The internal stress of epoxy resin generated during hardening process was analyzed by using simple viscoelastic model. The changes in the elastic modulus and volume of resin in the hardening process were measured. Their progresses were represented by the models with spring, dashpot, and shrinkage elements. The internal stresses and shrinkage behavior of resin were calculated by the finite element method and their results were compared with experimental results. Most of the internal stress was generated during the cooling process after curing. The effects of the internal stress on the strength of the adhesive bonded joints with epoxy resin were investigated. The joint strength was decreased by the internal stress. The effect was remarkable to the joint with short overlapped length.

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Corrosion-fatigue (CF) crack growth behavior of two high-tensile strength steel weldments, HT 50-TMCP and HT 80, have been investigated in ASTM synthetic seawater under free corrosion and a cathodic potential. Tests were conducted using sinusoidal loads at a frequency of 0.17 Hz and a load ratio of 0.1. The CF crack growth rates of the weldments in terms of the stress intensity factor range ΔK were considerably lower than those of the base matals, since the crack opening loads were increased by the compressive residual stress by welding, corrosion products, and calcareous deposits. The CF crack growth rate of the weldments agreed with those of base metal in terms of a modified effective stress intensity factor range ΔK_cont compared in the same environment. In the free-corrosion potential, effects of residual stress on the CF crack growth of the HT 50-TMCP weldment were scarcely observed because the crack growth was accelerated by dissolution, whereas that of the HT 80 weldment was almost the same as that in air. The cathodic protection of the weldment became effective at low ΔK_cont levels, while the crack growth rates at high ΔK_cont levels were much accelerated due to hydrogen embrittlement.

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Fatigue crack growth characteristics in air and in ASTM synthetic sea water have been investigated on four 50kgf/mm² TMCP steels and their weld-heat-affected-zone(HAZ). Tests were made under pulsating tension with a stress ratio of 0.1 and at a freqency of 30HZ in air and at a freqency of 0.17Hz in synthetic sea water. The da/dN-ΔK and da/dN-ΔK_eff relations of these steels were conlpared and the following results were obtained. If the conrparison is made on their da/dN-ΔK_eff relations, no appreciable differences are observed among the fatigue crack growth characteristics of these four steels and their HAZ, though some differences in fatigue crack growth behavior are observed if the comparison is made on da/dN-ΔK relations. In the da/dN-ΔK_eff relations, the fatigue crack growth rates of these steels are accerelated by a factor of two to three in synthetic sea water compared with those in air, and the amounts of this accerelation in growth rate in synthetic sea water are about the same for these four steels and their HAZ. The fractographic observations were also made.

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For annealed and prestrained carbon steels, the relation between the change in fatigue damage of the specimen surface and the value of half breadth of X-ray diffraction lines in the fatigue processes has been investigated. The place observed by a microscope is included in the area irradiated by X-ray. For annealed carbon steels the half-value breadth increases remarkably in the early period of stress cycles, while for prestrained steels, it decreases remarkably. The period of abrupt change in the half-value breadth corresponds to the period of abrupt change in the density of slip lines in both steels. In the process of the initiation and propagation of microcracks, the change in the half-value breadth is not marked.

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We carried out the repeated internal pressure test for an A 7075-T 73 cylindrical specimen, and obtained accurate fatigue data in large quantities. According to the fractography by SEM analysis, the most important factors which affect fatigue life are the Stage 1 and Stage 2 a crack propagation processes. In this paper, we could well explain the statistical feature of fatigue life data using stand-by distribution which consists of two kinds of weibull distributions (two-parameters).

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The circumferentially notched medium carbon steel specimens of root radii of 2, 3 and 5 mm were low-cycle fatigued. Meanwhile the stress-strain response was calculated at the notch root by means of the F. E. M. and the Neuber's rule. The crack initiation lives of the notched specimens were controlled well by the equivalent stress, the equivalent plastic strain and the axial plastic strain produced at the notch roots. The axial plastic strain versus crack initiation life curve estimated through Neuber's rule predicts the shorter and the longer lives in the higher and the lower plastic strain regions, respectively. The applicability of Neuber's rule to the estimation of the crack initiation life extends much more in the notched specimen of the smaller root radius. The above three quantities are also the dominant factors for the failure life of the notched specimen, nevertheless the stress and strain gradients develop in the cross section of the notched specimen. The necessity of the fracture mechanics approach to the surface crack produced at the notch root was suggested.

