In this study, rotating bending fatigue tests were carried out on three kinds of carbon steel with nearly equal sizes of ferrite but different volume fractions of pearlite. The role of pearlite in the fatigue process of the carbon steels is discussed through successive surface observations using the plastic replica method.

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The S-N curves, where fretting fatigue life under block loading simulating practical loading was arranged using the equivalent stress based on the modified Miner's rule, were identical with those under constant amplitude loading at both room and elevated temperatures. The results indicated the effectiveness of the modified Miner's rule to fretting fatigue under variable loading at elevated temperatures. The S-N curves, where fretting fatigue life under random loading was arranged using the rms value of stress amplitudes, were almost identical to those under constant amlitude loading. The proposed method of life prediction based on the fracture mechanics analysis was successfully applied to variable-loading fretting fatigue at elevated temperatures.

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In order to elucidate the microstructural effect on initiation and growth of intergranular small cracks under creep-fatigue conditions, we discuss the randomness of grain-boundary length and inclination. This study consists of the following investigations; (1) the length and inclination of grain boundaries of a stainless steel, SUS 304, are measured by means of image analysing system; (2) a numerical generation method of polycrystal grains is developed on the basis of an isotropic grain growth model; and (3) the crack length and inclination are measured by means of an image analysing system under creep-fatigue conditions. The results obtained from each investigation are summarized as follows, respectively. (A) The grain-boundary inclination of the steel is uniformly distributed and the length between adjacent triple points has a wide scatter between 10 and 100 μm. The length and the inclination are independent of each other (B) The simulated length and inclination of grain-boundaries coincides well with the actual grains of the steel. This method is useful for the stochastic simulation of initiation and growth of microstructurally small cracks, which will be reported in the next paper. (C) Cracks preferentially initiate on the grain boundaries perpendicular to the stress axis by a span between adjacent triple points. The crack growth rate shows a little dependence on the crack tip angle.

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Numerical simulation was conducted on the initiatior1 and growth of multiple small cracks under creep-fatigue condition based on a three-dimensional stochastic model. It was assumed in the model that ( 1 ) (quasi) three-dimensional polycrystal grains were numerically generated on the basis of an isotropic grain growth model ; ( 2 ) the fracture driving force on each grain boundary was given as a function of the grain boundary's angle to the stress axis ; ( 3 ) each grain had a different fracture resistance, and ( 4 ) cracks did not initiate and grow inside the stress relaxation zone of the preexistent crack. Crack density, angle of an initiated crack, crack propagation rate, and cumulative probability of crack length were examined by the simulation. As a result, they coincide well with the experimental observation of Type 304 stainless steel under slow-fast fatigue at 923 K in a vacuum.

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The propagation behavior of fatigue crack from pre-cracks in smooth or notched specimens of a low-carbon steel was studied. The development of crack closure with crack growth was measured through the compliance method. An interferometric displacement gage was used to measure the opening displacement of surface cracks. All cracks started to grow from the pre-cracks at the maximum stress intonsity factor equal to the threshold value of the effective stress intensity range ΔK_effth∞ for long cracks. As a crack grew, the crack closure developed and the effective stress intensity range ΔK_eff decreased. The crack stopped growing when ΔK_eff dropped below ΔK_effth∞. The relation between the crack propagation rate and the effective stress intensity range was unique, irrespective of the crack length or the atress level, and agreed well with that for leng cracks. Non-propagating cracks made under the fatigue limit in smooth specimen were mostly Stage I cracks, and the fatigue limit of smooth specimen was determined by the propagation threshold of these Stage I cracks.

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In previous papers, the authors discussed the J-integral range, ΔJ, evaluated by the path integral and by Dowling's simple estimation formula and showed that ΔJ was a good parameter for characterizing the crack tip stress and strain field under uniaxial and elastic-plastic conditions. In this paper, finite element simulations of fatigue crack growth in a plate under biaxial stresses are conducted in order to clarify whether ΔJ is also applicable under biaxial conditions. It is found that ΔJ-values evaluated by the path integral are almost path-independent irrespective of the depth of crack and ratio of transverse and longitudinal applied stresses. Furthermore, the examination of the relationship between ΔJ and the crack-tip-opening displacemint leads to the conclusion that ΔJ evaluated on the basis of crack opening level is the most appropriate parameter for representing the mechanical state near the crack tip under biaxial loading. ΔJ evaluated by the simple estimating formula is found to agree well with ΔJ evaluated by the path integral.

