In recent years, mechanical structures such as railway wheels, rails, offshore structures, bridges, engine components, load bearing parts of automobiles, etc. have to endure for a long term up to 10⁸-10¹⁰ loading cycles in order to save resources and to reduce the cost together with the environmental load to the globe. Thus, the fatigue behavior of structural materials in the very high cycle regime of 10⁸-10¹⁰ cycles has become an important subject of the research. In this paper, a review of the current studies in this area performed by many researchers is described in order to provide a certain milestone in the history of the research on fatigue behavior of the metallic materials in the very high cycle regime.

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Reducing the weight of a machine structure is an increasingly important consideration both for the conservation of resources during production and for the energy saving during operation. With these objectives in mind, thin-walled ductile cast iron has recently been developed. Because rapid cooling could result in brittle microstructure of cementite (chill) in this cast iron, it is necessary to investigate the effect of cementite on the fatigue properties. Therefore, fatigue tests were carried out on a ductile cast iron of block castings which contained a relatively small amount of cementite. Fracture surface observation indicated that the fracture origins were located at graphite clusters and cast shrinkage porosity, not at cementite. It appears that when the size of the cementite is smaller than that of the graphite, the cementite does not affect the fatigue properties of ductile cast iron. Not surprisingly, the fatigue lives were found to increase with decrease in the size of the fatigue fracture origin. The threshold initial stress intensity factor range ΔK_ini,th for fatigue failure was found to be about 3-4MPa√m, independent of microstructure.

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Researchers proposed the methods of creep-fatigue evaluation, such as time fraction rules or ductility exhaustion rules. However, the microstructure change during creep-fatigue should not be directly considered in these methods. The hysteresis energy contributes to the microstructure change before the crack initiation and the crack initiation and propagation. The creep-fatigue has evaluated by the hysteresis energy in modified 9Cr-1Mo steel which is a candidate for structural material in Fast Breeder Reactor (FBR) plant. Creep-fatigue and fatigue tests were carried out at 723-873K in air. The hysteresis energy per hour at the middle of life (N_f / 2, N_f is the number of cycles to failure) has been evaluated. It is clear that the relationship between this parameter and the time to failure can be expressed by the power-law function. The creep-fatigue life can be evaluated based on the hysteresis energy an hour at N_f / 2 using this relation.

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It is known that high temperature tensile strength increases with increasing Cr content in Cr containing heat resistant steels. Recently, however, it was found that long-term creep strength decreased with increasing Cr content in the heat resistant steels containing 8.5-12%Cr. In this study, precipitation behavior of M₂₃C₆ carbide and the Z phase after creep tests was investigated using two kinds of high Cr ferritic steels (9Cr and 10.5Cr). As a result, 10.5Cr steel exhibited larger average particle size of M₂₃C₆ than 9Cr steel irrespective of creep stress levels, but the amount of M₂₃C₆ carbide was almost the same in both steels. On the other hand, the amount of the Z phase became large in 10.5Cr steel compared with 9Cr steel. These experimental results indicate that high level of Cr content accelerates precipitation and coalescence rate of both M₂₃C₆ carbide and the Z phase, resulting in degradation of long term creep strength in 10.5 Cr steel compared to 9Cr steel.

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Creep strength of welded joints in high Cr steels decreases due to the formation of Type-IV creep damage in the heat-affected zone (HAZ) during long-term use at high temperatures. This paper aims to elucidate the processes and mechanisms of Type-IV failure. Creep tests for the welded joints with different groove configurations of Mod.9Cr-1Mo steel were conducted. Distributions of Type-IV creep damages in HAZ of these welds were measured quantitatively, and were compared with FEM computations using damage mechanics analysis. For the welded joints with double U groove, creep voids were observed mostly at 20% below the surface of the plate, and scarcely near surfaces and center of thickness. For the welded joints with single U groove, creep voids were observed inside the plate thickness more than 3mm below the surfaces. From the comparison of experimental damage distributions with FEM analysis, it is considered to be important to take the stress triaxiality into account for the prediction of damage location and fracture life of high Cr ferritic steel welds.

