Papers in JOURNAL OF THE JAPAN SOCIETY FOR TECHNOLOGY OF PLASTICITY
(vol.43 no.502 November 2002)
An Approximation Model of Contact State between Roll and Strand
-- Computation of Three-Dimensional Deformation Behavior of
Continuously Cast Steel Strand in Multiroll Spans 1 --
Shiro TOYOSHIMA， Manabu GOTOH and Kiminori NAKAYAMA
(Received on March 21, 2001)
Continuously cast strands can be deformed during solidification by thermal stresses, ferrostatic pressure due to molten metal, mechanical interaction with the rolls, bending, unbending, and roll misalignment. When the deformation becomes large, various internal cracks appear at the solidification front. In order to investigate the cause of the internal cracks, the strain rates and the strains at any position of the strand should be evaluated as accurately as possible, and therefore three-dimensional deformation analysis is required. In this paper, a computational method to analyze the three-dimensional deformation behavior of continuously cast steel strands in the steady state in multiroll spans is proposed. Two approximations for the contact state between the cast strand and the support roll are introduced using penalty functions, that is, (a)the strand passes through only the roll gap and (b)the inner product of the strand velocity and the normal vector on the roll surface at the roll gap point is zero. A computational method for the two approximations and an example of the three-dimensional deformation behavior of a slab at an unbending zone are shown.
Key words : continuous casting, internal cracks, bulging, misalignment, multiroll spans, contact model, penalty functions, three-dimensional analysis, FEM
Prediction of Bulging by Approximation Model of Contact State between Roll and Strand
-- Computation of Three-Dimensional Deformation Behavior of Continuously Cast Steel Strand in Multiroll Spans 2 --
Shiro TOYOSHIMA，Manabu GOTOH and Kiminori NAKAYAMA
(Received on March 21, 2001)
In our previous paper, a computational method to analyze three-dimensional deformation behavior of continuously cast steel strands in the steady state in multiroll spans has been proposed, where two approximations for the contact state between the cast strand and the support rolls have been introduced by penalty functions, that is, (a) the strand passes through only the roll gap and (b) the inner product of the strand velocity and the normal vector on the roll surface at the roll gap point is zero. In this paper, the bulging deflections of a slab in a single roll-span and multiroll (4 and 8) spans are considered as computational examples for examining (i) the validity of the proposed approximations and (ii) the influence of the penalty value, Kn, in approximation (b) on the bulging deflections. The comparison of the computed results with the experimental results by Wuennenberg confirms the validity of approximation (a). From the computational results, it is found that the approximation (b) is valid for a short roll span (the length of the roll span, L, is less than 430mm) and Kn>9.8x106Nmm-1s.
Key words : continuous casting, bulging, multiroll spans, three-dimensional analysis, contact model, penalty function, FEM
Method of Calculating Load and Torque in the Rolling of Lumber Using the Stress-Strain Curve Obtained by Uniaxial Compression
-- Studies on the Rolling of Wood 2 --
Keisuke YAMAGUCHI, Hiroyuki SHIOZAKI,
Tadahiro KAWASE and Tadao MUROTA
(Received on October 25, 2001)
A method of calculating load and torque in the rolling of lumber is presented and evaluated by comparison between experimental rolling data and calculated results. In this method, it is assumed that the stress-strain curve of lumber in the roll gap is coincident with that of uniaxial compression by flat dies, the stroke of which exhibits the same motion as that of the roll gap. The results of the comparison between calculated and experimental data show that the calculated load is 5% smaller than the experimental value, and the calculated torque is 25% smaller. It is also verified by experiments that no friction hill was generated in the compression of lumber plates. In conclusion, this method is applicable for the estimation of load and torque in the rolling of lumber.