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Although a number of models for the formation of extrusions and intrusions have been proposed, most of them are not considered to be sufficient. It is not yet clear whether or not the same mechanism may be responsible for the formation of extrusions in 70/30 brass, 85/15 brass and pure copper with different capability of cross slip. In this paper, investigations on dislocation structures of strain localized regions and fatigue crack initiation in these metals subjected to a long term stress cycling in vacuum were carried out by means of transmission electron microscopy. The strain localized regions bounded by two adjacent active glide layers were observed in the favorably oriented grains. Such strain localized regions were in close association with the formation of extrusion and transcrystalline cracking. At the intersections of the strain localized regions and the grain boundaries, extrusion-type deformations were sometimes formed due to the restraints of slip motions by the neighbouring grains.

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In order to investigate the effects of cathodic protection on small corrosion fatigue crack growth behaviors, we conducted high-cycle reversed plane bending fatigue tests in sodium chloride solution using high-tensile-strength steel HT50 smooth plate specimens. The small corrosion fatigue crack growth rates under conditions of free corrosion potential and - 1.1 V (saturated calomel electrode SCE) showed a stress amplitude dependence at a constant stress intensity factor range, while those under the condition of - 0.8 V (SCE) did not show the stress amplitude dependence at a constant stress intensity factor range. The crack growth rates of small strface cracks were reduced remark-ably by the cathodic protection compared to those of the through thickness cracks. In the crack growth behaviors of the surface cracks, crack size dependence was observed in the effect of cathodic protection; that is, the degree of suppression of the crack growth rate by the cathodic protection became high with decreasing crack size.

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Effects of residual stresses on the fatigue crack propagation behavior from surface precracks were studied using either water-cooled or oil-quenched plate specimens where the residual stress changed along the thickness but the hardness was nearly constant. The surface crack shape during fatigue was approximated by a half-ellipse, the depth of which was influenced by the residual stress distribution. The weight function method was used to evaluate the stress intensity factors, K_r, at the deepest point of the surface crack in the residual stress field. The fatigue crack propagation toward the depth was accelerated or decelerated according to the positive or the negative values of K_r by the tension or the compression residual stress generating inside, respectively. Their propagation rate was evaluated quantitatively by including the value of K_r in the maximum stress intensity factor, K_max, for the parameter (ΔK)^P (K_max)^q controlling the fatigue crack propagation rate, where ΔK is the stress intensity factor range and p, q the empirical coefficients satisfying the equation of p + q = 1.

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Growth characteristics of large and small fatigue cracks have been investigated in dual-phase stainless steel consisting of ferrite and austenite phases. The results of large crack-growth tests revealed the extremely high crack-growth resistance of the present material, and showed high threshold-stress intensity ranges, ΔK_th, of 15 to 17 MPa √(m). This behaviour is attributed primarily to significant roughness-induced crack closure resulting from Mode III displacement. Small cracks grew much faster than large cracks subjected to the same nominal stress intensity ranges, because the pronounced crack closure observed for large cracks was restricted for small cracks. This was supported by the close correspondence of small crack results for cracks larger than 100μm in length with large crack-growth rates plotted in terms of ΔK_eff. Small cracks mainly initiated at ferrite phase, and showed a growth perturbation due to microstructure in the region below 100μm. Therefore, the cracks smaller than 100μm could be considered to be microstructurally small cracks, for which the use of the continuum mechanics approach is inappropriate.

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A new method for measuring the strain around the high-temperature-creep-crack tip is proposed in the present paper. A grid pattern was described in a space of about 30μm with a diamond stylus in the area ahead of the precrack of the specimen. Then the distortion of the grids and the change in specimen thickness which were induced by the creep deformation were measured by means of the photomicroscope and the roughness-measuring system, respectively. The three-dimensional components of the strain were calculated through the Lagrangian equation, into which the above measurements were introduced. The route of creep-crack extension was examined in association with the local strain measured through the proposed method.

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The J-R curve, fatigue crack growth rate and characteristics of ductile unstable fracture under monotonic and cyclic load were investigated using 1TCT test specimens which were cut out from STS 42 carbon steel for piping. All the tests were carried out at 100°C. The main results obtained are as follows. (1) The J-R curve under the cyclic load is not a material constant but is dependent on the test conditions. (2) da/dN from typical fatigue data cannot be extrapolated byΔJ if the value of da/dN is above 3×10^-5 mm/cycles. However, it can be extrapolated by using the following equation in which J_max is used. da/dN = C{√(ΔJ)/(B - √(J_max)}^m (3) The J values at instability obtained from the ductile unstable fracture test carred out under the cyclic load of stress ratios R = 0.1 and -1.0 were compared with those from the monotonic increasing load. Both J values at instability were about the same for the loading histories used and the system compliances chosen.

