Jong-Bong Kim

The effect of plastic anisotropy on compressive instability in sheet metal forming

Abstract The wrinkling behavior of a thin sheet with perfect geometry is associated with compressive instability. The compressive instability is influenced by many factors such as stress state, mechanical properties of the sheet material, geometry of the body, contact conditions and plastic anisotropy. The analysis of compressive instability in a plastically deforming body is difficult considering all the factors because the effects of the factors are very complex and the instability behavior may show a wide variation for a small deviation of the factors. In this study, the bifurcation theory is introduced for the finite element analysis of puckering initiation and growth of a thin sheet with perfect geometry. All the above mentioned factors are conveniently considered by the finite-element method. The instability limit is found by the incremental analysis and the post-bifurcation behavior is analyzed by introducing the branching scheme proposed by Riks. The finite-element formulation is based on the incremental deformation theory and elastic–plastic material modeling. The finite-element analysis is carried out using the continuum-based resultant shell elements considering the anisotropy of the sheet metal. In order to investigate the effect of plastic anisotropy on the compressive instability, a square plate that is subjected to compression in one direction and tension in the other direction is analyzed by the above-mentioned finite-element analysis. The critical stress ratios above which buckling does not take place are found for various plastic anisotropic modeling methods and discussed. Finally, the effect of plastic anisotropy on the puckering behavior in the spherical cup deep drawing process is investigated. From the results of the finite-element analysis, it is shown that puckering behavior of sheet metal is largely affected by plastic anisotropy.

Investigation into wrinkling behavior in the elliptical cup deep drawing process by finite element analysis using bifurcation theory

Abstract The initiation and growth of wrinkles in sheet metal forming processes are influenced by many factors such as the stress state, the mechanical properties of the sheet material, the geometry of the body, and the contact conditions. It is difficult to analyze wrinkling initiation and growth considering these factors, because the effects of the factors are very complex and the wrinkling behavior may show a wide variation for small deviation of the factors. In this study, bifurcation theory is introduced for the finite element analysis of wrinkling initiation and growth. All the above mentioned factors are conveniently considered by the finite element method. The wrinkling initiation is determined by checking the determinant of the stiffness matrix at each iteration and the wrinkling behavior is analyzed by successive iteration with the perturbed guess along the eigenvector. The finite element formulation is based on the incremental deformation theory and elastic–plastic material modeling. The finite element analysis is carried out using continuum-based resultant shell elements. The initiation and growth of wrinkling in the elliptical cup deep drawing process are analyzed by the proposed algorithm. The effect of the aspect ratio of a punch on the wrinkling behavior in the elliptical cup deep drawing process is investigated.

A Phenomenological Constitutive Equation to Describe Various Flow Stress Behaviors of Materials in Wide Strain Rate and Temperature Regimes

A simple phenomenological constitutive model has been proposed to describe dynamic deformation behavior of various metals in wide strain rate, strain, and temperature regimes. The formulation of the model is, σ=[A +B{1-exp(-Ce)}][DIn(e/e 0 ) + exp(E·e/e 0 )][1 - (T - T ref ) / (T m - T ref ) ] m , where σ is the flow stress, e is the strain, e is the strain rate, e 0 is the reference strain rate, T is the temperature, T ref is the reference temperature, T m is the melting temperature, and A, B, C, D, E, and m are the material parameters. The proposed model successfully describes not only the linear rise of flow stress with logarithmic strain rate for many metals, but also the upturn of the flow stress at strain rate over about 10 4 s -1 for the case of copper. It can also describe the exponential increase in the flow stress with logarithmic strain rate for the case of tantalum, and is capable of predicting thermal softening of various metals at high as well as low temperature. The current model can be used for the practical simulation of many high-strain-rate events with improved precision and as a more rigorous comparison standard in the development of a physical model.

Enhanced strain of InAs quantum dots by an InGaAs ternary layer in a GaAs matrix

The present work demonstrates via numerical analysis that the presence of a thin InGaAs ternary layer around InAs quantum dots (QDs) reinforces the in-plane (err) and vertical (ezz) strain components of InAs quantum dots as compared to the QDs embedded directly in GaAs matrix, contrary to the general belief of strain relief. It has been further shown that such reinforced err and ezz states yields a decreased band-gap energy, i.e., the experimentally observed redshift in the literature.

