Masaru Zako

Finite element analysis of damaged woven fabric composite materials

Since fiber reinforced composite materials have been used in main parts of structures, an accurate evaluation of their mechanical characteristics becomes very important. Due to their anisotropic nature and complicated architecture, it is very difficult to reveal the damage mechanisms of these materials from the results of mechanical tests. Therefore, there is a need to conduct reliable simulations and analytical evaluations. In this paper, the damage behavior of FRP is simulated by finite element analysis using an anisotropic damage model based on damage mechanics. The proposed procedure is applied to an example; the finite element analysis of microscopic damage propagation in woven fabric composites. Experimental tests have been conducted to evaluate the validity of the proposed method. It is recognized that there is a good agreement between the computational and experimental results, and that the proposed simulation method is very useful for the evaluation of damage mechanisms.

Structural optimization using kriging approximation

An optimization method using Kriging approximation is applied to a structural optimization problem. The method involves two main processes. The first is a space estimation process that uses the Kriging method, and the second is an optimization process. The use of the Kriging method makes it easier to perform the approximation optimization. As an example of the estimation performed as part of structural optimization, a response surface for layout optimization of beam reinforcement is estimated. To evaluate the applicability of the Kriging method, Kriging estimation is compared with neural network approximation. As a numerical example, the optimization of a stiffened cylinder for an eigenfrequency problem is illustrated. The obtained results clearly show the applicability of the method.

Intelligent Material Systems Using Epoxy Particles to Repair Microcracks and Delamination Damage in GFRP

The objective of this study is to propose an intelligent material system that can perform a self-repairing operation against initial damage that might occur in GFRP laminates. Specifically, we highlight the development of a novel actuator to be used in such self-repairing operations. There has been much research on sensor systems to detect damage and some actuators to control the shape of the structure or to control the vibration. However, no literature can be found on the actuator aiming at the self-repair of damage. For this purpose, a small grain particle-type adhesive is embedded in a glass/epoxy composite (GFRP) laminate. The diameter of the particle is approximately 50 gim. Hence, in the developed intelligent material system, coldsetting epoxy resin is used as the matrix, uni-directionally arranged glass fiber is used as the reinforcement, and a thermosetting epoxy particle is used as a repairing actuator. The volume fraction of the particles in the matrix was approximately 40%. The embedded particles can repair the damage, when melted by heat. Basic characteristics of the particles were investigated first, and we confirmed that the embedded particles in the matrix can melt by heat and flow to repair the crack. We also confirmed that the embedded particles do not deteriorate the stiffness of the GFRP laminate. Then we investigated the efficiency of the repairing operation against initial damage such as microscopic matrix cracks and delamination, by conducting two typical tests, i.e., static three-point bending of [0/90] laminate and tensile fatigue of [O/90], laminate. Damage was observed by CCD camera. As a result, the decrease in the stiffness due to initial damage has been recovered and consequently increased the residual fatigue life.

Nesting in textile laminates: geometrical modelling of the laminate

The nesting of reinforcements in textile laminates is studied using a 3D geometrical model of a woven, braided and non-crimp stitched fabrics in the relaxed and sheared state. The following fabric parameters were varied in the numerical experiments: flatness of the yarns, tightness and balance of the fabric, fabric weaving/braiding/knitted pattern, number of layers and degree of shear. Monte-Carlo modelling of the random nesting generated data on the influence these parameters on the average laminate thickness and fibre volume fraction and distributions of these characteristics of the laminate. The results show that the nesting effect becomes more pronounced with the decrease of the fabric tightness and the decrease of the float length in the weave. For non-circular yarns, an average dimension of the cross-section proved to be a valid normalizing parameter to generalize the nesting behaviour of fabrics. Shear deformation of the fabric decreases the nesting. For non-crimp stitched fabrics the nesting is defined by the stitching pattern.

Microstructure-based stress analysis and evaluation for porous ceramics by homogenization method with digital image-based modeling

Multi-scale analysis using the asymptotic homogenization method is becoming a matter of concern for microstructural design and analysis of advanced heterogeneous materials. One of the problems is the lack of the experimental verification of the multi-scale analysis. Hence, it is applied to the porous alumina with needle-like pores to compare the predicted homogenized properties with the experimental result. The complex and random microstructure was modeled three-dimensionally with the help of the digital image-based modeling technique. An appropriate size of the unit microstructure model was investigated. The predicted elastic properties agreed quite well with the measured values. Next, a four-point bending test was simulated and finally the microscopic stress distribution was predicted. However, it was very hard to evaluate the calculated microscopic stress quantitatively. Therefore, a numerical algorithm to help understanding the three-dimensional and complex stress distribution in the random porous microstructure is proposed. An original histogram display of the stress distribution is shown to be effective to evaluate the stress concentration in the porous materials.