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The reasons for relatively low fatigue strength and large scatter of fatigue strength were quantitatively elucidated considering the combined effects of hardness and nonmetallic inclusions on fatigue strength. Nonmetallic inclusions are equivalent to small defects or cracks from the viewpoint of fracture mechanics. The effects of nonmetallic inclusions on fatigue strength depend on their size, shape and location where they exist, and this becomes the cause of large scatter of the fatigue limit. However, it is possible to predict the upper (σ_wu) and lower limits (σ_wl) of the fatigue strength from the hardness (H_v) of a matrix and the maximum size of inclusions (√(area)_max) defined by the square root of the projected area of an inclusion. The expected value of √(area)_max in a definite number of specimens or machine components can be estimated by statistics of extreme values.

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Cracking behavior in low cycle fatigue regime is affected by stress level and biaxiality, and also by material microstructure. More reasonable estimation for fatigue life requires an appropriate modeling of crack growth, including not only crack initiation and propagation, but also crack linking during the whole fatigue process. In the present study, the growth of fatigue cracks of the grain-boundary type under biaxial stresses was modeled to analyze cracking behavior and to evaluate fatigue life. In the modeling, deformed hexagonal elements with a double-slip system were employed as constituent grains in a polycrystalline material. An analytical procedure for crack growth was established as a competition between the coalescences among initiated and propagating cracks during a whole fatigue process and the propagation of a dominant crack as a single crack. The evaluation of fatigue life described by the size of the dominant crack was made based on the same procedure combined with a statistical analysis of the Monte Carlo type. Fatigue lives obtained for pure copper under several stress conditions were found to lie in the ranges of results simulated from fifty trials. Characteristics of intergranular cracking in the copper were very well-simulated using the present analytical procedure.

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The behavior of fatigue crack growth in the single spot weld tension shear specimens was studied by experimental and analytical fracture mechanics. Variation of the shape and size of fatigue fracture surfaces was observed and measured by beach mark techniques, and crack growth rate was determined. The crack growth rate in the plate thickness direction was related with the stress intensity factors which were detemined by the analyses of a plate with a semi-elliptic surface crack by the influence function method and the super-position method.

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This paper is concerned with the tension of infinite solids containing a doubly-periodic array and a zig-zag array of cracks. We define suitable unit regions, assume the stress potentials as eigen function expansions, and determine the unknown coefficients from the boundary conditions of the used unit regions. Numerical results of the stress intensity factors, the crack opening displacements and the longitudinal stiffnesses of the cracked solids are given for various values of the parameters, and they are fitted by reliable formulae for convenience of engineering applications.

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In this paper, we studied an impulsive propagation of elastic waves in an inhomogeneous half space. The inhomogeneity for SH-wave velocity is assumed to be a steplike function with depth. Applying the ray expansion method and Cagniard's techniques, we obtained a short-time solution that is valid near the wavefront. Numerical computations are carried out to clarify the effect of the inhomogenity on the response.

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Dynamic crack response to Mode II shear wave loading was studied by ultrasonic fractography. The maximum crack deflection angle ξ' and the modulation depth h were evaluated using a surface roughness-measuring instrument. The result showed that ξ' depends on the amplitude of the applied shear waves and decreases with the crack velocity V_f. The modulation depth h changes as a function of product ξ'V_f and increases linearly with the crack velocity when ξ' is constant.

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The present paper proposes mixed variational theorems of classical rate-independent elastoplasticity at finite strain based on the energy equation of Toupin, which takes into account the effects of non-symmetric stress. The proposed variational principle can easily incorporate the internal work related to angular momentum balance, which has not been treated exactly in the previous works. Attention is also focused on systematic and unified derivations for total Lagrangian formulation in terms of the non-symmetric first Piola-Kirchhoff stress as well as the symmetric second Piola-Kirchhoff stress. Also discussed and clarified is the explicit expression of complementary energy in rate type to be applicable for the finite element analysis.

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An experimental system is devised to investigate the asymmetric snap-through process of a pin-ended elastic-plastic arch under a concentrated load. A special device is used to bear the compressive reaction in the initial stage and the tensile reaction after the snap-through at the arch ends. In the system, the deflection at the loaded point is increased gradually and the resulting transverse load and thrust are continuously measured. The deformed shape of the arch line and the strain at certain locations are measured at several stages during the snap-through. The numerical results in which the reversed plasticity is taken into account are found to agree well with the experimental ones, while the results neglecting the reversed plasticity give a far smaller deflection after the snap-through.

