Interaction of crack growth in hybrid bodies subjected to cyclic loading is investigated using the coupled compact tension specimens model. Coupled CT specimens of 0.45% C steel, JIS S45C and aluminium alloy, A2017-T4, individually precracked to their initial lengths are loaded by common pins in the grip of a fatigue machine. The crack propagation behaviour of coupled specimens fatigued under a stress ratio of 0.05 is compared with that of a single specimen. It is found experimentally that crack growth rate of one of the coupled specimens is accelerated by the plasticity induced crack closure of another specimen. This behaviour is affected by the difference in residual plastic stretch on the crack wall in each specimen. An interaction curve for coupled hybrid specimens is theoretically predicted, and the interaction law is discussed. It is concluded that multiple ended fatigue cracks may propagate with a mechanism such that the increment of total energy release rate in a hybrid body is distributed to each crack with the ratio of the strain constraint factor.

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The fretting fatigue strength of low strength medium carbon steel (S 45 C) under two-step block loading was examined by clamping the contact pads of the same material. The linear cumulative damage rule did not always hold good for fretting fatigue under two-step block loading, while it held good for plain fatigue. When the number of cycles in the block was large enough and the number of blocks to failure was smaller than 5 or 6, the two-step block loading reduced the fretting fatigue strength by a factor of five or ten. The coefficient of the friction and the slip amplitude reached constant values within a few hundred cycles after changing the stress level. Prediction of fatigue life was made on the basis of the analysis in the previous paper, where the frictional force between the fretting pad and the specimen was taken into consideration. The predicted lives were in good agreement with the experimental results.

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Previously, a general expression of fatigue crack growth rate was derived by one of the authors, based on the concept of crack energy density. In this paper, the meanings of that expression and the parameters of which that expression is composed are considered ; and the meaning of conventional expression like the law of Paris is also made clear. Experiments of fatigue crack growth and finite element analyses corresponding to these experiments are carried out, the influences of the differences of material, type of load and crack length or the like on the parameters and crack growth rate are discussed based on the results and it is verified that such influences can be evaluated by the general expression above. It is also pointed out that, if the constitutive relation of the material is given, it may be possible to evaluate the growth rate as well as influences of various differences.

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The dependence of ΔK_th on crack size and geometry, and Vickers hardness H_v under stress ratio R=-1 was studied. The effects of crack size and geometry are unified with a geometrical parameter √(area) which is the square root of the area occupied by projecting defects or cracks onto the plane normal to the maximum tensile stress. The dependence of ΔK_th on √(area) is expressed by ΔK_th ∝ (√(area))^1/3 and that of ΔK_th on H_v is expressed by ΔK_th∝(H_v+C). For small cracks and defects with √(area)≤1000 μm, the following equation for predicting ΔK_th and the fatigue limit σ_ω are available : ΔK_th=3.3×10^-3(H_v+120)(√(area))^1/3 σ_ω=1.43(H_v+120)/(√(area))^1/6 where the units in these equations are ΔK_th : MPa·m^1/2, σ_ω : MPa, √(area) : μm. For cracks and defects with √(area) >1000 μm, the dependence of ΔK_th on crack size gradually changes from (√(area))^1/3 to (√(area))⁰ and this causes the difference in the exponent n in the equation of the type σ_ωⁿl=C which was first obtained by N.E. Frost, and was confirmed later by other researchers. Although the tendency of many data indicates that there may be a linear correlation between ΔK_th for a large crack and H_v, more systematic studies are necessary to establish the exact relationship between ΔK_th and H_v.

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The plane elastostatic problem for two bonded elastic half planes consisting of isotropic and anisotropic materials is consisdered. It is assumed that the anisotropic half plane contains a straight crack normal to the bimaterial interface, and the bonded plane is subjected to a constant strain away from, and perpendicular to, the crack. Singular stress fields at the tips of a crack fully embedded into the anisotropic half plane and terminating at the interface are investigated. Mathematical formulations are made using the method of continuous distribution of dislocations and singular intergral equation method. Numerical calculations are carried out for the stress intensity factors and the order of stress singularities at the tips of the crack.