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The tension problem for a transverse crack in the two half-planes bonded by an infinite layer is studied. The body force method is used to analyze the problem. Based on the numerical results, the effects of crack size, layer width and the material properties of the composite on the stress intensity factor are discussed. The approximation formula for a crack normal to the bond lines is also given.

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A magneto-elastic analysis is presented for the bending problem of a soft ferromagnetic thin plate of finite width with a through crack under a uniform magnetic field. Fourier transform method is used to solve the magneto-elastic problem and the result is expressed in terms of an integro-differential equation for the deflection. The integro-differential equation is solved by the standard iteration method and the mixed boundary value problem is reduced to the solution of a Fredholm integral equation of the second kind. The moment intensity factor is computed and the influence of the magnetic field on the normalized values is displayed graphically.

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To evaluate the LBB (leak before break) of a pressure vessel and piping, it is important to analyze the surface crack extension behavior under fatigue conditions. It is also necessary to analyze the stress intensity factors for a surface crack in a structual component. In this study. three-dimensional boundary element elastostatic analysis is carried out for various surface crack problems. The present BEM uses Mindlin's solution as well as Kelvin's solution as a fundamental solution. Thus we can obtain accurate solutions for a surface crack just before or after penetration. The obtained solutions for various shapes of surface cracks are stored as the data base, in terms of the influence function method. We develop the surface crack extension analysis system using the stress intensity factor data base and also the fatigue crack growth law. Our system seems to be useful especially for the analysis of the surface crack just before or after the penetration, and also under residual stresses.

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The growth characteristics of small fatigue cracks in room air, dry air and 1%NaCl solution were investigated for a high-strength steel, SNCM439. The growth rates of small fatigue cracks in room air accelerated slightly in contrast to long cracks, owing to the vapor in the air. The growth characteristics of small cracks in dry air were equivalent to those of long cracks. On the other hand, small cracks in a 1%NaCl solution showed a marked acceleration in fatigue crack growth as compared with long cracks. This was caused by the decrease of the threshold value of stress corrosion cracking (K_ISCC), that is, K_ISCC lowered with decreasing the crack length. The acceleration of small fatigue cracks in a 1%NaCl solution was predicted by the superposition method. Consequently, the predicted crack growth rates agreed well quantitatively with the experimental results.

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The growth characteristics of small cracks in distilled water were investigated for the high-strength steel SNCM439. The results were compared with the results obtained in a 1%NaCl solution. The fatigue and the stress corrosion cracking (SCC) behaviors of long cracks in distilled water were the same as those in the 1%NaCl solution. However, the growth rates of small fatigue cracks in the 1%NaCl solution were faster than the rates in distilled water. It was found from the SCC tests of small cracks in distilled water that K_ISCC decreased with decreasing crack length in the range of less than 0.6mm. At a crack length of more than 0.6mm, K_ISCC was equivalent to that of long cracks. In the 1%NaCl solution, K_ISCC decreased for the range of crack lengths of less than about 2mm. It was suggested that the difference in the results obtained from both environments was caused by the chlorine ion (C1^-) contained in the 1%NaCl solution.

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An elastic-plastic analysis program using the finite element method and a J-integral post-processor using the virtual crack extension method are developed. The program accuracy is examined by two test problems: a plate with a hole in tension and a single -edge notched specimen in bending. This program solves the Battelle/NRC finite element analysis round-robin problem regarding an elastic-plastic analysis of a pipe with an internal circumferential crack in bending. An investigation is made into the effect of the finite element mesh on the results of the elastic-plastic analysis. It is found that a finer mesh gives greater J-integral and COD values, while the mesh does not affect the load-load point displacement curve.

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Dynamic, elastic responses of rocks against the sudden growth of a subsurface penny-shaped reservoir crack ane analyzed in order to study the characteristics of elastic waves from the crack and particle motions observed at observation stations in an intermediate region where the distance from the crack is several ten times the size of the crack. In the analysis, a singular intergrodifferential equation was derived in Laplace image space, and the equation was solved numerically by a collocation method. The results show that the radial and circumferential displacements rise steeply just after P and S wave arrivals, respectively, where small oscillations are superimposed on the steeply rising portions. It is also shown that the displacement vectors are pointing to the crack tip where the crack growth is taking place, not the center of the crack.

