The corrosion current variation was measured during low cycle corrosion fatigue with stress hold time in a simulated electrochemical system. The flow out of substantial corrosion current from the strained metal continued for more than several hours and then decayed. The charge transfer per cycle which is related to the amount of anodic dissolution per cycle depended on the length of hold time and stress level. The variation in the charge transfer per cycle was considered to have caused the hold time effect which decreased the fatigue crack initiation life in low cycle corrosion fatigue.

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Fatigue Strength and stress-strain response of plain woven glass fibric laminates subjected to pulsating tension/pulsating torsion combined loading were studied in this paper. In order to evaluate the biaxial fatigue failure strength, the normalized fatigue strength that a cyclic biaxial stress is divided by the static strength was used in S-N curves. According to the test results, it is found that all data locate in a slightly wide band on the S-N plot in spite of different biaxial stress ratios, but the tendency that the slope of the S-N curve becomes low in case of a high shear stress component, can be distingushable. The tendency of modulus decays in both tension and shear even under combined loading is almost the same as those under uniaxial tension and pure torsion loadings, respectively. The direction of matrix cracking seems dependent on the principle stress direction under pulsating tension/pulsating torsion combined loading although it is also strongly influenced by fiber orientation.

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In this paper, the micromechanism of the deformation process during fatigue testing was discussed. ABS and polyacetal, which are applied in industrial service using were used. Quantitative analysis of the damaged area on the tensile and fatigue specimen by scanning acoustic microscope (SAM) was performed. Furthermore, TEM observation of the fracture surface was carried out to clarify the micromechasism of the damaged area. As a result, it was found that ( 1 ) in tensile testing, the damaged area of the specimen was widely dispersed. On the other hand, in fatigue testing, the damaged area was concentrated near the fracture surface: ( 2 ) the micromechanism of the deformation process could be explained by the nucleation and coalescence of crazes or microcracks.

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In this paper, rotating-bending fatigue tests of the SiC-whisker-reinforced 6061-T6 aluminum alloy and 6061-T6 aluminum alloy made by powder metallurgy were carried out to investigate the fatigue characteristics of plain and notched specimens at room temperature. The fatigue mechanisms in both materials were clarified through successive surface observations using the plastic replica method. In the case of the SiC-whisker-reinforced composites, there are whisker rich and poor zones and the fatigue crack is nucleated from the end of whiskers near the boundary. On the other hand, in the case of the aluminum alloy, the fatigue crack is nucleated from defects and propagates by shear. Moreover, the results were discussed based on linear notch mechanics.

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Fatigue crack propagation and crack closure have been investigated on spheroidal-graphite cast irons (SGI's) with four different microstructures, i. e., ferrite, pearlite, bull's eye and aus-ferrite. The crack propagation rates plotted against the stress intensity factor range showed the microstructure dependence due to a different contribution of crack closure. However, as crack closure was taken into account, the crack propagation rates became insensitive to the microstructures, indicating that the intrinsic propagation resistance was the same in all the microstructures studied. Furthermore, the published propagation data on SGI's with a wide variety of microstructures were reviewed, and an overall discussion is developed on the effect of microstructure on fatigue crack propagation.

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In this paper, rotating bending fatigue tests of two kinds of spheroidal graphite cast iron were carried out in order to clarify the effects of elasticity and compactness of graphite on the fatigue strength of the two cast iron samples. One is as-received cast iron whose graphites are compressed by the matrix and the other is cast iron annealed at 550°C whose graphites exist more loosely. The crack initiation limit of the as-received material is about 10% higher than that of the annealed material in the plain and notched specimens. The effects were discussed through the behaviour of the microcrack, based on successive observations using the plastic replica method.

