A new fatigue testing method was proposed by which fatigue crack propagation could be caused in a film attached to elliptical and circular holes on a base plate subjected to push-pull cyclic loads. In a Boundary Element Analysis of this method, stress intensity factors were almost constant during the greater part of crack propagation. With the use of commercial-grade iron films of 100-μm thickness, the fatigue crack propagation rate was expressed by a power law of stress intensity factor range under various stress amplitudes with a stress ratio of R=0 for the film attached to the base specimen. However, a considerable residual plastic layer was left in the wake of propagating cracks on the film. Effective stress intensity factor ranges were considered to be a good parameter controlling the fatigue crack growth in both film and bulk specimens.

View full abstract

In the first report, it was shown that, as far as the mode I (opening type) fracture occurs, the criterion ( ε^I_<ψmax> criterion) based on the mode I contribution of E_ψ (crack energy density in an arbitrary direction) is effective from completely elastic fracture to elastic-plastic fracture with large yielding region through the application of ε^I_<ψmax> criterion to the fractures of an inclined crack under tensile type loading. However, the mode II (shear type) fracture may occur under some conditions. So, in this paper, the criterion (ε^II_ψmax criterion) based on the mode II contribution of ε_ψ is proposed as the criterion for the mode II fractψre first. Subsequently, the fracture experiments of an inclined crack under shear type loading are carried out and, based on the experimental results, its applicability to mode II fractures is shown in addition to the applicability of ε^I_<ψmax> criterion to mode I fractures and, moreover, the criterion for judging fracture mode is discussed. Finally, by summarizing the results in this paper and those in the first report, the most generalized mixed-mode fracture criterion which can also judge fracture mode is given.

View full abstract

In the series of papers, the authors proposed the fracture criteria for mode I (opening type) fracture and mode II (shear type) fracture in a mixed-mode crack based on the CED (crack energy density) in an arbitarry direction, ε_ψ, and the applicability of these criteria to mixed-mode crack has been investigated through the fracture experiments of specimens with an inclined crack under tensile/shear type loading. In this paper, the evaluation method of ε_ψ by finite element method is studied. Elastic-plastic finite element analyses are carried out for the above mentioned fracture experiments and ε_ψ and its contribution of each mode are evaluated by path-independent integrals and the method based on load-displacement curves. Based on the results, we examine the fundamental properties in the evaluation of ε_ψ and so on in elastic case and, simultaniously, develop a practical method to evaluate ε_ψ and so on in elastic-plastic case which makes the application of the fractrure criteria to the fracture of a mixed-mode crack realistic and easy.

View full abstract

In order to exmaine the effect of stress ratio and the difference in loading type on the frictional force acting on a crack surface, fatigue tests under mixed mode are carried out. Namely, a plate specimen made of SK-5 carbon steel with a center through crack at a 90° angle to the specimen axis is used for combination tests of plane bending and cyclic torsion with various stress ratios and that at 52°, 57° and 63° angle is used for plane bending tests. The warping of the plate by torsion is one of the main factors responsible for the frictional force under mixed mode and the warping at the threshold of crack propagation becomes remarked with the decrease of plate thickness. Thus, the difference between the threshold stress obtained and that calculated using the strain energy density criterion increases with the decrease in plate thickness. On the other hand, the increase in stress ratio cancels the effect of frictional force.

View full abstract

An elastic plastic fracture toughness test was carried out at 4K and 290K to clarify the fracture mechanism of Inconel 718. It was revealed, at 4K, that pop-in behavior was dominant until final fracture and that this material was quite brittle. The elastic plastic fracture toughness corresponds well with plane strain fracture toughness. The tearing modulus is comparatively low if the energy level just before final pop-in is employed to obtain the J-R curve. On the other hand, at 290K, this material is ductile although the fracture toughness is less than that at 4K. The material strength contributes to the difference in fracture toughness between 4K and 290K. Microscopic examination shows that, at 4K, a small dimple zone is often located at the initial crack front although a cleavage facet or twinning is dominant at the fracture surface. However, at 290K, only a dimple zone is found on the fracture surface.

