The fatigue behavior of a gas-nitrided Ti-15Mo-5Zr-3Al alloy has been studied under rotating bending, and the results were compared to those of annealed materials on the basis of detailed observations of crack initiation, growth and fracture surfaces. Nitriding was performed for 20 h and 60 h at 750°C in pure nitrogen gas using smooth specimens, and the depths of the obtained nitrided layers were approximately 130μm and 200μm. The fatigue strength was reduced by nitriding for 20 h. On the other hand, the fatigue lives of the material nitrided for 60 h were shorter than those of the annealed material, but the fatigue limit was slightly increased. The decrease in the fatigue strength of the nitrided materials was primarily attributed to premature crack initiation in the nitrided layer. Furthermore, the role of the nitrided layer in crack initiation is also discussed in terms of the results for pure titanium and Ti-6Al-4V alloy in previous reports.

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The effect of tensile overload on fatigue crack propagation behavior of Fe-3% Si alloy was investigated by the measurement of surface crack length and crack closure level. Crack propagation after the overloading was observed to be delayed under constant stress amplitude. The delayed propagation was predominated by the crack closure behavior, and when the crack propagation rate da/dN became lower, the crack closure level became higher. Also, the crack propagation law could be reasonably evaluated with the effective stress intensity factor range ΔK_eff independent of the delayed propagation. It is expected for this reason that crack tip blunting hardly affected the crack propagation in the case of the present material.

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Rotating bending and torsional fatigue tests were carried out on plain specimens and small-hole specimens of rolled round carbon steel bars which were quenched and tempered. The present specimens are regarded as isotropic materials although the original materials have a banded structure. The fatigue limit ratio between rotating bending and torsional fatigue (τ_w/σ_w) in the specimens is different from that in an annealed rolled round carbon steel bar, and is approximately the same as that in isotropic cast carbon steel. We should use isotropic materials in discussing effects of combined stresses on fatigue. In the torsional fatigue tests, crack propagation on plain specimens was of the shear type in the initial stage and of the tension type in the later stage. Cracks of the shear type were generated in both the circumferential and axial directions. The crack growth laws in bending and torsion are expressed by dl/dN∝ σ _aⁿl or dl/dN∝τ_aⁿl. The dependency of 1/N_f on the stress amplitude σ_a and τ_a in bending and torsional fatigue is approximately the same as the dependency of the crack growth rate on σ_a or τ_a, respectively.

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Mesh dependence in finite-element analysis of creep crack growth by means of the continuum damage mechanics approach is discussed. A series of numerical analyses are first performed for a plate specimen with a central crack to show the characteristics of the mesh dependence. Then, strain localization is discussed in relation to the mesh dependence phenomenon. It is shown that the bifurcation localization, if any exists, will have no obvious effects on the mesh dependence. Finally, stress singularity due to boundary constraints, such as those observed at the crack-tip, is shown to be a controlling factor in the present mesh dependence problem. In order to prevent mesh dependence induced by the stress singularity, incorporation of ideal plasticity into the analyses is suggested and the validity of the procedure is discussed briefly.

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Fracture behavior of silicon nitride ceramics was investigated in oxidizing environments at high temperature. Flexural strength tests were performed under two loading rate conditions at high temperatures up to 1300°C in air, 10% oxygen gas, nitrogen and vacuum. Flexural strengths of specimens precracked by Knoop indentation were measured under three loading rate conditions at 1250°C in the same oxidizing environments. The effect of loading rate on static strengths of silicon nitrides was analyzed in the oxidizing environments. Oxidation tests were also performed under applied loading conditions at 1200°C in air, and the flexural strengths of oxidized specimens were evaluated at room temperature. The changing strength behavior of silicon nitrides was distinguished between tensile loading and compressed loading. Stress-time-dependent tests of silicon nitrides were performed in air at 1000°C and 1200°C. The relationship between applied stress and time to failure exhibited two curves due to flexural deformation at 1200°C.

