Plane bending and cyclic torsion tests, and a combination of them are carried out using aged cracked specimens made of carbon steel under the condition of a stress ratio R=-1. Taking account of the residual compressive stress around the crack in Model I and the friction stress acting on the crack surface in Model II, and adopting the criterion that and aged crack begins to propagate when the circumferential principal stress range reaches a critical value peculiar to the material, the threshold condition of micro fatigue crack propagation under a mixed mode can be deduced from the results of plane bending and cyclic torsion tests.

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A model is proposed to evaluate the effect of notch plasticity on the development of crack closure for a short fatigue crack propagating from a notch root under the zero mean stress or compressive mean stress. The model assumes that a fatigue crack closes completely at the minimum applied stress and that compressive plastic deformation take place near the notch as if there were no crack. Plastic yielding of the Dugdale type is made from the root of an elliptical notch in an infinite plate. The crack opening stress and the effective stress intensity range are computed as functions of crack length, applied stress, and notch geometry.

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To investigate the effect of material degradation on life prediction, fatigue crack propagation in a degraded steel was studied. Fatigue crack growth rate, da/dN, vs stress intensity factor range, ΔK, relationships were obtained for 72 crack tips in degraded 2 1/4 Cr-1 Mo steel due presumably to temper embrittlement during long service, a recovered one made from the above degraded steel and an unused carbon steel S50C. The main results are : (1) High intergranular fracture surface ratio and preceding cracks ahead of main cracks are remarkable characteristics of the degraded steel. (2) The da/dN vs ΔK relationship was not well represented by a single line for the degraded steel. Above 13 to 15 MPa √(m), da/dN in the degraded steel was higher than that in the other two steels. (3) The m and C in the da/dN = C(ΔK)^m for each steel tested followed normal and log normal distributions, respectively. (4) The coefficients of variation in the values of m and C were larger in the degraded steel than in the other two steels. (5) Almost the same linear relationship was obtained between log C and m for the three steels tested. (6) The predicted fatigue crack growth life given by Monte Carlo simulation was shorter at higher stress levels, and the scatter of lives was larger in the degraded steel than in the recovered steel.

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Fatigue crack growth rate of several high strength steels has been examined in laboratory air at different stress ratio, covering almost entire range of stress intensity, from nearly threshold stress intensity to fatigue fracture toughness K_fc. It is cleared that this crack propagation behaviour can be well expressed by four parameter Weibull function. The fatigue characteristic stress intensities, K_e and K_v, are proposed to define the transition behaviour of fatigue crack growth rate, from so called region I to II, and from region II to III, indicating that the maximum stress intensity, K_max, is reached to the constant values, K_e and K_v respectively. The correlation between K_fc, which is one of the four parameters in the Weibull function, and the other three parameters is also analysed and, hence, the stress ratio dependency of the fatigue crack propagation curve can be predicted successfully.

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In order to estimate the corrosion fatigue property of SUS 403 stainless steel, a corrosion fatigue test was performed under rotating bending in 3% NaCl aqueous solution at frequencies from 0.03 to 30 Hz up to ten thousand hours. Fatigue strength was monotonously decreased with increasing numbers of cycles and decreasing test frequency, except for the case of 30 Hz where fatigue limit was observed. The depth of corrosion pits at the origin of fatigue cracks was linearly correlated to the failure time on log-log coordinates. Microscopic observations revealed that the initiation of fatigue crack from a pit became possible when the growth rate of a hypothetical crack having the same depth as the pit exceeds the growth rate of the pit. Thus the corrosion fatigue life could be predicted from the crack initiation period and propagation period.

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Corrosion fatigue (CF) growth rate of a high-tensile strength steel has been measured in ASTM synthetic sea water at free corrosion and under a cathodic potential. The CF crack growth rate in synthetic sea water at free corrosion potential is nearly equal to the one in 3.5% NaCl solution at R=0.1 and 0.8. The CF crack growth characteristics under a cathodic potential can not be explained in terms of ΔK_eff, since Ca and Mg deposits-induced wedge effect enlarges the region II in the load-strain hysteresis loops. A revised effective stress intensity factor range ΔK_cont, deduced from the load range shared by regions I and II, is useful to explain the influence of cathodic potential on crack growth rate. The da/dN in synthetic sea water under a cathodic potential is almost the same as the fatigue crack growth rate in dry air near a threshold value of ΔK_cont. The cathodic protection becomes effective at a low ΔK_cont, whilst the one at a high ΔK_cont is much accelerated due to hydrogen embrittlement.

