Engineering Plasticity and Its Applications

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Authors: Kisaragi Yashiro, Masaomi Nishimura, Yoshihiro Tomita
Authors: Y. Doi, Akihiro Nakatani
Abstract: Manipulation of the intrinsic localized modes (ILMs) or discrete breathers (DBs) in the one dimensional anharmonic lattice systems is investigated. We can make a static ILM into a moving one without any collapses of localized structure by introducing the suitable linear plane into the system. Also we can make a moving ILM into a static one by the same way. Using these procedures, ILM’s position in the system can be controllable. This result indicates the possibilities of applications of ILMs in practical discrete systems in the future.
Authors: Takuya Uehara, Naoki Wakabayashi, Nobutada Ohno
Authors: Wing Bun Lee, Chi Fai Cheung, Suet To
Abstract: A multi-scale model is proposed to explain the effect of material induced vibration and the quantitative relation between cutting force and the surface quality from dislocations, grain orientations, cutting tools, machine tools used in the simulation of the nano-3D surface topology in single-point diamond turning. The model-based simulation system composes of several model elements which include a microplasticity model, a dynamic model and an enhanced surface topography model. The multi-scale model brings together knowledge from various disciplines to link up physical phenomenon occurring at different length scales to explain successfully the surface generation in single-point diamond turning of crystalline materials, and offers a new direction of research in ultra-precision machining.
Authors: Yoshihiro Tomita, K. Azuma, M. Naito
Abstract: The constitutive equation of rubber is derived by employing a nonaffine molecular chain network model for an elastic deformation behavior and the reptation theory for a viscoelastic deformation behavior. The results reveal the roles of the individual springs and dashpot, and the strain rate dependence of materials and disentanglement of molecular chains in the monotonic and cyclic deformation behaviors, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress-stretch curves under cyclic deformation processes.
Authors: Isamu Riku, Koji Mimura
Abstract: In this study, we employ the two-dimensional homogenization model based on molecular chain network theory to investigate the micro- to macroscopic mechanical behavior of plastic foam under macroscopic uniform compression. A parametric study is performed to quantify the effect of a characteristic value of matrix, distribution and initial volume fraction of voids, and the macroscopic triaxiality of loading condition on the deformation behavior of the foam. The results suggest that the onset of localized shear band at the ligament between voids together with the microscopic buckling of the ligament leads to the macroscopic yield of the foam. The initial modulus and the macroscopic yield stress of the foam have no dependence on the characteristic value of matrix. Furthermore, as the microscopic buckling of the ligament is promoted in case of high initial volume fraction of voids and high triaxiality loading condition, the macroscopic yield point appears at early deformation stage. After the macroscopic yield, macroscopic strain hardening appears in the macroscopic response and a remarkable strain hardening is shown in case of high initial volume fraction of voids and high triaxiality loading condition due to the considerable increase of the density of the foam in these cases.
Authors: Shōji Imatani, Daisuke Fujiwara
Abstract: Porous materials such as engineering ceramics and metal foams have a specific feature such that internal structure has a significant influence on the mechanical properties from the viewpoint of porosity and morphology. This paper discusses the relationship between microscopic morphology and macroscopic properties of the porous materials based on the homogenization technique, in which pores are randomly distributed over the domain. Various types of pores are examined and the conjunction between different elemental types is discussed. A wide range of porosity is covered from a low porosity of 5% such as engineering ceramics to 80% of foam-like materials within the same numerical strategy. It is found that the macroscopic property with low porosity shows good agreement with both experimental curve and micromechanics prediction, in which the elasticity coefficient is affected by morphology of internal structure. In contrast with the low porosity, the morphology effect diminishes and is hardly observed in high porosity region where the macroscopic stiffness is almost linear on the porosity.
Authors: Shuji Takashima, Noriyuki Miyazaki, Toru Ikeda, Michihiko Nakagaki
Abstract: In this study, we focus on the modeling of solid structures that include microstructures observed in particle-dispersed composites. The finite element modeling can be used to clarify how the macroscopic behaviors of solid structures are influenced by the microstructures. In such a case, if the whole structure including the microstructures is modeled by the finite elements, an enormous number of finite elements and enormous amount of computational time are required. To overcome such difficulties, we propose a new method for modeling microstructures. In this method, an explicit form of the stress-strain relation covering both elastic and elastic-plastic regions is derived from the equivalent inclusion method proposed by Eshelby that provides mathematical solutions for stress and strain at an arbitrary point inside and outside the inclusion. The derived elastic-plastic constitutive equation takes account of the microstructures, so that the effect of microstructures on the macroscopic behaviors can be obtained from the conventional finite element method by using such a constitutive equation without modeling microstructures in the finite element analysis. The effectiveness of the proposed constitutive equation is verified for a simple problem by comparing the results of the one-element finite element analyses using the proposed constitutive equation with those of the detailed finite element analyses using multi-element finite element modeling.
Authors: Tetsuya Matsuda, Dai Okumura, Nobutada Ohno, Masamichi Kawai
Abstract: Microscopic stress distributions at an interlaminar area in a CFRP cross-ply laminate are analyzed three-dimensionally using a homogenization theory in order to investigate microscopic interaction between 0°- and 90°-plies. It is first shown that a cross-ply laminate has a point-symmetric internal structure on the assumption that each ply in the laminate has a square array of long fibers. Next, the point-symmetry is utilized to reduce the domain of homogenization analysis by half. Moreover, the substructure method is combined with the homogenization theory for reducing consumption of computational resources. The present method is then employed for analyzing stress distributions at an interlaminar area in a carbon fiber/epoxy cross-ply laminate under in-plane off-axis tensile loading. It is thus shown that microscopic shear stress significantly occurs at the interface between 0°- and 90°-plies. It is also shown that the microscopic interaction between two plies is observed only in the vicinity of the interface.
Authors: Yuichi Tadano, Mitsutoshi Kuroda, Hirohisa Noguchi, Kazuyuki Shizawa
Abstract: In this study, a three-dimensional finite element formulation for polycrystalline plasticity model based on the homogenization method has been presented. The homogenization method is one of the useful procedures, which can evaluate the homogenized macroscopic material properties with a periodical microstructure, so-called a unit cell. The present study focuses on hexagonal metals such as titanium or magnesium. An assessment of flow stress by the presented method is conducted and it is clarified how the method can reproduce the behavior of hexagonal metal.

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