The homogenization method with characteristic deformation mode superposition is presented in this paper for geometrically nonlinear problems. It is well known that in nonlinear homogenization method, at every Newton-Raphson iteration, characteristic deformations are required to evaluate the homogenized moduli and these process needs huge computation. In the proposed method, the characteristic deformations are approximated by initially computed ones with scaling factors. The scaling factors can be statically condensed when macro element equations are evaluated. Some simple numerical results demonstrate the validity of this method.

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The axial crushing behavior of a triangulated cylindrical shell constructed by one set of helical strips and circles lying on the surface, is simulated by the finite element method. This paper also discusses the affection to the crushing characteristic of the angle and the number of the helix as well as the number of the circles along the axial direction of the cylinder. Based on the numerical analyses, minimizing problems of the axial crushing force of triangulated cylindrical shells are solved by using the crashworthiness maximization technique for tubular structures which combined the techniques of design-of-experiment, response surface approximation as well as usual mathematical programming. Moreover, the behavior of the triangulated cylinders when subjected simultaneously to axial crushing and twisting forces is optimized.

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This paper presents a method for identifying the Gurson's material constants by inverse analysis. Firstly, in order to improve the accuracy, the measurement condition, such as geometries of specimens, locations of measurements and types of measurements, is optimized. This approach is based on the Kalman filter technique. The optimization is achieved by minimizing the maximum eigen value of a posteriori estimate error covariance matrix. Mathematically, this procedure is reduced to solve a combinational/discrete optimization problem. Secondly, the Gurson's material constants is estimated by using Kalman filter. A numerical identification is presented to demonstrate the validity and usefulness of proposed method.

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Structural topology optimization has been applied to the various kind of problem in many industrial fields. And the homogenization method which is the base technology of topology optimization has been improved by introducing the 'Frame based unit cell'. This paper presents a methodology for a topology optimization based on the Frame based unit cell to satisfy both static and dynamic requirements which sometimes conflict in structural design. The mean compliance for the structural stiffness is used as the objective function and the mean eigenvalue and the structural mass are dealt with as constraints. The optimization problem with multiple constraints is solved by using a convex linearization method which was originally introduced by Fleury in 1989. The result of the proposed method is compared with the weighting objective method which is usually applied to the multiple objective problems. Illustrative examples are shown and the effectiveness of the proposed method is discussed.

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In order to establish the assessment method of creep damage for high temperature piping components made of mod. 9Cr-1Mo steel with circular seam welded joint, the internal pressure creep tests and FEM stress analysis were done. Internal pressure creep tests showed the creep rupture occurred in the coarse grained heat affected zone (C. G. HAZ), caused by cracking originated from the formation of voids on grain boundaries. The void parameters such as void area fraction, density of void population and "A" parameter correlated well with time fraction in internal pressure creep tests. Vickers hardness decreased with creep times and correlated well also with time fraction of internal pressure creep tests. Stress distribution of cylinder with circular seam welded joint under internal pressure creep showed the maximum circumferential stress in C. G. HAZ where creep rupture occurred. The distribution of circumferential stress and creep damage calculated by using circumferential stress along specimen thickness were quite similar to that of void area fraction. The creep damage of circular seam welded joint under internal pressure creep could be estimated by the observation of void and the FEM stress analysis.

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Microcracks at tips of longer fibers aligned in the straining direction are more likely to form in a short-fiber composite. An analytical model for a composite is developed to estimate effects of such fiber-end cracks on stiffness reduction by applying the Eshelby's equivalent inclusion method to two kinds of inhomogeneities, i.e., crack and fiber. Additionally a frequency distribution of fiber-end stress at crack occurrence is obtained from in-situ tensile test in SEM using injection-molded specimens, and used in the analytical model. Good agreement between the theoretical results based on the present model and the experimental ones is shown about a nonlinear stress-strain relationship of carbon-fiber/polycarbonate composite. Furthermore the effects of crack radius, fiber volume fraction, fiber orientation distribution and fiber aspect ratio on crack occurrence and the stiffness reduction are investigated.