Wrinkling initiation and growth in modified Yoshida buckling test: finite element analysis and experimental comparison

Wrinkling is one of the major defects in sheet metal products and may also play a significant role in the wear of the tool. The initiation and growth of wrinkles are influenced by many factors such as stress ratios, mechanical properties of the sheet material, geometry of the workpiece, contact condition, etc. It is difficult to analyze the wrinkling initiation and growth considering all the factors because the effects of the factors are very complex and the wrinkling behavior may show a wide scatter of data even for small deviations of factors. In this study, the bifurcation theory is introduced for the finite element analysis of wrinkling initiation and growth. All the above-mentioned factors are conveniently considered by the finite element method. The wrinkling initiation is found by checking the determinant of the stiffness matrix at each iteration and the wrinkling behavior is analyzed by successive iteration with the perturbed guess along the eigenvector. The effect of magnitude of perturbation on the wrinkling behavior can be avoided by the Newton-type iteration method. The finite element formulation is based on the incremental deformation theory and elastic-plastic material modeling. The finite element analysis is carried out using the continuum-based resultant shell elements considering the anisotropy of the sheet metal. For the verification of the analysis, the postbuckling of columns and circular plates are analyzed by finite element analysis using the bifurcation algorithm introduced in the study, and the results are compared with the exact solutions. In order to investigate the effects of geometry and stress ratio on the wrinkling initiation and growth, a modified Yoshida buckling test is proposed as an improved effective buckling test. In the modified Yoshida buckling test, the dimensions of the sheet specimen are varied to change the stress ratio and the degree of constraint. The finite element analysis is carried out for the modified Yoshida buckling test and compared with the experimental results.

Evaluation of Clamping Characteristics for Subminiature Screws According to Thread Angle Variation

Recent trends in the miniaturization and weight reduction of portable electronic parts have driven the use of subminiature screws with a micrometer-scale pitch. As both screw length and pitch decrease in subminiature screws, the resulting clamping force becomes diminishes. In this work, Finite element (FE) analysis is performed to evaluate clamping force of a screw assembly, with a comparison with experimental result. To improve clamping force of subminiature screws, a new screw design is considered by modifying screw thread angle: the thread angle is varied as an asymmetric way unlike the conventional symmetric thread angle. FE analyses are then performed to compare the clamping characteristics of each subminiature screw with different thread angle. The effect of thread angles on the clamping force is then discussed in terms of structural safety for both positive and negative screws.

Investigation of Deep Drawability and Product Qualities of Ultra Thin Beryllium Copper Sheet Metal

