The plane strain elastostatic problem for short fiber reinforced composite material is examined. Using the eigen function expansion method, stress singularities at the corner point of a fiber end and the tip of a fiber end crack are estimated. The effect of material combinations of fiber and matrix on the singularities are investigated. The singularity at the fiber end crack is numerically examined for carbon fiber reinforced epoxy by the boundary element technique. Based on the concept of linear fracture mechanics, the coefficient of the singular term for the fiber end crack problem is obtained by the numerical technique.

View full abstract

Carbon fiber reinforced plastics (CFRP), which is one of the advanced composites, have excellent properties of specific strength and rigidity. They have been used for lightening the mass of machines and the structures. It is thought that the fracture mechanisms of composite materials are so complicated that an investigation is necessary to make clear the fracture behaviors and mechanisms of the materials. Therefore, by using the results of frequency analysis of the acoustic emission of the model CFRP in the previous paper, it is found, in this paper, that the acoustic emission which is produced by the deformation and the fracture of unidirectional composite laminates and three directional ones are classified by the frequency, and that the fracture mechanisms of these composite materials can be clarified.

View full abstract

Rotating bending fatigue tests of a spheroidal graphite cast iron with a pearlite matrix were performed in the rage from room temperature to 450°C. The behavior of both the nucleation and the propagation of a small surface cracks were observed. The fatigue limits were verified to be the critical stress required to propagate the microcracks nucleated in the material faults of the graphites and shrinkage pores. Because of the retardation effect in crack propagation stage due to cyclic strain aging, the maximum value of the fatigue limits and the maximum length of nonpropagating cracks observed in unbroken specimens were seen at about 350°C. At all testing temperatures, the values of threshold stress intensity factor range calculated by incorporating the values of fatigue limits and the length of nonpropagating cracks were decreased down to about 0.38 when compared to the values of CT specimens with a long crack represented by the effective stress intensity factor range.

View full abstract

Single-edge-notched specimens of a low-carbon steel with three different notch depths were fatigued under completely reversed in-plane bending. The propagation and non-propagation of a short fatigue crack at notches were studied on the basis of crack closure measurement. A small amount of crack closure was found to be mainly responsible for the anomalous, fast growth rate of a short crack at the notch root. As the length of a non-propagating crack got longer, the threshold stress intensity range and the amount of crack closure increased. The Tanaka-Nakai-Akiniwa model gave a good prediction of the fatigue limit for crack nucleation and a slightly conservative estimate for the fatigue limit for fracture.

View full abstract

Effects of artificial small defects (drilled hole, shallow notch and the indentation of the Vickers hardness) on the fatigue strength of a maraging steel which received various aging treatments for the attainment of various hardness levels were studied. The fatigue strength σ_w can be predicted by σ_w = 0.65(H_V+960)/(√(area))^1/6………(a) where H_V is the Vickers hardness number and √(area) is the square root of the projected area of the artificial defect onto the plane normal to the direction of the maximum tensile stress. Equation (a) explains the reason of relatively low fatigue strength σ_w0 of maraging steel even with high hardness, because the maraging steel used in this study contains spherical inclusions of TiC with approximately 10 μm diameter and the value of √(area) of TiC was estimated to be about 9 μm by the investigation of the microstructure. Substituting this value and H_V into Eq. (a), we can obtain the values of σ_w0 which are in good agreement with the experimental results. These results suggest that the improvement in fatigue strength of maraging steel and hard steel may be achieved from the viewpoint of Eq. (a).

View full abstract

Rotating bending and push-pull fatigue tests in a low cycle region were carried out with plain and notched specimens of machine structural steels. Fatigue strength and cyclic strain amplitude at the surface of the specimen under the above applied stress were compared with each other. In addition, the notch effect on rotating bending fatigue properties under low cycle fatigue were investigated. The conclusions are summarized as follows; (1) In the case of expression by nominal stress, which is usually used, rotating bending fatigue strength is remarkably higher than push-pull. This is because the cyclic strain amplitude at the surface of the specimen under rotating bending is considerably smaller than the push-pull one. (2) It is found that the fatigue strength of both applied stress types shows good agreement by re-arranging the cyclic strain amplitude at the surface of the specimens. (3) Low cycle fatigue strength of notched specimens under rotating bending can be also arranged with plan specmens by re-arranging the cyclic strain amplitude at the notch bottom surface of notched specimens.

