• 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.

• Magazine of the Korean Society of Agricultural Engineers
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• v.45 no.2
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• pp.86-95
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• 2003

During this study, constant stress ratio tests with previous compression anisotropic stress history are performed on compacted decomposed granite soil sampled at Iksan, Jeonbuk. Yielding points are determined from stress-strain curves. The shape and characteristics of compression anisotropic yield curves is examined. In addition, the measured value of yielding curve and stress-strain behavior is predicted by Yasufuku's anisotropic constitutive model based on non-associated flow rule. The main results are summarized as follows : 1) Shape of yielding curves shows almost ellipse but asymmetry with respect to stress path during previous consolidation stress. 2) Yasufuku's anisotropic constitutive model is suitable in evaluation of yielding curves on anisotropic consolidated decomposed granite soil. 3) The predicted stress-strain curve shows reasonable agreement to measured behaviours.

• Transactions of Materials Processing
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• v.20 no.8
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• pp.595-600
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• 2011

This paper investigates the effect of strain rate on the anisotropic deformation behavior of advanced high strength steel sheets. Uniaxial tensile tests were carried out on TRIP590 and DP780 steel sheets at strain rates ranging from 0.001/sec to 100/sec to determine yield stresses and r-values at various loading angles from the reference rolling direction. R-values were determined by the digital image correlation technique. Hill48 and Yld2000-2d yield functions were tested for their capability to describe the plastic deformation anisotropy of the materials. Initial yield loci were constructed using the Yld2000-2d yield function, which adequately described the anisotropic behavior of the materials. The shape of the initial yield loci was found to change with different strain rate, and the anisotropic behavior decreased with increasing strain rate.

• Nuclear Engineering and Technology
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• v.53 no.10
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• pp.3379-3397
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• 2021

In this study, a multi-physics modeling method was developed to analyze a nuclear fuel rod's thermo-mechanical behavior especially for high temperature anisotropic creep deformation during ballooning and burst occurring in Loss of Coolant Accident (LOCA). Based on transient heat transfer and nonlinear mechanical analysis, the present work newly incorporated the nuclear fuel rod's special characteristics which include gap heat transfer, temperature and burnup dependent material properties, and especially for high temperature creep with material anisotropy. The proposed method was tested through various benchmark analyses and showed good agreements with analytical solutions. From the validation study with a cladding burst experiment which postulates the LOCA scenario, it was shown that the present development could predict the ballooning and burst behaviors accurately and showed the capability to predict anisotropic creep behavior during the LOCA. Moreover, in order to verify the anisotropic creep methodology proposed in this study, the comparison between modeling and experiment was made with isotropic material assumption. It was found that the present methodology with anisotropic creep could predict ballooning and burst more accurately and showed more realistic behavior of the cladding.

• Design & Manufacturing
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• v.10 no.2
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• pp.34-38
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• 2016

In this paper, a transversely isotropic behavior of AZ31 Mg alloy produced by equal-channel angular pressing (ECAP) process was investigated through tensile test and microstructure observation. The effects of initial ECAP pass number on the anisotropic behavior and mechanical properties of the Mg alloy are evaluated after conventional direct extrusion test, which are carried out at a temperature of $200^{\circ}C$. As a result of the tensile test in three directions ($0^{\circ}$, $45^{\circ}$, and $90^{\circ}$ to the extrusion direction of the sheet) at room temperature, elongation of as-extruded AZ31 alloy(ECAP for 0 pass) showed an unusual anisotropic behavior depending on the extrusion direction although the yield strength and tensile strength are similar to the ECAPed AZ31 alloy. After ECAP for 4 passes at $200^{\circ}C$, microstructural observations of ECAPed magnesium alloy showed a significant grain refinement, which is leading to an equiaxed grain structure with average size of $2.5{\mu}m$. The microstructures of the extruded billet are observed by the use of an electron back-scattering diffraction (EBSD) technique to evaluate of the influence on the grain refinement during extrusion process and re-crystallization mechanism of AZ31 Mg alloy.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.10a
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• pp.75-78
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• 2003

In order to describe the Bauschinger and transient behavior of orthotropic fiber-reinforced composites, a combined isotropic-kinematic hardening law based on the non-linear kinematic hardening rule was considered here, in particular, based on the Chaboche type law. In this modified constitutive law, the anisotropic evolution of the back-stress was properly accounted for. Also, to represent the orthotropy of composite materials, Hill's 1948 quadratic yield function and the orthotropic elasticity constitutive equations were utilized. Furthermore, the numerical formulation to update the stresses was also developed based on the incremental deformation theory for the boundary value problems. Numerical examples confirmed that the new law based on the anisotropic evolution of the back-stress complies well with the constitutive behavior of highly anisotropic materials such as fiber-reinforced composites.

• Smart Structures and Systems
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• v.17 no.6
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• pp.1055-1065
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• 2016

An anisotropic ultrasonic transducer is proposed for Lamb wave applications, such as passive damage or impact localization based on ultrasonic guided wave theory. This transducer is made from a PMNPT single crystal, and has different piezoelectric coefficients $d_{31}$ and $d_{32}$, which are the same for the conventional piezoelectric materials, such as Lead zirconate titanate (PZT). Different piezoelectric coefficients result in directionality of guided wave generated by this transducer, in other words, it is an anisotropic ultrasonic transducer. And thus, it has different sensitivity in comparison with conventional ultrasonic transducer. The anisotropic one can provide more information related to the direction when it is used as sensors. This paper first shows its detailed properties, including analytical formulae and finite elements simulations. Then, its application is described.

• Journal of Powder Materials
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• v.29 no.4
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• pp.303-308
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• 2022

The plastic deformation behavior of additively manufactured anisotropic structures are analyzed using the finite element method (FEM). Hill's quadratic anisotropic yield function is used, and a modified return-mapping method based on dual potential is presented. The plane stress biaxial loading condition is considered to investigate the number of iterations required for the convergence of the Newton-Raphson method during plastic deformation analysis. In this study, incompressible plastic deformation is considered, and the associated flow rule is assumed. The modified return-mapping method is implemented using the ABAQUS UMAT subroutine and effective in reducing the number of iterations in the Newton-Raphson method. The anisotropic tensile behavior is computed using the 3-dimensional FEM for two tensile specimens manufactured along orthogonal additive directions.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2008.10a
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• pp.304-307
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• 2008

In order to evaluate the effect of permanent softening behavior on springback prediction, 2D-draw bending simulations were compared with experiments for friction stir welded DP590 steel sheets. To account fur the nonlinear hardening behavior, the combined isotropic-kinematic hardening law was utilized with and without considering the permanent softening behavior during reverse loading. Also, the non-quadratic orthotropic yield function, Yld2000-2d, was used to describe the anisotropic initial-yielding behavior of the base sheet while anisotropic properties of the weld zone were ignored for simplicity.