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Rotating bending fatigue tests were conducted on SCM 420 steel specimens with three types of carburizing, i.e., eutectic carburizing, supercarburizing and plasma supercarburizing to examine the effect of carburizing conditions on the fatigue strength. The X-ray diffraction method was used to measure the residual stress. The stress intensity factor was calculated using the boundary element method on the basis of the residual stress. The fatigue strength decreased with increases in the amount of internal oxide. The fatigue strength of the polished specimen was almost constant irrespective of carburizing conditions. The crack propagation behavior obtained in rotating bending tests agreed with that obtained in axial loading tests when the effect of the residual stress was taken into account.

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The atomic changes of structure around the crack-tip in fcc crystal under in-plane shear (Mode II) loading is analyzed by means of molecular dynamics (MD) simulation. The interatomic force interaction is assumed to be derived from the many body potential proposed by Finnis and Sinclair. The crack surface and its front are assigned to (1) [110] (001), (2) [110] (111), and (3) [110] (110). Both fixed displacement and fixed stress boundary conditions are adopted. The ductile deformation with emission of edge dislocations from crack tip is observed in every case. When the dislocation nucleates, potential energy of the system decreases and kinetic energy increases. Similar problems are analyzed using the continuum model with FEM based on the crystalline plasticity theory. The trail of dislocation in the atomistic model corresponds with shear slip in the continuum model. From the result of MD simulation, the dislocation emission condition may be described as that the shear stress at a distance of a lattice constant from the crack-tip reaches the ideal shear strength of perfect crystal. The critical stress intensity factor estimated with this condition agrees well with Rice's theoretical prediction.

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It has been found that the boundary integral equations for potential and displacement can be regularized by introduction of their relative quantities. This study attempts to establish a method for accurate calculation of the boundary integral equations for the potential gradients or the flux. According to Cruse's method, a lengthy calculation process is needed in order to derive them. It is shown that, contrary to this, they can be easily obtained if the relative quantity is introduced. On the other hand, there still remains a singularity in the order of Cauchy's principal value. For this reason, accurate solutions of flux and traction on the boundary can never be obtained by means of the usual numerical integration scheme. This study has succeeded in regularizing the boundary integral equations for flux and traction with the help of the regularization technique of Cauchy's principal value integral.

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Linear stress analysis wtihout body force can be easily solved by means of the boundary-element method. Some cases of linear stress analysis with body force can also be solved without a domain integral. However, domain integrals are generally necessary to solve the linear stress problem with complicated body forces. This paper shows that the linear stress problem with complicated body forces can be solved approximately without a domain integral. In order to solve the linear stress problem with complicated body forces, the domain is divided into small areas using contour lines of body force. In these areas, the distributions of body force are assumed to approximately satisfy the Laplace equation.

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The combination method, which makes use of both the finite element method and the boundary element method is applied for analyses of nonlinear magnetic field. Using magnetic vector potential, the basic formulation for combining the both methods in the closed space problem is given. For treating nonlinearities arising due to material properties, the Newton-Raphson and over-relaxation schemes are used and the convergence of the solutions are examind. The results are compaired with those obtained using finite element analysis. It is shown that owing to the sparceness of the whole matrix, the convergency of the combination method is not so good as the finite element method, however, the accuracy of the converged solutions are sufficiently high especially in space region, then, this method is useful for the computation of two-dimensional nonlinear magnetic field.

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The boundary element method (BEM) for thin elastic plate bending analysis uses two different integral equations for the displacement and the slope. It is difficult to integrate the integral equation for rotation accurately, because the equation has hyper-singularity. In the present paper, these boundary integral equations are nomalized by the superposition of the rigid rotation mode. Through some numerical results of square plates under several boundary conditions, it is shown that unknown nodal values along the boundary are more accurately obtained that those of the usual methods, and the accuracy of deflections, moments and shear forces at internal points has been clearly improved.