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The caustics method as applied to the measurement of the impact fracture toughness K_Id is studied by using a three-dimensional finite-element method (3D-FEM). A semi-infinite crack in an elastic plate with a finite thickness is considered, and a time-dependent (ramp) uniform pressure is assumed to be applied to the crack surfaces. The dynamic J-integral, J, is calculated for various points on the crack front and is converted to the dynamic stress intensity factor K_I(t). The crack is assumed to begin to propagate when the value of K_I(t) at the mid-thickness of the plate reaches a critical value K_crit. The caustics in reflection are generated by using the reflection law of light. The "measured" K_I(t) is obtained from the diameter of the caustics, and the "measured" K_Id is determined from the peak of the time history of the "measured" K_I(t). It is found that the delay time to detect the crack initiation is larger than that predicted by 2D-FEM, and the "measured" K_Id depends on the shape of a propagating crack front.

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A standard test method for the fracture toughness of High-Polymer Materials has not been established. In this paper, according to ASTM standard E399 fracture toughness tests were conducted using three point bend specimens of Polycarbonate to investigate the effect of plate width on fracture toughness. The tests results were summarized as follows: ( 1 ) The values of fracture toughness depend on the plate width. They decreesed and converged a constant value as the plate width increased. ( 2 ) The valid K_Ic was obtained from the specimens with the plate width of above 40 mm. Finite element analyses were also carried out. It was shown that the load-displacement curve passed 5% offset line for the specimens of W<30 mm, and a yielded zone around the crack tip became larger as the decrease of plate width.

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This paper describes a probabilistic fracture mechanics ( PFM ) program based on the parallel Monte Carlo (MC) algorithm. In the present parallel algorithm, a sampling space of probabilistic variables such as fracture toughness values and crack depth and aspect ratio of initial semi-elliptical surface cracks is divided into a number of small cells. Fatigue crack growth simulations and failure judgements of samples are performed cell by cell on a parallel computing system consisting of multiple micro-processors, TRANSPUTERs (T800). As an example, the developed PFM computer program was applied to the analyses of PFM problems of aged RPV material. The results showed that break probabilities of the analyzed model were of an order of 10^-7 and that the performance of parallel processing was over 90%. It was also demonstrated from these analyses that degradation of fracture toughness values due to neutron iraddiation influences significantly influences failure probabilities.

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This paper describes the investigation of brittle to ductile transition in alpha-iron using an approximation in which fluctuations are neglected and a molecular dynamics simulation. By introducing two kinds of forces, the tendency for slip or cleavage is evaluated, using an approximation in which the atom position fluctuations are neglected. For ideal crystals, expanded alpha-iron single crystals are apt to be more ductile than compressed ones in the case of uniform tensile deformation. Crack propagation and blunting processes are simulated in alpha-iron using a molecular dynamics approach, utilizing the Johnson potential. The simulations show that expanded crystals are likely to undergo shear breakdown and that compressed ones are likely to fail due to cleavage. The results obtained with molecular dynamics simulations are found to be consistent with those obtained with analysis that neglects fluctuations.

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Molecular dynamic simulation is used to investigate the atomic mechanism of dynamic friction behavior associated with the atom arrangement utilizing the soft-core potential for the contact surfaces. The Johnson potential is used for α-iron single crystal bulk in an elastic contact condition. The effect of the shape of the soft-core potential is examined, and the resulting thermal distribution is discussed. A frictional model is composed of two specimens, an upper one and a lower one. As the upper specimen slides along the lower in one direction, atomic friction force is generated. The dynamic friction force is evaluated at the point of decreasing slip velocity. The results are summarized as follows : ( 1 ) An increase in the load applied to the contact surface raises the temperature of the contact surface. ( 2 ) The coefficient of dynamic friction calculated by the friction force generated at the contact surface is decreased due to the increasing core-radius of the soft-core potential. It remains almost constant regardless of variation in the load.

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A new approach to a sensitivity analysis in dynamic nonlinear problems has been investigated in this study. The objective of the study is to increase the crash energy absorption of vehicle body structures. In the first and second reports, we investigated the dynamic collapse behavior of elastic columns under axial compression. The relationship between impact velocity and collapse mode was shown. The sensitivity of buckling load matches the gain of collapse load of redesigned columns at slow impact, whereas it does not always match it at fast impact. In this report, the effect of the direction of design domains against the direction of the impact wave is investigated. The effectiveness and the limitation of a sensitivity analysis in dynamic problems are also discussed.