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This paper deals with the dynamic interaction between penny-shaped cracks in an infinite solid. Laplace and Hankel transforms are used to reduce the mixed boundary value problems to a set of dual integral equations. The solution is expressed in terms of a Fredholm integral equation of the second kind having a kernel with fast rate convergence. A numerical Laplace inversion technique is used to recover the time dependence of the solution. The dynamic stress intensity factor is determined and its dependence on time and the geometry parameter is discussed.

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An analytical method to determine the optimum shapes of orthotropic inclusions in orthotropic infinite plates (matrix) to which are applied uniformly biaxial tension or compression at infinity, is proposed. The method is based on the solution of an anisotropic plate with an elliptic inclusion found by Yang and Chou. The optimum inclusions, which have the optimum length ratios between the principal axes of the ellipses under the applied stress ratios, produce uniform stress distributions along the boundary between the inclusion and the matrix. Optimum shape diagrams for deciding the axis ratios of ellipses, which are plotted numerically for models with typical elastic stiffness ratios of inclusion to the matrix, show quantitatively the relationship between the effect of the anisotropic factors and the shapes. From the diagrams, it is appeared that the ellipse becomes more slender as the applied stress ratio or the anisotropic factors become larger or smaller than unit ; and that the factor of the inclusion produces an opposite effect on the shape, in comparison with that of the matrix

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The theoretical analysis of propagation and closure of two-dimensional hydraulic fractures subject to the compressive tectonic stress of a linear gradient has been made by Secor and Pollard. They have found the existence of a length limit for these hydraulic fractures. In the however, the rock in the earth's crust is assumed to be in an isothermal state. By developing Secor and Pollard's work, the present paper is concerned with the discussion of the length limit of an artificial geothermal crack in a hot dry rock with a linear temperature gradient. The rock is assumed to be homogeneous and isotropic with respect to thermal and elastic constants. By use of the singular point method, a set of nonlinear singular integral equations is derived. The results suggest that a very large artificial geothermal crack could be created in a hot dry rock with a large temperature gradient.

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Ordinary numerical computation methods (i.e., FEM and BEM etc.) lack the ability to present crack tip stress singularity, and meaningful procedures are required to determine stress intensity factors by use of the results from very near the crack tip. From this point of view, hybrid determination techniques are newly proposed to obtain reliable stress intensity factors with no special attention given to stress singularity. Crack tip stress and displacement behavior are expressed in the form of an infinite series expansion due to Williams and, usually, only the first terms of the series are considered when determining stress intensity factors (for example, extrapolation techniques). The hybrid determination techniques are based on considering the effect of including higher order terms, and results in solving simultaneous equations of the first degree derived by use of stress and displacement distributions. The characteristic of these techniques is that they are based on computation results from not very near the crack tip, and also that the higher order stress factors can be determined. These techniques are applied to BEM and FEM analyses of two dimensional and axisymmetric crack problems.

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Analyzing the stress distribution of an elastic body on which an impact load is applied has become important in relation to the reliability and vibration of machine elements. But stress distribution has seldom been analyzed because of lack of knowledge of the stress function, including the term of inertia. In earlier paper "85-081 B", the stress functions which satisfies this condition was derived The current paper deals with the stress distribution of an elastic body like as threads by using this function.

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The displacements and the stresses of an elastic half space loaded in the elliptical area on the surface are expressed by the series involving Hankel integrals. The general formula of the Abel transform is given to transform the series into ones involving Fourier integrals. By using the expressions, we are able to analyze theoretically the mixed boundary value problems such as the contact problems between the elliptical punch and an elastic half space and the crack problems of an elastic space with elliptical cracks. As an example, we apply the expressions to analyze the contact problem between the flat ended elliptical punch and the half space.

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This paper deals with the stress concentration problem of a circular solid cylinder with a central notch and two supplemental notches under torsion. Stress mitigations due to interference effects of stress concentrations are investigated. The influences of the distances between a central notch and two supplemental notches and the radius of the semicircular notches on the mitigations of stress concentration are considered. The principle of the method of solution used here is to distribute torsional body forces in the interior of a solid cylinder so as to satisfy boundary conditions of the notched surfaces imagined in the solid cylinder with no notch. For this purpose, we apply Green's functions for torsional body force problems of an infinite solid cylinder. Numerical results are shown for stress concentration factors of the problem.

