The fatigue behaviors of metals containing small defects or inclusions are so complicated that the prediction of the influence of defects or inclusions is very difficult. However, recent advances in fracture mechanics have led to quantitative treatment of this problem. In this paper, first, the characteristics of the effects of small defects and inclusions are discussed by reviewing the existing literature, which mostly reports the defect and inclusion problems qualitatively. Next, it is revealed that the clue to solving the problems quantitatively is the concept that defects and inclusions are virtually equivalent to cracks from the viewpoint of fatigue strength. A method of evaluating the fatigue limits of metals containing small defects based on this concept is introduced. Finally, it is shown that the method is useful in predicting the lower limit of fatigue strength of high-strength steels containing nonmetallic inclusions which cause a distinct decrease in fatigue strength and a large scatter of fatigue strength.

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In this paper a review is made of the stress concentration and the stress intensity factor approaches to dealing with fatigue crack growth. For small cracks, i.e., those which initiate in unnotched specimens, and for short cracks, i.e., those which initiate at notches, the stress intensity factor approach is not useful because the factor goes to zero for such cracks. On the other hand in the stress concentration approach the limiting stress is always the applied stress. A modification to include a material constant in the expression for the stress intensity factor is proposed based upon an analogy with the stress concentration approach. The modified stress intensity factor is used in the analysis of surface crack growth. The growth of small/short cracks is also analyzed with consideration being given to the effects of crack closure, and the observation that at a given ΔK level in the short crack range the shorter the crack the higher the rate of growth is discussed. Comparisons are also made between experimental results for short cracks growing from notches and predictions based upon the proposed method of analysis.

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This paper is concerned with the complete adhesion problem when an elastic half space is subjected to moment by an elliptical rigid punch. By using Abel transform, we reduce the problem to solve the inhomogeneous simultaneous Hilbert problem with infinite unknown functions. A general method for solving the problem is given. Numerical results are shown for the distribution of contact stresses and surface displacements in several cases of the punch aspect ratio.

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This paper deals with the numerical analysis of large elastic-plastic deformation of shells in contact with each other. The penalty function method is used accurately to treat the contact condition involving a finite amount of sliding. Axisymmetric large deformations of contacting spherical shells are analyzed, and it is shown that elastic unloading resulting from the sliding definitely affects the crushing of one shell by another. The possibility of nonaxisymmetric bifurcation of deformation is examined on the basis of the J2-deformation theory.

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A bar is made using the hot rolling method. It is important to make the temperature distribution clear for the precise estimation of the material shape and the controlling texture. Thus, we analyzed the flow of the material in bar rolling by the energy method using finite element division. In this paper, we deal with the temperature distribution in bar rolling. The temperature distribution near the material-roll contact surface changes drastically. We propose the following new method for the analysis in the neighboring region of the contact surface. We apply the finite difference method to this region, and apply the finite element method to the other region. Consequently, the following results are obtained. (i) Temperature at the material-roll contact surface depends highly on the frictional condition and the circumferential velocity of the roll. (ii) Temperature becomes high at the central part of the material near the contact surface, in the square-diamond pass and round-oval pass; whereas in the square-oval pass, the temperature becomes high at the side part of the material near the contact surface.

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The free vibrations of an infinitely long cylindrical shell under axisymmetrical hydrodynamic pressures due to external and internal fluids are studied theoretically. The basic equations of motion for axisymmetric vibrations of such a shell are given, based on the bending theory. These equations are solved analytically by means of Fourier cosine transformation, and the general frequency equation for the coupled systems is obtained by consideration of the dynamic interaction between the shell surface and fluids. Furthermore, seven special cases are derived from the general coupled frequency equation. The general frequency equation is calculated for some kinds of mass density of the internal fluid. Hence, it is shown that the effect of the motion of the external and internal fluids on the free vibrations of a shell is notable.

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This paper considers propagation of plane P- and SV-waves in an inhomogeneous elastic medium with harmonic variation of density. By assuming a small inhomogeneity in the density and using the perturbation method of multiple scales, the wave propagation phenomenon is discussed within a frame of the first order solution. Three unstable(resonant) frequencies are found. Near the unstable region, the amplitude of an internally reflected wave is of the same order as that of the incident wave. However, the wave is stable when the amplitude of an internally reflected wave is a higher order of a small parameter or when the amplitude of an internally refracted wave is the same order as that of the incident wave. It is concluded that unstable wave propagation in the harmonically inhomogeneous elastic medium occurs when an internally reflected wave appears and then its amplitude increases to the same order as that of the incident wave.

