Ryoji Yuuki

Crack-morphological aspects in fracture mechanics

Abstract Fracture mechanics can be regarded as a methodology to characterize the actual crack by using the parameters given by the analysis of a simple mathematical crack model. Therefore, the selection of these crack models has very significant meanings. In recent years, several precise crack models have been proposed. In this paper, we paid attention to the influences of the two-dimensional crack geometry and presented the numerical value of the elastic analytical solutions for the non-linear shaped cracks, those are, the bent, the curved and the branched crack. On the basis of these results, the characteristics of these cracks were discussed and the methods of approximate replacement to a simple straight crack were proposed. We examined a zig-zag growth of crack and the crack branching observed in actual fracture processes.

Effect of microstructural parameters on the fracture behavior of fiber-reinforced ceramics

A bridging law which includes both interfacial debonding and sliding properties in fiber-reinforced ceramics is applied to fiber bridging analysis and crack growth problems by treating bridging fibers as a distribution of closure stress. A numerical method to solve distributed spring model of a penny-shaped crack is provided to determine the bridging stress, debond length, crack opening displacement and stress intensity factor. By introducing fracture criteria of the composite and fiber, crack growth behavior in R-curve for the penny-shaped crack are simulated and the effects of such microstructural parameters as interface debonding toughness, compressive residual stress, frictional sliding stress, and fiber volume fraction on the R-curve are quantified in an explicit manner. On the basis of R-curve results, the toughening mechanism of fiber-reinforced ceramics is discussed.

Efficient error estimation and adaptive meshing method for boundary element analysis

Abstract This paper describes a new and efficient error estimator by using the Direct Regular Method and h or h - r adaptive meshing for BEM analysis. This posteriori error estimator correctly indicates the discretization errors on each element. Based on the error distribution, and the adaptive meshing is generated automatically. The accuracy and convergence of this method are demonstrated by the numerical results on the stress concentration problem and the crack problem.

Boundary Element Analysis of the Stress Intensity Factors for an Interface Crack in Dissimilar Materials

This paper describes the boundary element elastostatic analysis of a crack along the straight interface between two dissimilar materials. It is well known that the interface crack has an oscillation singularity at the crack tip which is quite different from a crack in homogeneous materials. Therefore, the definition of the stress intensity factor is not clarified yet and it is very difficult to analyze the interface crack by the numerical methods, such as FEM and BEM. We proposed a method to determine the stress intensity factors K1 and K2, for the interface crack by means of extrapolating the solutions at the points apart from the crack tip to avoid the oscillation singularity. This method can be widely applied to the BEM and also FEM analyses with any changes of the programmes. It is confirmed that the present results of the stress intensity factors for an interface crack in the infinite plate are completely consistent with the exact solutions. The stress intensity factors for various interface cracks in the finite plate and the adhesive joint are analyzed by the present method and BEM analyses, which is specially developed for this study.

The usefulness and limit of the direct regular method in boundary element elastostatic analysis.

A Boundary Element Method(BEM) has been developed as a new efficient numerical analysis method, and is applied widely to various fields of engineering problems1,2 these days. The mainstream of them is the Direct (Singular) Method, in which a boundary integral equation is discretized directly. Very accurate results have come to be obtained by introducing the sophisticated discretization techniques of FEM3. In the Direct Method, a special care must be taken to carry out the singular integral, since both the load point and the object point of the fundamental solution are located on the boundary. Therefore much computation time is necessary for the numerical integration.

Accurate BEM Elastostatic Analysis for Very Slender Body and Thin Plate

Recently it becomes very important to analyze the bonded structures with thin plates, the dissimilar materials, the adhesive joints, and the laminate plates. But in the usual boundary element elastostatic analysis (DSM) of very slender body and very thin plates, it is known that the unstable and inaccurate solutions are sometimes encountered. In the present paper, we point out the factors of this inaccuracy and provide the strategies for each factor to obtain an accurate solution. From this study, the highly-accurate solutions can be obtained even If the aspect ratio of slender beams and thin plates is in thousands and hundreds.

On the Improvement of the Boundary Element Analysis for the Crack Problems

The boundary element method has attracted special interest as a powerful method to analyze the crack problems. However, there still remain some problems to be improved for the accuracy and efficiency. In this study, it is attempted that some simple and accurate methods for determining the stress intensity factors are developed and introduced into the BEM analysis. In the three dimensional BEM analysis, Mindlin’s solution has been used as a fundamental solution for a point load acting within a semi- infinite medium instead of the ordinary Kelvin’s solution. It is expected that the accuracy of solution is improved and that the cost for computation is reduced because there is no necessity for dividing into elements on the surface where boundary conditions are satisfied by the fundamental solution.

BOUNDARY ELEMENT ELASTOSTATIC ANALYSIS OF DISSIMILAR MATERIALS AND THE INTERFACE CRACK

ABSTRACT To analyze the interface crack problems in dissimilar materials easily and efficiently, a boundary element elastostatic analysis program using two kinds of fundamental solution(Hetenyis and Kelvins solutions) is developed. By this program, we can analyze the dissimilar material problems without discretization of the interface. In this paper, we also propose a method to analyze an interface crack with a partially closed crack tip under shear or mixed loadings. By the comparison with Comninous theoretical solution, it is found that the method is useful. This paper also presents the method to deal with residual thermal stress which is due to the manufacture process. There exists quite large residual stress at the interface, especially around the edge point, if the materials have different thermal expansion coefficients.

SHAPE OPTIMIZATION FOR STRESS CONCENTRATION PROBLEMS IN ORTHOTROPIC MATERIALS BY USING BOUNDARY ELEMENT METHOD

ABSTRACT The shape optimization problem for finding minimum stress concentration in orthotropic plate is solved. Boundary element method has been developed for analysis of orthotropic materials involving arbitrary principal material direction by using the rotations of fundamental solution, and the good accuracy and efficiency were shown. The optimization algorithm described in this paper is to introduce the Complex Method, which is an efficient method for finding the minimum value of a general constrained nonlinear function without calculating derivatives, to the mentioned boundary element method. As an important application, the stress concentration problem of the fiber-reinforced composite with a center hole is discussed and optimal hole shape with minimum stress concentration are given for various angle-plys of the fiber and under various biaxial loadings.

APPLICATION OF NEW METHODS TO THE BOUNDARY ELEMENT METHOD ANALYSIS OF STRESS INTENSITY FACTORS

ABSTRACT It is necessary to develop the method suitable for Boundary Element Method (BEM) to determine the stress intensity factors (K) simply and accurately. New methods are proposed, using the solutions of the stress or the displacement near a crack tip obtained by BEM analyses. The methods can determine the accurate values of the stress intensity factors without any modifications of the given BEM programs. These methods proposed are applied to the BEM analyses for various two dimensional as well as three dimensional crack problems. From these numerical results, it is concluded that the present methods can be successfully applied to BEM analyses of K and can satisfy both demands of simplicity and high accuracy.