Papers by Author: Tetsuo Naka

Abstract: The framework for the complex step derivative approximations (hereafter CDSA) to calculate the consistent tangent moduli is studied. The present methods is one of the most effective methods to implement any material constitutive equations to the commercial finite element codes and does not suffer from calculation conditions and errors. In order to confirm the efficiency of CDSA, we developed the user subroutine code based on the CDSA using associative J2 flow rules with general nonlinear isotropic hardening rules that is commonly and widely utilized in commercial finite element codes. In this study, the user material subroutine ‘Hypela2’ of MSC.Marc (ver.2013.0.0) was utilized. The finite element calculation result by the proposal method shows a good agreement with the corresponding result by the MSC.Marc default setting. Also we apply the Yoshida-Uemori back stress model to the CDSA and evaluate this new technique to predict the deformation behavior of high tensile strength steel sheet.

Abstract: Magnesium alloy sheets have a potential to be widely used in many fields of industry due to their excellent lightweight property. Although magnesium alloys have low ductility at the room temperature due to their hexagonal close-packed structure, their formability can be improved at elevated temperatures. Therefore, warm press-forming of magnesium alloy sheets is an attractive technology. The objective of the present work is to investigate the cyclic plasticity behavior of an AZ31 sheet at elevated temperatures by performing cyclic tension-compression experiments. The cyclic deformation mechanism is examined by measuring the crystallographic orientation distributions by means of X-ray diffraction method at each stage of the cyclic deformation. The present findings are summarized as follows: (1) Stress-strain responses of an AZ31 sheet were investigated at various temperatures (R.T, 100, 150 and 200°C) at strain rates of 0.001, 0.01 and 0.05 s^-1. The flow stresses were insensitive to the strain rate at the room temperature, however the strain rate dependency of the flow stress becomes dominant at elevated temperatures of over 100 °C.(2) Cyclic plasticity behavior of the sheet at various elevated temperatures (R.T, 100, 150 and 200 °C) at strain rates of 0.001, 0.01 and 0.05 s^-1 were investigated by performing warm in-plane cyclic compression-tension test. Similarly to the uniaxial tension test, apparent temperature and strain rate dependencies of the flow stress were observed at temperatures of over 100 °C. (3) At the room temperature an unusual cyclic stress-strain curve, which is very different from that of bcc and fcc metals, was observed. From the texture measurement it was found that such a specific stress-strain characteristic is due to its twinning and detwinning deformation mechanism.(4) In contrast, at an elevated temperature of 200 °C, the usual cyclic stress-strain response, which is similar to one appearing in most of metallic materials, was observed. This is because the major deformation mechanism at an elevated temperature is the slip, rather than twinning/detwinning, since the CRSS decreases drastically with increasing temperature.

Abstract: Aluminum alloy sheet metals have been widely utilized for a light weight construction of automobile. However, Aluminum sheet metals still remain one of the difficult materials to predict the accurate final shapes after press forming processes, because of several mechanical weak features such as lower Youngs modulus, strong plastic anisotropy of yield stress, Lankford values, and so on. In order to solve the problems, the present author has developed a new constitutive model called Modified Yoshida-Uemori model. The present model can describe accurate non-proportional hardening behaviors of Aluminum alloy sheet metals. In the present research, several experimental procedures were carried out to reveal the mechanical properties of Aluminum alloy sheet metals. From the comparison between experimental data and the corresponding calculated results by our constitutive model, the performance of our model was evaluated. In addition to the above mentioned research, the evaluation of some springback analyses were also carried out. The calculated results show good agreements with the corresponding experimental data.

Abstract: Square cup drawing experiments were performed on an AZ31 sheet at various temperatures (T) ranging from room temperature to 200°C with three different punch travel speeds (V) of 3, 30 and 300mm/min. From the experiment, the highest drawability was observed either at T=175°C with V= 30mm/min or at T=200°C with V= 300mm/min. The effects of temperature and forming speed on the formability were discussed by comparing the result of drawing experiment with the high temperature tensile properties of the material. The forming limits were well predicted by FE simulation using a temperature and rate dependent constitutive model.

Abstract: The magnesium alloys, that have high specific strength, are often applied to the industrial products. However, the magnesium alloys exhibit low ductility at the room temperature on account of its hexagonal close-packed structure. It is difficult to give large deformation to the magnesium alloys at room temperature. Therefore, the plastic forming of a magnesium alloy sheet needs the process at warm temperature. In the present work, the procedure of thermal-mechanical coupled analyses are employed. The numerical simulations of warm deep drawings have been performed in order to evaluate the dependence of the temperature on the plastic forming of a magnesium alloy AZ31 sheet. The mechanical properties of the magnesium alloy AZ31 shall be described as the functions depending on temperature. The shapes of punches and die holes are rectangle whose aspect ratios are 1.5 or 2.0. The corners of punches and dies are heated locally at 473K. The influence of local heating on the formability have been investigated. The relation between the blank size and the formability has been also estimated. As the results of numerical simulations, it was shown that the formability of deep drawing was improved by local heating to the punch and the die. When the blanks of various sizes were tried, the distributions of the plastic strain rate around the die corner were changed. Therefore, the deviation of the plastic flow and the temperature distribution arose in a sheet. Consequently, it is necessary to optimize the blank sizes according to the shape of die holes in addition to the forming temperature.

Abstract: In the present work, FLDs of AZ31 magnesium alloy sheet for non-proportional strain paths were investigated by performing two-step stretch forming experiments at various forming speeds (3, 30 and 300 mm.min^-1) at elevated temperatures of 150, 200 and 250°C. The forming limit strains, both for proportional and non-proportional deformations, increased with temperature rise and with decreasing forming speed. A FLC after a uniaxial pre-strain lies outside of the proportional FLC for a given condition of temperature and forming speed, whereas a biaxially pre-strained FLC lies inside of the proportional FLC. It was found that the accumulated effective plastic strain and the direction of plastic strain increment at the final stage of forming are two major factors that influence the forming limits for non-proportional deformations.

Abstract: This paper deals with experimental observations and modeling of plastic deformations of a high strength steel sheet (HSS sheet) under biaxial stress conditions. Using a cruciform specimen of a HSS sheet of 980MPa-TS, experiments of proportional and non-proportional loadings were performed. Numerical simulations for the biaxial stress-strain responses were conducted using a constitutive model of large-strain cyclic plasticity (Yoshida-Uemori model), and the results were compared to the experimental data. The results of numerical simulation show a good agreement with the experimental results, which is attributed to accurate modeling of the backstress evolution of the anisotropic yield surface.

Abstract: The yield locus of type AZ31 magnesium alloy sheet was obtained by performing biaxial tensile tests, using cruciform specimens, at temperatures of 100, 150, 200, 250 and 300 P o PC at strain rates of 10P -2 P, 10P -3 P and 10P -4 PsP -1 P. Based on the experimental results, the effects of strain-rate and temperature on the yield locus was discussed. The size of yield locus drastically decreased with increasing temperature and decreased with decreasing strain-rate. Neither von Mises’s criterion or Hill’s can well predict the shape of the yield locus of this sheet metal. Instead of these quadratic yield functions, the yield criterion of Logan-Hosford or Barlat is a better choice for the accurate description of biaxial stress-strain responses at high temperature.