View full abstract

Crack growth behavior was investigated under static and cyclic loads in gas-pressure-sintered silicon nitride (EC-141) using a combined loading technique for stabilizing crack growth and a surface film technique for monitoring crack length. Load shedding tests were performed on two speciments at the loading frequencies of 1 and 10 Hz to evaluate fatigue crack growth until the crack became dormant, in order to determine the threshold stress intensity factor K_th. Then, one of the specimens was used in a fatigue test without the combined loading technique, in which K_th values for different crack lengths were determined. The other specimen was used in the quasi-static test under a monotonic loading condition, in which the fracture resistance curve for the fatigue precrack was measured. The results were compared to those reported in the literature for the same material and for other silicon nitrides. Based on the crack growth characteristics, the fracture strength under various loading conditions involving static, cyclic and monotonic loads was discussed.

View full abstract

Spheroidized cementite steel which consists of ferrite matrix and cementite particles is regarded as a kind of particulate-reinforced metal composite. Uniaxial tensile and fracture toughness tests were conducted on three kinds of spheroidized cementite steels. In the uniaxial tensile test, yield and fracture stresses increase and ductility decreases with an increase in cementite volume fraction. The fracture process is described in terms of the growth and coalescence of voids nucleated from cementite particles. Quantitative examination shows that the damage is accumulated mainly by the void growth for the material with a low volume fraction of comentite and by the void nucleation for a high volume fraction of cementite. Fracture toughness decreases with an increase in the cementite volume fraction. A crack is initiated by the growth and coalescence of voids except in the material with a high content of cementite particles, which shows a mixed fracture process combining the void coalescence type and the cleavage type. It is suggested from the present results that a new approach which takes account of the damage process is necessary for characterizing the performance of particulate-reinforced composites.

View full abstract

The stress-induced failure in an aluminum conductor of a microelectronic package was investigated in terms of diffusion along the surface and grain boundary. The mechanism of the growth of groove, which initiated at and progressed along a grain boundary perpendicular to the stress at elevated temperature, was proposed and the failure process was numerically simulated. The grooving process was found to be sensitive to thermal stress as well as the diffusion ratio, F=(grain boundary diffusion)/(surface diffusion). The active grain-boundary-diffusion brought about a crack-like groove at high magnitudes of F and/or stress, whereas the low magnitudes led to a V-shaped groove and marked thinning of the conductor.

View full abstract

A study has been made on the evaluation of the mechanistic condition for the critical behavior of Quasi-Cleavage (QC) and Intergranular (IG) cracks in the hydrogen charged quenched and tempered ASTM A-490 steel. SEM fractographic examination revealed that the QC facet can be regarded as the critical length of the Griffith Crack independent of the variety of hydrogen charging condition ; i.e., the transitional behaviour of QC to IG can be formulated as the following equation. σ·d^0.51_max=6.2{σ : stress [MPa], d_max : QC fracture length [m]} Transition of fracture mode from IG crack to MVC could be dependent on the amount of hydrogen. This transitional behaviour of the crack from IG to MVC was also discussed with the measurements of the distance from the surface to the crack front of both QC and IG facets on the fractured surface.

View full abstract

In this paper, we present a method for monitoring fatigue damage of steel specimens with no contact using the laser speckle method. This method is based on the phenomenon whereby the intensity distribution of the laser speckle changes depending on surface profile change invoked by fatigue damage. Analysis of the laser speckle distribution can be made quantitatively using an image processing system. Distribution of the speckle intensity was observed under cyclic tensile load with a constant stress amplitude. Surface roughness and surface profile were also investigated during the experiment. Intensity distribution of the laser speckle was found to be related to frequency distribution of the surface profile. This is the same as in the case of the static tensile test reported in the previous paper. The results showed that distribution of the laser speckle changes with the number of loading cycles. It was found that there is a possibility of estimating fatigue damage by observing the distribution of laser speckle intensity.

