Ken-ichiro Mori

Finite element method for rigid-plastic analysis of metal forming—Formulation for finite deformation

Abstract For the finite element analysis of metal forming processes, a method based on the equilibrium of nodal forces is proposed by assuming the deforming metal to be a slightly compressible rigid-plastic material. As an extension of the method, a formulation for finite deformation is derived on the basis of the equilibrium of nodal forces at the end of incremental deformation. The effects of work-hardening and shape change of element during incremental deformation are incorporated. This formulation is more accurate than that of the simple extension of infinitesimal deformation when dealing with non-steady problems, and is particularly effective for the processes in which the mode of deformation is sensitively changed by the distribution of flow stress and variation of shape. The effectiveness of the method is demonstrated by the examples of a tension test on an axi-symmetric specimen and of the plane-strain compression of blocks.

Warm and Hot Stamping of Ultra High Tensile Strength Steel Sheets Using Resistance Heating

A warm and hot stamping process of ultra high tensile strength steel sheets using resistance heating was developed to improve springback and formability. In this process, the decrease in temperature of the sheet before the forming is prevented by directly heating the sheets set into the dies by means of the electrical resistance, the so-called Joule heat. Since the heating time up to 800°C is only 2 seconds, the resistance heating is rapid enough to synchronise with a press. The effects of the heating temperature on the springback and formability of ultra high tensile strength steel sheets were examined. The springback in hat-shaped bending of the high tensile strength steel sheets was eliminated by heating the sheet. In addition, the ultra sheet having a tensile strength of 980MPa was successfully drawn by the heating. The heating temperature is optimum around 600°C due to the small springback and oxidation and the increase in hardness.

Simulation of plane-strain rolling by the rigid-plastic finite element method

Abstract The rigid-plastic finite element method for a slightly compressible material is applied to steady and non-steady state strip rolling. Solutions for some technical problems using a finite element analysis for rolling process are given. Stress and strain distributions in steady state plane-strain strip rolling under the condition of a constant coefficient of friction are calculated for work-hardening and non-hardening materials. The calculated distribution of roll pressure exhibits a peak at the entry which does not appear in the analysis by the slab method. Non-steady state deformation of the front and tail ends is also analysed. The calculated end shapes are in good agreement with the experimental ones for aluminium strip.

The application of some criteria for ductile fracture to the prediction of the forming limit of sheet metals

Abstract The possibility of the application of ductile fracture criteria to the formability prediction of sheet metals is examined. Some criteria in simple forms are employed and combined with the finite element simulation of sheet metal forming. From the calculated histories of stress and strain in each element, the fracture initiation site and the forming limit are predicted by means of the criteria for ductile fracture. The material constants in the criteria are determined from uniaxial and plane-strain tension tests. The calculations are carried out for the axisymmetric deep drawing of various aluminium alloy and steel sheets. A comparison between the calculated and experimental results shows that the present approach using the ductile fracture criteria gives fairly good predictions.

FINITE ELEMENT ANALYSIS OF LIMIT STRAINS IN BIAXIAL STRETCHING OF SHEET METALS ALLOWING FOR DUCTILE FRACTURE

To predict limit strains in biaxial stretching of sheet metals, a criterion for ductile fracture is combined with the finite element simulation. The limit strains are determined by substituting the values of stress and strain obtained from the finite element simulation into the ductile fracture criterion. Material constants in the criterion are obtained from the fracture strains measured in the biaxial stretching tests. Calculations are carried out for various strain paths from balanced biaxial stretching to uniaxial tension of aluminium alloy sheets, and compared with the experimental results. The predicted limit strains are in good agreement with the measured ones not only just at the fracture site but also at outside of the fracture site. It is demonstrated that the forming limit diagrams are successfully predicted by the present approach.

Finite element simulation of warm deep drawing of aluminium alloy sheet when accounting for heat conduction

Abstract The deformation behaviour and the temperature change in cylindrical deep drawing of an aluminium alloy sheet at elevated temperatures are simulated by the combination of the rigid-plastic and the heat conduction finite element methods. The comparison with the experimental results shows that the forming limits and the necking sites are successfully predicted by the simulation. It is clarified that the appropriate distribution of flow stress depending on temperature must exist in the sheet for the higher limiting drawing ratio. The numerical as well as the experimental results show that the limiting drawing ratio in the warm deep drawing increases with the die profile radius.

Plastic Joining of Ultra High Strength Steel and Aluminium Alloy Sheets by Self Piercing Rivet

Ultra high strength steel and aluminium alloy sheets were plastically joined by a self piercing rivet driven through the upper sheet and spread in the lower sheet with a die. The self piercing rivet directly pierces into the sheets without drilling the sheets beforehand unlike the conventional rivets. Insufficient driving though the upper sheet and fracture of the lower sheet occur due to the high hardness and low ductility of the ultra sheet, respectively. An ultra high strength steel sheet having a tensile strength of 980MPa and an aluminium alloy sheet were successfully joined by optimising shapes of the die.

Simulation of three-dimensional deformation in rolling by the finite-element method

Abstract A method for simulating three-dimensional deformation in plate rolling and edge rolling is established on the basis of the rigid-plastic finite-element method. For the simulation with small number of elements, simplified elements which represent three-dimensional deformation in rolling with grooveless rolls are developed. Solutions for some problems associated with simulation of steady-state rolling of work-hardening plates are given. The three-dimensional behaviour of deforming plate in single-pass plate rolling and multi-pass edge rolling is simulated by assuming a constant coefficient of friction between the rolls and the plate. The computed shapes of the plates and loads are found to be in good agreement with the experimental ones carried out with aluminium plates.

Prediction of forming limit in bore-expanding of sheet metals using ductile fracture criterion

Abstract To predict the forming limit in sheet metal forming, a criterion for ductile fracture is introduced into the finite element simulation. From the histories of stress and strain in each element calculated by the finite element simulation, the initiation of fracture is predicted by means of the fracture criterion. Calculations are carried out for axisymmetric bore-expanding processes of mild steel and high strength steel sheets using flat-, hemispherical- and conical-headed punches. Comparison with experimental results shows that the fracture initiation site and the critical stroke are predicted successfully by the present approach.

Prediction of forming limit in deep drawing of Fe/Al laminated composite sheets using ductile fracture criterion

Abstract Axisymmetric deep drawing processes of laminates composed of mild steel and various aluminium alloy sheets are simulated by FEM. From the calculated stress and strain histories of elements in each layer, the fracture initiation site and the forming limit are predicted by using the ductile fracture criterion. The predictions so obtained are compared with experimental observations. The results exhibit that various types of fracture initiations in deep drawing of the laminated composite sheets are successfully predicted. Furthermore it is found that the drawability is improved by setting the mild steel sheet on the punch side for the case of aluminium alloy sheet with comparatively high ductility, and by sandwiching the aluminium alloy sheet with the mild steel sheets for the case of low ductility.