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Near-threshold corrosion fatigue crack growth characteristics and crack closure of high strength steels AISI 4340 with two yield strengths (σ_Y=1 446 and 1 089 MPa) below K_ISCC were investigated. Compact specimens were exposed to synthetic seawater under ΔK-decreasing conditions at two stress ratio (R=0.1 and 0.7) and at a cyclic frequency of 5 Hz. The results obtained are summarized as follows : (1) A da/dN-ΔK_eff relation in air can give a conservative estimation of da/dN-ΔK relations in seawater. (2) Corrosion products formed within the crack are FeOOH and Fe₃O₄ and exist behind the crack tip. (3) The crack opening stress intensity factor K_op detected by the back-face-strain method is result of crack surface contact with the corrosion products and gives overestimation of K_op at the crack tip.

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Rotating bending fatigue tests of a spheroidal graphite cast iron with a ferrite matrix were performed at temperatures between room temperature and 450°C. The behaviors of both the nucleation and the propagation of small surface cracks were observed. Because of the strengthening effect due to cyclic strain aging, the maximum fatigue limit could be seen at about 350°C. The peaking phenomenon of fatigue limit, however, was not so striking as that seen in carbon steels. The contribution of cyclic strain aging to the increase in fatigue life was not made so much that the peaking phenomenon could not be readily identified, differing from the remarkable peaking phenomenon in carbon steels. It is concluded that the existence of graphites in a ferrite matrix promotes not only the nucleation of small surface cracks but the coalescence of them and cancels the strengthening effect of ferrite matrix due to cyclic strain aging.

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The fatigue lives of surface-hardened metals depend chiefly on a laminated inhomogeneity and a change of residual stress incidental to the surface micro-structural change. The effects of each factor on the fatigue lives, however, have not been stated quantitatively as yet, because it is difficult to separate these factors experimentally. In this paper, the steel specimens with longitudinal thermal residual stresses which are created by cooling in water from 873K temperature without martensitic transformation are prepared to examine effects of the only residual stress on fatigue crack initiation and propagation behaviors. The expression of fatigue life evaluation, proposed in a previous paper, is discussed in the light of the fatigue crack growth law and is used to estimate the fatigue lives of the specimens with and without residual stresses.

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In order to develop a prediction method for the fatigue strength of spot welds in thin steel structures such as automobile bodies, bending fatigue tests were made on T-shaped members. The fatigue test results expressed in terms of the strain range, measured on the outer surface near the nugget, did not coincide with predictions from the fatigue strength data of standard tensile shear specimens. FEM analysis and strain measurement showed the difference to be due to the fact that loads acting on spot welds and the stress states are different between the standard specimens and the members. A joint specimen having flanges under a combined load of a tensile shear force and a bending moment, which simulates the stress distribution near the nugget, has been proposed. It was confirmed by fatigue tests that the strength of the specimen is an accurate prediction of the strength of the member in terms of the strain rage.

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The influences of small vibratory stresses and the loading axis against grain flow directions on the initiation behavior of stress corrosion cracking (SCC) have been investigated on high-strength aluminum alloys sensitive to active path corrosion type SCC. Irrespective of loading directions, the strength of dynamic SCC under a sustained load with small vibratory stresses (>59 MPa) super-imposed was considerably lower than that of static SCC under a sustained load, σ_SCC. The static SCC resistance in the TT orientation, where the loading axis is normal to the rolling direction, was superior to that in the LL orientation, where the loading axis is parallel to the rolling direction. Under dynamic loading, on the contrary, the strength in the LL orientation was higher than that in the TT orientation. Static SCC cracks were initiated at intergranular cracks, whereas the initiation sites of dynamic SCC were intergranular cracks, hydrogen-induced {111} plain cleavage fracture, and transgranular cracks associated with corrosion fatigue.

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Crack propagation behavior was investigated under creep-fatigue interaction conditions. The interaction was classified into two types : (1) the interaction between creep damage and fatigue damage introduced at the same time in each cycle : (2) the interaction between pre-creep (or pre-fatigue) damage and fatigue (or creep) damage introduced in the following cycle. In order to discuss these interactions, three kinds of crack propagation tests were conducted. The results obtained were sumarrized as follows : (a) There was a remarkable effect of interaction (1) on the intensity of the stress (strain or strain rate) field in the vicinity of the crack-tip but little effect on the fracture criterion in the fracture process zone. (b) The pre-creep or the pre-fatigue damage had little effect on the following crack propagation. (c) The result (a) was supported by the detailed observation of the crack propagation in a cycle by means of a d.c. electrical potential drop technique. The observation also revealed that the pre-damage affected the following crack propagation when the damage was extremely large.