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In the present paper, based on the general solution for an elliptical crack in an infinite solid, subjected to arbitrary tractions (the VNA solution), the analytical solution of the first order variation of displacement field due to geometrical changes in the shape of an elliptical crack is derived. The analytical solution is related to the partial derivatives of the displacement field with respect to the lengths of the major and minor axes of the ellipse, respectively. Since the VNA solution involves the generic elliptic integrals. The partial derivatives of the generic elliptic integrals with respect to the lengths of the major and minor axes of the ellipse are required. A systematic procedure for the evaluation of these derivatives is also developed in this paper. The presently developed analytical solution will be effectively utilized to establish the three-dimensional weight function method for elliptical crack problems, in the forthcoming paper.

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Surface-cracked specimens are analyzed precisely using the three-dimensional finite element method, and the stress fields at the crack tip are compared with HRR solution. First, a plate with a surface crack subjected to a bending load is analyzed. It is shown that the stress field does not agree well with the HRR solution when the crack depth is not large. But as the crack depth increases, the stress field becomes nearer to the HRR solution. It is also shown that a displacement field similar to the HRR solution exists in a small region wheich is very near to the crack tip. Then the surface crack in a pipe is analyzed. The results show that the stress field is significantly different from the HRR solution. The reason for this difference is considered to be the difference of the stress distribution in the ligament of the specimen.

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Fatigue crack growth rate in a residual stress field has been predicted by using the superposition technique. In this method, a residual SIF (stress intensity factor) is computed and, by taking into account a real stress ratio of the summation of applied and residual (real) SIFs, a fatigue crack growth rate is predicted. When a crack grows from a compressive residual stress field, however, it is necessary to compute a SIF due to partial crack surface contact. In our previous paper, this effect was discussed and simple method of computing the SIF was shown. In this paper, by using this method, we stdudied the effect more precisely for some specimen geometries and loading types. Results obtained are as follows; (1) When the specimen completely unloaded, the real SIF is not affected by specimen geometries. (2) Partial crack surface partial contact is affected by loading types. (3) The bending loading reduces the loading when the crack surfaces contact compared with the tensile stress. Moreover, the partial crack contact does not occur at a crack in the residual tensile stress field. (4) A notch induced in the specimens reduces the SIF of partial crack surface contact.

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The axisymmetric dynamic response of an infinite cylinder with a circumferential edge crack under normal impact is considered. Laplace and Hankel transforms are used to reduce the transient problem to a pair of dual integral equations in the Laplace transform plane. The solution is given in terms of a singular integral equation of the first kind which has a generalized Cauchy kernel as the dominant part. A numerical Laplace transform routine is used to recover the time dependence of the solution. Numerical results on the dynamic stress intensity factor are obtained and are presented in a graphical form.

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The time-dependent stress intensity factor of a semi-infinite crack has been obtained when an infinite plate is heated uniformly in a circle near the crack tip. The intensity depends on the heating location D and the radius R. But the radius dependence is small and the total amount of heat gives almost the same intensity as point heat as long as R/D remains small. This is preferable for cleavage cutting in which surface melting should be avoided. Glass plates were heated by an exposure of the CO₂ laser beam and crack opening displacements were measured by an interference method. The measured crack deformation corresponds well with the thermal stress analysis. At the onset of the crack extension, similar stress intensity was attained for the same plate thickness irrespective of the heating intensity and location.

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The steady-state temperature and thermal stress fields have been calculated in the case that the heat source moves with constant velocity along a line in an infinite plane. Stresses were evaluated in two ways: one method is based on the superposition of body forces corresponding to the thermal strains and the other, superposition of axi-symmetric stress fields caused by an instantaneous heat source. When a semi-infinite crack follows the heat source in the plane, thermal stresses show singularities at the crack tip. The estimated mode I stress intensity is strongly affected by a heat dissipation rate to surroundings, moving velocity, heating rate, and a distance between a heat source and a crack tip. This model gives a stable crack configuration and hence will provide appropriate conditions for cleavage-cutting of brittle materials, which uses no machining bits.