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It is emphasized that the sinusoidal response of the shear stress τ to large shear strain γ in a simple shear is not unreasonable at least in a mathematical sense (although it has long been considered unreasonable), and is dependent on the material property. Also it is found that the up-dated form of the constitutive equation is not necessarily equivalent to its original one except when the current rates of stress and strain are completely independent of the deformation state and history in a tensorial sense, which are commonly used unconditionally in the numerical deformation analysis by the incremental method. A new plastic constitutive equation is proposed which involves a new material constant ρ with 0≦ρ≦1. It reduces to the so-called J₂-flow theory for ρ=0, and resembles the deformation theory for ρ=1. Its stress response to simple shear is discussed with various values of ρ, and the well-known axial extension of a cylinder subjected to torsion is explained using an appropriate value of ρ. The spin to be used in the constitutive equation and the evolution equation of thee internal variables are also discussed.

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Fatigue crack growth rates under elastic-plastic conditions have been reported to correlate well with the J-integral range, ΔJ, evaluated experimentally from load-point displacement using formula developed for specific specimen configurations. However, the theoretical basis of ΔJ still remains unestablished. in this paper, path-integral expressions of ΔJ and their approximate path-independence in the presence of the effects of strain hardening and crack closure were discussed. Finite element simulations of elastic-plastic crack growth under cyclic loading were conducted. It was found that ΔJ values evaluated by the path-integral were almost path-independent when the minimum load point or the crack opening point was selected as a reference point for evaluation. The examination of the relationship between ΔH and crack-tip opening displacement or strain distribution near the crack tip led to the conclusion that ΔJ evaluated on the basis of the crack opening point was the most appropriate parameter in characterizing the near-tip-stress and strain fields under fatigue conditions.

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Circumferentially grooved specimens were low - cycle fatigued, and the local stress-strain relation was calculated at the notch root by F.E.M. (finite-element method). The fatigue lives for crack initiation and final failure were satisfactorily evaluated by both the axial and equivalent plastic strain ranges existing at the notch root, and Coffin-Manson law held for the notched specimens as well as for the smooth specimen. The growth behavior of surface cracks at the notch root was examined in association with the growth rates of the surface crack in the smooth specimen and of the long through-crack. The fatigue crack growth rates, da/dN, were successfully plotted against the cyclic J-integral range, ΔJ, and the strain intensity factor range, ΔK_ε, which were estimated using the stress-strain hysteresis loop analyzed at the notch roots by F.E.M: The plots of log da/dN versus log ΔJ and log da/dN versus log ΔK_ε for the notched specimens were expressed by linear lines which were nearly in accord with these relations for the surface crack in the smooth specimen.

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A boundary element application to inverse problems associated with galvanic field response due to anodic/cathodic interactions is discussed. The galvanic corrosion rate is usually estimated by solving Laplace's equation with nonlinear boundary conditions which are imposed based on experimentally determined electrochemical polarization curves. However, the electrochemical polarization curves of the materials considered are not always available. In this case, the inverse approach, in which the current density across the materials is estimated from the potential values in the electrolyte, is necessary. This inverse problem generally yields an ill-conditioned system of linear equations. A regularization method is introduced using the singular value decomposition of the coefficient matrix, and a criterion for determining an effective rank of matrix is presented. A numerical example of coating damage detection is presented to illustrate the usefulness of the method.

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A supercomputer-based software which enables reconstruction of a three-dimensional shape without human assistance using a stereo-pair of scanning electron micrographs has been developed. It is based upon computer image processing and pattern recognition techniques, and can reconstruct a three-dimensional shape of a wide variety of fracture surfaces of corrosion fatigue as well as crack initiation sites in an aggressive environment line a corrosion pit. We discuss the optimum algorithm according to the morphology of the fracture surfaces. A sequential similarity detection algorithm is available in transgranular fatigued surfaces, whereas in the case of corrosion fatigue fracture surfaces and crack initiation sites, the mutual correlation coefficient technique is well suited. The shape and size of the window area, and the run time required in reconstruction are also discussed.