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The accurate prediction of the fatigue fracture at elevated temperature will depend on the elucidation of the small crack initiation and propagation laws. In this study, smooth specimens of a 304 stainless steel were subjected to the slow-fast cyclic strain of 1% range at 650°C in air and in a vacuum (about 10^-2 Pa), respectively. All small cracks on the fixed surface of a specimen were observed with an optical microscope, and their propagation curves and propagation rate were mesured in detail. The surface length and the depth of small cracks covered a wide range, from 10μm to 1 mm. The propagation behavior was classified into two types : propagating cracks with coalescence ; and non-propagating cracks blocked by grain boundary triple points. On the other hand, the statistical treatment of the crack propagation rates showed that the mode of the distribution of their rates agreed with the through macro-crack propagation law, but that their upper and lower limits largely deviated beyond the bounds of the factor of two on the macro-crack propagation rate.

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Low-cycle fatigue properties were investigated for low-alloy steels differently heat-treated to obtain strength levels of 2 000, 1 500, and 1 000 N/mm². The results were compared with those reported in the previous works where 15 grades of carbon steels, low-alloy steels and stainless steels (σ_B=470∼1 100 N/mm²) were examined, on the basis of cyclic softening or hardening behavior, cyclic stress-strain relationship and strain-life properties. SNCM 439 steel was cyclically stable when tempered at 200°C, while those tempered at 400 and 600°C, as well as other tempered-martensitic steels, cyclically softened. The relationship between total stain amplitude, ε_ta, and number of cycles to failure, N_f, was independent of material at the low-cycle region of N_f<10⁴ cycles. The Coffin-Manson relation was not satisfied for all the tempered-martensitic steels. This behavior was explained by a model assuming that the plastic strain was concentrated at the ferritic portion in the tempered-martensitic microstructure.

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Normalized JIS S 35 C medium carbon and quenched & tempered JIS SNCM 439 alloy steels were low cycle fatigued under the push-pull and the axial strain controlled conditions. The fatigue crack of a=8∼12μm in depth originates at the cycle ratio of N/N_f=0.10. The cyclic J-integral range, ΔJ and the strain intensity factor range, ΔK_ε become good parameters for evaluating the growth rate of the small surface crack under low cycle fatigue. The prior cyclic deformation slightly accelerates the crack growth rate in SNCM 439 steel. The cyclic deformation history dependence of crack growth rate seems to be associated with the existence of a non-metallic inclusion in the material. The fatigue life curves evaluated on the basis of small crack growth are in quite good agreement with the test results.

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Ceramic fibers, e. g., boron fibers and carbon fibers etc., are known to contain several kinds of strength-limiting defects, and in this case the statistical analysis of their strength is mainly evaluated by the theory decided due to the weakest defect among all defects, the so-called "Weibull's weakest link theory". In this paper, from the tensile-test data of two types of boron fibers, we try to analyze from the view point that tensile strength is governed by the weakest defect, which is decided by competition among the several kinds of defect groups. The resukt is that the strength distribution curves predicted by multi-modal Weibull's distribution fitted to experimental plots better than those predicted by single Weibull's distribution for every gage length tested. The application of the multi-model Weibull's distribution also showed that the analysis gives the exact expected value of the bundle strength at a certain gage length. The multi-modal Weibull's distribution function may be applied to the statistical strength anblysis for ceramic fibers accompanied by several kinds of defects.

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Stress intensity factors for cracks emanating from a circular hole in a circular disk under diametral compression are analyzed by the body force method. The stress intensity factors K₁ for several cases of the ratio β of the inner to the outer radius and the ratio λ of crack length to the inner radius are numerically calculated. The main results are summarized as follows : (1) In the case of λ≤0.1, an approximate equation for K₁ on the basis of the maximum tensile stress at the edge of a hole is derived. (2) In the case of β≤0.3 and λβ≥0.1, K₁ can be estimated by the results of a circular disk containing a central crack without a hole. (3) With increasing β, K₁ approaches the results for the pure bending problem where the width is equal to the difference between the inner and the outer radius.