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An explosive shock pressure treatment at 930 MPa was given to polycrystalline molybdenum (99.9 mass % purity) in water to examine the change in the tensile behavior of the metal. Findings in the present study are summarized as follows. (1) No sharp yielding appeared in the specimen in the annealed state and its yield stress was increased with decreasing temperature and increasing strain rate. Increasing strain rate raised the ductile-brittle transition temperature of the specimen. (2) The transition temperature of the annealed specimen remained unchanged even after the specimen was prestrained by 6% in tension at a warm temperature of 673 K. (3) Neither deformation twins nor detectable macroscopic plastic deformation were observed in the specimen shock-loaded at 930 MPa. The shock loading at this pressure lowered not only the yield stress but also the transition temperature. As interpreted from the behavior of iron, steel and chromium, it is supposed that the free dislocations generated at the elastic discontinuities in the shock-loaded specimen are responsible for the decrease in the yield stress, by which the ductile-brittle transition temperature is lowered.

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This paper is concerned with the ductile-brittle transition behavior in sheet specimens of carbon steels under mode I -II mixed mode loading conditions. Mixed mode tests were carried out on 1.6 mm thick center-cracked sheet specimens of S50C and HT50 under various mixed mode loading conditions in the ductile-brittle transition temperature region using the testing method proposed by the present authors. In this method, the loading condition can be varied by changing the angle between the loading direction and the crack plane. The specimen width and the crack length were also changed. From the experiments, it was shown that the fracture appearance varied with decreasing test temperature, independent of the loading direction, as follows : ( a ) a ductile crack initiates and then extends, ( b ) a ductile crack initiates and then extends as a brittle cleavage crack, and ( c ) a cleavage crack initiates and extends. The upper limit temperature below which cleavage fracture can occur showed a tendency to decrease with increasing mode II component in the case of S50C, but it was almost constant and independent of the loading direction in the case of HT50.

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The singular stress fields near a corner of fiber can be expressed as the sum of two terms: a symmetric term and a screw-symmetric term. The stress singularities for the two terms are different. The intensities of the mode I and mode II singular stress fields are defined in terms of constants K_{I, λ1} and K_{II, λ2}, respectively. In this study, a new method for calculating K_{I, λ1} and K_{II, λ2} based the body force method is developed. In the numerical analysis, the singularities of stress field are characterized by introducing the proper basic density functions of body forces. The use of the basic density functions enables one to obtain accurate solutions. K_{I, λ1} and K_{II, λ2} are obtained simply from the values of weights of the density functions at the corner of the fiber.

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Stress functions in the anisotropic elasticity theory are firstly introduced, from which the well-known stress functions in the isotropic elasticity theory are derived through a suitable limiting process, and it is shown that there exists a correspondence relationship between them. When the stress functions for an isotropic elasticity problem are known, the use of this relationship makes it possible to solve the corresponding anisotropic elasticity problem. Some basic anisotropic elasticity problems are shown to be solved easily through this relationship.

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This paper presents the simplified estimation equations of J-integral at the surface and maximum depth point of a surface crack. These equations are based on finite element analysis with the surface cracked large plate specimen. The equations are expressed as the functions of crack length, crack depth, plate thickness and plate width for bending loads. The J-integral equations are used to develop the analysis given by finite element method for semielliptical surface cracks in finite elastic plastic plate subjected to bending loads. A wide range of configuration parameters was included in the equations. The ratios of crack depth to crack length ranged from 0 to 1 and the ratios of crack depth to plate thickness ranged from 0 to 0.75. The effects of plate width on the J-integral variations along the crack front were also included. Comparing the values of J-integral computed by the equations with those from the finite element analysis, the mean errors are within ±2.6 percent. The equations were used to predict patterns of surface crack propagation under bending fatigue loads for a SUS304 steel at 550°C. The curves of crack length, crack depth vs number of cycles predicted by the equations describe the experimental data well.