View full abstract

Fretting fatigue cracks appear very early in the fatigue life of metals. Fretting fatigue life is dominated by the propagation process of small cracks. Characteristics of fretting fatigue cracks are analysed using stress intensity factors which are obtained at the tip of cracks growing from contact edges. Stress intensity factors are calculated using contact pressure and tangential stress distributions across contact surfaces. Contact pressure and tangential stress distributions are anaysed using the Finite Element Method. Fretting fatigue limits are estimated by comparing the above mentioned calculated results of stress intensity factor ranges with the threshold stress intensity factor range of the material. These calculated results are compared with experimental results of fretting fatigue tests.

View full abstract

Fatigue tests with two-step cyclic loading (Low-High and High-Low stress change tests) were carried out on mild steel and stainless steel specimens with different slip characters. Plastic strain range Δε_p changed rapidly with the stress change, and it was investigated from a stand-point of rearrangement of dislocation structures, and compared with the analytical values by dislocation dynamics. The dislocation structures were rearranged easily in the Low-High stress change test. On the other hand, in the High-Low test, the specimen fractured before full rearrangement of dislocation because of surface micro-cracks growth resulting from initial high stress amplitude, but the rearrangement was performed sufficiently by the removal of cracks and by sufficient cycling of second low-stress amplitude. The rate of dislocation rearrangement was expressed clearly by the change of cell structure area and was higher in mild steel because of its ease of cross-slip.

View full abstract

Two methods of predicting fatigue lives of cracks propagating in residual stress fields were proposed. In these predictions, effective loads near the crack tip in components containing residual stresses are determined by superposition of the stress intensity factors for the residual stresses and for the applied stresses. One method uses the effective stress ratio R and the stress intensity range ΔK of the effective loads to estimate the effective stress range ratio U = ΔK_eff/ΔK. The fatigue crack growth lives are predicted by using ΔK_eff and the da/dN-ΔK_eff relation. The other method replicates simultaniously the variation of both R and ΔK with crack length by using specimens free form initial residual stresses, in order to simulate the mechanical state near the crack tip in the components with residual stresses. The life of the specimen directly provides the predicted value of the component life. Experiments were conducted by using specimens of S 35 C carbon steel with residual stresses. Good agreement was observed between the experimental and predicted values, for cracks emanating either from the tensile residual stress region or from the compressive residual stress region.

View full abstract

Fatigue crack growth rates in the base metal and the welds of HT80 steel welded joints were evaluated at temperatures ranging from room temperature down to 93 K. For the welds, the crack growth rates between room temperature and 174 K were dominated by residual stresses rather than temperatures. As the temperature decreased below 123 K, the crack growth rates of the base metal and the welds increased markedly because of cyclic cleavage during striation growth. The crack growth rates of the welds correlated with the effective stress intensity factor range, ΔK_effR, which was estimated by superposition of the respective stress intensity factors for the residual stress fields and for the applied stresses, when the crack growth was dominated by striation formation.

View full abstract

Crack closure characteristics in fatigue crack growth were examined using the modified Dugdale model developed by Newman. The model can leave elastic-plastic asperities in the wake of the growing crack tip. The analysis shows the influence of the rigidity, E, of the asperities, asperity length, asperity thickness and the distance from the crack tip. The results are compared with the experiments. It is noted that the experimentally detected closure level can't give correct informations regarding actual one under some conditions. Especially, under corrosive environment, the crack closuer level is overestimated than the actual level. On the other hand, near threshold region in air environment, it is underestimated.