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Instead of the conventional Kelvin's solution Mindlin's solution has been introduced into boundary element analysis as a fundamental solution. Since Mindlin's solution satisfies analytically a traction free condition of one flat surface, the discretization of the surface becomes unnecessary. Therefore, the use of this solution reduces the memory region and the c. p. u. time for computation, and improves the accuracy of the solution. Moreover, it is expected that the displacement or the stress on and beneath the surface can be obtained accurately without the divergence of solutions which are shown in BEM analyses using Kelvin's solution. Mindlin's solution has been experessed as a sum of Kelvin's solution and the other function so that it can be easily incorporated in the usual BEM programmes. Three dimensional elastic analysis are carried out on some fundamental problems and surface crack problems by BEM using this solution ; and the usefulness of this solution is discussed.

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In recent years the boundary element methods (BEM) have been widely applied to the computation of stress intensity factors in elastostatics. Several methods are available at present for an efficient computation of K-values from boundary element calculations. One of the most attractive methods seems to be the approach using crack elements near the crack front. This paper is concerned with the crack element approach, and a new type of crack element is proposed. The proposed crack element can simulate in a more reasonable manner the behavior of displacements and tractions or stresses near the crack front. Several sample problems are computed by use of the proposed crack element as well as the other ones available in the literature, whereby the usefulness of the proposed method is demonstrated.

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The Direct Regular Method is applied to BEM elastostatic analysis. In this method, the domain of the problem is discretized by defining freedoms on its boundary, as usual ; but the load point of the foundamental solution is located outside the domain so that the singular integral can be avoided. Stress intensity factors for a crack and stress concentration for a hole are analyzed by this method and the usefulness and limit of this method are discussed in comparison with Direct BEM. It is shown that this method can give an acculate solution for these problems if the load points are arranged very near the boundary. It is found that his method is especially useful for the problem with a corner point where the tractions on both edges are unknown. This method can be used combined with the Direct Method.

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Most rotating machines such as turbines and flywheels, involve the use of fast rotating components. To optimize their dimensions and to ensure their safety in service, a practical study of the strength under centrifugal force is necessary. This paper deals with the applicability of linear-elastic fracture mechanics under centrifugal force. Stress intensity factors K are calculated as a function of the inclination crack of length 2a, the position at different angular velocities 1 300 rpm, 2 100 rpm and at different values of the inclination crack angle φ(φ=0°, 30°, 45°, 60°, 90°) and are measured in models of rotating disks using a photoelastic stress freezing method. The ratio (K_II/K_I) of the stress intensity factor is determined by using the isochromatic fringe loops angle θ_m near the crack tip. Especially, stress intensity factors K_I and K_II obtained separately from the isochromatic fringes of the mixed mode, were used to further investigate the influence of K_I and K_II on fracture in rotating disks. The results of this experiment coincided favorably with the theoretical analysis results of Ishida.

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The influence of sheet thickness on the fracture resistance of a stably growing crack evaluated by crack energy density based on the method proposed in the 1st Report is investigated. That is, the experiments of stable growth fracture similar to those in 2nd Report are carried out varying the sheet thickness, and the fracture resistances expressed by additional rate of crack energy density and crack energy density are evaluated. The results are as follows : (1) The fracture resistances are almost independent of initial crack lengths and specimen types for any sheet thickness. (2) With the decrease of sheet thickness, the fracture resistance expressed by crack energy density at the initiation of crack growth decreases and, on the other hand, the fracture resistance expressed by crack energy density and additional rate of crack energy density of stably growing cracks increase under the uniform slant fracture mode. These effects of sheet thickness can be explained by considering the admissible types of plastic deformation around a crack tip.

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In the previous 2nd and 3rd Reports, the method proposed in the 1st Report to evaluate the fracture resistance of a stable growing crack by crack energy density was applied to the stable crack growth problems of thin plates, and its applicability was confirmed. In this report, the fracture resistances based on the J-integral are evaluated using the experimental data obtained in the 2nd and 3rd Reports. They are compared with the fracture resistances evaluated before by crack energy density and the superiority of the proposed method is shown through the comparison. The results are as follows : (1) The fracture resistances by the J-integral at the initiation of crack growth almost accord with those by crack energy density, as was predicted before. (2) The change of the fracture resistance of a growing crack evaluated by the J-integral does not correspond to the change of the fracture mode, although the fracture resistance by crack energy density varies corresponding to the change of the fracture mode.