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This work is a preliminary investigation carried out in an attempt to develop a software system which detects the possible sources of degradation in the original design of machines and structures and provides alternatives to improve their integrities in terms of strength by noting their geometrical distinctions. The computer stores their topological data using a boundary representation model. The system detects the distinctive geometrical features and reasons based on them whether they might be triggers for degradation or not by referring to the attributes attached to each geometrical feature. The fundamental validity of the approach is verified on a personal computer using Prolog. What should be stressed as the originality of this paper is that although the design models cannot be modified without numerical data in the conventional strength-related designs, they can be improved or better alternatives can be suggested as long as their topological data are available in our system.

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The fretting fatigue strength of SUP 9 spring steel under random loading was examined by clamping the contact pads of the same material. Random loading reduced the fretting fatigue strengths by a factor of 1.5. The linear cumulative damage rule held well for fretting fatigue under random loading. The relationship between the coefficient of the friction and the slip amplitude using root-mean-square values under random loading agreed well with that under constant amplitude loading. Prediction of fatigue life was made on the basis of the fracture mechanics analysis proposed in the previous paper, where the frictional force between the fretting pad and the specimen was taken into consideration. The predicted lives were in good agreement with the experimental results.

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An estimation method of long-term growth characteristics of corrosion fatigue (CF) cracks using laboratory data is proposed based upon a linear summation model in terms of modified effective stress intensity factor range, ΔK_cont, which eliminates the corrosion products-induced wedge effect. Long-term CF crack growth curves of a 50 kgf/mm² high-tensile strength steel, HT50 and HT50-TMCP, and a 80kgf/mm² one, HT80, in synthetic seawater are estimated supposing that ΔK_cont is identical to the nominal stress intensity factor range, ΔK. The threshold values for long-term CF, ΔK_CF, deduced from these curves are nearly equal to the threshold values for crack initiation at corrosion pits, ΔK*_CF, which are calculated assuming the pits as sharp cracks.

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A study was conduced on the effect of crack size or surface roughness on the tensile strength of ceramics used to the lower-quality fueled gas turbine or diesel engine. In general, removal of the surface defects and/or forming of the correct shape of the ceramic materials requires machining of the part at enormous cost and a large expenditure of time. Even if the materials were carefully machined, the fact that their surfaces would still be extensively attacked by corrosive ashes causing considerable damage, makes such an effort seemingly useless. The experimental results show that in the case of partially stabilized zirconia at 650°C°C, the existence of artificial corrosive ash containing vanadium pentoxide and sodium sulphate on flaws significantly enhances the tensile strength of the ceramic. However, in the case of silicon carbide at 900°C, no remarkable differences could be found between the results with or without corrosive ash. In this experiment, the hardness indentation method was used as a quantitative tool to simulate mechanical surface defects.

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The effect of a water environment on the near-threshold growth of delamination fatigue cracks was investigated with unidirectional laminates made from Ciba Geigy prepregs 914 C (T300/914) and from Toray prepregs P305 (T300/#2500). Tests were carried out under mode I opening loading using double cantilever beam specimens. The crack growth rate was correlated to the equivalent stress intensity range regardless of the stress ratio. For the 914 C laminate, the crack growth rate in water was about one tenth of that in air in the power-law region. For the P305 laminate, the effect of a water environment was small in the power-law region. Near the threshold, the crack grew slower in water than in air for both laminates. When the 914 C laminate specimen was moisture-conditioned, the growth rate in water was about 300 times faster than that of the specimen in water without conditioning. These environmental effects were explained on the bases of fractography and fracture mechanisms.

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The influence of notches on the static tensile strength of plates was studied for a composite material. Tension tests on notched plates made of fiber glass/epoxy laminates have been carried out for a wide range of notch root radii. All notched specimens failed in a brittle manner through the formation of a small deformation near the notch root. This experiment shows that the nominal stress at failure decreases with decreasing notch root radius, and it approaches a constant value when the notch root radius is less than about 0.2 mm. It has been verified that the maximum elastic stress at the notch root when the specimen fails is governed by the notch root radius alone and is independent of notch depth. On the basis of the concept of linear notch mechanics, the experimental results mentioned above can be clearly explained, and the limiting condition for the fracture of notched plates of composite materials is determined. This condition is the same as that of notched engineering plastics.

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