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A constitutive equation by which strain rate sensitivity, strain rate history effect, temperature dependence and strain hardening can be described, covering a wide range of strain rates, is proposed. The proposed equation is expanded to describe the strain rate history effect and strain hardening using the constitutive equation given by Kocks et al. To describe the strain rate history effect, the plastic work is taken into account in a manner of fading memory. It is illustrated that the material behavior observed not only in constant strain rate tests but also in jump tests, at temperatures between 77 and 523 K, can be represented fairly well by the proposed equation.

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A method employing finite-element simulation is proposed to identify the uniaxial stress-strain relationship of polymeric material from the load-elongation curve exhibiting neck propagation under the quasi-static isothermal condition. In this method, independent parameters in the uniaxial stress -strain relationship are determined such that the predicted load-elongation curve coincides with the given one. Then, the propriety of the proposed method is examined by the determination of the uniaxial stress-strain relationship from load-elongation curves.

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The recovery stress associated with the R-phase transformation in TiNi shape memory alloy was investigated experimentally concerning constant residual strain. The results are summarized as follows. ( 1 ) The recovery stress in the heating process is larger than the R-phase transformation stress in the loading process at low temperature. ( 2 ) In the heating process, the recovery stress occurs at about 320 K and takes a maximum value at about 335 K. The recovery stress increases along the reverse transformation line on the stress-temperature plane. ( 3 ) The higher the shape memory processing temperature, the larger is the recovery stress. ( 4 ) The larger the maximum strain at low temperature, the larger is the recovery stress.

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An analytical method was proposed to evaluate the unsteady temperature and stress fields during the ceramic coating process. The proposed procedure was developed by means of finite element modeling. In the modeling, the temperature and stress fields were assumed to be one-dimensional and axi-symmetric, respectively. This assumption was based on the fact that the thickness of the coating layer is small compared with the dimensions of the coated surface area. A simulation using the proposed model was conducted for the detonation coating of alumina on steel as a discontinuous coating process. The temperature variation with respect to time during and after the coating process was simulated by the selection of a suitable combination of heat-transmission parameters. The results almost coincided with the experimental observation. The simulated results for the stress field indicated that the residual stress generated in the coated ceramic layer was tensile and extremely large.

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In the present paper, a one-dimensional theory of elastic-plastic-viscoplastic stress wave propagation is evolved. The concepts of understress and overstress are introduced to the constitutive equation used. The strain dependence and the strain-rate dependence of the wave propagation speed of the stress wave are given. A few forms of the wave propagation speed of the elastic-plastic-viscoplastic stress wave are newly derived. It is also shown that the theory of elastic-plastic-viscoplastic stress wave propagation given here contains a theory of elastic-plastic stress wave propagation and a theory of elastic-viscoplastic stress wave propagation. Moreover, a precursor and an unloading wave are also mentioned.

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The cyclic deformation properties of shape memory polymer of the polyurethane series were investigated experimentally. The main results are summarized as follows. ( 1 ) As thermal cycles progress, the residual strain increases, the recovery strain decreases and the deformation resistance increases. ( 2 ) The recovery strain in the heating proccess under no-stress conditions appears above the glass transition temperature. The temperature at which recovery of strain starts rises with cyclic deformation. ( 3 ) The recovery strain at high temperature increases significantly during the first 10 min when the temperature is kept constant, but varies slightly after that. ( 4 ) The characteristic values in ( 1 ) - ( 3 ) vary significantly in the early cycles, but vary slightly after these cycles. ( 5 ) The strain obtained at low temperature following the predeformation at high temperature does not vary under thermomechanical cycling, which demonstrates the stable shape fixity of the material for cyclic deformation.