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The extension behaviour of a hydraulically induced crack under the simplified conditions of tectonic stresses was simulated experimentally by use of brittle epoxy specimens with boreholes. The results were described by means of linear elastic fracture mechanics, where a criterion for the onset of crack extension is a critical tensile stress at a characteristic distance deduced from the experimental results. Based upon the criterion with a maximum stress criterion for fracture angles, a predictive procedure for breakdown pressure and fracture angles during hydraulic fracturing was proposed.

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J and J^^- integrals are evaluated for an assumed crack in a rector pressure vessel under pressurized thermal shock (PTS) conditions. First, two dimensional analyses are carried out assuming the cladding on the inner surface of the vessel wall. Several kinds of PTS conditions are treated, and it is shown that the RFT condition gives the most severe results. J values are compared with J_Ic and J_Ia and the possibilies of the crack growth in the vessel wall are discussed. Second, three dimensional analyses are conducted and the results are compared with those of two dimensional analyses.

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A versatile automated system for X-ray stress measurement using a microcomputer has been developed on the basis of conventional techniques and the fundamental study on X-ray stress measurement using the Gaussian curve method previously proposed by the author. The simultaneous control of the three stepper motors on the goniometer by use of three motor controllers allows both rapid measurement and the use of various measuring methods. The most appropriate method for each material is programmable in this system. Residual stress values of a hardened steel were measured by the iso-or side-inclination method using the fixed time or fixed count method agreed within the scatter of the measured values. The η oscillation method was found to be most useful for stress measurement of coarse grained steels. The system can also be used for evaluating diffraction line widths by using the Gaussian curve parameter.

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Using dynamic loading at a test velocity range of 3 mm/s to 2 m/s, fracture toughness tests were made on type A508 class 3 steel. Fatigue precracked 2T type Compact Tension specimens were used. Tests were performed according to ASTM E399 ANNEX 7 using a high flow and high response tensile machine. In this investigation, load, strain and displacement outputs were obtained with quite small oscillations. Then it was shown that the rapid load plane strain fracture toughness was able to evaluate with high accuracy at a K rate range of 10 to 10⁵ MPa·√(m)/s according to ANNEX 7.

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Firstly, the thickness effects of the CCT specimen are discussed from the experimental aspect. The distributions of the plastic strain energy absorbed in the intense strain region at the crack tip along the crack front are measured by using the recrystallization method. From the fractographic observation, the distributions of the stretched zone width and the increment of stable crack growth along the crack front are investigated. The experimental results are compared with distribution of J_x along the crack front obtained from the three-dimensional elasto-plastic analysis. Secondly, for CCT specimens of three kinds of thickness (B=18, 6, 4 mm), J(J_in) at the stable crack growth initiation are measured by the stretched zone and R-curve methods, and then those are compared with the valid J_Ic. Finally, the J value is estimated by the average J_x obtained from the distributions of J_x along the crack front and the R-curve are rewritten, and then the J_in values are determined. Moreover, the comparisons between the CCT specimen and the CT specimen are carried out by using R-curves.

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By use of the resonance method in a cylindrical specimen, anisotropic elastic constants of an axisymmetrical specimen have been measured. Two Young's moduli, E_z, E_r=E_θ, two shear moduli, C₄₄, C₆₆, and Poisson's ratio ν_zr are determined in a JIS-C 3604 brass (60/40) specimen which is mono-axially deformed in compression up to 49% of nominal strains. The elastic anisotropy factors, E_z/E_r=1.08 and C₆₆/C₄₄=1.11, are obtained in this specimen. Finally, isochronal recovery experiments have been performed in the deformed specimen, so that these elastic anisotropies in Young's moduli and shear moduli are almost removed by the annealing up to 450°C.

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Fracture toughness tests were performed on four kinds of rock samples of granite, andesite, tuff and mudstone to evaluate the fracture behavior of subsurface rock materials in geothermal areas. The effects of temperature, confining pressure and water environment on the rock fracture toughness were shown through experiments using a pre-notched cylindrical specimen in the presence of pressurized water, ranging from 0.1 to 30 MPa at a maximum temperature of 224°C. The rock fracture toughness (K_iAE) is defined by the critical stress intensity factor of crack tip region at the onset of the main crack propagation, which corresponds to an abrupt increase of ΣE_AE before the maximum differential pressure. For granite, the value of K_iAE at 200°C and 20 MPa decreases by approximately 20% of the value at room temperature and atmospheric pressure. On the contrary, the value of K_iAE of andesite is independent of high temperatures and confining pressures provided that the test environment conditions are less than 224°C and 24 MPa. Intermediate value of KiAE_&lt;/SUB> between granite and andesite are obtained in the same manner as for tuff and mudstone.