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This paper proposes an inverse analysis method for identification of unknown defects and/or unknown boundary conditions of an elastic body in a steady elastodynamic state. An extended Kalman filter and the boundary element method are combined and applied to the inverse analysis method. The extended Kalman filter algorithm enables estimation of state variables of a stochastic system. It is expected that the algorithm is also applicable to analysis of other identification problems for which only noisy data are available at certain measuring points. The effectiveness of the proposed inverse analysis method is demonstrated through numerical simulation for several example problems.

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A method of rigid plastic finite element analysis including the inertia effect has been developed in order to determine the mechanical behavior of penetration caused by collision of a flying projectile with a target. The analysis is based on the double-nodes method and is treated as an axisymmetric problem. The penetrating process is clarified via a method of node separation, which satisfies the condition that plastic deformation energy extends beyond a threshold value. Experiments on collision of two bodies, a cylindrical projectile of steel and a disc target of plasticine or plumbum, were carried out using a test apparatus with projection of compressed air. The experimental results were compared with the calculated results, and it is shown that the calculated results of the residual speed of the projectile and the final shape of the disc target after penetration are in agreement with the experimental results. It is expected that the calculation time of the developed method is less than that of the conventional elasto-plastic approach.

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Stress distributions in single-lap adhesive joints are analyzed using an elasto plastic finite-element method in order to predict joint strength. With an increase of tensile shear load, adherends tend to be yielded and the interface then starts to peel. The peel process and the yielded regions of the adherends are examined with an increase of the tensile shear load. The effects of rigidity and yield stress of adherends and so on are clarified on the peel process. It is seen that the peel stress increases with a decrease of adherend rigidity. In addition, the joint strength is estimated taking the peel produced at the inter face, by the von Mises's criterion. Experiments concerning joint strength were performed. The numerical results are in fairly good agreement with the experimental ones concerning joint strength. It is shown that joint strength increases as the adherend rigidity increases.

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In the metal forming process, the roughening of the free surface of products is one of the most important problems. In order to clarify the relationship between wavelength and applied strain, uniaxial compressive load and tensile load were applied to iron specimens. A stylus instrument was used to measure the surface roughness at the same position on a specimen during plastic deformation. The maximum entropy method was employed for the spectrum analysis of the surface roughness curves. Photographs of the grains on the surface were taken with a scanning electron microscope. The results show that in the compression test, the primary wavelength of surface roughness becomes shorter in the longitudinal direction and longer in the transverse direction as the applied strain increases. The opposite results were obtained in the tensile test.

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The remaining life estimation method based on creep deformation behavior was developed in this study. Constant load creep tests in Cr-Mo-V steel was used for 91600 h experienced start/stop operation and 131 times in a turbine rotor were performed at 773 K, 823 K and 873 K in air. Creep strain curve was approximated by the modified theta-projection method, which was proposed by K. Maruyama et. al. as the following equation : ε=ε₀+A{1-exp(-αt)}+B{exp(αt)-1}. A determination method for cut-off strain was proposed in this study and it is 2% offset strain due to stationary creep. From this investigation, the following conclusions were obtained. (1) Modified theta-projection method was able to express the entire creep region from primary stage to tertiary stage except just before the rupture of the material. (2) Coefficients A and B were invariable with tested conditions. Constant a was related to applied stress, tested temperature and degree of damage. It was found that the α is related to the vickers hardness of the material. (3) Estimation of creep curves up to the tertiary stage was possible from the knowledge of vickers hardness of the material, and remaining lives under actual conditions were estimated on the basis of the creep curve prediction.

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In plastic processes such as deep drawing, it is important to evaluate the anisotropy of the material, especially the Lankford value in the sheet, nondestructively. The microstructure of the materials introduced by rolling, drawing, or other materials processing relates to the mechanical properties of the materials such as the strength and anisotropy, and influences the velocity and attenuation of the ultrasonic waves propagating in the materials. Therefore, we are able to investigate the growth of the plastic anisotropy using the ultrasonic waves. In this paper, in order to establish an ultrasonic method for nondestructively evaluating the Lankford value of the material, we examined the correlation between the changes in the Lankford value and the subsequent yield surfaces numerically simulated using the parameters of the plastic anisotropy which were determined from the velocity changes in the longitudinal waves propagating in the directions of width and thickness of the aluminum alloy specimen in a uniaxial tensile test.