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This paper is concerned with the contact problem between an elastic half-space and a rigid elliptical punch subjected to a torsional moment. It is assumed that the contact is completely adhesive and that the normal pressure within the contact region cannot be neglected. This problem is a mixed boundary value problem in which the displacements are specified inside the elliptical region and the surface stresses are specified and zero outside. The problem is reduced to solving simultaneous integral equations with kernels involving Bessel functions of the first kind of integer orders. It is further reduced to solving the Hilbert problem with infinite unknown functions by using the Abel transform and the Plemelj formulae. A general method for solving the problem is given. Numerical results for contact stresses and surface displacements are shown in graphical form for various aspect ratios of the ellipse.

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A solution is presented for a doubly axisymmetric contact problem of the torsion in two dissimilar elastic layers by an annular rigid punch attached to its surface. The problem is solved under the assumptions that the layers are bonded together, and the other face of the layers is clamped to a rigid foundation weakened by an annular hole which is coaxial to the punch and of the same radius. The problem is reduced to infinite systems of simultaneous equations in which both the displacement on the lower face of the layers and the contact stress under the punch are expressed as an appropriate series. The disturbances due to the presence of the hole are shown in the curves calculated numerically, and the effects of various parameters on the stress field are studied.

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The body force method is a method based on the principle of superposition. By inserting the region in question into the supplementary region and reducing the given problem to the problem of an infinite body without any cavity or additional, the most general formula based on superposing of fundamental solutions can be obtained. The direct method of BEM can be regarded as a special case of the proposed general formula in which the deformation in the supplementary region is put to be zero.

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The analytical solutions are given for both a steady-state heat conduction problem and an associated plane thermal stress problem expressed in elliptical coordinates in a confocal hollow elliptical plate subjected to nonaxisymmetric heatings on the elliptical boundaries, and with heat loss from the upper and lower surfaces into the surrounding media. The temperature function can be expressed in the form of an infinite series of Mathieu and modified, Mathieu functions. The associated plane thermal stress problem can be formulated in terms of Airy's stress function. In this formulation, a single-valuedness of the rotation component is assured by using Michell's condition in elliptical coordinates derived already by one of the present authors. The numerical calculations of the distributions of the temperature and circumferential thermal stress in the confocal hollow elliptical plates are carried out for the cases of various aspect ratios of the elliptical hole and various Biot's numbers on the upper and lower surfaces.

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A relationship of axial force and compressive displacement is presented theoretically for bin spheres of equal size and material. The deformations of the spheres are limited to an elastic region and the case of loading process. The displacement of the packing body is derived, in consideration of the local displacements by the Hertz contact theory for the elastic spheres piled in the vertical direction, and by considering vertical movements of the spheres due to slidings and the Hertz's contacts of some spheres in the horizontal direction. The latter displacement due to the sliding and the horizontal compression is determined by introducing a probability theory to the random distribution of contact angles of two spheres in contact. The relation agrees fairly well with experimental results for steel spheres packed in a cylinder of steel.

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Some initial out-of-plane distortions, occurring as a result of the errors during working and assembling members or by the thermal deformations during welding, often exist in the members of various structures. A large strain concentration at the distortion regions is induced by an application of tensile load to such members. In spite of the importance for practice, the quantitative relation between the initial distortions and the strain concentration has scarcely been investigated so far. In the present paper, theoretical formulae for the strain concentration at the distortion regions, with various types of the initial out-of-plane distortions, are derived on the basis of the large deformation theory by infinitesimal strain. The theory is then compared with experimental strain concentration and shown to agree well with each other. The present formulae are very useful for estimating the amount of allowable distortions in various structures.

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This study was carried out to decrease the residual stress that developed during cooling a ceramics-metal joint. The analysis connected with thermal stresses and residual stresses was performed using the finite element method and the boundary element method. The analysis clarified the effect of some factors (E^B/E^A, v^A, v^B, h^A/b, h^B/b) on the residual stress in ceramics. Several kinds of test pieces that differed in the shape of the joint were devised for decreasing the residual stress in ceramics in the neighborhood of bond line. The experimental results of bonding of Si₃N₄ to Cr-Mo steel using a copper insert showed that the devised joint shapes were decreasing the residual stress.