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In this study, experimental and numerical analyses for thermal stresses or strains of electronic circuit board models are performed. The circuit board models are constructed of two layers of copper and phenol resin with a width of 30mm, length of 80mm and thickness of 2mm. The shape is similar to that of some of the integrated circuits for practical use. The thermal stresses and strains of the models are analyzed by means of the finite-element method proposed in the previous paper. These numerical results are compared with the values obtained by the experiments. Furthermore, the influence of the circuit shapes for the thermal stresses distributions is discussed.

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A mapped (effective) stress defined by a linear transformation of four rank was applied to formulate an anisotropic creep constitutive equation. First, a reduced version of the polynomial representation of isotropic strain rate function was discussed in connection with an effective stress mapped by a four-rank anisotropic tensor. Then, a rational effective stress defined by the four-rank anisotropic tensor proposed by Baltov-Sawczuk was examined, and it was extended so as to incorporate both isotropic and anisotropic hardenings. By using the proposed anisotropic effective stress tensor, a form of anisotropic creep constitutive relation was develpoed and embodied by using the functional form of Bailey-Norton creep law. The proposed model was applied to the anisotropic creep behavior after plastic deformation for 316 stainless steel at elevated temperature. A comparison between the predicted and experimental results showed reasonable agreement.

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This paper describes the method of determining the Mode I stress-intensity factor (K_I) by using the electrical strain gage. When fracture mechanics is applied to engineering, The stress-intensity factor near the crack tip must be accurately determined by way of a convenient measuring method of the strain. Usually, electrical strain gages are used for the strain measurement of the structure material. Thus the strain gage is used in this study. The type of strain gage used in this study is the chain strain gage consisting of 5 measuring grids. It is used in the experiments which examine the center-cracked test specimens (CCT) and single-edge-cracked plate tension specimens (SECT) as well as the compact-type specimens (CT). The accuracy of the stress-intensity factor (K_I) determined by the experiments is within ±10 percent, compared to the analytical value.

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The present paper describes the theoretical treatment of the updated Lagrangian formulation expressed by quantities in the current configuration through mathematically equivalent transformation of the fundamental equations in the reference configuration. Since no subsidiary condition is imposed on the transformation, the obtained variational principle can employ the constitutive equation as it is. Discussed are the relative advantages of the total or updated Lagrangian approaches from the viewpoint of numerical analysis. Also derived are the work theorem and constitutive equation to ensure objective numerical integration in the moving as well as rotating coordinate system.

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The present paper discusses rate-type elastic-plastic constitutive equations with the stress rates being taken as the Jaumann derivative and the Green derivative from the viewpoint of reference configuration and spin tensors. These equations are shown to be transformed in the rate-type forms so as to exclude the effects of rigid rotation. The obtained ordinary differential equations can be implemented to ensure objective numerical integration during finite deformation increment. The simple shear problem is taken for an example to demonstrate the accuracy of the present formulations based on the Euler method or the Runge-Kutta method of the second order.

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A new method is proposed to evaluate the strength of a sharply notched structure with a large notch angle. A new parameter, K_e which is to be called the equivalent stress-intensity factor and which prescribes the singularity of stress distribution near the notch tip, is defined to evaluate the effect of a sharp notch on the fatigue and static strength. This method enables one to predict the strength of a notched structure by using the well-known parameters ΔK_th and K_IC. Fatigue tests of HT60, SS41 and a brittle fracture test of an acrylic plate were conducted and the applicability of the parameter was verified.

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This paper describes the strength evaluation of surface mount solder joints. Recently Surface Mount Technology (SMT) has advanced with high density assembly of circuit. However, the reliability of surface mount solder joints may be lower than that of through-mount solder joints. So, the strength evaluation of surface mount solder joints is required. In this study, tensile tests for various specimens of butt-leaded surface mount solder joints have been conducted at first. Secondly, two-dimensional elastic-plastic analyses of the joints have been carried out by finite element method. From these results, the relation between the geometry and the strength of butt-leaded surface mount solder joints has been obtained.

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A universal program is developed with which impulsive responses of framed structures consisting of straight-bar elements are analyzed. The matrix method described in this paper constitutes superposition of analytical Laplace transformed solutions given from longitudinal, bending and torsional dynamic equations for each element. For inversion of the Laplace transformed solutions, a fast Fourier transform method is used. Numerical and experimental results are compared for problems of two-and three-dimensional framed structures having rigid or pin joints. Then, it is found that the program can be used to obtain accurate numerical results with a fewer number of elements.

