Seung Chul Baik

Analysis of the deformation of a perforated sheet under uniaxial tension

Abstract Two-dimensional (2D) and three-dimensional (3D) finite-element methods (FEM) have been used to analyse the deformation behaviour of a perforated sheet during uniaxial tension. The 2D results analysed under plane stress and plane strain have been compared with the results of 3D analysis. As the thickness and the diameter of holes increase, the deformation behaviour at the yield point becomes closer to plane strain. A shadow mask was used for the tensile test of the perforated sheet, the shadow mask containing holes the size of which varied across the thickness. Because the apparent plastic contraction ratio of the perforated sheets was dependent on hole size, the tensile specimens of the shadow mask suffered bending when subjected to unaxial tension. The calculated radii of curvature of the bent specimens as a function of strain were found to be in good agreement with measured data.

Forming limit diagram of perforated sheet

The proper design and manufacture of tube sheets in heat exchangers and shadow masks in color picture tubes require the characterization of the deformation behavior of perforated sheets containing a large number of holes. The limit or failure strains in sheet metal forming are best represented by a forming limit curve (FLC) which indicates the onset of necking over all possible combinations of strains in the plane. A number of theoretical treatments have been developed to predict the FLC of continuum materials. However, there are few reports on the experimental and theoretical studies on FLC for a perforated sheet. The purpose of this paper is to propose a model which can explain the FLC of a perforated sheet for dot-type shadow mask.

Plastic behaviour of perforated sheets under biaxial stress state

A yield criterion of sheets with a uniform triangular pattern of round holes under biaxial loading has been proposed in terms of apparent stresses. The yield criterion was confirmed by finite element analysis results in the whole range of ligament efficiency of the perforated sheet. In order to analyse stretching of a perforated sheet for dot-type shadow mask by the finite element method, a yield function which can incorporate the apparent yield stress and the apparent plastic contraction ratio has been obtained. The agreement between the measured and calculated results of stretch forming of the perforated sheet was satisfactory.

Plastic behaviour of perforated sheets with slot-type holes under biaxial stress state

A yield criterion of sheets with slot-type holes under biaxial loading has been proposed in terms of apparent stresses. The yield criterion was confirmed by finite-element analysis results. In order to analyse stretching of a perforated sheet for slot-type shadow mask by finite-element method, a yield function which can incorporate the apparent yield stress and the apparent plastic contraction ratio has been obtained. The agreement between the measured and calculated results of stretch forming of the perforated sheet was satisfactory.

Analysis of heat transfer in hot rolled coils for optimum condition of forced cooling

A new equation was proposed to investigate the heat transfer in the hot rolled coils by taking account of the variation of contact between coiled layers. The proposed equation was represented by the equivalent radial thermal conductivity as a function of radial normal pressure. It was found that the analytical results were in good agreement with the experimental data. The cooling times of the hot rolled coils of various dimensions cooled by air or water have been calculated by using the proposed equation. It was shown by finite element analyses that the cooling time was decreased from 32–53 hours to 6–13 hours for spray water cooling.

Effects of centerline macrosegregation on necking of P-added extra low carbon steel sheet

Effects of centerline macrosegregation on necking was examined by the stretching experiment for cold rolled P-added extra low carbon steel sheets. The centerline macrosegregated zone containing high concentration of Mn and P was elongated in the rolling process. The elongated macrosegregated zone induced instability in the strain state when the sheet was stretched, thus resulted in the waved sheet surface. The formability of cold rolled steel sheet was deteriorated due to the wave formed by the macrosegregation. The waved surface was thought to be caused by the higher hardness in the macrosegregated zone compared to the segregation free zone. The experiments on the stretching of sheet including macrosegregation showed that the macrosegregation was the important source of instability in that of the cold rolled steel sheets. A 3D FEM analysis was carried out for the quantitative evaluation of waved surface. It was confirmed that the main source of the waved surface was the macrosegregation. Stretching in the transverse direction under the plane strain condition made the cold rolled steel sheet more inhomogeneous than stretching in any other strain condition. The thickness difference in the stretched sheet was linearly increased when the ratio of hardness in the macrosegregated zone to that of the segregation free zone was increased. The macrosegregation formed in the internal crack close to the surface was more harmful to the formability in the cold rolled steel sheet than the centerline macrosegregation.