View full abstract

The existing computational damage mechanics models for brittle microcracking solids are improved, based on the results of mesoscopic simulations previously presented by the authors. The relations between the elastic compliances and the microcrack density, especially in the compressive stress state, are modified for the isotropic theory. For the anisotropic model, the damage evolution equations are modified so as to give positive values of the damage rates in an arbitrary stress state. These enhanced damage mechanics models are applied to the two-dimensional finite element analysis of brittle microcracking solids in order to test their validities.

View full abstract

An attempt was made to clarify the effect of a surface-hardened layer produced by gas-nitriding (880°C, 24 hours) on the fatigue strength of pure titanium through experiments concerning the fatigue properties of nitrided pure titanium whose surface-hardened layer was removed to a thickness of 12-60μm. The results are summarized as follows : (1) the fatigue strangth of nitrided pure titanium is improved by removing the compound layer, (2) the fatigue strength of nitrided pure titanium can be reduced because the compound layer posesses a very low fracture toughness compared with that of the matrix, and in addition to this, residual compressive stress in the compound layer is cancelled out by tensile stress developed by the stress magnification effect due to a difference of Young's moduli between the marix and the compound layer.

View full abstract

Many kinds of engineering ceramics have been developed and used as parts of mechanical structures. These ceramics are often used as machine parts which are exposed to elevated temperatures. The strength distribution of those materials significantly depends upon the temperature. In this study, distribution characteristics of the flexural strength for alumina ceramics were examined at the temperatures of room temperature (RT), 800°C, 1000°C and 1200°C, respectively. Based on the temperature dependence of distribution parameters, the Probability-Strength-Temperature characteristics were quantitatively analysed. An analytical model for the temperature dependence of the strength distribution was finally proposed by introducing the defect sensitivity and its temperature dependence. Analytical results thus obtained were in good agreement with the experimental aspect of the strength distributions.

View full abstract

In order to investigate the fatigue strength and fracture mechanism of ceramic-sprayed steel, rotating bending fatigue tests have been conducted at room temperature using specimens of medium carbon steel (S 45 C) with sprayed chromia coating. The results obtained were discussed based on detailed observation of fatigue cracks and on the experimental fatigue data on specimens subjected to individual treatment during the ceramic spraying process. It was found that at an extremely early stage of fatigue, fatigue cracks were initiated at the interface between under-and top-coated layers, and then grew rapidly into the ceramic-sprayed layer. However, these cracks did not propagate continuously into the substrate, and the final failure was led by the growth of a crack newly initiated at the surface of the substrate steel. Therefore, it was concluded that the fatigue strength of the ceramic-sprayed steel could be evaluated to be due to the property of the substrate.

View full abstract

Superplasticity is the ability of a polycrystalline material to exhibit, in a generally isotropic manner, very high tensile elongations prior to failure. Various models explaining the deformation behavior in superplastic materials have been proposed. As superplasticity is a thermally activated process, diffusional flow plays a dominant role in the deformation mechanism. In order to determine the controlling mechanism during the deformation process, the activation energy for superplastic flow associated with the diffusional flow process needs to be measured for two powder metallurgically processed Al-Mg-Mn alloys. The apparent activation energies between 181 to 190 kJ/mol for superplastic flow measured in Al-Mg-Mn alloys were higher than that for self-diffusion of aluminum (142 kJ/mol). The activation energies for superplastic flow measured in both alloys were found to be similar to grain boundary diffusion (84 kJ/mol) by incorporation of the temperature dependence of threshold stress and shear modulus into the constitutive equation, whereas, by additional incorporation of the temperature dependence of grain size, the true activation energies were equal to that of lattice self-diffusion of aluminum base metal, and all data in both alloys can be represented by a single equation. This indicates that a single mechanism exists in both alloys. The rate-controlling step in the deformation process is considered to be controlled by diffusional-flow-related phenomena within the grains during the superplastic flow.