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Hardness is influenced by the different mechanical properties of the spherical indenter in the elastic-plastic transient indenting process. To clarify that point, we indented steel and tungsten-carbide spherical indenters in the several standard blocks for hardness. In order to establish the relations of the elastic-plastic transient indenting process experimentally we related the hardness P_m(mean contact pressure) with a true profile coefficient of the permanent indentation : (d/D_p), not with an apparent profile coefficient : (d/D) used traditionally, and formulated as follows ; P_m=P_up(d/D_p)^xp. We can calculate the hardness affected by the different mechanical properties of the spherical indenter using this formula for arbitrary conditions. Further, we compared the Brinell hardness obtained by Yoshizawa with our calculated values, and we obtained a good coincidence between them.

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A design formula has been derived to obtain stress concentration factors of grooved shafts with several kinds of groove shapes in this investigation. This formula was derived based on the analytical result for infinitesimal grooves and experimental values of the author et al., and numerical values of other investigators for finite grooves. The formula agreed fairly well with the numerical values of Nishitani et al. for a wide range of groove sizes. A comparison with Neuber's formula showed that Neuber's formula gives much lower values than the present one, especially for deep grooves.

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The three-dimensional axisymmetric boundary value problem of the torus of a closed hollow circular cross section under uniform internal pressure is analysed by the indirect fictitious-boundary integral method. The configuration parameters are the mean radius of the torus, the mean meridional radius of the hollow circular cross section, and the thickness. Moreover, using the results, the applicability of the shell theory solution by Novozhilov is investigated.

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In the linear couple-stress theory, three-dimensional elastic stress analysis of a plate is carried out in order to examine the effect of thickness ratio. The problem treated here is the axisymmetric bending of a clamped circular plate subjected to an annularly distributed load. For this analysis, use is made of the indirect fictitious-boundary integral method. From the results, the effects of thickness ratio are investigated. Further, the effects of various material constants, such as the characteristic length and the ratio of bending-twisting moduli, on the mechanical behaviour of a plate are made clear with various thickness ratios.

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Transient thermal stress problems for an infinite plate with two unequal circular holes heated by fluids are solved analytically in the framework of linear thermoelasticity. The effects of Biot's numbers, ratio of hole radii and pitch of holes on thermal stress concentrations are clarified for two cases of the fluid temperatures being equal and unequal. The results show that the above mentioned effects and the location of maximum stress are quite different for the two fluid temperature conditions. In this paper the general procedure for calculating the temperature and thermal stress distribution are presented, and the numerical results for the case of unequal fluid temperatures are shown in the form of figures.

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The purpose of this sequence of two papers is the calculation of the transient thermal stresses in an infinite plate with two unequal circular holes heated by fluids. In Part 1 the general procedure for calculating the temperature and stress distribution was presented, and the numerical results were shown for the case of fluid temperature being T₀ and T₀ in the two holes respectivily. In this paper numerical calculations are performed for the case of fluid temperature being T₀ and T₀ by using the method described in Part 1. The results are compared with those of Part 1, and the difference of the mechanism of thermal stress concentration for the both fluid temperature conditions is explicitly considered.

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A semi-infinite shear fracture initiated from notch roots and the other stress concentrators in unidirectional fiber-reinforced composites is considered on the basis of the two-dimensional theory of orthotropic elasticity. By use of the Wiener-Hopf technique, simultaneous Wiener-Hopf equations are derived for the semi-infinite shear fracture in an infinite strip of the composites under tensile loading at infinity. The stress intensity factors at the tip of the shear fracture are obtained through asymptotic properties of the equations with the aid of some numerical computations. As a consequence, it is revealed that the considerably large stress intensity factor for the opening mode appears in addition to the stress intensity factor for the in-plane-shear mode. Furthermore, when the results for the stress intensity factors is compared with one obtained by the well-known method of energy balance, it is found that the results do not coincide and the latter is inappropriate to estimate the stress intensity factors.