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A newly developed ultrasonic reflectivity measurement technique is applied for the evaluation of surface-weve velocity in a small surface area in polycrystalline materials. The surface-wave velocity is determined by observing either the phase change or the amplitude change of the ultrasonic reflection coefficient on the specimen surface. The measurement system, with a sensor unit consisting of a transmitter with a planar lens and a receiver with a spherical lens, provides high spatial resolution for estimation of frequency dependence of the velocity using impulse waves. Measurements of steel with various elastic properties and structures have been carried out in a frequency range from 40 to 120 MHz. The measurement resolution and accuracy were dependent on the frequency. The velocities on quenched and tempered steels could be estimated accurately by measuring the phase change, while the velocity on annealed steel was estimated by measuring the amplitude change, because the phase change of the annealed steel was anomalous due to significant attenuation in the solid in the high-frequency region.

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Unified descriptions of the constitutive and evolution equations of elastic-brittle-damage materials are developed on the basis of irreversible thermodynamic theory for constitutive equations. The Helmholtz free energy is assumed to be a function of modified elastic strain ε^e and second-rank symmetric damage tensor D by taking account of the effects of crack closure and damage anisotropy, and a damage dissipation potential related to the entropy production rate is expressed in terms of damage-conjugate force Y. The constitutive equation and the damage evolution equation derived by these potentials were applied to an elastic-brittle-damage material. The anisotropic elastic-brittle-damage behavior of high-strength concrete under uniaxial, proportional and non-proportional combined loading was analyzed to elucidate the utility and the limitations of the present theory.

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In this paper, we discuss the influence of the temperature dependence of material properties on transient thermal stresses in functionally gradient materials (FGMs). We consider a circular plate of FGM (ZrO₂ and Ti-6 Al-4V) subjected to one rapid heating-cooling cycle. We analyze the transient thermal stresses by means of a finite element method. When the temperature dependence of material properties is considered, the maximum tensile stress is 10% less than the FGM with constant material properties at 300 K, and the maximum compressive stress is 30% less than that at 300 K. The maximum tensile stress is the lowest when the material properties of FGM are distributed linearly. The influence of the heating condition is also discussed.

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Many cracks have often been found in the ceramic substrate of power modules during operation, which were induced by cyclic thermal stress. In this paper, the thermal stress singularity in different material wedges was studied by elastoplastic FEM analysis and the actual fracture mode was evaluated. The results are as follows. Maximum principal stress was produced in a cyclic cooling process near a free bonded edge, which was regarded as a dominant factor for fracture. Actually, a type of peel and crack propagation into the ceramic substrate at the free bonded edge was induced by this cyclic tensile stress singularity.

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In this paper, a simple method for analyzing the singular thermal stress field near the corner tip in jointed materials caused by the thermal mismatch of different moduli was developed. It is found that the singular thermal stress fields can be replaced by the singular elastic stress fields caused by biaxial tension. This finding enables us to obtain the stress intensity factors of a singular thermal stress field from the available data on the stress intensity factors of a singular elastic stress field caused by biaxial tension.

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Since joined axisymmetric dissimilar materials have constant hoop stress distribution around the edge near the interface, the basic data concerning residual stress should be evaluated. To solve a 2-dimensional joined dissimilar materials system with a theoretical Thermal elastic problem, analysis under the plane-strain condition is needed, but it is possible or not possible to apply the axisymmetrical condition. In this paper, correlation between an axisymmetric condition and plane-strain analysis is discussed for a cylindrical joined material with a suitable residual stress problem.

