Consideration of crack growth under creep-fatigue conditions can be the dominant factor in determining the allowable maximum stress and temperature as well as the design and remaining lives of elevated temperature components. Several advancements in the concepts of linear and nonlinear fracture mechanics have occurred over the past fifteen years which address creep-fatigue crack behavior growth. These developments are reviewed in this paper. The available data strongly demonstrate the importance of loading frequency and waveform on the creep-fatigue crack growth behavior of high temperature alloys. There is considerable data and analytical support in the literature to show that crack growth under gross plasticity conditions can be treated by the ΔJ-integral. Further, (C_t)_avg and ΔJ_c parameters are needed if creep deformation accompanies crack growth. Several examples of creep-fatigue crack growth data correlated with (C_t)_avg and ΔJ_c parameters are shown. It is also shown that (C_t)_avg and ΔJ_c are equivalent parameters when extensive creep conditions occur. Under small-scale and transition creep conditions, ΔJ_c is not rigorously defined but (C_t)_avg is related to the average creep zone expansion rate. Methods for determining (C_t)_avg and ΔJ_c are described. Experimental methods for obtaining creep-fatigue crack growth data are also described and critically evaluated. Models for predicting creep-fatigue crack gowth in components are also described. It is shown that in some materials, (C_t)_avg does not uniquely characterize the behavior during early crack growth. The reasons for these trends are discussed. Several recommendations for future research in this area are made.

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By using the thermoporoelasticity theory proposed previously by the author, thermal stresses induced in a fluid-saturated porous hollow cylinder whose inner surface is heated by burning gas, and the wall of which is cooled by the fluid injection from its outer surface, are analyzed. Two situations of loading conditions are considered : (A) the cylinder is subjected to a sudden rise in temperature of the gas and is simultaneously pressurized at its outer surface to cool the wall, and (B) steady-state cooling is abruptly disturbed by a sudden loss of pressurization, and after a while it is recovered. The main focus is placed on the effect of heat advection due to active fluid pressurization and injection on the reduction of temperature and thermal stresses. Since the formulated problem is an axisymmetric one, the displacement field is decoupled from the temperature and pore-pressure fields which are still coupled to each other. The coupled nonlinear diffusion equations are solved by the implicit Crank -Nicolson method. It has been shown that the active fluid pressurization and injection is effective in suppressing the maximum thermal hoop stress at the outer surface without the occurrence of the excess compressional stress at the inner surface.

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The plane elastic problem of an interface crack of a rectangular inclusion is considered. The inclusion is assumed to be completely bonded to the interior of an elastic infinite medium, except for a portion which is regarded as an interface crack. Muskhelishvili's stress function is determined for m terms of finite series of the function for the conformal mapping, by which the inclusion is mapped onto the unit circle. Then, the stress intensity factors for the interface crack are determined under the equal biaxial loading condition.

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This paper presents a new method for stress intensity factor analysis of a two-dimensional interface crack between dissimilar materials. In the present paper, the virtual crack extension method which is a powerful tool for evaluating the stress intensity factor is combined with the boundary element method. A stress analysis is carried out using the boundary element method, and then virtual finite elements are assumed around a crack tip. The nodal displacements of these virtual finite elements are evaluated as internal points of a boundary element analysis. At first, we applied the present method to a center-cracked homogeneous plate under tension. Furthermore, we analyzed a bimaterial plate with a center interface crack and a bimaterial plate with a center slant interface crack subjected to tension. In such mixed mode problems, the M₁-integral was applied to the mode-separation to obtain the individual mode stress intensity factors. It is found from these analyses that the present method gives very accurate results whose accuracy is insensitive to the size of virtual finite elements.

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In this paper, a finite-element method (FEM) system of non-steady thermal stress analysis has been developed to analyze the problem of metal-fiber-reinforced plastic (FRP) bonded joints. The authors have presented a new algorithm for the system, which can provide an effective thermal stress analysis for metal-carbon-FRP (CFRP)bonded joints. The effectiveness, in terms of the accuracy and central processing unit (CPU) time, has been discussed by analyzing some typical problems. The thermal fatigue strength of Al-CFRP bonded joints has been studied through a series of thermal cyclic fatigue tests. It has been shown that the thermal fatigue strength of the joints can be well described by the maximum equivalent stress at the adhesive layer, which can be calculated by the developed FEM system.

