Katsumi Tao

The Mechanical Behavior Analysis of CFCC with Overall Anisotropic Damage by the Micro-Macro Scale Method

In this paper, a micro-macromechanical approach is used to establish the macroscopic constitutive model with anisotropic damage in continuous fiber reinforced ceramic matrix composites (CFCC). For microlevel analysis of unit cell, the homogenization method based on double-scale asymptotic expansion is used to derive the material properties of composites. The macrolevel analysis is conducted to compute the macrostresses and strains with anisotropic damage. The two analyses are conducted by using Finite Element Method (FEM). An overall anisotropic damage tensor for the whole composite is used to describe all types of damage that composite undergoes, such as matrix cracking, fiber breakage, and interfacial damage between matrix and fiber. The damage evolution equation is obtained by using thermodynamic theory. The numerical calculation is carried out to investigate and to predict the onset and evolution of anisotropic damage for composites with different types of laminate. The damage material parameters are determined by fitting the numerical results to the experimental data, and some results are compared well with experimental results in the literature [Wang, S.W. and Parvizi-Majidi, A. (1992). Experimental Characterization of the Tensile Behavior of Nicalon Fiber-Reinforced Calcium Aluminosilicate Composites, Journal of Materials Science, 27: 5483-5496.]. By using the proposed model, the stiffness and nonlinear stress-strain response of brittle composite materials are predicted, and the macroscopic elastic brittle anisotropic damage behavior is also described

Application of fracture mechanics to the surface crack propagation in stainless steel at elevated temperatures

Abstract The propagation of small surface cracks in SUS 304 stainless steel is examined at elevated temperatures. In the temperature region studied, the crack growth is mainly cycle-dependent. When temperature is higher than 500°C, creep-dependent crack growth becomes dominant which results in a larger crack growth rate. By confirming that the surface crack maintains a semi-elliptic shape during its growth and by investigating the cyclic deformation behavior of the material, elastic-plastic fracture mechanics parameters are evaluated and used to correlate the crack growth rate. Both the J integral range ΔJ, and the effective J integral range ΔJeff, which accounts for the crack closure effect, are found to be excellent to consolidate crack growth rates for the high temperature fatigue conditions.

Nonlocal elastic damage near crack tip

A constitutive modeling for nonlocal elastic damage near crack tip is proposed. A calculation method for nonlocal elastic damage is introduced and the computational results for stress and damage are given by means of finite element method.

Effect of loading frequency on fatigue crack growth under high temperature

Abstract The effect of loading frequency on the fatigue crack growth under high temperature is studied. The high temperature fatigue crack growth tests for pure titanium (99.5%) are carried out under three loading frequencies (2, 6, 20 Hz). An elasto/viscoplastic constitutive equation which fully couples strain to continuum damage is used to analyse fatigue crack growth at high temperature. A damage criterion is employed for predicting the crack growth which is related to the actual material failure ahead of the crack tip. By means of FEM, the mechanical fields ( σ ij , e ij , D ) and the dependence of crack growth rate on loading frequency and viscoplastic strain at the crack tip are investigated in detail. The numerical simulation results of the fatigue crack growth are shown and compared with the experimental ones. The results in the present study show that: (1) the stress at the crack tip element decreases rapidly with the cyclic numbers. There is no stable state of stress distribution in the fatigue process when material damage is taken into account. (2) The crack tip stress is lower than the peak stress and the peak stress takes place at a location away from the crack tip. No stress singularity is present at the crack tip. (3) The fatigue growth rate dl/dN is closely related to the Δe y vp obtained by numerical analysis. If d t /d N is plotted against Δ e y vp , the relation can be expressed by a straight line in logarithmic coordinates for any loading frequency.

A nonlocal damage mechanics approach to high temperature fatigue crack growth

Abstract A nonlocal damage constitutive model is developed for elasto/visco-plastic materials and is used to analyze fatigue crack growth at high temperature. In this model, no kinematic hardening rule is needed to account for the subsequent yielding and strain hardening behavior of the materials. A calculation method for nonlocal damage is introduced. The fatigue crack growth tests at high temperature for pure titanium (99.5%) are carried out. By means of FEM, the mechanical fields (σij, ϵij, D) and their redistribution due to damage effect near the crack tip are investigated. The numerical simulation results of the fatigue crack growth are shown. The validity of the presented damage model is verified by comparing the FEM numerical simulation with experimental results.

