Eiji Nakamachi

Drawability assessment of BCC steel sheet by using elastic/crystalline viscoplastic finite element analyses

Abstract Elastic/crystalline viscoplastic finite element (FE) analyses were carried out to asses the drawability of three kinds of BCC steel sheets, such as mild steel, dual-phase steel and high-strength steel, in the cylindrical cup deep drawing processes. In this study, the crystal orientations were obtained by X-ray diffraction and orientation distribution function (ODF) analyses. The measured ODF results have revealed clearly different textures of sheets, featured by orientation fibers, skeleton lines and selected orientations in Euler angle coordinate space, which can be related to the plastic anisotropy. An orientation probability assignment method, which can be categorized as an inhomogenized material modeling, was used in this FE modeling. The orientations were determined from the measured ODF and assigned to FE integration points one by one. Numbers of integration points, which represent crystallites and can rotate individually, are employed to represent textures of the sheet metals for taking account of the initial and evolutional plastic anisotropy without introducing Taylor or Sachs homogenization assumption. The FE analyses showed how the fiber textures affect the strain localization and earing in the deep drawing operation. It was confirmed by comparison with experimental results that this FE code could predict the extreme strain localization and earing with good accuracy and assess the sheet drawability.

Development of optimum process design system by numerical simulation

Abstract Now, the development of optimum forming process design system based on computer simulation to reduce the time consumption is strongly required in the industries. In this study, the optimum process design system is newly developed in conjunction with the nonlinear FEA code and the nonlinear optimization code. In the latter code, “Sweeping Simplex Method” is newly proposed, which can find the global minimum. The accuracy and quickness of this method to find the global minimum of objective function, which have several local minimum points, is confirmed by comparison with the grid method. This numerical system is applied to the process design of complicate shaped cup deep drawing. In order to form the sheet metal with uniform thickness, “Deviation of thickness from uniform average thickness” is employed as the objective function, and the global minimum point in the design variable space is searched by “Sweeping Simplex Method”. For the design variables, the heights of two punches in first stage forming are employed. The optimum process condition was determined by using this numerical code and also the validity of this code was confirmed by the comparison with the experimental observation results.

Elastic/crystalline viscoplastic finite element analyses of single- and poly-crystal sheet deformations and their experimental verification

Abstract The elastic/crystalline viscoplastic constitutive equation, based on a newly proposed hardening-softening evolution equation, is introduced into the dynamic-explicit finite element code “Itas-Dynamic.” In the softening evolution equation, the effective distance and the angle between each slip system of a crystal are introduced to elucidate the interaction between the slip systems, which causes a decrease of dislocation density. The polycrystal sheet is modeled by Voronoi polygons, which correspond to the crystal grains; and by the selected orientations, which can relate to the texture, they are assigned to the integration points of the finite elements. We propose a direct crystal orientation assignment method, which means that each integration point of finite element has an assigned orientation, and its orientation can be rotated independently. Therefore, this inhomogeneous polycrystal model can consider the plastic induced texture development and subsequent anisotropy evolution. The parameters of the constitutive equation are identified by uni-axial tension tests carried out on single crystal sheets. Numerical results obtained for sheet tensions are compared with experimental ones to confirm the validity of our finite element code. Further, we investigate the following subjects: (1) how the initial orientation of single crystal affects slip band formation and strain localization; (2) how the grain size and particular orientations of the grain affect the strain localization in case of a polycrystal sheet. It is confirmed that the orientation of a single crystal can be related to the primary slip system and the deformation induced activation of that system, which in turn can be related to the slip band formation of the single crystal sheet. Further, in case of a polycrystal sheet, the larger the grain size, the more the strain localizes at a specific crystal, which has the particular orientation. It is confirmed through comparisons with experiments that our finite element code can predict the localization of strain in sheets and consequently can estimate the formability of sheet metals.

Development of optimum process design system for sheet fabrication using response surface method

Abstract The aim of this optimum process design system is to assist the decision of material process condition for making a sheet metal which has better formability for stamping. This system is realized by combining finite element analysis and discretized optimization algorithms. In this system, optimization algorithm is required to search the optimum condition quickly. Therefore, the response surface method was newly suggested to improve the efficiency of the retrieval. This system is applied to find the annealing conditions suitable for a sheet forming condition. Annealing temperature and time are chosen for the process parameters. Formability is evaluated by thickness uniformity of stamped part. As the result, this system could search optimum condition quickly. The effectiveness of this system was confirmed through experimental verification. It is demonstrated that this optimum process design system is a useful tool for deciding a material process and sheet metal fabrication design.

Formability assessment of FCC aluminum alloy sheet by using elastic/crystalline viscoplastic finite element analysis

Abstract This study looks at the influence of crystallographic texture on the formability of FCC aluminum sheet metal using our elastic/crystalline viscoplastic finite element (FE) analysis code “ROBUST-CRYSTAL”. First, the crystallographic textures of Al–2.5% Mg aluminum alloy generated by employing different annealing temperatures were obtained by X-ray diffraction and orientation distribution function (ODF) analyses. The measured ODF results revealed clearly different textures of sheets, featured by orientation fibers, skeleton lines and selected orientations in Euler angle coordinate space, which can be related to plastic anisotropy. The orientation probability assignment method was used in FE modeling. The orientations determined from the measured ODF results were assigned to FE integration points. A large number of integration points, which represent crystallites and can rotate individually, are employed to represent textures of the sheet metals, which take into account the initial and evolutional plastic anisotropy without introducing Taylor or Sachs homogenization assumption. An actual sheet metal forming process, VDI benchmark problem, was adopted to assess the texture effects on strain localization and failure. It was confirmed by comparison with experimental results that our crystalline plasticity FE code could predict strain localization and assess formability with good accuracy.