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This study discusses multiaxial low cycle fatigue life of notched specimens under proportional and non-proportional loadings at room temperature. Strain controlled multiaxial low cycle fatigue tests were carried out using smooth and circumferentially notched round-bar specimens of two types of steels, SUS316 and SGV410. Two kinds of shallow notched specimens were employed of which elastic stress concentration factors, K_t, are 1.5 and 2.5. The strain paths include proportional and non-proportional loadings. The former employed a push-pull straining or a reversed torsion straining. The latter was achieved by strain path where axial and shear strains had 90 degree phase difference but their amplitudes were the same based on von Mises' criterion. The notch dependency of multiaxial low cycle fatigue life and the life predictability were discussed. The lives for both steels depend on both K_t and strain path. The data correlations also showed the different trend between the steels. The strain parameter for the life prediction was discussed with the non-proportional strain parameter proposed by one of the authors with introducing K_t. The proposed parameter gave a satisfactory correlation with multiaxial low cycle fatigue life of notched specimens for two steels under proportional and non-proportional loadings.

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In order to make clear the mechanism of the directional coarsening of γ' phases (rafting) of Ni-base superalloy under uni-axial strain, molecular dynamics (MD) analysis was applied to analyze the effect of strain on the diffusion characteristics around the interface between different materials. In a Ni (001)/Al (001) interface structure, the stress induced diffusion of Al atoms perpendicular to the interface was found. The stress induced anisotropic diffusion of Al was also found in a Ni (001)/Ni₃Al (001) interface. These results imply that it is highly possible the rafting occurs predominantly by the stress induced anisotropic diffusion of Al atoms.

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Fatigue strength of electroplated copper thin films was measured under uni-axial stress. Two kinds of electroplated films were prepared for the fatigue test. One was a commercial film mainly used for interconnections in printed wiring boards. The other film was grown on a stainless steel substrate by using acid copper sulfate bath without any additive agent. The micro texture of each film was observed by using SEM (Scanning Electron Microscope) and SIM (Scanning Ion Microscope). It was found that the micro texture of each film was quite different with each other. The mechanical properties such as the yield stress, fracture elongation and Young's modulus of each film changed significantly from those of bulk copper depending on their micro structure. The low-cycle fatigue strength also varied drastically with each other, while the high-cycle fatigue strength was almost same. The fracture surfaces were observed by SEM after the fatigue test. It was found that there were two fracture modes under the fatigue test. One was a typical ductile fracture, and another was brittle one even under the fatigue load higher than its yield stress. Transgranular crack propagation was observed when the ductile fracture occurred. On the other, Intergranular crack growth appeared when the brittle fracture occurred. These results clearly indicated that the fatigue strength of electroplated copper thin films varies depending on their micro structure.

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This paper describes the creep-fatigue life assessment of Sn-3.0Ag-0.5Cu solder under pull-push loading using fast-fast, fast-slow, slow-fast and strain-hold strain waveforms. Strain controlled creep-fatigue tests were carried out using solid bar specimen, and the effect of strain waveform on the creep-fatigue life was discussed. Creep-fatigue damage was evaluated by the linear damage rule, the frequency modified fatigue life, the ductility exhaustion model, the strain range partitioning method and the grain boundary sliding model. The strain range partitioning method and the grain boundary sliding model only predicted the creep-fatigue lives within a small scatter.

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A new method is proposed to detect a tilted planar flaw on the back surface of a plate using the interference of ultrasonic waves. Parameters for flaw evaluation are developed and examined through experimental results for artificial flaws. The existence of the flaw and its height are estimated by parameter B_h, which shows the first amplitude of the interference fringe. The effect of tilt angle of the flaw on parameter B_α, which indicates the amount of asymmetry of the interference fringe along the direction normal to the flaw, is investigated. Flaws larger than 0.5 mm in height can be detected using the present method with a tilt angle of 20°from the normal direction of the inspection surface.

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Numerical analysis was conducted to solve the problems encountered in the thermal stress cleaving of borosilicate-glass plate of 50μm thick using CO₂ laser with the speed over 100mm/s. We investigated the influence of constraint and the effect of heat dissipation from the surface. It is concluded that the constraint of out-of-plane deformation does not influence the distribution of thermal stress intensity factor in the thickness and higher cleaving velocity may be attained with increase of heat dissipation.

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We apply a finite-element analysis method based on first-principles density functional theory, to evaluate the nonlinear large elastic deformation of single-crystal diamond. The stress-strain relations are obtained during finite-element analysis on the fly based on the first-principles calculations and their numerical database is simultaneously constructed, which enables us to obtain high-precision stress without any empirical parameters even under finite strained conditions. The shear strength and mechanical behavior of diamond crystal are analyzed under various stress conditions, and then the uniaxial deformation of a diamond-crystal pillar model is examined through the present analysis method.