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The finite three-point bending of a fiber-reinforced straight beam with a central step attached on the beam bottom is analysed in the framework of the theory of ideal fiber-reinforced composite materials. The beam is reinforced in its axial direction and simply supported at its ends. It was found that the exact solution reached by the rule of trial and error is statically and kinematically admissible only for a linear elastic (or quasi-elastic) shear response. The equilibrium condition of the part of the beam corresponding to the step edge is reduced to a Fredholm type integral equation of the second kind with respect to the curvature radius of the uppermost fiber.

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An optimum configuration for a stepped bar under torsion is obtained. The optimum configuration is obtained to minimize the stress concentration factor, when a length of the stepped region and two radii of the bar are given. First, the torsion problem of the stepped bar, whose configuration is given, is analyzed by the series expansion technique. Next, the optimum configuration is obtained by the Simplex method. Furthermore, stresses of the bar with the optimum configuration are obtained and are compared with stresses of the bar with the circular notch.

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An inverse procedure is developed for obtaining an exact solution for the travel time of seismic rays transmitted through an inhomogeneous media in which the seismic velocity depends only on depth from surface. If the inhomogenity is the form of distinct, horizontal layers (graded material), then the procedure of insuring continious displacement and stress across the interface between homogoneous layers is straight-forward and involves a considerable amount of algebra. However, if the inhomogeneous media has a continuous variation of properties (gradient material), then the problems are redused the Abel's integral equation.

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The strength of joints between a carbon steel shaft and a glass fiber reinforced plastic (GFRP) tube connected with adhesive resin was investigated analytically and experimentally. The stress distributions under the combined tensile and torsional loads were calculated using the finite element method. It was shown that stress concentrations occurred at the edges of the overlap between two shafts. The strains measured by the strain gauges on the surface of the shaft joints were in close agreement with the calculated results. The strength of the adhesive shaft joint was predicted by applying the strength laws of GFRP, carbon steel, the adhesive layer and their interfaces to the calculated stress distributions. The predicted strength of the adhesive shaft joint under the combined loads was in good agreement with the experimental results of the initial cracking load.

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The deformation and strength of adhesive shaft joints were investigated analytically and experimentally. The meal shafts were adhesively connected with a coupling and epoxy resin. The outer diameters of the coupling and the shafts were identical. The joint configuration was straight through the shafts and the coupling. The strain and stress distribution of the adhesive straight shaft joints were calculated for various dimensions using the finite element method. It was shown that stress concentrations occurred in the adhesive layer and the adhesive interface near the edges of the coupling. The strains measured by the strain gauges on the surface of the straight shaft joint were in close agreement with the calculated results. The strength of the joints was predicted by applying three kinds of strength laws of GFRP, carbon steel, the adhesive layer and their interfaces to the stress distribution. The predicted strength for initial failure loads of the adhesive shaft joints under combined loads was in good agreement with the calculated results.

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The stress state of a continuum is represented by the stress tensor Σ which is specified by the stress components dependent on a coordinate system in a physical space. For a geometrical representation of a stress state, a stress space having a Cartesian coordinate system of five or six dimensions with stress components as axes is used. When Σ is specified by two different coordinate system, two different stress vectors result in spite of the same Σ. The relation is presented with respect to the eigenvectors between the physical space and the stress space. By this relation, yield surfaces are able to be compared with each other, even if they are obtained in different coordinate systems. When two yield surfaces, F and F^^- obtained ion different coordinate systems are taken to be plastic potentials, the relation between two strain increment vectors proportional to ∇F and ∇^^-F^^- is consistent with that which holds good in vectors of stress space.

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A new constitutive model of cyclic plasticity in non-proportional loading conditions is developed on the basis of previous experimental results by the present authors. Namely, by examining the characteristic features of the cyclic hardening elucidated in previous paper, the notions of a perfect non-hardening region and a proportional non-hardening region are first introduced. In the former region, neither proportional nor non-proportional loading brings about any isotropic hardening ; whereas no isotropic hardening is induced by any proportional loading in the latter region. In view of the experimental results, we further assumed that the cyclic-hardening caused by arbitrary strain paths can be described by a single scalar isotropic hardening variable. Finally, a relevant constitutive equation is formulated by incorporating these notions into Krieg's two-surface plasticity model. The methods of the determination of the material functions and the material constants as well as the comparison of the theory with the corresponding experiments will be reported in the succeeding paper.

