Torsional fatigue tests were performed on 60Sn-40Pb solder under strain control, and a method for the solder fatigue life prediction was investigated. The type of specimen was a thin-walled cylinder. Two cycling frequencies of 0.001 Hz and 0.01 Hz were used at 303 K. Using the test data at 0.03-1.0 Hz shown in the previous paper, as well as the present test data, the following results were obtained. ( 1 )The fatigue life and the plastic shearing strain range, which was found by a partition of the inelastic shearing strain range, could be correlated by the Coffin-Manson law for each cycling frequency. ( 2 )A life prediction formula was obtained on the basis of the strain-range partitioning approach and the linear cumulative damage rule for the superposition of both plastic and creep deformations. The values calculated by the formula nearly coincided with the test results.

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Fatigue properties were examined on base metals and butt-welded joints for 5-and 20-mm-thick 5083-O aluminium alloy plates with three heats for each thickness. The fatigue strength was independent of the heat and the thickness both for base metals and welded joints. However, it was much lower for butt-welded joints than for base metals because of the tensile residual stresses introduced in the butt-welded joints. The fatigue properties for 5083-O aluminium alloys were compared with those for SM50B and HT80 steels. The relationΔσ/E versus N_f was found to be unique for those materials in the case of welded joints, but was dispersed in the case of base metals. Here, Δσ, E and N_f are stress range, Young's modulus and fatigue life, respectively.

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We carried out a repeating internal pressure test on the thin wall cylinder of austempered ductile iron (ADI) which has been noted for its good combination of high static strength and elongation. We examined the effect of the austempering and surface hardening treatments using roller burnishing which affects fatigue strength. As for the lathe-turned specimen (not roller-burnished), the fatigue life of ADI was longer than that of the as-cast sample at high pressure level. But this difference of fatigue life became less clear with decreasing pressure level. At the lowest pressure level, most of the specimen was unfractured at 1×10⁷ cycles ; the fatigue life of the ADI sample was shorter than that of the as-cast specimen. On the other hand, for a roller-burnished specimen, the fatigue life of ADI was longer than that of the as-cast specimen at all pressure levels. After the SEM observation of the fracture surface, it was clarified that most of the fracture origins were 0.10.15 mm microshrin-kages produced under the casting process.

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The effects of surface abrasion on crack initiation and variation of the characteristics of the material surface in the fatigue process were studied. Hardness of the specimen surface decreased and residual stress induced by abrasion was released with advance of the fatigue process. Fatigue cracks were initiated while hardness was constant, and after that, compressive residual stress was released. From these results, fatigue crack initiation was predicted by the variation of hardness on a surface and crack initiation duration could be monitored through the X-ray stress measurement method.

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In order to investigate the basic properties on pseudoelasticity of TiNi shape memory alloy, tensile tests with various maximum strains under constant temperature were performed. Based on the experimental results, dependence of the stress-strain curve in the pseudoelastic region on maximum strain and temperature was discussed. The results are summarized as follows : ( 1 )If maximum strain occurs in the stress-induced martensitic (SIM) transformation region, the reverse transforma-tion stress assumes a constant value at each temperature. ( 2 ) The modulus of elasticity decreases in proportion to maximum strain. This occurs due to the fact that the fraction of the martensitic phase increases. ( 3 ) The residual strain increases in proportion to the amount of SIM transformation strain and temperature. ( 4 ) The dissipated strain energy increases in proportion to the amount of SIM transformation strain, but depends slightly on temperature. ( 5 )The recoverable strain energy increases in proportion to maximum strain and temperature.