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A method of real time stress analysis by a scanning infrared camera has been developed. The stress concentrations have been measured for the notched and cracked specimens made of aluminium alloy and mild steel. A macroscopic pattern of the stress distribution can be visualized momentarily according to the variation of the applied load. Data of the stress distribution can be stored in a video tape recorder, and accuracy has been improved by smoothing these data. Results are in good agreement with those by the finite element analysis. By means of this system, fatigue crack propagation can be monitored and the hysteresis energy in the cyclic plastic zone at the crack tip can be measured as well.

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When an impact load is imposed to a finite body, the dynamic stress state generated in it is very complicated and different from the static loading case. The purpose of this paper is to study the effect of the contact condition and specimen length on the size of the yielding zone generated by an impact compression in prismatical steel specimens, which were piled to a total height 60 m. The lengths of the respective specimens were 20, 30 and 40 mm. An impact compression was imposed on a pile of specimens by a drop weight superposed upon a static compression load at 3, -72 and -184°C respectively. The strain-time diagrams were measured by a strain gauge and discussed based on a one-dimensional stress wave propagation model taking into account the reflection and transmission at the contact surface. The yielding zone was generated near the upper end, the lower end and the contact surface of the specimens. The length of the yielding zone was larger for a large static load superposed, and smaller at a lower temperature. Swelling over the yielding zone was observed by an interferometer and distribution of hardness on the specimen surface was also examined.

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With special attention to the fracture modes, flat mode and slant mode, ductile crack growth was examined over a wide range of crack extension of ran aluminum alloy 7 NO 1-T6 using compact specimens with various thicknesses and notch geometries. Results obtained are as follows : (1) The conventional concept that the ductile crack growth resistance of the slant mode is higher than that of the flat mode, does not hold true ; (2) The mode I, plane-strain, ductile crack growth resistance can be obtained from the J-Δa_max curve, where Δa_max is the maximum crack extension of the flat mode fracture near the midthickness of the specimens ; (3) It is not possible to evaluate both the ductile crack growth resistances of the flat mode and of the slant mode, using specimens with side grooves and with slant notches, respectively.

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The governing equations of the dynamic problems in elastic-viscoplastic three-dimensional soil containing spherical cavities are formulated by means of bipolar coordinates adapting constitutive equations of normally consolidated clay. The stress wave propagation in the ground containing a spherical cavity of 0.5 m diameter at 5 m depth from the ground surface is analyzed by the method of direct integration of the basic equations of the problem, when an axisymmetric dynamic load is applied to the boundary of the cavity. In the calculation, the change of pressure with the depth from the ground surface is also taken into account for the initial state of the soil.

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The local buckling characteristics of elastic plates with a central crack subjected to a uniaxial tensile load are analyzed by the finite element method based on the linear bifurcation theory. The accuracy of analysis is discussed in conjunction with the nature of the crack buckling phenomena. The influences of the loading conditions, the plate aspect ratios, and the plate width to crack length ratios on the buckling load are investigated in detail. The comparison shows fairly good agreement between the experimental and predicted results, under the condition of small-scale yielding at the crack tips. Finally, an approximate formula for estimating the elastic-tensile buckling load of the cracked plate is proposed.

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The local buckling characteristics of centrally cracked rectangular plates subjected to a uniaxial tension are analyzed by the finite element method, taking into consideration the effect of plastic deformation developing near the crack tips. There is remarkable agreement between experimental and calculated results. The results obtained in this investigation indicate that the effect of elastic-plastic deformation is predominant on reductions in the tensile buckling loads of cracked plates. It is shown that the buckling loads of either plates with a short crack or thick cracked plates tend to be so much smaller than values predicted by the elastic buckling analyses. Finally, a empirical relation based on the conception of the equivalent elastic-crack-length is proposed, for estimating the elastic-plastic buckling loads of the center cracked plates.