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This paper discusses a perturbation-based stochastic homogenization analysis procedure for a fiber reinforced composite material. For the purpose of estimating a stochastic characteristic of a homogenized equivalent elastic constant of composites for a microscopic random variation of a material property or geometry of a microstructure, the first order perturbation technique is applied to the equivalent inclusion method. The homogenized equivalent elastic constants can be computed from a homogenized compliance in case of an orthotropic material, therefore, the perturbation term of the homogenized compliance for a microscopic random variation is also computed. From numerical results, validity and effectiveness of the proposed method are illustrated.

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Welding residual stress is one of the most important factors of stress corrosion cracking (SCC) growth in pressure boundary piping. The effect of excessive loading, such as an earthquake, on the residual stress is evaluated by axisymmetric thermo-elastic-plastic analyses based on the finite element method. After conducting welding residual stress simulation, several loading patterns of prescribed displacement for piping butt-welds have been applied in the axial direction by varying the maximum displacement and the combination of tension and compression. A greater displacement causes greater relaxation of welding residual stress near piping welds after the loading and unloading cycle. We conclude that the SCC growth rate could decrease as the amount of prescribed displacement increased.

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MEMS structures and machines fabricated by photolithography and/or etching have often repeated unit microstructure. We need to design not only the global parameters but also microscopic and local parameters. In pursuit of this, a dynamic analysis of global/local problem is essential, and especially fast computational method and convenient modeling technique are both required for the MEMS design. Hence, this paper presents the application of model order reduction (MOR) for fast dynamic analysis combined with the finite element mesh superposition (FEMS) technique for practical and convenient modeling of the above-mentioned microstructures. Through two examples, the accuracy is carefully investigated for both global and local responses associated with the base vectors in MOR algorithm. The first example is analyzed by a kind of homogenization technique and MOR. The number of DOFs was finally reduced by a factor of approximately 1/6 (47,362/296,268). In addition, MOR enabled us to reduce the coefficient matrix size to only 300. The second example is analyzed by both FEMS and MOR, and it was found that MOR is also applicable to an unusual matrices generated by FEMS.

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The effects of variables, such as the dimensions of a test specimen and the friction between the plate specimen and the tools, on the average stress measured in the usual split Hopkinson-Davies pressure bar (SHPB) compression test are estimated, and a method, which is a variant of the well-known Cook and Larke extrapolation method, is established for a constant-strain-rate test using some tapered striker bars to determine the curves of dynamic resistance to homogeneous deformation, i.e., the intrinsic stress-strain curves, by trial and error. The research involves the SHPB compression tests on metal specimens with four or five initial ratios of diameter to height and an analysis of the resulting curves. It is shown that the friction coefficient for various conditions is somewhat complicated and hence it is difficult to estimate the friction coefficient by the SHPB compression test. Then we formulate an extrapolation method to reduce friction to a minimum for the SHPB compression test at a constant strain rate: approximately 1000 [1/s] for metal plate specimens. We conclude that this kind of SHPB system with a constant-strain-rate test followed by the extrapolation procedure is a standard SHPB compression system for metal plate specimens.

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A set of simplified formulae is proposed for estimating the dynamic spring constants of rubber bushes used in suspension systems. These formulae are structured by extending a set of elastic solutions[Editor2] proposed before to calculate the dynamic spring constants according to the associated law (pseudo-elasticity) of the linear viscoelasticity theory. A unique feature of this method is that it helps in the easy and quick evaluation of the dynamic behavior of rubber bushes for all the six degrees of freedom (axial loading, loading normal to an axis in two directions, wrench in two directions, and torsion[Editor3]) with no direct involvement of the FEM. In order to validate this method of calculation, the results obtained for all the degrees of freedom are compared with those obtained using the FEM. It is verified that this approach is capable of qualitatively reproducing the results obtained by using the FEM analysis.

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Aiming at the practical use of polyethylene glycol (PEG) microneedles for transdermal drug delivery system (DDS), a testing apparatus for their insertion into cultured human skin has been developed. To simulate the variety of conditions of human skin, biaxial tension can be applied to the cultured human skin. An adopted testing scheme to apply and control the biaxial tension is similar to the deep-draw forming technique. An attention was also paid to the short-time setup of small, thin and wet cultured skin. One dimensional array with four needles was inserted and influence of tension was discussed. It was found that tension, deflection of skin during insertion and original curvature of skin are the important parameters for microneedles array design.

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