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For clarifying fracture strength and estimating structural integrity, a simple procedure has been developed to evaluate the stress intensity factors for some cracked structures in our recent studies. This procedure is the application of a matrix method to the analysis of cracked structures, as in the analysis of statically indeterminate structures based on the energy principle. In this paper, the above procedure is extended to nonlinear elastic structures using the fact that the complementary energy of cracked members can be easily calculated using fully plastic solutions. Therefore, it is shown that this procedure enables us to easily carry out some parametric studies systematically without full numerical calculation as in finite-element analysis. Furthermore, this procedure is applied to the evaluation of the J-integral for one or more axial cracks in circular cylinders, where matrix formulation is shown to be useful for both computer-aided calculation and the discussion on some influential parameters: such as external forces, diameter ratios, relative crack depths, and the number of cracks.

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The stress intensity factors of a small crack have been analyzed when an infinite plate is heated around the crack due to a rotating heat source changed step-functionally with time at a start point. The stress solution can be obtained by superposing the stress disturbance by the crack on the transient thermal stresses due to the rotating heat source in an infinite plate. The problem is reduced to a singular integral equation which satisfies the boundary condition on the crack face. The numerical results of stress intensity factors are obtained for the case of a uniformly distributed heat source in a circular region. The effects of the angular velocity of the heat source on the variations of stress intensity factors are considered.

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This paper is concerned with a theoretical treatment of thermal stress and thermal bending problems involving a multilayered anisotropic laminated plate due to partially distributed heat supply in a transient state. As an analytical model, we consider a laminated rectangular plate consisting of an orthogonal pile of layers having orthotropic material properties, i. e. a cross-ply laminate. By introducing the methods of finite consine transform and Laplace transform for the temperature field, we obtain the three-dimensional temperature solution with the aid of the residue theorem and evaluate the characteristic behavior of thermal stress and thermal deformation of a simply supported plate in a transient state using the classical plate theory based on Kirchhoff-Love's hypothesis. As an example, we carry out numerical calculations for a 5-layered cross-ply laminate and closely examine the numerical results.

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Recently, nonlocal effects were introduced in thermodynamics by the author, and materials with these effects were called thermopolar materials. We imagine that each point of a thermopolar continuum has an internal structure which allows distributing thermodynamic quantities on the analogy of mechanical polar materials. First and second laws of thermodynamics are coupled and each term is averaged over the microscopic volume. The obtained formulae have simple forms compared with the expressions in the previous reports, though second-order terms are estimated rigorously. Reciprocal temperatures are used for the series expansion, and new thermodynamic potential is introduced. Finally, a form of the constitutive equation of the stress is presented, which includes the terms of temperature gradient.

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Thermopolar theory explains nonequilibrium processes, introducing the nonlocalities of thermodynamic quantities in continuum mechanics. In a previous report considering this concept, thermodynamic laws and the balance law for fluctuations of thermodynamic quantities were formulated, and the constitutive equations for thermopolar materials were constructed. In this paper, the basic equations governing thermopolar materials with microscopic gradient of temperature are discussed on the basis of previous results. Moreover, these basic equations are applied to thermopolar materials, and relations among the moduli, which were defined when the constitutive equations were constructed, are derived. As the result of these investigations, it is clarified that the heat conduction of thermopolar materials with microscopic gradient of temperature is governed not only by the equation of heat conduction but also by the equation for the balance of the microscopic gradient of temperature.

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The thermal stress during growth and the residual stress after growth in a Czochralski-grown crystal are calculated numerically for three kinds of growth conditions by using an isotropic ther-moelastic model. The maximum stress which the crystal experiences is obtained from the thermal and residual stress histories. The cross-sectional patterns of the total of twelve resolved shear stresses and the resolved shear stress direction patterns are shown for the [100] and [111] grown crystals. It is found that the features resulted from the maximum stress distribution and the resolved shear stress direction patterns agree well qualitatively with the dislocation density and array patterns observed in GaAs and InP single crystals.

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This paper presents a computational method of dynamic stress intensity factors(DSIF) in two-dimensional problems. In order to obtain accurate numerical results of DSIF, the boundary element method using the Laplace transform based on regularized boundary integral equations is applied to the computation of transient elastodynamic responses. A computer program id newly developed for two-dimensional elastodynamics. Numerical computation is carried out for computation of DSIF for a rectangular plate with a center crack under impact tension. Accuracy of the results is investigated from the viewpoint of computational conditions such as the sampling number of the inverse Laplace transform and the number of boundary elements.