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Postbuckling behaviors and load-carrying capacity of thin laminated plates under uniaxial compression have been discussed by many researchers. However, little research has been performed on the postbuckling behaviors and the secondary buckling phenomenon for thin laminated curved plate which occurs with further increase of load. In this paper, angle-ply laminated curved plates under uniaxial compression which are simply supported along four edges is considered as an example. By a proposed method based on the second variation of total potential energy to judge the stability of postbuckling equilibrium state, the inevitability of secondary buckling is proven analytically, and the effects of various factors, such as dimension of curved plate, assumed virtual displacement pattern, postbuckling deflection pattern and average axial shortening, on the secondary buckling values are clarified.

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Recently composite laminated structures have been applied to many structures of vehicles. Because of its low interlaminar strength, delamination can be generated in the structures easily by external impact forces. Since the existence of delamination degrades compression stiffness of the structures, it is very important to identify delamination nondestructively. In the present study, we propose the delaminated domain location method of CFRP laminated beams using anti-resonance frequency change. The anti-resonance frequencies on a frequency response function are changed from an intact state by existence of delamination. The criteria for judging existence of a delamination between the actuation point and the measurement point on vibration test is devised. The present method is applied to delaminated domain location of CFRP laminated beams and the effectiveness of the present method is shown.

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Equivalent expression is derived for an ellipsoidal double inhomogeneous inclusion which consists of a nested sequence of two inhomogeneous inclusions whose elastic constants are different both from that of a matrix and from each other. By using the resultant equivalent expression, the elastic strain energy and the total potential energy of such an ellipsoidal double inhomogeneous inclusion are formulated as a function of two equivalent eigenstrains. In addition to this, for two types of the mixed double inclusions, i.e., one is the mixed double inclusion of the first kind which is defined as an ellipsoidal inhomogeneous inclusion surrounded by an annular inclusion and the other is that of the second kind which is vice visa, equivalent expressions, elastic strain energies, and total potential energies of the system are also derived successfully.

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In a partially stabilized zirconia (PSZ) containing tetragonal ZrO₂ particles, a crack may be closed due to dilatational transformation strain of the particles induced in both a process zone and its wake surrounding the crack by enhanced stress at the vicinity of the tip of crack. In this study, micromechanical analysis on the toughness of such a PSZ is performed by modeling a crack surrounded by a process zone and its wake as a mixed double inclusion of the first kind which is defined in the previous paper as an ellipsoidal inhomogeneous inclusion surrounded by an annular inclusion. Energy release rate of the crack G in the PSZ is derived and then its decrease ΔG due to stress induced transformation of particles is formulated as a function of the transformation strain, the thickness of zone wake, and the volume fraction of particles. Numerical results of ΔG is good agreement with the experimental ones obtained by Swain et al.

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In these days, crashworthiness design has been required more frequently in rail vehicle. The results of static strength test of an end underframe that absorbs most of the crash energy were presented, as well as numerical simulations. By comparing both results, the numerical simulations were found to be adequately accurate. Then, a new and highly crashworthy structure was proposed. Both of the test and the numerical simulation confirmed that the structure worked well to absorb the crash energy. Further, effects of welding strength, geometrical initial imperfection, and strain rate on the crashworthiness were discussed. Especially, strain rate effect of materials is important to evaluate crashworthiness accurately.

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Quantitative characterization of surfaces of anodic dissolved nickel films was performed using the roughness exponent, the Hurst rescaled range analysis and the Fourier transform of their AFM images. Of three methods, the first and second methods give almost the same fractal dimension 2.06 and 2.02 respectively, which indicate the roughness exponent α interchanged with the Hurst exponent, but the third method determines a little larger fractal dimension 2.25. The value of the fractal dimension, 2.0, implies that the anodic dissolved nickel films surface have no fractal structure.

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Lamb waves generally consist of many dispersive modes, which makes mode identification difficult. This study discribes the extraction of a single mode from multiple modes. The single mode extraction is based on two dimensional Fast Fourie Transform (2 D FFT) in time and space, signal filtering and 2 D inverse FFT. Air-coupled ultrasonic technique were adopted for non-contact fast measurements. Using this technique, the A 0 and S 0 modes were clearly detected in preliminary tests of intact plates. Furthermore, multiple reflections of the A 0 mode, which were shown only in the computer simulation, were experimentally confirmed in reflection tests of plates with a square notch. In the reflection tests, two reflected waves were extracted in the intervals corresponding to notch widths.