A nonlocal damage approach to analysis of the fracture process zone

Abstract A two-zone fracture process model with a crack-bridging zone (CBZ) and a microcracking zone (MCZ) is proposed to describe the fracture process around the tip of a macrocrack. A nonlocal damage approach based on previous work is used to determine the size of the fracture process zone (FPZ). The experimental analysis given by Horii and Ichinomiya [Int.J. Fracture51, 19–29 (1991)] supports the proposal that the existence of the crack bridging effect brings out an increase in load-carrying capacity of materials, whereas microcracking leads to the deterioration of the capacity. Based on the above and utilizing Westergaards complex function, the distribution functions of stress arid damage in the FPZ are given. Applying these to the concrete-like material mortar, we can determine the distribution functions of stress and damage in the FPZ if load and crack opening displacement (COD) at a point are given. Additionally, a nonlocal damage failure criterion is proposed to judge the propagation of the macrocrack.

Elasto/Visco-Plastic Dynamic Response of Moderately Thick Shells of Revolution under Consideration of Rotatory Inertia

An analytical method for the elasto/visco-plastic dynamic problems of general moderately thick shells of revolution is developed in consideration of the effect of the shear deformation and rotatory inertia. The equations of motion and the relations between the resulting stresses and displacements are derived by extending the Naghdi theory in elastic shells with given consideration to the effect of shear deformation and rotatory inertia. For the constitutive relations, the elasto/visco-plastic equations by Fyfe based on the model developed by Perzyna are employed. The numerical method selected for this problem is a method using finite difference in both space and time. As a numerical example a cylindrical shell under a semi-sinusoidal internal pressure with respect to time is analyzed, and the results are compared with those from the theory which neglects the effect of rotatory inertia.

Dynamic Stress and Deformation of Non-Homogeneous Poroelastic Moderately Thick Shells of Revolution Saturated in Viscous Fluid

This paper describes an analytical formulation and a numerical solution of the elastic dynamic problems of non-homogeneous poroelastic moderately thick shells of revolution saturated in viscous fluid. The porosity and porous diameter of the material are assumed to be continuously varied along the shell thickness. The equations of motion and the relations between strains and displacements are derived from the Reissner-Naghdi shell theory. As the constitutive relations, the consolidation theory of Biot for models of fluid-solid mixtures is employed. The flow of viscous fluid through a porous elastic solid is governed by Darcys law. In the numerical analysis of the fundamental equations an usual finite difference form is employed for the spatial derivatives and the inertia terms are treated with the backward difference formula proposed by Houbolt. As a numerical example, the simply supported cylindrical shell under a semi-sinusoidal internal load with respect to time is analyzed. Numerical computations are carried out by changing porosity and mean void radius along the shell thickness, and the variations of pore pressure, displacements and internal forces with time are analyzed.

Dynamic Stress and Deformation of Non-Homogeneous Poroelastic Shells of Revolution Saturated in Viscous Fluid

This paper describes an analytical formulation and a numerical solution of the elastic dynamic problems of non-homogeneous poroelastic shells of revolution saturated in viscous fluid. The porosity and porous diameter of the material are assumed to be continuously varied along the shell thickness. The equations of motion and the relations between strains and displacements are derived by extending the Sanders shell theory. As the constitutive relations, the consolidation theory of Biot for models of fluid-solid mixtures is employed. The flow of viscous fluid through a porous elastic solid is governed by Darcys law. In the numerical analysis of the fundamental equations an usual finite difference form is employed for the spatial derivatives and the inertia terms are treated with the backward difference formula proposed by Houbolt. As a numerical example, the simply supported cylindrical shell under a semi-sinusoidal internal load with respect to time is analyzed. Numerical computations are carried out by changing porosity and mean void radius along the shell thickness, and the variations of pore pressure, displacements and internal forces with time are analyzed.

Thermal Stress and Deformation in Moderately Thick Shells of Revolution of Functionally Graded Material under Thermal Loading due to Fluid.

This paper is concerned with an analytical formulation and a numerical solution of thermal stress and deformation for moderately thick shells of revolution made of functionally graded material (FGM) subjected to thermal loading due to fluid. The temperature distribution through the thickness is experessed using a curve of high order, and the temperature field in the shell is determined using the equations of heat conduction and heat transfer. the equations of equilibrium and the relations between strains and displacements are derived from the Reissner-Naghdi shell theory. The fundamental equations derived are numerically solved using the finite difference method. As numerical examples, functionally graded cylindrical shells composed of SUS 304 and ZrO2 subjected to thermal ioads due to fluid are analyzed. The results show that the present method gives correct temparature distributions and that the temperature distributions, stress distributions and deformations vary significantly depending on the compositional distribution profiles in FGM.