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The deformation properties of the shape memory polymer of the polyurethane series were investigated through thermomechanical cycling with loading at low temperature and heating with no load. The main results are summarized as follows. ( 1 ) The stress-strain curves vary significantly in the early cycles. In particular, the increment in the residual strain is large. ( 2 ) The recovery strain obtained by unloading is about 10-20% of the maximum strain. In order to obtain a certain amount of deformation with forming at low temperature, it is necessary to estimate an accurate amount of spring back. ( 3 ) The recovery strain due to heating with no load subsequent to loading at low temperature appears at a temperature near the midpoint glass transition temperature. ( 4 ) The shape recoverability and the shape fixity with loading at high temperature are better than those with loading at low temperature.

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The flexural vibration of laminated fiber-plastic composite structures can be simulated by the finite element method (FEM). The numerical analysis of flexural vibration must consider three-dimensional deformation of objects. Therefore, the numerical model for the vibration analysis must have a large number of three-dimensional elements since the thickness of the composite laminate is very small as compared with other dimensions. In this study, we propose a new numerical model for the vibration analysis of the composite laminate. This model is constructed of shell elements and beam elements. The vibration analysis of the composite laminate is carried out to evaluate this proposed model. It is revealed that the proposed model is effective for simulating the free vibration of composite laminates and reduces the calculation time as compared with the conventional model. Furthermore, we confirm that this proposed model can simulate the vibration of the composite laminates with interlaminar delamination.

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Optical birefringence is measured by a high-frequency modulation method using a photoelastic modulator and polarized laser. This measurement method has the high sensitivity required to measure very small birefringence. The distributions of optical birefringence corresponding to stress distributions are measured for a glass plate with notches and a bonded glass plates with epoxy resin. The residual stress caused by the bonding process is evaluated.

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General higher-order approximation theory to analize static and/or dynamic behaviors of laminated composite structures is established. Theoretical and accurate characteristics of the theory are made clear by numerical examples. The theory is established by using modified Hamilton's principle for relaxed displacement continuity requirment, after expanding displacements of each lamina using power series of the thickness coordinate. The independent unknown variables of this theory are displacement coefficients of each lamina and interlamina stresses. It is shown that the present theory includes the previous theories, and improves the defects of those theories.

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The strength of adhesive shaft joints between carbon-fiber-reinforced plastics (CFRP) and stainless steel bonded with epoxy resin was investigated in room temperature and low temperature (-70°C) both analytically and experimentally. The distributions of stress for tensile load and thermal stress for cooling in the joint were analyzed by applying the elastic finite-element method. The strength of the joints was predicted by applying the strength law of CFRP, stainless steel, adhesive layer and their interfaces to the calculated stress distributions. The predicted strength was compared with the experimental strength of the joints. The effects of the overlapped length and diameter ratio on the joint strength were examined at both conditions of room and low temperatures. The joint strength for the initial failure is saturated by a certain overlapped length, but the strength decreases with increasing diameter ratio. The final joint strength in low temperature is larger than that in room temperature.

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Thermal stress distribution and thermal strength were examined when butt adhesive joints with rigid fillers in an adhesive were in steady-state temperature distribution. In the analyses, the thermal stress distribution in the adhesive was given using the two-dimensional theory of elasticity in the case where adherends composed of the same size and the rigid material were kept at a constant temperature and the side surfaces of the joint were surrounded with fluid of a different temperature. Numerical calculations showed that the thermal stress was tensile near the end of the interface between the adherend and the adhesive and around the interface where the filler was included underneath, the thermal stress concentrated at the periphery of the filler, and large concentration of thermal stress was generated when the filler size was large. Photoelastic experiments were carried out, and the analytical results were consistent with the experimental ones.