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This paper presents the fatigue response of high strength steel, SNCM 439, depending on work hardened layer and humidity. Tests were conducted in laboratory air and in dry air using cantilever type rotating bending fatigue testing machines. The dew point of dry air is -60°C. Specimens with two different surface conditions were prepared, i.e., buff finished and electro polished specimens. In the buff finished specimens, a step wise S N curve was seen in both environments, but the horizontal part of the S N curve below which subsurface crack initiation occurred shifted to a higher stress level in dry air. In the electro polished specimens, a step wise S N curve was not observed in laboratory air, but seen in dry air. At stress levels where cracks initiated at the surface, the fatigue lives of the electro polished specimens decreased compared to the buff-finished. On the contrary, at stress levels where subsurface cracks were generated, the fatigue lives of both specimens were the same, indicating no influence of surface finishing condition and environment.

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The objectives of this study were to investigate the effectiveness of a compliance method for analyzing the fatigue crack growth of GLARE 3 fiber/metal laminates, and to ascertain the influence of specimen thickness, notch length, and fiber orientation upon fatigue crack growth. The materials tested were GLARE 3-5/4 and GLARE 3-3/2. Centrally notched specimens with two kinds of notch length and two kinds of fiber orientation were fatigue tested under constant amplitude loading. The experimental stress intensity factors, K_exp, for the 2024-T3 aluminum-alloy layers of a GLARE 3 were obtained from the relationship between crack length and specimen compliance. The test results clarified that da/dN-ΔK_exp relationships are roughly independent of maximum stress level, specimen thickness, notch length, and fiber orientations and that the compliance method is effective for analyzing fatigue crack growth in GLARE 3 laminates.

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Fatigue properties of a bearing steel (SUJ 2) including long life region were experimentally examined under axial loading and discussed from viewpoints of fractography and fracture mechanics. Thus, the complicated S-N property in the wide life region was well explained as the duplex S-N characteristics superimposed two different S-N curves for surface induced fracture and interior inclusion induced fracture. Fish-eye was formed on the fracture surface of each specimen in the interior inclusion induced fracture. Fine granular area (FGA) was necessarily observed around the inclusion at the center of the fish-eye. Stress intensity factor ranges at FGA, fish-eye and final fracture stage were in good agreement with their corresponding levels in the crack propagation law confirmed by CT specimens.

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Fatigue tests up to (10)⁸ cycles were carried out for two spring steels (heats A and D 1) and one valve spring steel (heat F) with tensile strength, σ_B, of 1720, 1725 and 1764 MPa, respectively. The size and composition of inclusions in heats D 1 and F were controlled. The surface type fracture occurred at the shorter life below (10)⁶ cycles, while the fish eye type fracture occurred at the longer life. The fatigue limit, σ_W, at (10)⁸ cycles was 640 MPa for heats A and D 1, and 700 MPa for heat F. Al₂O₃ inclusion for heat A and both of TiN inclusion for heat A and matrix crack, i.e., internal facets, were observed at the fracture sites, while only matrix cracks were observed for heat D 1. ODA, i.e., optically dark area, which is considered to be related to hydrogen embrittlement were formed around Al₂O₃ and TiN inclusions. Fatigue tests were also conducted after specimens were heated up to 300°C in the high vacuum of 2×(10)⁶Pa. The heat treatment eliminated matrix cracks for heat D 1 and the fatigue limit at (10)⁸ cycles recovered to the estimated value of 920 MPa from the equation σ_W=0.53σ_B for the surface type fracture. These results suggest that the inclusion control and hydrogen embrittlement influence the giga-cycle fatigue properties for the high strength steel. In addition, it is expected that the creation of martensite structure with the high resistance against hydrogen enbrittlement in the inclusion controlled steel could achieve the higher fatigue limit estimated for the surface type fracture.

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In this paper a plane bending fatigue tests have been performed to investigate the effect of die pressing on fatigue strength of the plate specimens with a central circular hole. The main results are as follows : (1) The fatigue limit of notched specimen by die pressing is increased by 60% as compared to that of the same notched specimen without die pressing and is equal to that of plain specimen. (2) The reason of increase in the fatigue limit is attributed to the work hardening and compressive residual stress, which are generated by die pressing to the edge of the hole, which increase the resistance against crack initiation and suppress its initial growth. (3) In the case of die pressing, the lifetime summations of the period of the fatigue crack initiation and short crack propagation within 1mm is about 80% of the total number of cycle to failure.