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The ductile-brittle transition of α-iron single crystals under a constant tensile stress is simulated by a molecular dynamics approach, focusing on thermal distribution in the crystals, where the Newton equations of motion are solved utilizing the Johnson potential. The simulation uses the ad-hoc velocity scaling method to control the crystal deformation at a low temperature, and showed brittle fracture starting at a notch in the plane perpendicular to the direction of stress. Another simulation where no scaling was used, and hence the temperature of the crystal increased during the deformation, showed plastic deformation at slip planes. From these two simulations, the brittle-to-ductile transition of α-iron can be explained by the temperature effect under deformation. With the use of a definition for local temperature at a nonequilibrium state, a substantial temperature increase was observed near the crack.

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A numerical method is given for the solution of counterformal rolling contact problems. The theoretical basis of rolling contact problems is described in a manner where the physical meanings of the problems can be directly understood. The difference in rolling velocities and the gap in the leading edges of two contacting wheels are calculated as functions of driving forces. Only the contact area is divided into triangular elements. Linear contact pressures are applied on a triangular element. The contribution from a triangular element is calculated analytically.

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In the first paper, it has been shown that in 304 austenitic stainless steels, the martensitic phase induced by cold working, generates a flow stress growth according to deforming conditions given to the material. Moreover, constitutive equations for the aggregate have been formulated under a uniaxial stress state. In this second paper, the study has been extended to develop an incremental formulation to analyze multiaxial plastic deformation problems. The incremental constitutive model is formulated by considering the austenite-martensite phase transformation, flow stress under a multiaxial stress state, compliance of each phase and temperature, whose effects are included simultaneously in each parameter. A method of rigid-plastic finite-element analysis is proposed in order to estimate the distributions of transformed martensite and flow stress growth of materials subjected to general kinds of cold working such as forging, extrusion, and deep drawing. The temperature rise distributions due to plastic deformation have been co-analyzed using the above formulation. Some compression tests accompanied by temperature changes have been carried out and they were compared with the theoretical results. Good agreement was confirmed between them. It is demonstrated that the proposed method can be used successfully to determine distributions of both strain-induced martensitic phase and flow stress in austenitic stainless steels under cold-working conditions.

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In the thin plate theory, shear deformation is neglected. This theory is unreliable for plates of considerable thickness in the vicinity of the point of application of load, and for sandwich plates with shear rigidity which is very low compared with bending rigidity. A widely accepted theory which includes the effects of shear deformation was developed by Reissner and Mindlin. In recent years, composite materials have been widely employed as structural elements, and it is important to understand their characteristics for designing structures. Plates of composite material are characterized by strong anisotropy and low out-of-plane shear rigidity. This paper provides a convenient representation for the stiffness matrix of the finite element in order to analyze a sandwich plate with anisotropic face plate and core. The formulation is based on the non-conforming element of Zienkiewicz and is obtained with a modified stiffness matrix in the condition in which the out-of-plane shear strain is constant in two directions within an element.

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Buckling behavior of square tubes under bending load depends on the direction of the bending moment. This paper considers two directions. The first has an axis which crosses at right angles to a side of a cross section ; the second has an axis which crosses at right angles to a diagonal line of a cross section. Four-point bending tests are conducted at room temperature and at 300 ^C, using square tubes of three thicknesses (2.0, 2.5, and 3.0 mm), but having the same inside width (115 mm, excluding corner radius) and length (4000 mm). Local deformations and ultimate bending loads are measured. An empirical formula of the relationship between buckling wave growth and bending load is obtained by analogy with an equation derived from the results of bending theory for plates with an initial curvature. An empirical formula of the ultimate bending moment is also obtained by applying Karman's effective width theorem for critical loads in plates to square tubes. These formulas are proven to represent the behavior of test and analysis values very well.