View full abstract

A physical-metallurgical interpretation of the modified kinematic hardening (MKH) model presented in the previous studies is discussed in detail. Physically based expressions which are equivalent to the phenomenological MKH model are also given. First of all, we examined the relationship between the apparent stress exponent (b) and the effective one (m) which is predicted by the MKH model, and compared it with the reported results. As a result, the physical-metallurgical observations that b>m and the magnitude of the internal stress in the steady state is proportional to the applied stress were not predicted simultaneously by the present model. If b=m, however, the proportional relation was satisfied. Second, using the relationship between the internal stress and the dislocation density, we constructed a physically based constitutive model. The structure of the derived model was slightly more general than the multiaxial version of Lagneborg's dislocation-density model. Finally, incorporation of an anisotropic aspect into this dislocation-density-based constitutive structure was discussed.

View full abstract

In this paper, theoretical analysis of a three-dimensional transient thermal stress problem is developed for a nonhomogeneous hollow circular cylinder. We assume that the hollow circular cylinder has nonhomogeneous thermal and mechanical material properties in the radial direction. The heat conduction problem and the associated thermoelastic behavior for such a nonhomogeneous medium are developed by introducing the theory of laminated composites as one of the theoretical approximations. The transient heat conduction problem under the condition of three-dimensional heat supply due to the inner or outer surrounding medium is evaluated with the aid of the methods of Fourier cosine transform and Laplace transform. The associated thermoelastic field is analyzed by making use of the thermoelastic displacement potential, Michell's function and Boussinesq's function. Thereafter, the numerical results for the temperature change and the stress distributions are shown in the figures, and the influence of the nonhomogeneous material properties is briefly discussed.

View full abstract

The boundary element method (BEM) does not require a domain integral in steady thermoelastic problems without heat generation. However, in problems with heat generation, the domain integral is necessary. This paper shows that the axisymmetric problem of steady thermoelasticity with nonuniform heat generation over the region can be easily solved without a domain integral by means of BEM. This method can also be applied to steady thermal stress Problems under complicated general heat generation. However, for general heat generation the domain must be divided into small areas, in which distributions of heat generation approximately satisfy the Laplace equation.

View full abstract

With the recent increase an composite laminate applications, a number of issues affecting their use have been discovered. In particular, the decrease in buckling load for laminates with interlaminar delaminations is very serious. Accordingly, it is very important to estimate the residual buckling strength after delamination. We attempted a quasi-three-dimensional analysis to clarify this issue. The model is constructed of beam and shell elements. Here the former indicate matrix, the latter indicate fiber, and the deletion of some beam elements indicates interlaminar delaminations. Therefore we confirmed that a quasi-three-dimensional model was very effective for simulating the flexural elastic modulus and buckling strength of a composite laminate with an interlaminar delamination.

View full abstract

In previous research, the modified equivalent inclusion method developed by Taya and Chou was extended to be applicable to the case where there were many kinds of inhomogenities and inhomobeneous inclusions. By using this extended method, micromechanical analysis was performed on a discontinuous fiber-reinforced composite showing interfacial sliding between fiber and matrix, and analytical experssions such as for energy release rates and the overall elastic modulus as a composite were derived. In addition, the fracture toughness of such a composite was evaluated in terms of the critical size of a crack which travels across the composite in an unstable manner. The effect of material parameters on the toughness can be explained by the interfacial phenomenon, whose results are consistent with common experimental results. In the present paper, by applying the extended modified equivalent inclusion method, micromechanical analysis is done of the unidirectional fiber-reinforced composites producing interfacial debonding between fiber and matrix. The expressions of energy release rates both for a matrix crack and a debonding one can be obtained.

View full abstract

In the 3rd report of the sequential papers which dealt with analysis of the composite showing interfacial phenomena, micromechanical analysis was performed on a unidirectional fiber-reinforced composite producing interfacial debonding between a fiber and a matrix, and analytical expressions for energy release rates of a matrix crack and a debonding one were derived. In the present paper, evaluation of mechanical properties of a composite with such an interfacial debonding like a resin-based composite, is carried out based on the theoretical analysis of the 3rd paper. As a result, fracture toughness of such a composite can be evaluated in terms of the critical size of the crack at which the unstable propagation of the matrix crack will be arrested and then the debonding between a matrix and a fiber will occur. The effect of material parameters such as the volume fraction of a fiber, and the length of the debonding, etc., on the toughness can be explained by the interfacial phenomenon. The results obtained are consistent with the common experimantal facts. It should be particularly emphasized that there exists an optimal value of the surface energy of the interface for obtaining a tougher composite.