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This paper presents an analysis of in-plane problems for isotropic semi-infinite body due to single force, single dislocation, dipole-force, dipole-dislocation, and so forth, with various surface boundaries such as free, fixed and two sliding conditions. Distributions of stresses and displacements under applied singular forces for the above four boundaries are illustrated by some graphical representations as numerical examples.

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The nonlinear plate and shell theory employing the anisotropic plastic theory is developed for implementing the finite-element simulation code. For the anisotropic plasticity, Gotoh's 4th-order yield function and Barlat's m-th-order one are employed. I defined the spacial orthogonal coordinate, derived from the deformed (surface-embedded) coordinate through normalizing one of those bases, which coincides with the anisotropic axis at the initial configuration. The anisotropic axis spin, obtained by the decomposition of the continuum spin, is newly introduced to obtain the objective stress rate. For the nonlinear contact problem, the explicit-rate-type formulation for the contact force is also developed, using Seguchi's friction law. Finally, the static explicit method is employed for the time integration of the updated Lagrange-rate-type finite-element equation.

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In tightening structural members with bolts or studs, hydraulic bolt tensioners are frequently used in cases where the clamping force should be controlled with high accuracy. The most important factor in the operation is the ratio of axial tension desired to initial tension applied with a hydraulic pump, which is termed "effective tensile coefficient" here. In this study, five spring constants of parts constituting of the joint are used to estimate the effective tensile coefficient. The relationships between the effective tensile coefficient and grip length are discussed and the influences of Young's modulus of fastened plates are also evaluated. The validity of the elementary calculation method proposed here is ascertained by comparing the results to those obtained by FEM and experiment.

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In reliability-based design and reliability testing, the reliability and confidence level are used together when distribution parameters are unknown. Determination of the design allowable stress in the MIL Handbook is a typical example. This conventional method of using the two-dimensional measure is somewhat complicated, and makes it difficult to compare allowable stress based on different confidence levels. In the present paper, the idea of using the mean reliability as a one-dimensional measure was proposed. This idea was applied to the determination of the design allowable stress S_a for the case when the strength follows a normal distribution N(μ, σ²). The factor k in the expessions of S_a= μ-kσfor the case of unknown μ, and S_a= μ-kσ for the case of unknown μand σ was derived based on this idea, where μand σare estimated values. A method for specifying the design goal of the mean reliability was also proposed. Furthermore, the meaning of the product of reliability and confidence level was clarified.

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This paper describes an experimental study on crack propagation properties of conventionally cast and directionally solidified Ni-base superalloys, Mar-M247CC and DS, under creep-fatigue loading. The following points were made clear: ( 1 )The crack propagation properties of Ni-base superalloys under creep-fatigue loading were divided into cyclic and time-dependent types as reported before. The result is due to a difference in fracture modes, transdendritic fracture in cyclic-dependent crack propagation and interdendritic fracture in time-dependent crack propagation. ( 2 )In time-dependent crack propagation, the resistance to crack propagation under CP loading was smaller than that under CC loading because of a difference in creep in the process of compression, similar to those of polycrystalline austenitic stainless steel and single-crystal Ni-base superalloy at elevated temperatures. ( 3 )In time-dependent crack propagation, nominal crack propagation rates of Mar-M247CC were lower than those of Mar-M247DS, because the crack traces a zigzag course along the dendrite boundaries in the case of Mar-M247CC crack propagation. ( 4 ) From conventional and present studies, it was clarified that the transitions of fracture modes from polycrystalline heat-resisting steels to a single crystal changed from transgranular through transdendritic to gamma prime transphasic ftactures in cyclic-dependent crack propagation, and from intergranular through interdendritic to gamma prime interphasic fractures in time-dependent crack propagation.