View full abstract

In order to clarify whether da/dN depends on cycle only, or on time only or on both cycle and time, crack growth behaviour, in a 3.5% NaCl solution, of low alloy Cr-Mo steel at a lower frequency range was experimentally studied, stress frequency f being controlled by stress rise time t_R and tress hold time t_H independently. From the results and the analysis, a new experimental formula was obtained for da/dN in non-linear terms of f, t_R and t_H. A stochastic process concept is proposed for the significance of the equation of this type. As a special case, a simple and convenient expression for da/dN and da/dt in corrosion fatigue (t_H =0 s) was proposed in terms of frequency.

View full abstract

A CrMoV turbine rotor retired after long service operation (22 years at 500°C) was investigated to characterize the material degradation due to temper embrittlement by use of three different kinds of techniques ; the electrochemical polarization curve (EPC) method, the electrochemical noise analysis (ENA) and the small punch (SP) test. Grain boundary embrittlement due to phosphorous segregation can be detected as a change in repassivation behavior in the EPC method ; a significant difference in corrosion potential fluctuation in ENA ; and a shift of SP transition temperature. Diagrams for evaluating the temper embrittlement of a CrMoV turbine rotor were also proposed. Furthermore, a realistic and rational procedure for evaluating material degradation during service operation has been also discussed by combined EPC, ENA and SP methods.

View full abstract

Static-fatigue crack behavior for different sizes of artificial flaws in sintered silicon nitride was measured at elevated temperatures. The growth process of cracks consists of three stages. In the first stage, the crack shows a rapid growth, but the growth rate decreases in the second stage. In the third stage, the growth rate increases again and the material begins to fracture under high applied stresses, otherwise, the growth rate continues to decrease under low stresses. Consequently, a static-fatigue limit, below which cracks are arrested, exists for each condition. The effect of crack size on the static fatigue limit show a similar tendency as that for short time strength. That is, the threshold stress intensity for cracks smaller than 200μm becomes lower than that for large cracks. Furthermore, interpretation using the Larson-Miller parameter can be applied to the results with fractured specimens, but it does not hold for the results with specimens reaching the static-fatigue limit.

View full abstract

Rotating bending fatigue tests were carried out to study the cyclic fatigue properties of sintered silicon nitride at room temperature. Thirty-eight specimens were used with the purpose of statistical analysis. The fracture surface was observed using a scanning electron microscope. A large scatter was observed in the fatigue life, but a lower limit S-N curve could be drawn within the range of the present study. Mirror-mist-hackle areas were clearly observed on the fracture surfaces, and it was confirmed that the relation σ·γ^1/2 = const. holds between the mirror or mist radius γ and the stress amplitude σ. Furthermore, a cyclic slow crack growth region surrounding the fracture origin was observed on some of the fracture surfaces. Finally, supposing the slow crack growth under cyclic loading, the scatter of fatigue lives was explained as a first approximation from the scatter of defect sizes inherent to the material.

View full abstract

An acoustoelastic technique using ultrasonic was applied to nondestructive measurements of welding residual stress. Redistributions of the residual stresses in weld joint CT specimens were measured by the acoustoelastic and strain gauge techniques in fatigue crack growth tests. The redistributions of the residual stresses due to saw-cuts were also measured. The acoustoelastic technique is able to successfully measure the redistributions of the residual stresses. The validity of the principle of superposition is confirmed by the measurements of the redistributions of the residual stresses.

View full abstract

The boundary element method (BEM) to analyze the stress intensity factors for a crack in dissimilar materials is developed using Hetenyi's solution as a fundamental solution of BEM. Since Hetenyi's solution, which is a solution for a point load in an infinite dissimilar plate, satisfies exactly the boundary condition at the interface, this method with use of this solution does not require the discretization of the interface and only require the division of elements on the boundary of a finite plate. Therefore it is expected that this method can give an accurate solution for a crack on and near the interface. Moreover this solution includes Kelvin's solution and Mindlin's solution. After formulating and incorporating this solution in the BEM programmes, several numerical results of the stress intensity factors for a crack in dissimilar materials as well as a homogeneous material are presented. The usefulness of this solution for BEM analysis is discussed.