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It was shown previously that a crack in a weld line between high tension steel and mild steel causes mode II type fracture, even under so called mode I type loading, due to the difference of material properties, especially, to the difference of yield stress. In this study, the fracture experiments of the specimen with a crack in a weld line between two different steels were carried out changing the yield stress ratio of two steels from 1.0 to 2.67 (smaller value is taken as a unit). In the experiments, it was observed that fracture mode changes from mode I type to mode II type around yield stress ratio of 1.22 with the increase of its value. Finite element analyses corresponding to the experiments were also carried out taking the variation of yield stress in the weld line and heat affected zone by welding into account and the CED (crack energy density) in an arbitrary direction was evaluated through the results. It is demonstrated that the fracture criterion based on the CED in an arbitrary direction works well to explain the growth initiation behavior of a crack in a weld line between different steels and, moreover, the fracture mode change with the increase of yield stress ratio can also be explained based on the criterion.

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High speed holographic microscopy is applied to take three successive photographs of fast propagating cracks at the moment of bifurcation. The cracks are propagated in PMMA plate specimens at a speed of about 660m/s. From the photographs, crack opening displacement (COD) is measured along the cracks as a function of distance γ from the crack tips. The measurement results show that the COD_S are proportional to √(γ) before bifurcation. After bifureation, the COD_S of mother cracks are proportional to √(γ), however, those of bifurcated cracks are not always proportional to √(γ). The energy release rate is obtained from the COD data, and is found to be continuous across the bifurcation point. The continuity of the energy release rate is explained through the fact that the bifurcated cracks appear as three dimensional cracks, not as through cracks.

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Local approach of fracture in damage mechanics based on an anisotropic damage tensor in applied to analyse the anisotropic aspect of crack problems. The stress analyses of a plane stress model with a crack inclinated toward the load direction were conducted to evaluate the validity of the damage tensor. The results of the FE analysis using the present model were compared with those by the standard code. Although some differences were found between the present and the conventional analyses at the crack tip probably owe to the F. E. approximation, good agreements were obtained between them in general.

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In this paper, a singular integral equation method is applied to calculate the distribution of stress intensity factor along crack front of an elliptical internal crack near the free surface. The stress field induced by the force doublet in a semi-infinite body is used as the fundamental solution. Then, the problem is formulated as an integral equation with a singularity of the form of γ^-3. In the numerical calculation, the unknown functions of the density of body force doublet are approximated by the product of fundamental density function and polynomials. The numerical results show that the present method yields smooth variation of stress intensity factors along crack front very accurately even when the crack is extremely near from the free surface. The mode I, II and III stress intensity factors for an inclined elliptical crack are shown for various geometrical conditions.

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Fatigue tests of crack propagation from a pre crack in thin walled tubular specimens made of a medium carbon steel were performed under cyclic torsion with and without superposed static tension. The condition of the transition from shear to tensile mode and the propagation behavior during this transition were investigated from the viewpoint of fracture mechanics. The direction of fatigue crack propagation follows the direction of the maximum of the total range of the tangential stress, Δσ_{θ max} near the crack tip and then gradually changes to the direction perpendicular to the maximum of the total range of the principal nominal stress. The propagation rate is faster than the uniaxial data when compared at the onset of crack extension and at high stress intensity factors. The former acceleration is caused by crack closure and the latter acceleration is due to the non singular T stress. The negative nonsingular stress induces excessive plasticity ahead of the fatigue crack, and then accelerates the fatigue crack.

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In this paper a three dimensional crack perpendicular to and terminating at a bimaterial interface is considered under general mixed-mode loading. The solution utilizes the body force method and requires Green's functions for perfectly bonded elastic half planes. The formulation leads to a system of hypersingular integral equations whose unknowns are three modes of crack opening displacements. The main-part analytical method is used to investigate the characteristics of stress singularity around the crack front touching the interface. An explicit closed-form expression is given for the singular stress field, which is controlled by general stress intensity factors. The relations between three modes of crack opening displacements and stress intensity factors are also discussed.

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