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A general method for the solution of the dynamic problem in an elasto/viscoplastic solid is presented. This method reduces the elasto/viscoplastic problem to a sequence of elastic problems with initial strains. The solution of the elastic problem with initial strains is determined by using four displacement functions. Using the foregoing method, a solution is derived for a dynamic elasto/viscoplastic problem in a thick-walled spherical shell subjected to internal impact load. The numerical results show how the dynamic stresses in a sphere with viscoplastic properties vary with time.

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Special plate and curved shell elements have been developed for the finite element analysis of fiber reinforced laminated composite structures. The formulation is based on a modified Hu-Washizu variational principle. The independent quantities subject to variation are displacements and the transverse components of stresses. The continuity of displacements, strains and stresses is exactly satisfied along interlayer surfaces. The individual cross-sectional rotations and thickness changes of each layer are allowed for the accurate evaluation of transverse stresses, including interlaminar normal stress which may produce catastrophic delamination failures. The present elements, which have eight nodes regardless of the total number of layers, can be used in conjunction with standard isoparametric shell elements and can lead to realistic solutions of practical design problems dealing with notches, holes and other out-of-plane loads in laminated composite structures.

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In optimal structural design, a shape of a structure is determined so that it can utilize the materials uniformly for the given (deterministic) loading conditions. However, actual loads are not determinate, but often vary from the given condition. In this situation, variable loads may cause higher stresses or yield large differences in the stress distribution from point to point for the structure which was designed optimally for a particular load. In this paper, a shape determination method of structures considering variation of the load, such as variation in the position of the applying point, the direction and the magnitude of load, is proposed by extending the Inverse Variational Shape Determination Procedure, which was formulated for the deterministic case. In the present procedure, such a shape as makes the expected value of the potential energy stationary is searched for. Besides, and effective scheme is proposed to obtain the displacements as random variables.

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By use of the resonance method in a cylindrical specimen, the elastic constants of polycrystalline materials of pure aluminum are measured at a temperature range from about -190°C to about 300°C. The elastic constants agree well with the reduced values of polycrystals, which are converted from existing experimental results of single crystals of ultrasonic measurement. The influence of dimension and thermal expansion on elastic constants is also estimated. Finally, the applicability of this method to alloy systems is investigated.

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Cyclic elastic-plastic behavior was investigated experimentally under various temperatures and temperature changing conditions. The specimens were cyclically loaded between fixed strain limits at a strain rate of 0.2%/s at constant temperature in the range from room temperature to 600°C. The effect of strain range on the saturation property of cyclic hardening was obtained at various temperatures. To investigate the effect of temperature variations on the cyclic hardening, the cyclic tests were conducted at one temperature after the specimen was cyclically hardened at another temperature. The hardening models accounting for the cyclic behavior were discussed and the experimental results were compared with the calculated results for those models.

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A constitutive equation for stress, stress-rate, strain-rate and temperature effect is proposed and examined with the experimental results. The proposed equation is a combination of an Arrehnius equation and Malvern-type constitutive equation, which was proposed by the author previously, and indicated well the impact behaviors of various materials. The characteristics of the present equation are : (1) constants involved in the equation are clear and accurate physically, (2) the athermal stress component and maximum limit of strain-rate are considered, (3) at a high strain-rate, there are approximated linear relationships between stress, the reciprocal of absolute temperature and the logarithm of plastic strain-rate, (4) at a low strain-rate, there is a linear relationship between stress and the plastic strain-rate, (5) the proposed equation represents experimental results of constitutive relations of metals with a few exceptions, such as the blue brittleness range of steels.

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This paper proposes the branch-and-bound technique which generates stochastically dominant structural failure modes by using a lower bound of complete failure path probability. First, combinatorial properties of the failure paths are clarified and it is shown that there are many complete failure paths in a large-scale structure with a high degree of redundancy. Then, in order to reduce computational efforts, heuristic operations are applied to the branch-and-bound algorithm. Finally, the validity of the heuristic operations is demonstrated through numerical examples.

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