Papers relating to artificial subsurface cracks are reviewed, with special attention given to the fracture mechanics approach to the design of the artificial subsurface heat-exchange systems used in geothermal heat extraction. This approach is compared with the classical approaches which have been empoyed in oil and/or gas well stimulation. A variety of methods for mapping the artificial, subsurface cracks are also reviewed since the development of the methods is one of the key themes involved in the design of subsurface cracks. The demonstrative field experiments of extracting heat from hot dry rocks are also surveyed, since they are the best practical examples. Finally, the basic concept for the design of artificial subsurface cracks is briefly described following the successful results of the Γ-project at Tohoku university on geothermal heat extraction.

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A frictionless, axisymmetric contact problem is considered, where an elastic half-space is pressed onto a rigid foundation with a parabolic-ended pit or protrusion. It is necessary to find the extent of the contact region and contact stress between an elastic half-space and the rigid foundatin. Also required is the normal displacement on the free surface. The problem is solved by using Papkovich-Neuber equations in oblate spheroidal coordinates. The effects of various parameters on the contact stress are studied. Numerical results are compared with those for a flat-ended pit or protrusion, and they are found to be in agreement.

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The present paper deals with the combined effect of a spring support and a lumped mass on the stability of a tubular cantilever conveying fluid. The support and the mass are assumed to be attached to the cantilever at the same location. The validity of Galerkin's 8 term approximation is discussed from the view pont of predominanteigenmodes in critical flutter configurations. It is shown that for particular combinations of spring stiffness and lumped mass there exists an instability region which juts out from the main foutter domain. Both theory and experiment confirm that the instability in the region is of the mild flutter type, mot the violent type.

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The theoretical analysis of propagation and closure of two-dimensional hydraulicfractures 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 their model, 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 homegeneous 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 geotherma crack could be created in a hot dry rock with a large temperature gradient.

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The elastic stress analysis of a three-dimensional crack is carried out by the use of the indirect boundary integral method. The fundamental solutions of this method are simple- and double-layer potentials. This method has the advantage that the discontinuity of a layer potential across the crack surface is related to that of displacement, i.e., crack opening displacements of penny- and ring-shaped cracks are obtained. Also, the usefulness of this method in solving crack problem is shown by comparing the present results with other results.

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An expedient method to improve the accuracy in BEM and FEM is discussed in this paper. The concept of this method is based on the similarity of stress fields near notch roots. In this method, constant boundary elements are used for BEM and constant-strain triangular finite elements for FEM. Therefore, personal computer programs can be used in analyzing practical problems. This method is applied to some examples and its effectiveness is shown.

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Nowadays, due to the development of the sandwich core series and the higher degree of accuracy required for each thickness of sandwich plate, optimum design of the structural sandwich plate has been needed. We have found several papers relating to the optimum design of the laminated plates, but not for the optimum design of a sandwich plate with a hole or notch. Hereby, this paper presents the characteristics and some example data of the stress concentrations of a sandwich plate with a hole or notch. In analyzing the structural sandwich plate, we apply two bending theories, of which we name one the simple bending theory and the other the advanced bending theory. By using FEM analysis, which is based on these two bending theories, we determine stress concentrations of a sandwich plate, taking into account both the accuracy and cost efficiency of the calculations. We also examine the stress concentrations and raveal the characteristics of the stress concentrations under two types of bending load: anticlastic bending load and cylindrical bending load. To show examples of stress concentrations of a sandwich plate, we use the simple bending theory under the anticlastic bending load.

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Many automatic mesh generators for FEM are popularly in use, but in none of them is the finite element approximation error considered. This paper is concerned with an adaptive mesh refinement for FEM, in which the finite element approximation error is considered. In the analysis, the interpolation error gives the upper bound of the approximation errors. Here, we use interpolation error instead of approximation error. And we calculate the error measure; then, remesh is carried out by only relocating the nodes, without increasing the total number of nodes and elements. The method is applied to 3-node triangular elements and the stress analysis of linearly elastic structures. The γ-method is tested in two examples of stress analysis problems, and its effect is confirmed.

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The bucking problem of compressed coiled springs has been investigated by Haringx and that of twisted coiled springs by Hubbard. In this paper, the buckling condition of coiled springs is derived by considering coiled springs as elastic rods of equivalent rigidities. It is noticeable that the shearing-deformation of coiled springs is large enough to be taken into account in the analysis. Therefore, an equilibrium equation is set up by considering both the bending and shearing deformation of the rod element. The results confirm the theories of Haringx and Hubbard. The experimental results on coiled springs under combined axial deflection and torsion show good agreement with those predicted by the theory.

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This paper deals with a method for analyzing the random vibration of a vehicle running on a road whose surface is uneven probabilistically. The uneven road is represented by a two-dimensional filtered Poisson process in terms of sinusoidal shape function. A four-wheeled vehicle is modeled as a frame structure, into which the effect of the road surface is fed through spring-damper systems, in the framework of the finite element method. The shape function of the structural response is obtained through mode decoupling by means of complex eigenvalue analysis and time integration of the equation of motion. It turns out that the samples of response time history are calculated in addition to response power spectra, without using the coherence function. The numerical examples are carried out in regard to a model truck chassis, and the time history, power spectrum and number of occurrences of the internal bending moments generated are estimated by using the Monte Carlo simulation technique.