View full abstract

The energy method combined with the boundary element method is used to obtain the stress intensity factors of two-dimensional crack problems. The analyses are performed to examine the factors affecting the accuracy of solutions, that is, the method for crack extension, the value of crack extension and the type of element. It is shown from the analyses that the linear boundary element gives accurate solutions when the node at the crack tip is released by changing its boundary conditions. Then, the method proposed here is applied to center cracked plates subjected to tension and compact tension specimens to show the effectiveness of the present method.

View full abstract

The electric-potential CT method proposed previously by three of the present authors was applied to quantitative measurements of location, angle and size of two-dimensional inclined cracks embedded in steel plates. In this experiment, a D-C current was consecutively supplied between one of five pairs of electrodes placed on the top and bottom ends of the plates. Electric-potential distribution was measured along the side faces of the plate under each of these five current application conditions. Data on electric-potential were processed to reconstruct cracks by a least residual inverse analysis scheme, in which a least residual criterion was employed between the observed potential distributions and the computed ones for various assumed crack locations. When the residual was evaluated using a potential distribution obtained under any single current application condition, this scheme did not always give reasonable results. Simultaneous use of the potential distributions under five current application conditions made it possible to determine the location, angle and size of cracks with good accuracies.

View full abstract

Recently, with the rapid progress of computer technology, there is a growing need for large scale non-linear finite element analyses. However, These calculations take a lot of time and have large storage requirements. The authors have applied the ICCG method, which is one of the iterative solutions, to the three dimensional finite element analysis by supercomputer. Using the ICCG method, large problems with over 10 000 nodes have been solved in a short computational time and with good accuracy.

View full abstract

In this paper, a computer technique to analyze the contact stress distributions between two elastic bodies is proposed. The technique is the inverse analysis method using the information, which is forces or stresses measured by experimental techniques, on the surface of elastic body distant from the contact area. The finite element method is used to formulate the method. Under the assumed contact area the stresses of one of the elastic bodies in contact, of which the experimental information is used in calculation, are analyzed. Furthermore, by minimizing the square sum of stresses at the contact area the reasonable contact area and the stress distribution are obtained. The validity of this technique is proved numerically by the analysis of two-dimensional contact problem.

View full abstract

The contact problem between the magnetic tape and cylinder in a video tape recorder (VTR) is numerically analyzed, based on the virtual variable stiffness spring (VVSS) model iteration method. A head is assumed to have a uniform contact pressure. Green's function in tape deflection is first verified by the experiment on a commercially available VTR tape. The numerical iteration method based on VVSS model is next descried. From computer calculation, good convergent characteristics are shown for a wide range of iteration parameter values. Calculated results of the contact pressure and tape deflection around the head window are presented for various values of head protruding height. It is found that a fine division width less than 30 μm is necessary in the transverse direction in order to get a smooth contact pressure distribution.

View full abstract

A numerical method is given for the solution of frictionless counterformal contact problems. Only the contact area is divided into triangular elements. Linear contact pressure was applied on a triangular element. The displacements and stresses in the contact body were calculated. The contribution from a triangular element was calculated analytically. An example is given for a crowned roller pressed to a semi-infinite body.

View full abstract

An analytical evaluation method for the proof testing applied to ceramic components has been proposed. Based on this method, the effectiveness of a proof test whose loading pattern is different from that in a service condition can be evaluated. A statistical evaluation method for the small sample data of the fracture test of ceramic components after proof testing has been also proposed. The integrity of ceramic components subjected to complicated loading can be assured by the above mentioned methodology.

View full abstract

In order to investigate the size requirements for ductile fracture initiation under J-dominant conditions in tensile type specimens, finite deformation FEM analyses were performed on crack tip fields in center cracked and edge cracked plates subjected to tension. It was found that even when the stress distribution deviates from the HRR singular field, there exists a J-value range where the stress strain field in the immediate vicinity of the crack tip is in close agreement with that of small scale yielding. This suggests that for such a J-value range, the fracture process near the crack tip is the same as in the small scale yielding and that the fracture initiation can be characterized by the J-integral. The minimum value of the remaining uncracked ligament and (half) crack length for ensuring J-controlled crack tip characteristics, 80(J/σ₀), were σ₀ represents yield stress, is obtained for a center cracked tension specimen, while 50(J/σ₀) is obtained for an edge cracked tension specimen.