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This paper formulates a weight minimization problem of a 3-D truss structure with the constraints on stresses and natural frequencies of specified modes. Cross-sectional areas of truss members are optimized by sequential linear programming. When the object mode is in the same direction as that of the static load considered in the strength problem, the minimization can be carried out effectively. Moreover, it is observed that the structure obtained has good controllability in the context of the optimal regulator theory.

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The mechanical behavior of laminated graphite/epoxy tubes under multiaxial monotonic loadings was elucidated with special emphasis on the effects of fiber orientation, loading condition and laminate structure. Tubular specimens of symmetrically laminated graphite/epoxy of 5 different fiber orientations θ (the angle of fiber measured from the specimen axis) were tested under monotonic combined tension/compression and torsion. Based on the preliminary results of the proceeding paper, the angle θ was specified to be 0°, ±22.5°, ±45°, ±67.5° and ±78.75°. The results of the stress-strain relationships and fracture stress loci are presented. It is shown that stiffness and strength decreased with the increase in the angle θ of fiber orientation measured from the direction of principal stress, and the Tsai-Wu criterion applied very well.

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The interfacial structure formed with silane coupling agents influences the inter-facial properties between the reinforcement and matrix in glass fiber reinforced composite. However, the interfacial structure at the molecular level has not yet been evaluated sufficiently. Therefore, a numerical analysis method is expected to estimate the interfacial structure on a molecular level. In this study, we proposed a formation model of interfacial structure, and tried to evaluate the model with fractal dimensions that can classify complex shapes. We proposed a model of interfacial structure for the finite element method, and investigated the relationship between the interfacial structure and the stress transmission mechanism. Moreover, we compared the results of numerical analysis with interfacial transmissibility in order to verify this analysis method. It was clear that the difference in interfacial structure influenced the mechanical properties at the interface. The above result suggests that this analysis method is useful for the investigation of the effects of interfacial structure on the interfacial properties.

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Clad plates composed of low-carbon and high-carbon steels were prepared in order to investigate the effects of laminated inhomogeneity and residual stress distribution along the thickness on fatigue crack propagation behavior. The fatigue crack propagation rates of the tempered clad plate without residual stress were between those of both base metals, which showed behavior based on the law of mixture. The fatigue crack propagation rates of the quenched clad plates with residual stress were lower than those of either base metal under the same fatigue conditions. This was because the crack opening displacement, even in unhardened parts with tensile residual stress, was suppressed by the crack front curved due to the residual stress field balanced along the thickness, in which the stress intensity factor due to the residual stress was estimated to be almost zero.

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Strain-controlled creep-fatigue tests were carried out on smooth specimens of austenitic stainless steel SUS 316 L with the strain rate of ε=2×10^-5/s in tension and ε=2×10^-3/s in compression at 650°C in air. Replicas of the specimen surface were taken at a constant interval of strain cycles, and the lengths of all the cracks on the entire specimen surface (=628 mm²) were measured by means of image processing through the life. Based on statistics of extremes, the maximum crack length was estimated using the crack length data taken from the sample area of 16 mm², and the estimated maximum length was compared with the measured maximum length. It was found that before initiation of crack coalescence, the estimated value was in good agreement with the measured value. Thus, the limit and usefulness of statistics of extremes in the estimation of the maximum fatigue crack length were shown.

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The influences of martensite morphology on the characteristics of small fatigue crack growth were investigated under rotating bending using two kinds of dual-phase steels : Steel A, which has a microstructure containing isolated martensite phases in a ferrite phase, and Steel B, which has a continuous martensite phase filled with ferrite phases. Most of the fatigue life in plain specimens is occupied by the growth of small cracks less than 1 mm in the two steels, and in the region corresponding to about 50% of the total life, small-crack growth is affected strongly by microstructures such as the ferrite grain boundary and martensite phase. Even in the region where the growth behaviors are affected by microstructures and the fluctuation of growth rate is marked, the average crack-growth rate can be considered to be proportional to the crack length. That is, the resistance to the crack growth is approximately evaluated through the static strength. On the other hand, the fatigue limits in the steels are determined by each limit for crack growth which is affected by the microstructure. Consequently, there is a large difference between fatigue ratios (σ_w/σ_B) of the two steels (0.39 in Steel A, 0.49 in Steel B).

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