Abstract The present study is focused on the deep drawability and product qualities of ultra thin beryllium copper sheet metal. The goal of this research is to investigate the limit drawing ratio in deep drawing of ultra thin beryllium copper metal. For the experiment, beryllium copper(C1720, 50μm in thickness) is used. Tensile test are also carried out to find out the material properties. Deep drawing experiments are carried out in Universal Testing Machine(UTM) to obtain limit drawing ratio. Deep drawing tests are carried out for various specimen sizes. Teflon film is used as a lubricant and constant blank holding force is imposed. Sheet thickness and surface hardness are measured along radial direction after deep drawing. Thickness is measured using optical microscope. For beryllium copper(C1720), the maximum LDR of 2.4 is obtained when the die shoulder radius is 20 or 30 times of sheet thickness. Key Words : Micro Sheet, Deep Drawing, Limit Drawing Ratio 1. 서 론 최근 산업동향은 소품종 다량생산 체제에서 다품종 소량 생산체제로, 고부가가치를 창출하는 제품의 생산으로, 그리고 전통적인 생산방식에서 벗어나 초정밀 미세가공 분야까지 확대되고 있다. 또한, 정보통신, 생명공학 관련 기기는 경량화, 슬림화, 고집적화, 대용량화, 그리고 고기능화가 필수적이며, 이로 말미암은 부품의 소형화 추세가 두드러지고 있다. 마이크로 제품과 다품종 소량 생산에 대응하기 위한 성형성의 향상과 공정 단축 및 개선 할 수 있는 성형 기술의 개발이 요구되고 있는 실정이다. Han 등[1]은 마이크로 박판 소재의 물성 평가를 위한 시험 장비를 개발하였으며, Shim[2,3]은 미세 박판성형에서 블랭크 형상이 미치는 영향에 관하여 제시되었고, Lee 등[4] 은 마이크로 부품을 소성 성형하는 시스템에 대한 연구결과를 발표했다. Lee 등[5]은 일반 박판재의 드로잉 공정에서 설계변수 변화에 따른 성형품의 특성을 조사하여 발표하였고, Kang등[6]은 미세박판재의 드로잉성에 대한 기초실험연구를 하였고, Park 등[7,8]은 원형 컵 드로잉 공정의 설계에 적용 될 수 있는 프로그램을 제시하였다. Beak 등[9]은 1~3μm 두께의 금속 박판에 6~14μm의 폭을 가지는 다양한 형상의 채널성형에 대한 연구결과를 발표했다. 이렇게 마이크로 성형의 기

Investigation into hydromechanical reverse redrawing assisted by separate radial pressure : process development and theoretical verification

Abstract High-quality cups with a deep drawing ratio of more than four cannot be simply drawn by conventional drawing and redrawing. A special technology is required to form cups of a high deep drawing ratio. In the present study, after the conventional mechanical deep drawing process, subsequent hydromechanical reverse redrawing with controlled radial pressure has been developed. In order to increase the deep drawing ratio by more than four, the radial pressure is controlled independently of the chamber pressure and thus an optimum forming condition can be determined by varying the radial pressure. The process has been verified by a rigid-plastic finite element (FE) analysis considering all the external force boundary conditions induced by the hydrostatic pressure. The pressure distribution on the sheet is calculated numerically from the simplified Navier-Stokes equation. Through the experiment and the FE analysis, it has been shown that hydromechanical reverse redrawing assisted by separate radial pressure, developed in the present study, helps to increase the drawability of cylindrical cups, and thus it is useful when forming long cups.

Finite Element Analysis for Improvement of Folding Defects in the Forging Process of Subminiature Screws

1 서울과학기술대학교 기계시스템디자인공학과 (Department of Mechanical System and Design Engineering,Seoul National University of Science and Technology)2 서울과학기술대학교 기계자동차공학과 (Department of Mechanical and Automotive Engineering,Seoul National University of Science and Technology) Corresponding author: kpark@seoultech.ac.kr, Tel: +82-2-970-6358

Bifurcation Instability of sheet metal during spring-back

In automotive and home appliance industries, there are many complex-shaped sheet metal components which need to be fabricated in multiple stamping operations. For example, the manufacturing of an outer case of washing machine consists of stamping followed by a bending operation. After the first stage of the stamping process, a large amount of spring-back takes place, and therefore, it is difficult to proceed to the next stage of the bending process. In the stamping process of that kind of sheet component with low geometric constraint, the forming area is large compared to the forming depth. Therefore, the formed part is in an unstable state and is less geometrically constrained, which causes a large amount of spring-back. To investigate this phenomenon, finite element analyses are carried out. During a spring-back analysis after forming, bifurcation takes place and the finite element solution procedure using the Newton–Raphson scheme becomes unstable. To get a stable post-bifurcation solution, a bifurcation algorithm is introduced at the bifurcation point. The deformed shapes obtained from finite element analyses are in good agreement with the experimental data. From this study, it is shown that the bifurcation behaviour enlarges the spring-back and the degree of dimensional error. To obtain additional possible post-bifurcation solutions, non-bifurcation analyses using initial guesses obtained in a modal analysis are carried. For the initial guesses, lowed four eigenmodes are utilized. Finally, the post-bifurcation behaviour and spring-back amount are investigated for various process parameters including the forming depth, punch width and corner radius.