View full abstract

The present work deals with the two-dimensional stress wave in a semi-infinite stepped bar of circular cross section, subjected to torsional impact. The equations governing the dynamic torsional deformation of the stepped bar are solved by the method of numerical integration along bicharacteristics. The torsional impact experiments for the stepped bar were performed using a modified torsional Hopkinson bar apparatus. The numerical results for the dynamic shear strain on the stepped bar are shown to be in close agreement with the experimental results. The distributions of the dynamic shear stresses in the vicinity of the junction of the stepped bar are examined to determine the limitations of the elementary theory of torsional wave propagation.

View full abstract

An entimation method for dynamic consitutive equations using the experimental data of strain time curves and the residual strain profile induced in a finite-length bar applied to longitudinal impact is described. The estimation was performed by means of the nonlinear least squares based on the Gauss-Newton method assuming the constitutive equation forms were given. The previous report explained that the method was applicable to estimation of dynamic consitutive equations for aluminium, stress-strain relations for which are weakly dependent on strain rates. In this study, in order to confirm that the present method could be applied to the estimation of dynamic consitutive equations of carbons steels, stress-strain relationships of which are highly depndent on strain rates, the estimations were performed using actual experimental data. Furthermore, by the comparison of estimated results and experimental results regarding stress-strain relationships with strain rates, it was clarified that the method might be applied to estimation of the dynamic constitutive equations of carbon steels.

View full abstract

In the previous paper, we reported several results of the compressive test for ceramics, and also proposed a dumbbell-type specimen and suitable equipment for measuring actual compressive strength. This paper discusses the fracture mechanism of ceramics under a compressive load and the edge effects in the specimen, using additional results for an acoustic emission (AE) test and the brittle fracture criterion under multiaxial stress. The results are as follows. (1) The compressive strength of ceramics is about 11 times as much as the tensile strength for Si₃N₄. (2) AE sounds are detected at the early stage of the compressive load, whose value coincides with the value estimated by means of the fracture criterion ; namely, about 22% of the fracture load. (3) The dumbbell-type specimen is highly recommended for ceramics as an edge effect-free specimen.

View full abstract

In the present paper, the general higher-order theories of plates and beams with varying thickness are established. The theories are formulated by using the power series expansion of displacements along the thickness. Some lower-order theories with truncation of the displacement coefficients are shown for the case of stretching as well as bending behavior. Some interrelations among present theories and previously proposed other author's theories are discussed through theoretical considerations.

View full abstract

In this paper we consider the general fundamental solutions and their characteristics of nonlocal elastic theory. The solutions are obtained by means of a simple method and a direct integral method. The simple method combines a power series of α and classical fundamental solutions. In the direct integral method, by assumping a nonlocal kernel α solutions can be obtained by integrating Fourier form. As an example, the results of nonlocal and classical solutions of point force for a two-dimensional infinite region are shown by graphycal representation.

View full abstract

A simulation method has been proposed to estimate the effective elastic moduli of sintered spherical particles by analyzing the response of a random network of springs with 6 degrees of freedom to uniform deformation ; the network is constructed by computer simulation of a 3D random packing of spherical particles, while the spring constants of a pair of sintered particles are estimated by FEM. In order to verify the validity of the proposed method, its 2D version has been applied to an estimation of the effective Young modulus, and its specific procedures have been examined in detail.

View full abstract

In the field of tribology, the contact pressure is usually assumed to be distributed elliptically according to the well-known Hertz's contact theory. However, the existence of defects near the contact area may require some modifications of this theory. In this study, the effect of a surface crack in contact problems is investigated. In the present analysis, with considering the effect of the surface crack on the contact pressure distribution, the problem is formulated into the singular integral equations in which the dislocation density on the crack surface and the contact pressure distribution are unknown. Furthermore, the numerical method for solving the singular integral equations is shown and some typical examples are solved by the present method. Calculated contact pressure distributions are compared with those obtained by assuming the Hertz's theory. It is concluded that there are some cases when the Hertz's theory does not give sufficiently accurate solutions.