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In continuum mechanics, balance equations and constitutive equations are derived under the conditions of nonlocality and noninstantaneity. From the condition of nonlocality, Coleman's theorem is derived. In this paper, from the condition of noninstantaneity, another strong restriction is discussed whereby the 2nd-order strain rate cannot be introduced for the argument of the stress response function. This restriction is caused by the absence of terms of the 2nd-order strain rate in the dissipation function. In order to include these terms in the dissipation function, the 2nd law of thermodynamics should be modified. The author assumed that the increasing value in the entropy inequality is not an instantaneous value of entropy but is the average value in the short-range memory of entropy. With this assumption, the 2nd-order strain rate can be introduced in the argument of the stress response function.

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Combined tension-torsion creep tests of a nickel-base single crystal superalloy CMSX-2 are performed at 900°C under steady as well as nonsteady stress conditions using thin-walled tubular specimens with [001] oriented in the axial direction. Effects of anisotropy are observed conspicuously both on the magnitude of creep rate and the noncoaxiality between creep rate and stress. To identify operative slip systems in the present creep tests, the experimental data of steady-state creep are analyzed on the basis of a crystal creep theory of the power-law type. It is shown that the experiments are simulated well if we assume simultaneous operation of the {111}<112> octahedral and {100}<110> cubic slip systems.

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Thermal stress analyses of Si, GaAs and InP bulk single crystals during Czochralski growth are performed in the cases of [001] and [111] pulling directions, using a three-dimensional finite element program. Elastic anisotropy is taken into account in this program. The stress components obtained from the thermal stress analysis are converted into the parameter σ_tot representing the effective stress for glide strains. The values and distribution patterns of σ_tot obtained in the anisotropic analysis taking account of elastic anisotropy are compared with those obtained in the isotropic analysis using Young's modulus and Poisson's ratio in the {111} plane.

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In the first part of this work, the inelastic behavior of aluminium alloy was investigated experimentally using thin-walled tubular specimens subjected to combined loads of axial force and torque under varying temperature conditions. The temperature was selected to be between room temperature and 250°C. The strain rate was controlled to be constant (3×10^-5/sec). In the second part, the observed behavior under such complex conditions was confirmed to be reproduced by using a set of constitutive equations derived on the basis of crystal plasticity.

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Thermal stress analyses of a silicon bulk single crystal with 6 or 8 inches in diameter are performed in the case of [001] and [111] pulling directions by using a three-dimensional finite element program developed for calculating thermal stress in a bulk single crystal during Czochralski growth. Elastic anisotropy and temperature dependence of material properties are taken into account in this program. The temperature distribution and shape of a silicon bulk crystal which are required for the thermal stress analysis are obtained from a computer program for a transient heat conduction analysis. The stress components obtained from the thermal stress analysis are converted into the parameters related with dislocation density. The time variations of these parameters are shown in this paper. The relationship between these parameters and the shape of the crystal-melt interface is discussed.

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A New stress development mechanism in thin films, crystallizatin-induced stress, is discussed experimentally in P-doped amorphous silicon thin films. P-doped amorphous silicon thin films are deposited on thermally oxidized silicon wafers at 520°C using the CVD technique. The thickness of the oxide is 0.1 μm, and that of amorphous silicon is about 550 nm. The crystallization process, i. e., nucleation and growth of polycrystalline silicon, in the amorphous silicon thin films is observed using a scanning laser microscope. During the crystallization process of the amorphous silicon film, the silicon film shrinks and a large tensile stress of about 1000 MPa occurs in the film. The crystallization temperature of the P-doped amorphous silicon film decreases with higher P concentration. However, the crystallization-induced stress does not depend on the doped-P concentration. The developed stress decreases with high-temperature annealing at over 700°C. The stress relaxation ratio becomes higher in the higher P-doped films.

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A new design method based on the fuzzy set theory is proposed for optimizing semiconductor device structures which have various problems relating to heat dissipation and thermal stresses. The design region where all important design goals are satisfied is quickly obtained using this method. The validity of this method is confirmed through the sample calculation of a semiconductor chip mounting structure design.