Key words : rolling, lumber, rolling force, rolling torque, uniaxial compression, friction hill
Evaluation of Springback Analysis Accuracy for Stretch-Bending Simulation Using Four-Node Shell Element
-- Springback Simulation Using the Static Explicit FEM Code,
Using a New Algorithm for Canceling Nonequilibrated Forces 2 --
Naoto YAMAMURA, Toshihiko KUWABARA,
Akitake MAKINOUCHI and Cristian TEODOSIU
(Received on January 7, 2002)
In the previous study［Yamamura et al.:Proc. 7th Int. Conf. NUMIFORM 2001, (2001), 699‐704］, we developed a novel algorithm for canceling nonequilibrated forces between external and internal forces at each node of the static explicit finite element model, and were successful in improving the accuracy of springback analysis in the pure bending problem. In this study, we applied the algorithm to stretch-bending simulations. The results obtained in this study are as follows. 1）In order to predict the springback accurately, we have to reduce the global nonequilibrated moment after the bending process such that it be as small as possible.
2）The nodal nonequilibrium between the external and internal forces and the global nonequilibrated moment are reduced to almost zero by applying the algorithm, and consequently, 3）the results of the finite element analysis of springback are in complete agreement with the analytical solutions based on the elastic-plastic incremental strain theory, when fifteen integration points are taken through the thickness of the sheet.
Key words : finite element method, sheet metal, bending, static explicit FEM, elastoplasticity, nonequilibrated force, springback
Deformation Behavior of Al-Si-Fe Alloy Powder during Powder Forging Process
Toshikatsu KOIKE, Hiroshi YAMAGATA and Naoyuki KANETAKE
(Received on January 7, 2002)
To obtain a homogeneous billet of Al-Si-Fe alloy powder by powder forging, the initiation of macro- and microdefects and the deformation behavior of powder particles in the forged specimens were investigated and discussed the results of tensile tests. The alloy powder was cold-compacted and subsequently forged to the billet through one-step and two-step forging at 793K. In order to obtain a strength equivalent to that of the extruded bar, powder particles in the forged billet were required to be deformed unti1 the aspect ratio more than 4~5 without initiation of macro- and microdefects. Two-step forging (compressive strain, Epsilon=1.3) enabled the powder particles to be deformed until the aspect ratio more than 5~6 in all regions of the billet. The two-step forging after the first-step strain of 0.5 successfuly resulted in the compressive strain of 1.3 without any defects and an almost uniformly deformed billet that had the same strength as the extruded bar.
Key words : forging, powder forming, Al-Si-Fe alloy, aspect ratio, consolidation, extrusion, tension test
Tensile Properties and Press Formability of a Mg-9Li-1Y Alloy Sheet
Hirohiko TAKUDA, Shiomi KIKUCHI,
Noriyuki YOSHIDA and Haruo OKAHARA
(Received on January 21, 2002)
The formability of an experimentally produced Mg-9mass%Li-1mass%Y alloy sheet with a thickness of 0.6mm is investigated. Uniaxial tension tests and some fundamental press-forming tests, such as stretching, deep drawing and bore expanding, are carried out at room temperature. The sheet has sufficiently high ductility. However, ductility decreases with the increase in strain rate. Even at room temperature, the stress is also sensitive to the strain rate. The stress and the work-hardening rate increase with the strain rate. The strain rate sensitivity affects the formability of the alloy sheet in press forming. The critical punch stroke in the stretching test decreases with the increase in punch speed. However, the limiting drawing ratio increases with the punch speed due to the increase in work-hardening rate. The Erichsen value is estimated to be 8~9mm, and the limiting drawing ratio is 2.15. It may be concluded that the sheet has sufficiently high formability.