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Square plates of laminated glass, whose interlayer is the polyvinyl butyral, are impacted transversely by a circular steel ball. The impact critical energies Uc and Up, which are the energy to initiate a crack in the outerlayer glasses and penetration energy of the ball, are measured by changing the dropping height of the ball. The static bending strength and Uc are dependent on the total thickness T of glass in the laminated glass. But, Up is independent of T and dependent on the thickness of the interlayer. In the laminated glass, the crack initiates from the glass of the impact side, and the next cracks initiate from the glass of the side on the reverse of the impact side. The penetration fracture of the laminated glasses consists of three steps. The first step is until initial cracks initiate in the outerlayer glasses, the second step is the bending fracture of the laminated glass, and the third step is the fracture due to shearing of the interlayer.

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Damage ahead of notch tips in continuous fiber-reinforced cross-ply composites consists of microcracks extendibg in the directions parallel to fibers in each ply. We direct our attention to the behaviour of these micrcracks in order to clarify the essential factor which drivdes microcracks, i. e., governs the extension behaviour of the damage region. We first determine quantitatively the state of damage with parameters which are local microcrack densities averaged over the thickness of the specimen, and we derive the relation between the increment of macroscopic material compliance and the elastic strain energy released by microcrack extension. With an assumption that the released energy would control the process of microcrack extension, a computer simulation of damage extension is carried out and its results appear to be in agreement with experimental results. We finally come to the conclusion that the damage extension in continuous fiber-reinforced cross-ply composites is essentially the release of elastic strain energy.

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The large sized, multi-walled coaxial cylindrical tank has been studied in recent years because various kinds of oil can be stored simultaneously in one tank. In the design of this tank, the bifurcation buckling of the ring-stiffened inner shell plate under external liquid pressure becomes an important problem. The diameter/thickness ratio of the oil storage tank is considerably greater than that of the other cylindrical shells, and the ring-stiffened cylinders of such diameter/thickness ratio under the large external pressure have never been used so far. This paper presents the bifurcation buckling analysis of the inner shell plate by the finite element method. For the estimation of the minimum required number of ring stiffeners to prevent the buckling, the location where rings should be attached to the shell is determined considering the buckling mode.

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This paper is concerned with a contact problem for an elastic layer on a rigid substrate indented by multiple rigid concentric-annular stamps. This problem is a mixed boundary value problem in which the surface displacement of the layer is specified inside the concentric-annular regions and the traction is zero outside. It is assumed that contact is free from friction so that the shear traction on the whole surface of the layer is zero. The problem is reduced to infinite simultaneous algebraic equations by using Fourier series expansion of the normal traction within the contact region. General solutions for the contact stress and the surface displacement are presented. Sone numerical results are given in graphical form, and the interaction of the contact stresses caused by each annulus is investigated.

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Because of complex and multivalue properties of brightness function of isochromatic fringe, there exist enormous difficulties in automatic construction of fringe order distribution over the whole field of specimen in the framework of digital image processing using a microcomputer. In this study, the structure of the distribution function of fringe order is analyzed mathematically on a concept of unfolding, and a criterion for the reversal of rise of fall or fringe order is well established. Thus, on the basis of the criterion, the authors have successfully developed a general algorithm for the automatic calculation of fringe order over the whole field using a piece of isochromatic fringe pattern. Availability of the theory and algorithm are also shown in an example problem of three-point bending.

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Mixed mode (Mode I + II) elastic-plastic fracture tests were conducted using A5083-O aluminum alloy compact-tension-shear specimens. The behaviors of crack tip blunting and crack growth were studied by fractographic investigation. Mixed mode loadings were found to cause a blunting of one corner of the crack tip and a sharpening of the other corner. Under a load with relatively high mode II components, a fracture by shear localization initiated at the sharpened corner of the crack tip near the surfaces of the specimen, and then another fracture by microvoid coalescence occurred at the blunted corner of the crack tip near the midthickness of the specimen. This was explained qualitatively by taking into account of the stress and strain singularities and the triaxial stresses near the surface and the midthickness of the specimen. Fracture mechanics parameters appropriate for mixed mode elastic-plastic fractures were also studied based on the experimental data.