View full abstract

The stress of band adhesive butt joints in which the interfaces are partially bonded, was analyzed using a two-dimensional, theory of elasticity in order to establish fracture criteria for the case in which the joints of dissimilar adherends are subjected to tensile loads. In the analysis, when the interfaces are bonded by an adhesive at two regions, the dissimilar adherends and the adhesive are replaced with finite strips. In the numerical calculations, the effects of the ratio of Young's modulus of adherends to that of adhesives, the thickness of the adhesives, the bonding area and position and load distributions on the stress distributions at the interfaces were demonstrated. In addition, with use of the stress distribution, a method for evaluating joint strength was proposed. As a result, it was observed that band adhesive joints were available when the bonding area and positions were varied taking into account external load distribution. For verification, experiments were performed on the strain of adherends and the joint strength. Analytical results were consistent with the experimental ones.

View full abstract

The principles of adhesively bonded coaxial assemblies in power transmission gears provide some interesting design possibilities for example, in the attachment of gears to shafts, the savings in machining and material costs can be identified. To evaluate the durability of adhesively bonded coaxial joints applied in power transmission gears, a power circulating durability testing machine was constructed. Using this testing machine, we experimentally investigated the effect of applied mean torque, overlap length and rotational speed on the durability of joints. Static torsional tests were also conducted, and the relationship between durability in the testing machine and static torsional strength was discussed. Furthermore, the stress distribution in joints of this type was analyzed with the finite-element method to investigate the effect of stress distribution within the adhesive layer on the torsional strength and durability of the joint. The main results obtained are summarized as follows. (1) With increase in lap length, the static torsional strength increased. However, the maximum stress in the adhesive layer was almost constant irrespective of the lap length. (2) Durability test data obtained from different lap lengths can be normalized by utilizing the static torsional strength of the joint. (3) Applied torque with constant failure time decreases with increase in rotational speed. This phenomenon is apparently due to fatigue damage to the adhesive layer caused by vibration during rotation.

View full abstract

In this paper, stress and deflection of a multilayered plate subjected to thermal load, which is simulated by printed plate boards, are analyzed using the multilayered beam theory. That is, curvature in multilayered plate and axial forces in each layer are obtained using the continuous condition of strain at adhesive faces, balancing condition of axial forces and bending moments at each layer. Using the theory, stress and deflection in a two-layered plate composed of aluminum and copper are analyzed, and the results are compared with the corresponding finite element method solution. Furthermore, stress and deflection in printed plate boards are analyzed, and from the results, important factors in design are highlighted.

View full abstract

Generally, the ladder-type frames of heavy duty trucks consist of sidemembers and crossmembers. When the truck is driven, these frames receive static and dynamic loads from cargo and the road surface. Torsional stresses are generated by uneven surfaces of roads. Vertical bending and torsional stresses have previously analyzed, but the crosswise bending stresses of extremely slow speed turning have seldom been investigated. For 3-axle vehicle with non-steerable rear 2-axle alignment torque about vehicle centerline is created when cornering because of non-steerable rear 2-axle resulting in side force required at the front and rear axles. This paper presents a method for analysis of crosswise bending force which represents the rigid frame stresses.

View full abstract

In this study, we investigate asymptotic distributions of extremes for the case when the initial distribution is log-normal. We show theoretically by means of logarithmic transformation that the second asymptotic distribution is derived for the largest value. This result seems to be in contradiction to Gumbel's statement that the first asymptotic distribution is derived for the largest value, since it is not possible for two different types of asymptotic distributions of the largest value to correspond to the same initial distribution. This apparent contradiction is explained by the finding that the resulting first and second asymptotic distributions coincide with each other due to some relation between their distribution parameters. This result is also demonstrated graphically using probability paper. We also examine the asymptotic distribution of the smallest value.

View full abstract