Key words : sheet metal forming, tension test, non-ferrous metal (Mg-9Li-1Y), material property, forming limit
Theoretical Solution for Allowable Minimum Wrap Angle of Strip Coil
to Avoid Loosening against Expansion Force from Mandrel
Keiji MIZUTA and Tadashi NAKAGAWA
(Received on January 10, 2002)
The critical wrap angle required to avoid loosening of the wrapped strip during coiling without support (wrapper or unit) rolls is solved theoretically by considering the backward tension and the friction force between the mandrel and each wrapped coil layer. The moment just after separation of support rolls form the coil is analyzed. Balance equations for both radial and tangential force on each wrapped layer are derived and solved for tension and contact pressure from the coil end to the strip head in tangential direction. From the results, the allowable minimum wrap angle is determined using known mandrel expansion force, friction coefficient and backward strip tension.
Key words : bending, basic theory, forming limit, friction, process design, coiler, mandrel, strip
Effect of Forming Conditions on Cross-Sectional Shapes of Corners of Square Steel Pipes Formed by Draw Bench Method
Xin GUAN, Yoshitomi ONODA, Eiji WAKAMATSU,
Sadao KIMURA and Takeo KITAWAKI
(Received on January 25, 2002)
The deformation features of round welded steel pipes undergoing reshaping into square shapes by the draw bench method are discussed with reference to the results of experiments and calculations by the rigid-plastic finite element method. Calculated results were consistent with experimental data. In terms of the cross-sectional shape, the deformation features resulting from the draw bench method were similar to those resulting from extroll-forming. It was found that the longitudinal strain of the product formed by the draw bench method was larger than that of the product formed by extroll-forming. The increase rate of wall thickness
(ln(t/t0), t:wall thickness, t0:initial wall thickness) at the corners was slightly smaller, and the relative radius of external curvature (rhoO/t0, rhoO : radius of external curvature) and the relative radius of internal curvature
(rhoI/t0, rhoI:radius of internal curvature) were slightly larger for the draw bench method than for extroll-forming.
Key words : sheet metal forming, cold die forging, rigid-plastic FEM, deformation-load property, spur gear
Design of a Die Bending to the Variation of Product Size and Strength of Material
-- Research on Box-Shaped Reinforced Bumper Made of High-Strength Steel Sheet 2 --
Motoo ASAKAWA, Isao KUWAYAMA, Takayuki HAMA,
Hiroyuki HOSODA,
Yoshio FUJISHIRO and Ikuhiko HAYASHI
(Received on January 29, 2002)
The forming processes of box-shaped cross-section products by die bending using a high-strength 1180MPa steel sheet were studied. In a previous paper, the optimum shape of a die was determined. This paper describes the formability on the occasion of varying the product size and the strength of material. As for varying the product size, the forming processes using the newly developed dies were analyzed by FEM and it was found that the target shape could be obtained by simply changing the die dimensions of width and height. As for varying the strength of material, it was clarified that the influence of the U-bending processes direction on the final shape of the product was negligible and approximately identical shapes were obtained by changing the punch travels in the C-bending process. Furthermore, it was shown that the energy absorption of the novel product was superior to that of conventional one.
Key words : sheet metal forming, high-strength steel plate, spring back, multistage die bending, box-shaped cross section, most suitable die
Fabrication of Titanium-Based Composites with Intermetallics Using Shock-Induced Reaction for Mixed Element Powders
Jung-Suk LEE, Kazuyuki HOKAMOTO,
Shigeru ITOH and Masahiro FUJITA
(Received on February 25, 2002)
The process of shock-induced reaction for a mixture of element powders is investigated using underwater shock wave assembly. The critical condition for the reaction of Ti and Si powder mixture to synthesize Ti5Si3, which has a high melting temperature (2403K), is clearly suggested, but the recovered sample shows many pores due to excessive reaction heat. To improve the conditions for recovery, nonreactive powder is admixed with the mixture of Ti and Si, and the nonreactive powder is effective in releasing the excessive heat of reaction. Some composites such as Ti5Si3/Ti and Ti5Si3/TiAl are fabricated and show a good microstructure without defects.
Key words : high-energy-rate forming, explosive material processing, shock synthesis, intermetallics, composite of intermetallics, Ti5Si3, Ti5Si3/Ti, Ti5Si3/TiAl