View full abstract

The authors have developed an influence function method by which the stress intensity factor, K, for surface cracks can be analyzed easily for arbitrarily distributed surface stresses. The data of the influence coefficients. K_ij, have been obtained for a semielliptical or a quarter-elliptical surface crack in a flat plate and for a semielliptical surface crack in a round bar. In this paper, the authors have shown how these data can be applied to the analysis of K for a surface crack originating at the stress-concentrated portions such as notch roots, welding joints and circular holes. It has been found that the proposed estimation scheme gives approximate values of K at most 10% higher than the exact values.

View full abstract

This paper describes a method for the stress analysis in the 2-dimensional region of a model in a photoelastic experiment. The present method uses an approximate equation of a directly integrated stress-equation of equilibrium between two points in any direction. The equation of sums of normal stresses induced from the approximate equation etc. is applied to any set of two points in the region to analyze the stresses. The method of least squares is used to constitute the simultaneous equations for the sums of stresses. The sums of stresses are obtained by solving the simultaneous equations, and the stress components are determined. The present method is applied to a circular disk subjected to diametral compression, and the results agree well with theoretical solutions.

View full abstract

This paper describes a method for automatically drawing stress trajectories in a 2-dimensional region from a photoelastic experiment. The stress trajectories are considered a gathering of circular arcs with different curvatures, and approximately expressed by polygonal lines. The polygonal lines are determined by a repeat calculation to be in contact with true stress trajectories. The present method can apply to cases where the stress components are given and the directions of principal stresses are given from isoclinics.

View full abstract

Large deformations of a fiber-reinforced straight beam with a central crack on the beam bottom are analysed in the framework of the theory of ideal fiber-reinforced composite materials. The beam is reinforced in its axial direction and simply supported with fixed roller fulcrums. The equilibrium condition of the part of the beam corresponding to the crack is reduced to a Fredholm-type integral equation of the second kind with respect to the curvature radius of the uppermost fiber.

View full abstract

A frictionless, axisymmetric contact problem is considered, where an elastic half-space is pressed onto a rigid foundation with a parabolic-ended pit or protrusion. It is necessary to find the extension of the contact region and contact stress between an elastic half-space and the rigid foundation. Also required is the normal displacement on the free surface. The problem is solved by using a solution of the Papkovich-Neuber equations in oblate spheroidal coordinates. The effects of various parameters on the contact stress are studied. Numerical results are compared with these for a flat-ended pit or protrusion, and they are found to be in agreement.

View full abstract

This paper deals with a three-dimensional stress analysis of adhesive butt joints subjected to tensile loads in order to contribute to an establishment of the design of joints. Similar adherends and an adhesive bond are replaced with finite hollow cylinders in the analysis. Stress distributions in adhesive joints are analyzed strictly by using the three-dimensional theory of elasticity. The effects of stiffness and thickness of the adhesive bonds on the normal and the shear stress distributions are shown by numerical computations. The analytical result is also compared with the result obtained by F.E.M. in order to verify the stress distributions in adhesive bonds. It is shown that they are in fairly good agreement.

View full abstract

The adaptability of the electroplating method of stress analysis to variable test temperatures is examined by using nickel plating foil of 5 μm in thickness. The test temperatures vary gradually or stepwise in the range from 100°C to 200°C. The relations between the proper stress σ_p of the nickel plating foil and the number of stress cycles N, namely, the σ_p-N curves at variable test temperatures are obtained by the calibration tests in rotating bending in which N=(0.54.5)×10⁶ cycles are designated. It is found that the σ_p-values at variable test temperatures can be estimated by using the formulas of the σ_p-N curves at constant temperatures, which is based on the assumption that the appearance of slip-bands in the nickel plating foil owing to cyclic straining is subject to the linear cumulative damage law.