Investigations of the formability of BCC steel sheets by using crystalline plasticity finite element analysis

Abstract The effect of crystallographic texture on the formability of BCC steel sheets was studied by using crystalline plasticity finite element (FE) analysis. Three kinds of BCC steel sheets, mild steel, dual phase steel and high strength steel, were adopted as the examples in this investigation. At first, the crystal orientations of the three steel sheets were obtained by X-ray diffraction and orientation distribution function (ODF) analyses. The measured ODF results clearly revealed different preferred orientations — textures — of three kinds of steel sheets, featured by orientation fibers, skeleton lines and selected orientations in Euler angle space. Next, the crystal orientations were introduced into a FE model by using the orientation probability assignment method, which can be categorized as an inhomogenized material modeling. Huge numbers of integration points, which represent crystallites and can rotate individually, were employed to represent the textures for taking account of the initial and evolutional plastic anisotropy without introducing Taylor or Sachs homogenization assumption. The actual sheet metal forming processes, VDI benchmark and deep drawing problems, were adopted to assess the texture affects on the strain localization and failure. It was confirmed that the more {111} orientations — γ-fiber texture — and the less {001} orientations, the better the formability. Complex phase steel sheet (CP800), a high strength steel sheet, shows poor formability due to lack of γ-fiber texture.

Numerical investigation on ferroelectric properties of piezoelectric materials using a crystallographic homogenization method

Polycrystalline piezoelectric materials are aggregations of crystal grains and domains with uneven forms and orientations. Therefore, the macroscopic ferroelectric property should be characterized by introducing a microscopic inhomogeneity in the crystal morphology. In this study, a multi-scale finite element modelling procedure based on a crystallographic homogenization method has been proposed for describing a macroscopic property of polycrystalline ferroelectrics with consideration of the crystal morphology at a microscopic scale. The proposed procedure has been applied to two kinds of piezoelectric materials, BaTiO3 and PbTiO3 polycrystals; the influence of microscopic crystal orientations on macroscopic ferroelectric properties was verified numerically. From the computational results, it has been shown that piezoelectric constants of polycrystalline ferroelectrics can be maximized by design of microscopic crystal morphology.

Sheet-forming process characterization by static-explicit anisotropic elastic-plastic finite-element simulation

Abstract The Static-explicit finite-element simulation code has been proven to be a robust tool for prediction in highly non-linear sheet-forming processes. This code has been developed employing a rate-type formulation, based on non-linear shell theory, non-linear contact friction theory and an anisotropic elastic-plastic constitutive equation. The Euler method has been employed for the time integration of the equation of motion under the quasi-static condition. The C 0 continuity shell finite-element model has been proven to be an efficient model for large-scale finite-element computation. The sheet-forming process involves the highly non-linear phenomenon of a complicated mechanical system. The coupling of the contact boundary condition and the material properties causes instability phenomena, such as localization and wrinkling. These instability phenomena are studied using a “Forming Process Map”, which characterize thinning and draw-in deformation processes, and also the phase diagram. The investigations are carried out in the case of square-cup deep drawing adopting NUMISHEET93 materials, such as mild steel and aluminum alloy.

Elastic/crystalline‐viscoplastic finite element analysis of dynamic deformation of sheet metal

Describes the development of a dynamic‐explicit type finite‐element formulation based on elastic/crystalline‐viscoplastic theory to predict the dynamic forming limits of sheet metal. Formulates an evolution equation governing all the slip stages of a single crystal, by modifying Pierce and Bassani’s crystalline plasticity models. Interprets precisely the experimentally observed hardening evolution. Takes account of the importance of the strain rate and temperature sensitivity of the material in predicting dynamic plastic instability. Analyses the deformation and strain localization in a rectangular sheet under stretching, in relation to the plane strain assumption, using the numerical results to demonstrate the influences of tension force and temperature on strain localization, and to show the temperature dependence of shear band formation. Demonstrates that the deviation of tension direction from the axis of symmetry of a single crystal causes non‐simultaneous sliding between primary and conjugate slip systems, resulting in S‐shaped non‐symmetrical deformation.

Development of enhanced piezoelectric energy harvester induced by human motion

In this study, a high frequency piezoelectric energy harvester converted from the human low vibrated motion energy was newly developed. This hybrid energy harvester consists of the unimorph piezoelectric cantilever and a couple of permanent magnets. One magnet was attached at the end of cantilever, and the counterpart magnet was set at the end of the pendulum. The mechanical energy provided through the human walking motion, which is a typical ubiquitous presence of vibration, is converted to the electric energy via the piezoelectric cantilever vibration system. At first, we studied the energy convert mechanism and the performance of our energy harvester, where the resonance free vibration of unimorph cantilever with one permanent magnet under a rather high frequency was induced by the artificial low frequency vibration. The counterpart magnet attached on the pendulum. Next, we equipped the counterpart permanent magnet pendulum, which was fluctuated under a very low frequency by the human walking, and the piezoelectric cantilever, which had the permanent magnet at the end. The low-to-high frequency convert “hybrid system” can be characterized as an enhanced energy harvest one. We examined and obtained maximum values of voltage and power in this system, as 1.2V and 1.2 μW. Those results show the possibility to apply for the energy harvester in the portable and implantable Bio-MEMS devices.