The formulation of homogenization method applied to large deformation problem for composite materials

In order to analyze the mechanical behaviors of composite materials under large deformation, the formulation of the homogenization method is described. In this formulation, assuming that the microstructures in a local region of the global structure are deformed uniformly and that consequently the microscopic periodicity remains in the local region under large deformation, the microscopic deformation is precisely defined by the perturbed displacement and product of macroscopic displacement gradient and microscopic coordinates. Finally, microscopic and macroscopic equations are obtained. The above mentioned assumption of the periodicity of microstructures is experimentally validated. The computer program is also developed according to this formulation, and the large deformation is analyzed for the unidirectional fiber reinforced composite material and the knitted fabric composite material.

Hierarchical modelling of textile composite materials and structures by the homogenization method

For the simulation of mechanical behaviours of textile composite materials and structures, a novel hierarchical modelling technique is proposed. Not only the global deformation but also the stresses at multiscales are analysed precisely. Four-level hierarchy is defined for the textile composites such as woven and knitted fabric composites. The stresses at the mesostructure, which is a periodic unit cell of textile composite materials consisting of fibre bundles and matrix, can be evaluated accurately by the homogenization method and finite-element mesh superposition technique. The latter technique makes it possible to overlay arbitrary local fine mesh on the global rough mesh. Anisotropic damage mechanics is also utilized for strength evaluation at the mesoscale. Three-dimensional modelling of the mesostructure of woven and knitted fabric composite materials is shown. Localization analysis has been carried out within practical computational time and cost by the proposed hierarchical modelling.

Microstructure-based Evaluation of the Influence of Woven Architecture on Permeability by Asymptotic Homogenization Theory

A microstructure-based computational approach is taken to predict the permeability tensor of woven fabric composites, which is a key parameter in resin transfer moulding (RTM) simulation of polymer-matrix composites. An asymptotic homogenization theory is employed to evaluate the permeability from both macro- and microscopic standpoints with the help of the finite-element method (FEM). This theory allows us to study the relation between microscopic woven architecture and macroscopic permeability based on the method of two-scale asymptotic expansions. While the fluid velocity is introduced for Stokes flow microscopically, the macroscopic one is for seepage flow with the Darcys law. The latter can be characterized for arbitrary configurations of unit microstructures that are analyzed for the former under the assumption of the periodicity. After discussing the validity of this approach, we present a typical numerical example to discuss the permeability characteristics of plain weave fabrics undergoing shear deformation in the preforming in comparison with the undeformed one. Another notable feature of the proposed method is that the correlation between the macroscopic behaviors and the microscopic ones can be analyzed, which is important to analyze and/or design the RTM process. Hence, it is also demonstrated that the microscopic velocity field evaluated with macroscopic pressure gradient provides important information about the flow in RTM processes.

Microstructure-based deep-drawing simulation of knitted fabric reinforced thermoplastics by homogenization theory

Abstract Process simulation of fiber reinforced composite materials is an important research theme for the development of low-cost and advanced functional composite materials. This paper aims at the simulation of deep-drawing process of knitted fiber reinforced thermoplastics and its verification. The feature of the simulation is that the large deformation of the knitted microstructures can be traced everywhere in the deep-drawn product. The homogenization theory is applied to analyze the micro–macro coupled behaviors of the knitted fabric composite material. By employing a simplified nonlinear computational algorithm, the deep-drawing simulation was carried out on a personal computer. The predicted largely deformed microstructures were compared with the experimental results. The numerical results and experimental ones agreed quite well. This deep-drawing simulation requires us to prepare only the mechanical properties of the constituents, while it provides us all the necessary quantities such as the deformation, strain, stress and stiffness from both microscopic and macroscopic standpoints.

Multi-scale computational method for elastic bodies with global and local heterogeneity

A multi-scale computational method using the homogenization theory and the finite element mesh superposition technique is presented for the stress analysis of composite materials and structures from both micro- and macroscopic standpoints. The proposed method is based on the continuum mechanics, and the micro–macro coupling effects are considered for a variety of composites with very complex microstructures. To bridge the gap of the length scale between the microscale and the macroscale, the homogenized material model is basically used. The classical homogenized model can be applied to the case that the microstructures are periodically arrayed in the structure and that the macroscopic strain field is uniform within the microscopic unit cell domain. When these two conditions are satisfied, the homogenization theory provides the most reliable homogenized properties rigorously to the continuum mechanics. This theory can also calculate the microscopic stresses as well as the macroscopic stresses, which is the most attractive advantage of this theory over other homogenizing techniques such as the rule of mixture. The most notable feature of this paper is to utilize the finite element mesh superposition technique along with the homogenization theory in order to analyze cases where non-periodic local heterogeneity exists and the macroscopic field is non-uniform. The accuracy of the analysis using the finite element mesh superposition technique is verified through a simple example. Then, two numerical examples of knitted fabric composite materials and particulate reinforced composite material are shown. In the latter example, a shell-solid connection is also adopted for the cost-effective multi-scale modeling and analysis.