A microstructural design method is developed by utilizing the homogenization method and digital image-based (DIB) geometric modeling technique. The localization capability of the asymptotic homogenization method enables the evaluation of the microscopic deformation in the microstructure, i.e., representative volume element (RVE). This distinctive feature allows us to use the microscopic variables in the functional forms of constraints and objective function. In estimating the micromechanical responses, the systematic modeling method in terms of the pixel information of images and their processing make the construction of unit cell geometry easy and the homogenization results accurate. Therefore, while the specific microstructural geometry is taken into account in evaluating the micro and macroscopic variables, the optimal microstructural configurations can be determined depending on our objectives
This paper discusses modeling issues in the constitutive relation of a composite material in conjunction with the asymptotic homogenization method. Since the constitutive relations for basic materials of the composite material is given in the microscopic level, the identification of micromechanics and the geometric modeling of the microstructure directly affects the overall mechanical behavior of the structural components. Therefore the modeling in the microscopic level is essential in the analysis of composite materials especially for nonlinear cases. Several numerical examples show that the overall mechanical behavior depends on the constitutive relations defined in the microscopic level as well as the geometry of the microstructure. The FEM-based asymptotic homogenization method and Digital Image-Based (DIB) modeling are utilized to simulate such a global-local nature of the mechanical responses.
For easy and practical simulation of microscopic nonlinear mechanical behavior of composite materials, new homogenization analysis procedure named macro-micro uncoupled method is proposed. In this procedure, microscopic simulation of material strength test is carried out first, then nonlinear homogenized material properties are obtained. Both the homogenization method and RVE (Representative Volume Element) approach are shown for this microscopic simulation. Macroscopic nonlinear behavior of a structure made of composite materials can be analyzed by only referring the pre-calculated homogenized material nonlinearity. As an example, microscopic fracture propagation for textile composite materials and microscopic large deformation for porous elastic materials are analyzed.
Long glass fiber reinforced Nylon 6/Amine Terminated Butadiene Acrylonitrile (ATBN) block copolymer pellets were prepared by a pultrusion process. Optical microscope (OM) and scanning electron microscope (SEM) showed that the fiber dispersion and fiber-matrix bonding in the injection molded long glass fiber reinforced Nylon 6/ATBN block copolymer pellets are better than that from the conventional melt pelletized process. The fiber length distribution in the molded samples was calculated by image analyzer. The static tensile strength, tensile modulus, flexural strength, flexural modulus, notched Izod impact and heat deflection temperature (HDT) of injection molded long glass fiber reinforced Nylon 6/ATBN composites are superior to those of the short fiber reinforced Nylon 6 composites. Moreover, the effect of acrylonitride content on the degradation temperature of injection molded long glass fiber reinforced Nylon 6/ATBN composites was studied.
The present paper shows an identification method of bending stiffnesses of symmetrically laminated plates using bending deflections under static loading. Firstly, three bending stiffnesses of simply-supported orthotropic plates are identified by using an analytical expression. Secondly, four or six bending stiffnesses of symmetrically laminated plates are identified by using the finite element method and the nonlinear optimization technique. Effects of the number of measured deflections on the identified bending stiffnesses are examined numerically.
A theoretical analysis is presented for the post-buckling behavior of simply supported crossply laminated plates without initial imperfection subjected to in-plane biaxial compression. A method based on the second variation of total potential energy is then proposed for evaluating the stability of the post-buckling equilibrium state and the inevitable secondary buckling is derived analytically. Numerical results are obtained for carbon-epoxy composite square plates. The effects of the average axial strain, post-buckling deflection, biaxial compressive ratio are illustrated graphically and discussed.
A semi-analytical method is proposed for solving the free vibration problem of a rectangular parallelepiped. The parallelepiped is made of a unidirectionally reinforced fiber composite, which is modeled to have rectangular orthotropy. The method is based on the Ritz approach, and accommodates arbitrary boundary conditions on the six faces by introducing the boundary indices into the displacement functions. Numerical results are given for the first several frequencies of isotropic and orthotropic parallelepipeds, including the cube, and are compared to the existing results obtained by other three dimensional and plate theories.
A new scheme for estimating the intralaminar fracture toughness is proposed. Recent research on the transverse cracking damage in crossply composite laminates suggests the use of the energy-release rate (ERR) of the 90° layer as the fracture toughness of the 90° layer. A brief survey of the authors' formulation of transverse cracking damage is presented, which shows that the ERR of the 90° layer is constant during damage progress in spite of the fact that the transverse cracking is a stochastic process. The ERR of the 90° layer is a constant which completely characterizes the damage evolution process. Some benefits of using the ERR of the 90° layer as a measure of the intralaminar fracture toughness are discussed in comparison with the other parameters such as the transverse strength, the crack resistance and the ERR of the whole laminate.
To predict the strength of notched unidirectional (UD) fiber reinforced laminates, computational modeling method is shown as well as its verification. Both intra-laminar damage such as fiber breaking, matrix cracking and fiber-matrix interface debonding and inter-laminar damage such as delamination occur and propagate up to the final breaking. In the proposed numerical method, the occurrence of the intra-laminar damage is judged by Hoffman's failure criterion and its propagating behavior is theoretically formulated by anisotropic damage mechanics. The delamination is numerically treated by introducing inter-laminar element (IE) in the finite element analysis. Applying the proposed method to CFRP laminates with a hole under tensile load, the damage mode in each lamina and the notched strength have been predicted. By comparison with the experimental results, the validity and the reliability of our simulation have been recognized.
The purpose of this study is to evaluate the lifetime distribution of ceramic fibers by a time-dependent Weibull function, from the viewpoint of materials reliability engineering. Static loading tests and constant loading rate tests of a boron fiber, one of representative ceramic fibers, were carried out in air at 300°C, and the relevant Weibull parameters were estimated from the lifetime and the strength data obtained in the above tests. The results showed that the fibers fractured in a moment or a long-term period in the static loading tests, and the lifetime distributions predicted from the single time-dependent Weibull function were not in good agreement with the long-term lifetime data. The SEM observation for the fracture surfaces indicated that the cause of the long-term rupture was due to a creep damage, and completely different from that of the momentary fracture. Therefore, a mixed time-dependent Weibull function based on a mixed distribution model was proposed for evaluating again the lifetime data. It was clarified that, finally, the function proposed here was enough applicable for predicting the creep-rupture lifetime distribution of boron fibers.