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When strength degradation due to slow crack growth occurs during proof testing of ceramic components, it is desirable to determine proof test conditions such that S_{f min}≥S_d is satisfied and the probability of surviving the proof test becomes maximum, where S_{f min} is the minimum strength after proof testing and S_d is the required strength. In the previous paper, the optimum proof testing conditions were studied for the case of uniform stress distribution. In the present paper, the case of nonuniform stress distribution is studied. This case is important since real structural components are usually subjected to nonuniformly distributed stresses. It is shown that if a proof test is conducted such that S_{f min}≥S_d is satisfied at the point of maximum stress, then S_{f min}≥S_d is satisfied automatically at every point in the component. Hence, the optimum proof testing conditions for the case of nonuniform stress distribution can be determined by considering only the point of maximum stress.

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Commercial quarter-hard pure aluminum (Al-1/4H) sheets of 10 mm thickness are tested. A circular disk is sheared from a circular specimen concentrically. Clearance between punch and die is 1 and 0.5%. Two testing machines are used, one of which is aided by a drop hammer for high punch speed (10 m/s) and the other, driven by hydraulic pressure for low punch speed (0.1 mm/s). At high-speed shearing, not only the occurrence of the adiabatic shear band (ASB) but also melting along it is clearly demonstrated by measuring the micro-Vicker's hardness distribution over the sheared-off surface, by optical microscopy of the sheared section, which shows a thin layer with a different microstructure from the adjacent smooth shear flow region, by the mirrorlike appearance of the sheared-off surface, and above all, by a theoretical analysis of the shearing process.

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It is well known that plastic deformation is accompanied by microstructural material property changes, and also that these changes affect the macroscopic plastic response of the materials. For example, the elastic moduli and Lankford's value vary depending upon both the plastic flow localization and the texture change taking place under plastic deformation; therefore plastic anisotropy develops due to anisotropic changes of elastic properties. Moreover, inhomogeneous localization of plastic strain, such as localized slip bands, characterizes the plastic instability and the forming limits of the materials. This behaviour of the materials is known to influence ultrasonic propagation properties in solids; ultrasonic methods are alternatives to conventional approaches to characterizing microstructure and morphology. The purpose of the present paper is to evaluate microstructural changes of the aluminum alloy induced by plastic deformation by using the proposed ultrasonic nondestructive evaluation method.

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A new formulation is proposed to determine the minimal objective function under inequality constraint conditions. Taylor-series expansion of the objective function with respect to design variables is employed for the approximation up to the quadratic terms by use of the Hessian matrix, while linear approximation is employed for the inequality constraint conditions. The objective function is standardized on the basis of the eigenvalue analysis of the Hessian matrix so as to form a hypersphere in the design variable space. The center of the hypersphere is used directly for the minimization in the case that it is contained inside the feasible domain. In the case that the center is outside the feasible domain, the minimal objective function is searched for as the contact point of the hypersphere and feasible domain. The numerical examples in problems of beam vibration show that the proposed method is straightforward and efficient to search for minimal objective function.

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The three-dimensional configuration information of each vertebra is essential for surgery of a scoliotic spine. The authors have developed biplane X-ray photogrammetry for the cofiguration measurement and analysis. XCT (X-ray computer tomography) is generally applied to these patients, and more than two scout images of them from different angulations of the tube are taken to determine which part of the body is suitable for tomography. Two scout images from different angulations are sufficient for the reconstruction of the 3D configuration of the vertebra in the line of biplane X-ray photogrammetry. This new method will be called bidirectional CT scout imaging by the authors. This paper shows its basic equations and its accuracy. It was concluded that this is an effective clinical method for the reconstruction of the configuration of the spine.

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The unified inelastic constitutive equation suggested in the previous report is extended to cyclic inelastic deformation and creep deformation of 2 1/4 Cr-1 Mo steel at 550°C. Two of the parameters in the monotonic model decrease with respect to the accumulated inelastic strain, resulting in cyclic softening of the internal stress and the overstress. To describe creep deformation, rate-dependent strain hardening of the internal stress is investigated and introduced into its evolution equation. Through several numerical simulations, the agreement is again found to be good.

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