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The stress field near the apex of two-phase materials formed from two isotropic homogeneous wedges with arbitrary angles under surface traction has been obtained by Bogy. The singularity in the stress field is investigated using Dundurs' composite parameters α and β. The stress singularity depends on the values of α and β, and is represented by the order O(r^-s-2) for α(α-2β)>0, O(log r) for α(α-2β)=0, and O(1) for α(α-2β)<0. However, the order in the displacement field has not yet been clarified. In this paper, equations of the stress field and displacement field near the apex in bonded quarter-planes of dissimilar materials under surface traction are derived for α(α-2β)<0, α(α-2β)=0 and α(α-2β)>0. It is shown that the limiting behavior r→0 for the r-direction and θ-direction displacement differs from each other.

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Since light-weight, high-strength and hight-stiffness composite materials exhibit the degradation of both strength and stiffness in a hygrothermal environment, there is an urgent need to quantitatively assess the influence of coupling effects between transient heat and moisture diffusion on the temperature, moisture and hygrothermal stress distributions. In this paper, the coupled diffusion problem of temperature and moisture in a hollow circular cylinder subjected to unaxisymmetric hygrothermal loading is solved in a closed form. The associated plane-strain hygrothermoelastic problem is solved in terms of a stress function using the integral conditions necessary for the assurance of the single-valuedness of rotation and displacements derived by the present authors. The obtained closed-form solution is applied to the hygrothermoelastic problem in a hollow circular cylinder made of T300/5208 composite material subjected to unaxisymmetric transient hygrothermal loading on the inner and outer boundary surfaces. Numerical calculations of the distributions of temperature, moisture and hygrothermal stress are carried out for the cases of various hygrometric and thermal loading conditions. The coupling effects of temperature and moisture fields on the stress distribution are quantitatively estimated under various hygrothermal environments.

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This paper deals with numerical solutions of singular integral equations of the body force method in 3D stress concentration problems. As examples, the problems of ellipsoidal cavities and a toroidal hole under uniform tension are considered. The problems are formulated as a system of singular integral equations with Cauchy-type singularities, where the densities of body forces distributing in the r and z directions are unknown functions. In order to satisfy the boundary conditions along the notches, several types of fundamental density functions are proposed ; then, the body force densities are approximated by a linear combination of the fundamental density functions and polynomials. The accuracy of the present analysis is verified by comparing the present results with the results obtained by the conventional method. The present method is found to give rapidly converging numerical results for the stress distribution along the boundaries.

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Ion-beam processing such as absorption (deposition), sputtering or implantation creates a disordered crystalline structure in the thermodynamical nonequilibrium state. Intrinsic stress within the disordered surface layer caused by the incident ions was estimated using both molecular dynamics (MD) simulations and continuum mechanics considerations. We proposed one estimation of the anisotropic elastic stress derived from dilatation of the disordered layer which was obtained by applying the Voronoi analysis or the statistical treatment to the results of MD analyses. It was noted that the incident ions with lower accelerating energy induced the tensile stress in the layer. And the stress field became compressive as the accelerating energy increased because of the occurrence of interstitials. Some aspects of the local volume change were also analyzed from the distribution of the atomic volumes within the Voronoi polyhedra.

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Titanium carbide and its composites incorporated with 1, 3, 5 and 10 wt% of graphite were consolidated by hot-pressing at temperatures ranging from 1800°to 2100°C. Although significant grain growth occurred in the monolithic TiC at higher hot-pressing temperatures, the graphite addition inhibited the grain growth well in the composites. Room-temperature bending strength, σ, of the monolithic TiC correlated with the average grain diameter, d, through the Hall-Petch relation (σ∝d^-1/2). Such a correlation may be attributed to intrinsically existing surface flaws with size dominated by average grain size. Fracture toughness of the monolithic TiC increased linearly with the average grain diameter, in accordance with an increase in effective surface energy. The graphite addition resulted in strengthening of the TiC through the inhibition of both grain growth and crack propagation ; however, excess addition of graphite (more than 3 wt%) caused strength reduction in the composites due to graphite agglomeration which acts as a fracture origin. Fracture toughness of the TiC also increased with graphite addition through deflection and bridging of the cracks by graphite particles.

