• Research in Mathematical Education
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• 제13권2호
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• pp.171-180
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• 2009

This study investigates relationships between 7th and 8th grade students' achievements in forming and solving equations of. Study was conducted on randomly selected 7th and 8th grade students of elementary schools in Konya City, Turkey. 145 students (99 female, 46 male) participated in the research. Data were collected by an 'Equation Test'. The test which is suitable for equation types in 7th Grade Elementary Mathematics Curriculum. It was developed by the researchers. The relationships between achievements in forming and solving equations were examined by dependent samples t-test. The t-test results show that there is a significant difference. This difference is in the favor of equation solving (p>0.05). In other word, students are more successful in equation solving. In addition, students' achievements about different types of equations were investigated. The results show that the students have the highest achievement in ax=b type and the lowest achievement in (ax+b)/c=(dx+e)/f type of equations.

• Transactions of Materials Processing
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• 제8권3호
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• pp.252-261
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• 1999

The 3-dimensional finite element program is developed to analyze the non-isothermal forming processes of aluminum-alloy sheet metals. Bishop's method is introduced to solve the heat balance and force equilibrium equations. Also, Barlat's non-quadratic anisotropic yield function depicts the planar anisotropy of the aluminum-alloy sheet. To find an appropriate constitutive equation, four different forms are reviewed. For the verification of the reliability of the developed program, the computational try-outs of the non-isothermal cylindrical cupping processes of AL5052-H32 and Al1050-H16 are carried out. As results, the constitutive equation relating to strain and strain-rate, in which the constants are represented by the 5th-degree polynomials of temperature, is in good agreement with measurement. The computational try-outs can predict optimal forming conditions in non-isothermal forming processes.

• Transactions of Materials Processing
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• 제21권7호
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• pp.403-411
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• 2012

The aim of this study was to predict the results of superplastic forming on magnesium alloy, by considering the grain growth using numerical simulations. Superplastic behavior of AZ31 alloy was investigated through a set of uniaxial tensile tests that cover the forming temperatures ranges from 375 to $450^{\circ}C$. All the material parameters in the model, which consists of a constitutive equation and a grain growth equation, were determined. The model was used in the finite element analysis for uniaxial tensile tests and superplastic blow forming, through a user-subroutine available within ABAQUS. From this study, the effect of grain growth during forming was evaluated. The results show that it is essential to include the effect of grain growth in predicting the behavior during superplastic forming of this magnesium alloy.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 한국소성가공학회 1999년도 춘계학술대회논문집
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• pp.18-21
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• 1999

In this study in order to make doubly-curved sheet metal effectively a sheet metal forming process has been developed by adopting the flexibility of the incremental forming process and the principle of bending deformation which causes slight deformation to thickness The developed process is an unconstrained forming process with no holder. For this study the experimental equipment is set up with the punch-set which consists of two pairs of lower support-punches and one upper center-punch. In the experiments using aluminum sheet it is found that the curvature of the formed sheet metal is determined by controlling the distance between supporting punches in pairs and the forming depth of the center-punch. and the edge-forming method is proposed for forming the sheet metal into the balanced shape. The equation using process variables such as the distance between supporting punches in pairs and the forming depth of the center-punch is proposed for the prediction of the radii of curvatures of the formed shape and it is corrected by the experimental results and the FEM simulation results about whether springback takes place. It is found that according o the simulation there is a certain set of the distance between a pair of supporting punches and the forming depth of the center-punch which causes a little springback. It is thus shown that the radii of curvatures of the formed sheet metal can be predicated by the corrected equation unless significant springback occurs.

• Transactions of Materials Processing
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• 제16권4호
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• pp.276-281
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• 2007

The hardening and the constitutive equation based on the crystal plasticity are introduced for the numerical simulation of hemispherical sheet metal forming. For calculating the deformation and the stress of the crystal, Taylor's model of the crystalline aggregate is employed. The hardening is evaluated by using the Taylor factor, the critical resolved shear stress of the slip system, and the sum of the crystallographic shears. During the hemispherical forming process, the texture of the sheet metal is evolved by the plastic deformation of the crystal. By calculating the Euler angles of the BCC sheet, the texture evolution of the sheet is traced during the forming process. Deformation texture of the BCC sheet is represented by using the pole figure. The comparison of the strain distribution and punch force in the hemispherical forming process between the prediction using crystal plasticity and experiment shows the verification of the crystal plasticity-based formulation and the accuracy of the hardening and constitutive equation obtained from the crystal plasticity.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 한국정밀공학회 2007년도 추계학술대회 논문집
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• pp.401-402
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• 2007

• Transactions of Materials Processing
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• 제27권6호
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• pp.331-338
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• 2018

Electrohydraulic forming (EHF) process is a high speed forming process that utilizes the electric energy discharge in fluid-filled chamber to deform a sheet material. This process is completed in a very short time of less than 1ms. Therefore, finite element analysis is essential to observe the deformation mechanism of the material in detail. In addition, to perform the numerical simulation of EHF, the material properties obtained from the high-speed status, not quasi static conditions, should be applied. In this study, to obtain the parameters in the constitutive equation of Al 6061-T6 at high strain rate condition, a surrogate model using an artificial neural network (ANN) technique was employed. Using the results of the numerical simulation with free-bulging die in LS-DYNA, the surrogate model was constructed by ANN technique. By comparing the z-displacement with respect to the x-axis position in the experiment with the z-displacement in the ANN model, the parameters for the smallest error are obtained. Finally, the acquired parameters were validated by comparing the results of the finite element analysis, the ANN model and the experiment.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 한국소성가공학회 2008년도 추계학술대회 논문집
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• pp.234-237
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• 2008

It was reported that the semi-solid forming process has many advantages over the conventional forming process, such as a long die life, good mechanical properties and energy savings. It is very important, however, to control liquid segregation to gain mechanical property improvement of materials. During forming process, Rheology material has complex characteristics, thixotropic behavior. Also, difference of velocity between solid and liquid in the semi-solid state material makes a liquid segregation and specific stress variation. Therefore, it is difficult for a numerical simulation of the rheology Process to be Performed. General Plastic or fluid dynamic analysis is not suitable for the behavior of rheology material. The behavior and stress of solid particle in the rheology material during forging process is affected by viscosity, temperature and solid fraction. In this study, compression experiments of aluminum alloy were performed under each other tool shape. In addition, the dynamics behavior compare with Okano equation to Power law model which is viscosity equation.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 한국정밀공학회 2007년도 춘계학술대회 논문집
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• pp.585-586
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• 2007

• Transactions of Materials Processing
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• 제1권1호
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• pp.95-103
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• 1992

The plane strain analysis for simulating the stretch/draw forming operation with an arbitrarily-shaped tool profile 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 linear line elements are used for depicting the formed sheet, based on membrane approximation. The FEM formulation is tested in the sections of automotive inner panel and two-side draw-in. Not only the excellent agreement between measured and computed strains is obtained in the stretched section, but also the numerical stability of formulation is verified in the draw-in section.