View full abstract

The authors have developed a method of real time stress measurement by a scanning infrared camera. It has been shown that the cyclic plastic zone at the tip of a fatigue crack can be monitored. Further, the HRR singurality of 1/γ in the distribution of plastic strain energy in the cyclic plastic zone, where γ is the distance from the crack tip, has been verified experimentally. It has been shown that the fracture mechanics parameters such as stress intensity factor, K, and J-integral can be measured by the developed system.

View full abstract

This paper deals with a methodology to analyse randem vibration of a vehicle running on a road whose surface is uneven probabilistically. The uneven road is represented as a two-dimensional filtered Poisson process in terms of sinusoidal shape function. The four-wheeled vehicle is modeled as a frame structure, to which the effect of road surface is input through spring-damper systems, in the framework of the finite element method. The shape function of structural response is obtained through mode decoupling by means of complex eigenvalue analysis and time integration of the equation of motion. It turns out that samples of response time history are calculated in addition to response power spectra, without using the coherence function. A numerical example is carried out in regard to a model truck, and time history, power spectrum and frequencies of occurrence of bending mements generated are given.

View full abstract

In this paper, the dynamic similarity of transient response caused by the collision between a sphere and a cantilever beam is theoretically investigated and the results are compared with the experiments. The theoretical analysis of transient response in a cantilever beam is conducted by the use of classical beam theory and with the aid of a Laplace transform which extends the fast Fourier transform to an inverse transform under the condition that the spheres strike cantilever beams at arbitrary points. The dynamic similarity of a cantilever beam is studied to use those results. In the experiment, the bending strain is measured by a strain gauge cemented to a bar of rectangular cross section of the model or the real thing. It is shown that the variation in bending strain of the model multiplied by the coefficient of similarity is in agreement with the real thing.

View full abstract

In fastening structural members by using bolts and nuts, the so-called pre-tension method is frequently used now in cases where the axial tension in the bolt must be controlled with high accuracy. This method consists of two processes, i.e., (1) the pre-tension process using an oil pressure cylinder and (2) the fastening process releasing the pressure in the cylinder after rotating the nut to the contact surface. The ratio of the axial tension in the bolt in the process (2) to that in the process (1) is termed the "Effective tensile coefficient" here. It is important in design to estimate its value. In spite of the importance of the pre-tension method, no papers for the analysis of this process have been published yet. In this study, the above mentioned two processes are analyzed using the finite element method and the relations between the effective tensile coefficient and design factors such as the grip length or the nominal designation of screw thread are clarified.

View full abstract

The present paper deals with the combined effect of a spring support and a lumped mass on the stability of a tubular cantilever conveying fluid. The support and the mass are assumed to be attached to the cantilever at the same location. The validity of Galerkin's 8 term approximation is discussed from the view point of predominant eigenmodes in critical flutter configurations. It is shown that for particular combinations of spring stiffness and lumped mass there exists an instability region which jutts out from the main flutter domain. Both theory and experiment confirm that the instability in the region is of mild flutter type, not violent.

View full abstract

An analytical method to estimate the temperature distribution of a slab in a steady continuous casting process when considering solidification is presented in this paper in a spatial coordinate system to take into account the effect of the flow rate of the material. As an example, a vertical continuous casting model is examined by use of the finite element method, and the calculated results of temperature and shell thickness are compared with experimentally measured data to verify the proposed method.

View full abstract

An analytical method to simulate the deformation and stress in a slab due to a steady continuous casting process in a spatial coordinate system is presented in this paper. Considering both the solid and liquid states existing in the process, a viscoplastic constitutive relationship capable of describing the elastic-viscoplastic solid as well as viscous fluid is employed. As an example, a vertical continuous casting process is examined by use of the finite element method, and the calculated results of deformation and stress are revealed to simulate the actual behavior during continuous casting process.

View full abstract