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Composite pipes with structurally unsymmetric laminated configurations (SULC pipe) shows coupled deformations upon bending and torsion. Our previous study treated the static behavior of the SULC pipes, and this paper deals with their dynamic coupling behavior. The coupled bending and torsional vibration of a cantilevered SULC pipe with an eccentric weight at its free end is analyzed, neglecting the mass of the pipe and assuming that it is an undamped free vibration system with two degree of freedom, transversal and rotational displacements. It is found that the SULC pipe has an elastic principal axis apart from its geometric principal axis, and the vibration becomes uncoupled when the center of gravity of the eccentric weight is located on the elastic axis of the pipe. The effects of the fiber orientation angles and the eccentricity of the tip weight on the vibration behavior are also analyzed considering the dynamic center of rotation. The analytical results show good agreement with the experimental results.

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In order to determine the optimum fiber orientation angles with maximum reliability under probabilistic loading conditions, a simple analytical method, which is called the interior tangent ellipsoid (ITE) method, has been proposed by one of the authors and applied to unidirectional composites, but has not been applied to laminated composites. In this paper, the ITE method is extended and applied to multiaxial laminates, based on first-ply failure. With the use of the quadratic equation of a failure criterion transformed for multiaxial laminates, an analytical solution for the relative value of reliability is formulated. The results obtained using the ITE method show good agreement with those obtained using an accurate reliability method. The calculation time for the ITE method is much less than that for the sophisticated reliability method. The ITE method enables a clear interpretation of the optimum orientation angles of laminated composites under probabilistic loading conditions. As a result, it is found that the ITE method is applicable to for multiaxial laminated composites as well as undirectional composites.

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A method of estimating the intergrain strength of sintered ceramics is proposed by a means of simplified analytical crack propagation model. Numerical simulation is performed for crack propagation in polycrystalline brittle material such as ceramic materials. The analysis is focused on the determination of inter- or transgranular fracture path. The criterion of crack path selection is based on the total released energy rate of the system on the crack extension. A hexagonal system grain is chosen in the analysis featuring a silicon nitride crystal structure. The grains are distributed three-dimensionally ; however, the crack paths are analyzed on a cross sectional plane. Examples of crack propagation paths are shown with changing specific fracture surface formation energy. The inter-/transgranular fracture surface ratio is related to the fracture surface formation energy ratio, giving a comprehensive estimation method of the strength of sintered ceramics.

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A scanning tunneling microscope (STM) can provide atomic-scale images in various environments, such as a vacuum, air and aqueous solution. In addition, STM can offer a new approach to surface fabrication on a nanometer scale. In this study, we describe hardness measurement on a nanometer scale, using STM technology. Pyramidal indentations with side length less than 100 nm were created by the contact of the conductive diamond tips with the surfaces of gold and cementite-spheroidized S25C steel. The 16×16 indentations with 300 nm pitch were arranged on the surface of cementite-spheroidized S25C steel. The indentations were much larger in the ferrite portion than in the cementite portion.

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Chao (1980) and Mills (1991), according to Grood (1979) developed a link mechanism goniometer composed of three rods connected perpendicular to each other by collars. They claimed that three relative rotational angles of the rods correspond to three-dimensional clinical angles, that is, the flexion-extension, abduction-adduction and external rotation-internal rotation. However, the three angles are equal to Euler's angles obtained by using the three axis method proposed by Panjabi (1971). It is well known that Euler's angle obtaind by using this method has six cases and it is understood that the goniometer by Chao et al gives only one case of the six because three angles obtained have different values depending on the way of making the correspondence of local coordinate axis of two bones to the rods of the link. This paper describes kinematics of a goniometer using a link mechanism based on the similarity transformation and investigates the three-dimensional expression of the rotation angle.

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