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We constructed a dynamic fracture testing apparatus of caustics combining an ultrahigh-speed camera, Imacon 790, and a laser light source of 2 mW, and tried to apply the direct surface reflection caustic method to zirconium ceramic plates in order to investigate the dynamic fracture behavior using this system. Consequently, it is shown that the clear caustic patterns which are formed by direct surface reflection light under a dynamically loaded condition can be obtained and the applicability of this technique to dynamic fracture problems of ceramic materials is confirmed. Dynamic fracture toughness K_Id and the crack-propagation fracture toughness K_ID are determined from a sequence of caustic patterns. The dependence of K_Id on the stress intensity rate K and the relationship between K_ID and the crack velocity a of this material are revealed. Finally, we attempt to evaluate the crack arrest toughness value K_Ia by means of this technique.

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This study aimed at a theoretical approach which can be applied to the Fracture analysis of graphite cylinders with a transverse hole under torsion. It was found that the position of maximum tensile stress occurred at an intersection of hole and outer surface of the cylinder. Theoretical analysis has been carried out with the surface layer theory applied to the maximum tensile stress at the edge of the hole. The graphite is brittle material with a little ductility; therefore, we established the fracture criteria by taking the ductility into account. The fracture stresses of the solid and hollow cylinders were dependent only on the diameter of the hole, and were not influenced by the outer diameter of the cylinder. A hole with the comparatively small diameter had no effect on the fracture stress of the cylinder.

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In order to improve fatigue strength of ductile cast iron, effects of austempering from the (α+γ) phase region (partial austempering) and/or the (γ) phase region (full austempering) were investigated under axial load and rotating bending load. The results of tension, hardness and fatigue tests were compared with those of as-cast material. Although the tensile strength and hardness of fully austempered material were greatest in all of the materials used in this study, the greatest fatigue limit was obtained in partially austempered material. The reasons were discussed based on the Vickers hardness, the defect size and the threshold stress intensity range.

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This paper treats the bending problem of a uniformly or concentratedly loaded circular plate subjected to elastic constraint for the deflection at its edge, i. e., elastic support. It is assumed that the degree of the constraint varies periodically and stepwisely or continuously along the edge of the circular plate. The iterative method which was previously proposed by the authors for the problem of the circular plate with mixed boundary conditions is adopted in this paper. The case when the degree of constraint varies nonlinearly according to the deflection at the edge is also considered.

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A theoretical equation for particle velocity discontinutities across stress wave in linear viscoelasticity is derived. This equation is based on both a mathematical distribution model of linear viscoelasticity and ray theory. By applying this equation to the particular stress wave shape (2-dimensional noncurvature stress wave shape), the decreasing phenomena of stress and stress gradient across the stress wave are shown.

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The deformation behavior of the material is modeled by a thermoelasto viscoplastic version of the strain-gradient-dependent constitutive equation. Full plane strain thermocoupled finite-element analysis clarifies the effect of the gradient term added to the constitutive equation, deformation rate and heat conduction on the shear localization. Furthermore, the critical dependence of finite-element simulation with classical continuum theories in shear localization behavior on the employed finite-element mesh size and its partial solution are discussed.

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A method of rebound hardness testing is introduced in which a hammer propelled by a spring mechanism strikes a sample surface. The rebound hardness is obtained by dividing the rebound velocity of the hammer by its impact velocity. This method can be applied for any impact angle, but the values obtained at some angles deviate from the true hardness because the velocities are affected by the component of gravity and other factors such as friction. The impact and rebound velocities at various impact angles are measured and the relations between the velocities and the angles are distussed. The hardness value is found to increase as the impact angleθ, the angle between the impact direction and gravity direcction, increases. For less hard materials, the calculated hardness is more closely dependent on θ. In addition to this, the impact and rebound velocities have a linear relation to the cosine of θ. These results determine the relation between the rebound hardness and the impact angle. That is, the hardness values can be obtained by using an impact angle derived from the impact velocity.

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