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The X-ray elastic constants and the stress constant for the X-ray stress measumement of partially stabilized tetragonal zirconia with 2.5 mol% and 3 mol% yttria were determined for diffractions from plane (0 2 6) by Cu-Kα radiation and from plane (1 3 3) by Cr-Kα radiation. The X-ray value of E/(1+ v) (E=Young's modulus, v=Poisson's ratio) was rather insensitive to the conditions of sintering and surface finishing. The measured value for plane (1 3 3) was lower than that for plane (0 2 6). The accuracy of the X-ray stress measurement was found to be higher for the case of plane (1 3 3). The residual stresses measured on the ground, lapped and polished surfaces were all compressive. The Ψ splitting of the sin² Ψ diagram was observed for the cases of heavy grinding. The magnitude of the compressive residual stress became larger with increasing the diamond grain size of a cutting wheel, while it was insensitive to the cutting depth. The full width at the half maximum of the X-ray diffraction profiles and the amount of transformation from the tetragonal phase to the monoclinic phase also increased with increasing the diamond grain size of a cutting wheel.

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In a spherical pressure vessel, some initial distortions occur due to weld angular distortion and so on. In this case, the quantitative determination of an allowable amount of the distortion is very important for a reliability evaluation of the vessel. However, such an analysis is complicated since a large deformation analysis is generally necessary. The authors previously reported a theoretical analysis based on the large deformation theory of plates and shells. This analysis was, however, applicable only to a simple joint located at the position of the equator of the vessel. In this study, the authors analyzed the joint model with a concave angular distortion at ψ=0°, 22.5°, 45°, 67.5°, 90°(polar) (ψis latitude) by a nonlinear finite element method. It was found that the strain concentration at the distortion part is scarcely influenced by the latitude of a welded joint with the same shape of distortion.

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In a large pressure vessel built with 5teel plates, there often occur local distortions due to errors in assembling parts and thermal deformation during welding processes and so on. In these regions, large strain concentration is caused by internal pressure. The estimation of an allowable amount of distortion is therefore very important to maintain the reliability of the pressure vessel. In the present paper, stress-strain behavior was theoretically analyzed in distortion regions of a spherical pressure vessel with initial distortion. A large deformation analysis is generally necessary in this analysis because a pressure vessel has relatively thin walls. The formulations of the amount of strain in distortion regions were derived by the large deformation theory on the basis of infinitesimal strain for various types of initial distortion and boundary conditions. Comparing the results of calculation with those of experiment, the theoretical formulae were shown to be very useful for deterrninin9 the allowable amount of distortion.

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This paper describes the boundary element elastostatic analysis of a crack along the straight interface between two dissimilar materials. It is well known that the interface crack has an oscillation singularity at the crack tip which is quite different from a crack in homogeneous materials. Therefore, the definition of the stress intensity factor is not clarified yet and it is very difficult to analyze the interface crack by the numerical methods, such as FEM and BEM. We proposed a method to determine the stress intensity factors K₁ and K₂, for the interface crack by means of extrapolating the solutions at the points apart from the crack tip to avoid the oscillation singularity. This method can be widely applied to the BEM and also FEM analyses with any changes of the programmes. It is confirmed that the present results of the stress intensity factors for an interface crack in the infinite plate are completely consistent with the exact solutions. The stress intensity factors for various interface cracks in the finite plate and the adhesive joint are analyzed by the present method and BEM analyses, which is specially developed for this study.

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A Computer Aided Instruction System for the Finite Element Method has been developed. The system consists of a super-mini computer with 20 terminals and some software which is especially designed for mass instruction at the undergraduate level. It has been used in a 15-week FEM course with approximately 120 third year students in which each student is required to write his own program consisting of a main program and 11 subroutines. Their accomplishments of the assignments have been measured through the system which enables adaptation of the course in the following week. "QUESTION" and "SELF-LEARNING" systems have been also provided to assist students with the assignments. The statistical data thus obtained during the semester has been analysed to determine the effectiveness of the system. It is concluded that the present CAI system works satisfactorily.

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Recently, the plastic packages of ICs have been changing from insertion types to surface mounted types. Reflow soldering is used for surface mounted ICs onto printed circuit boards. During the process, packages are heated up above 200'C. If the encapsulant absorbs moisture, package cracking may occur during the reflow soldering. It is known that the cracks are caused by vapor pressure generated inside the packages which causes excessive stress in the plastic. A quantitative explanation of the mechanism of this phenomenon, however, has not been made. In this study, a moisture diffusion analysis in the plastic and deformation and stress analyses of the packages are performed. Also, the properties of the plastic at high temperature are measured and the strength evaluation method is investigated. It is found that the vapor pressure generated inside the package is lower than the saturated vapor pressure and depends on the moisture content distribution of the plastic.

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