are presented, involving isotropic and orthotropic plates, to assess the behaviour of the yield line approach. The YLM function is shown to perform extremely well, in predicting both the collapse loads and failure mechanisms.

• Journal of the Korean Society of Environmental Restoration Technology
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• v.10 no.1
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• pp.36-43
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• 2007

This study was carried out to know how erosion control function of forests varies as forests develop in watersheds. The erosion control function among the forest welfare functions can be estimated by comparing sediment yield in stocked with non-stocked area. Sediment yield of reservoirs in stocked area were collected from farmland improvement associations. The sediment yields in non-stocked area were using USLE (Universal Soil Loss Equation) in the same reservoirs. Forests' erosion control function estimated by differences of the sediment yield between stocked and non-stocked area was static model because of no consideration on forest aging. Dynamic model was developed to consider a forest stand age. The model comprises the relationship between average forest age in watershed and sediment yield. The amount of sediment yield was different depending mother rocks. It decreased exponentially according to the forest's grow up. In case of igneous rock, the volume of sediment yield $Y_{ig}=1.4431e\;^{0.023x}$(x=average forest age), metamorphic rock $Y_{me}=4.7115e\;^{0.0694x}$, and sedimentary rock $Y_{se}=1.2808e\;^{0.028x}$.

• Environmental and Resource Economics Review
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• v.9 no.4
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• pp.641-661
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• 2000

The study examines the relation between yield insurance and nitrogen fertilizer in Korea. Since the yield insurance has never been introduced in Korea, the simulation method developed by Babcock & Hennessy is used to see the effect. From the simulation, we obtained the following results: (1) When a farmer is assumed to have a risk-neutral utility function, the yield insurance reduces nitrogen fertilizer by 19.74% (2) When a farmer is assumed to have a risk-averse utility function, the yield insurance reduces nitrogen fertilizer by 24.53%.