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Cyclic internal stress was determined through a strain rate change test, and cyclic hardening and softening properties were measured during low cycle fatigue tests on structural steels greatly different in strength and ductility levels. The internal stress and the mechanical quantities on cyclic deformation were empirically formulated as functions of the yield stress and the work hardening exponent in a static tension, and the dislocation density. These formulated quantities were introduced into the Johnston-Gilman's equation modified by the authors, in which the macroscopic plastic strain rate was correlated with the dislocation motion. Then, the stress-strain hysteresis loops and the cyclic stress-strain response of the structural steels for machine components were analyzed in terms of dislocation dynamics. The analyses were in quite good agreement with the present test results. Consequently, it was shown that the cyclic stress-strain response of the steels could be analytically determined using the static mechanical properties.

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The stress-strain hysteresis loops and the cyclic stress-strain curves of structural steels for machine components were estimated through the use of analytical equations proposed in the previous report. The analysis on the loop profile describes well the Bauschinger effect which inherently appears in the cyclic deformation. The cyclic stress-strain curve calculated under the incremental step test condition was in quite good agreement with the test results, and that for the companion specimens method left some problems to be discussed only in the extremely low strain range. Moreover, the analyses on the hysteresis loops were successfully applied to predict the low cycle fatigue life curves plotted against a plastic strain range. Thus, the proposed analysis seems to make it possible to estimate the cyclic stress-strain curves and the low cycle fatigue lives to steels, using only the yield stress and the work hardening exponent in a static tension.

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The plastic behavior of metals (SUS 304, 2-1/4Cr-1 Mo steel Al alloy) after cyclic prestraining is systematically and experimentally investigated in a stress (strain) plane that consists of axial and torsional stress (strain) components. A useful multiaxial deformations sensor for both a cyclic test and a following large straining test is developed. The stress level in reloading after cyclic prestraining is never below the initial stress-strain curve, independently of the loading direction, even after cyclic softening, but may become strong depending on the prestraining direction, even after cyclic softening has occurred. An initial plastic anisotropy is never weak and never vanishes due to cyclic prestraining, but may become strong depending on the prestraining direction. The larger the cyclic strain hardening, the smaller the coefficient of work hardening in reloading. Therefore, it is suggested that the initial stress-strain relations should/can be used as basic material data for a strength and safty analysis of a structure that is subjected to both an usual cyclic load and an abrupt overload due to accident, earthquake and so on.

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A formula to describe the creep strain-rate based on the random barriers theory was presented by considering the process in which the movable dislocations could surmount the barriers in the field of resisting force with the help of thermal fluctuations. An effect of loading strain-rate on the stress-strain curves in cyclic loading at a slow rate was discussed with a new equation combined by the above formula and the equilibrium equation between the stress-rate and the strain-rate at any stress which had been derived in the previous paper. The results simulated by the above new equation show that the hysteresis curve at room temperature may shift conspicuously to the lower stress level as the loading strain-rate comes near to the creep strain-rate.

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This paper investigates the three dimensional rotation between the tibia and femur, which constitute the femorotibial joint, using the bi-plane photogrammetric system developed by the authors. Calculation method of rotational angles is presented based on the corrective rotation of tibial coordinates (r, a, s) to the femoral coordinates (R, A, S). Experiments are performed on two fresh human normal left joints (died at 53 years and 57 years). Internal and external torques of 2.5 N·m are applied to intact and anterior cruciate ligament (ACL) cut joints at flexions ranging from 0° to 80° and their 3-D rotational angles are measured. Known clinical facts relating to the present experiment of ACL cut from normal knee are : (1) By the application of the internal torgue, it causes the increase of the internal rotation at flexions ranging from 0° to 40°. (2) It has no effect on the adduction-abduction of the knee. Comparing the present results with the clinical ones, it is concluded that the proposed calculation method is adequate.

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An expression of the rotational angles of vertebrae which are measured by a system based on photogrammetry has been proposed by the authors. The angle is calculated as the corrective rotational angle of objective vertebrae coordinates to coincide with the reference vertebral coordinates. One of the reference vertebral coordinates can be selected as its rotational axis. Also, the axis of coordinates of the objective vertebra would be selected as its rotational axis. The former rotation is named as the other axes rotation and the latter as the self axes rotation. Two values according to the two cases in these expressions introduced a little confusion to the estimation of the rotated state of the vertebra. Then, the third expression, named the mean rotation, is proposed. By investigation of the proposed three expressions, it is concluded that the expression by mean rotation is useful for the analysis of spinal deformity.

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