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An analysis method to evaluate the gradient of structural response is developed for nonlinear systems which are governed by incremental finite element equations. The formulation originates in the perturbation method and retains its advantage. Namely a nonlinear finite element analysis needs to be done only once; based on which the gradients are evaluated. Although the formulation is written for elasto-plastic problems in the present paper, it is also applicable to a wider class of nonlinear problems, the solutions of which depend on the load paths. An elastic-plastic truss structure is solved to examine the validity of the method, and satisfactory results are obtained. The proposed formulation forms the foundation of the nonlinear stochastic finite element method.

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This paper is concerned with the residual stress and deformation of PMMA beam produced by rapid cooling from both sides under various temperature conditions. The theoretical value of the residual stress and deformation of this beam are calculated by using the fundamental equations based on the linear viscoelastic theory. On the other hand, the specimens were then actually subjected to rapid cooling under the same temperature conditions. After rapid cooling, the residual stress and deformation are measured. The experimental and theoretical results are then compared and discussed.

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Recently, attempts have been made to be join ceramics to metals in order to make up for the brittleness of ceramics. The difference in the coefficients of linear expansion of the two materials joined at high temperature will cause residual stress, which has a strong influence on the strength of the joined materials. The residual stress distribution of silicon nitride plates brazed to a carbon steel JIS-type S45C was determined by X-ray diffraction using thd Gaussian curve method. The measured residual stress distribution agreed approximately with the result from the three-dimensional thermo elastoplastic stress analysis by FEM, but did not agree with the result from the plane stress analysis. This is because the stress concentration occurs and the stress distributes three-dimensionally at the interface of the silicon nitride and metals. The tensile residual stress perpendicular to the interface on the surface of the silicon nitride has maximum values at the center and the edge of the interface.

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A model plant of strip casting system of two roll type was developed to obtain the fundamental data on optimum operating condition for production of strip or thin slab. In this first report, mode of solidification and temperature distribution in the strip of Pb-Bi alloy with low melting temperature during steady process was simulated by solving the heat conduction equation incorporated with latent heat due to solidification when considering material flow. And, the results of analysis on the shape of the solidified shell and the temperature distribution in molten metal was compared with measured temperature data by thermocouples, and the validity of the simulation method are also discussed.

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The simulation technique of solidification and temperature distribution developed and verified by experiment in the first report was applied to the process of strip casting of a steel. The effect of operating condition, such as casting speed, diameter of roll, depth of molten metal and roll gap, on the shape of solidified shell and the temperature were examined by numerical calculation. Mode of stresses in the shell under steady material flow was also evaluated by use of elastic-viscoplastic constitutive relation, and the comparison between the results and the stresses was carried out by simple elastic-plastic model.

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The test system was newly developed for evaluating precisely the tensile strength of ceramics at elevated temperatures. Four-point bending and tensile tests were performed on the sintered silicon-nitride ceramics in the temperature range from room temperature to 1300°C. The track of ductile fracture was observed on the fracture surface of tensile specimen tested at temperatures above 1100°C, suggesting the occurrence of plastic deformation. Fracture stress of bending specimens was about 1.18∼1.43 times as large as that of tensile specimen. The test temperature dependency, however, was very similar in both the fracture Stresses in the whole test temperature range. The fracture toughness from tensile and bending specimens were almost the same in the test temperature range from R. T. to about 800°C. The fracture toughness obtained from the chevron notch-type specimen was almost coincident with that from the Knoop-indented specimen in the temperature range from R. T. to 900°C. They, however, produced some difference in the temperature above this, suggesting occurrence of the adhesion at the crack tip in the Knoop-indented specimen.

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A structure optimized for a given determinate load is not optimum for other loads. This paper proposes a shape determination method by BEM for structures which are subjected to uncertain loads. In the case that the loads are represented by some random variables which obey certain probabilistic laws, response quantities such as displacements and strain energies can be expressed as random variables by the use of a method of "decomposition into fundamental loads" Then, only several runs of analysis can give optimum shapes where expected values of strain energy densities are uniform on every boundary element.

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Various kinds of low-alloy steels have been used widely for machines and structures. Accordingly, it is an important task to estimate the fatigue lives oflow-alloy steels. Although many fatigue data sheets have been published, they have large scatter, and it seems to be difficult to directly predict the fatigue lives from the raw data. In this study, using two kinds of low-alloy steels (SCr440 and SCM435) the systematic fatigue tests were carried out. An effective and convenient method based on the small-crack growth law and tensile strength is presented for estimating the fatigue life of plain members. Moreover, the validity of this method is checked applying it to the data sheets by the Japan National Research Institute for Metals.

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