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This paper describes a method for automatically drawing stress trajectories in a 2-dimensional region from a photoelastic experiment. The stress trajectories are considered a gathering of circular arcs with different radii of the curvature, and approximately expressed by polygonal lines. The polygonal lines are determined by repeating the procedures so that they may contact with true trajectories. This method can be applied to the case where stress components are given and the directions of principal stresses are obtained from isoclinics. By this method, the trajectories are drawn easily by selecting merely starting points for the drawing.

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The electric-potential CT method proposed previously by three of the present authors was applied to quantitative measurements of location, angle and size of two-dimensional inclined cracks embedded in steel plates. In this experiment, a DC current was consecutively supplied between one of five pairs of electrodes placed on the top and bottom ends of the plates. Electric-potential distribution was measured along the side faces of the plate under each of these five current application conditions. Data on electric-potential were processed to reconstruct cracks by a least residual inverse analysis scheme, in which a least residual criterion was employed between the observed potential distributions and the computed ones for various assumed crack locations. When the residual was evaluated using a potential distribution obtained under any single current application condition, this scheme did not always give reasonable results. Simultaneous use of the potential distributions under five current application condition made it possible to determine the location, angle and size of cracks with good accuracies.

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In the low-cycle fatigue design based on testing of geometrically similar models, the scatter of fatigue life is taken into account using the factor for the statistical variation in test results, K_ss = 1.470-0.044γ, the formula given by the ASME Boiler and Pressure Vessel Code, where γ is the number of replicate test. In the present paper, this formula has been examined by calculating the upper confidence limit of the probability of failure P_fU for the design service cycles as determined using the above formula. It was found that P_fU varied with η and γ, where η was the coefficient of variation of the fatigue life. An alternative formula was proposed which made P_fU independent of η and γ.

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Near threshold fatigue crack growth and crack closure were investigated in SS 41, SM 41 A, SUS 304 steels and A 2218-T 6 Aluminum alloy at elevated temperatures up to 500°C. Emphasis was placed on examining the role of crack closure on fatigue threshold at elevated temperatures. The fatigue threshold, Δ K_th, was found to increase with increasing test temperature in all the steels tested, while it was found to decrease in A 2218-T 6 Aluminum alloy. Oxide-induced crack closure was found to play an important role in the in crease of ΔK_th at elevated temperatures in SM 41 A, while it was found to play a less important role in SS 41 and SUS 304. It was concluded that oxide products on the fracture surface enhance crack closure only when the CTOD at threshold remains small at elevated temperatures.

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In this paper, an estimation method for fretting fatigue strength is proposed. Fretting fatigue cracks initiate very early in the fatigue life of metals, which is dominated by the propagation process of small cracks. Characteristics of fretting fatigue cracks are analysed using stress intensity factors at the tip of cracks growing from the contact edges. The stress intensity factors are calculated from the contact pressure and tangential stress distributions on the contact surfaces. Fretting fatigue limits were estimated by comparing the stress intensity factor ranges with the threshold stress intensity factor range of the material. These calculated results were then compared with experimental results of fretting fatigue tests.

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This report studies the failure phenomena of ductile thin metal sheets using conical punches and tries to estimate the total work done which is absorbed under penetration. Penetration tests on circular thin sheets of mild steel, at thicknesses of 1.0, 2.1 and 3.1 mm and at a blank diameter of 200 mm, are carried out at a quasi-static punch speed using conical punches. The punch angles are 30, 45, 60 and 90 degrees and the punch nose diameters are 5.5 and 20 mm. The effects of the sheet thickness, the punch angle and thee punch nose diameter on the failure mode of a thin sheet are investigated experimentally. In addition, the authors present formulae for estimation of the energy-absorbing capacity of ductile thin metal sheets under penetration. By comparing the estimated values with the experimetal ones, it is clear that the proposed formulae are valid for assessment of the energy-absorbing capacity of thin sheets, except for the case of large punch angle.

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This paper deals with the correlation between hardness (mean contact pressure) P_m by a spherical indenter and flow stress Y under the uniaxial stress field. Firstly, the mean strain of the deformed material around the indentation ε_ic, which corresponds to the total strain of the uniaxial stress field, is defined following Tabor's idea. Secondly, hardness/flow stress ratio C is obtained experimentally for C =9.8 P_m/Y, where Y is in MPa, and formulated for two conditions of material (1) elastic-plastic transient process : C=1.1+(2/3) ln(ε_ic E_s/Y), (2) ideal-plastic deformation : C=2.9; E_s is the Young's modulus of a material. Finally, by combining these relations, a method of estimating the flow stress-strain characteristic curve by spherical indentation is proposed. In addition, an example of estimation of the flow stress-strain characteristic curve of SUS 304 is shown over a wide range of strain by means of the proposed method.

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Fundamental equations based on the linear-thermovisco - elastic theory were established to determine the residual stress and deformation due to cooling in a multilayer laminated beam. The transient thermal stress distribution and deformation in an epoxy resin/aluminum alloy laminated beam during the cooling process was calculated using these fundamental equations, then these beams were actually subjected to the cooling process. The experimentally obtained values revealed a high level of correlation with values theoretically calculated by the thermoviscoelastic analysis. The results demonstrate the necessity of thermoviscoelastic analysis for obtaining the residual stress and deformation due to cooling of multi-layer laminated beams made of thermosetting resin and elastic material.

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The complex shear modulus of a thin adhesive layer may be determined from the torsional resonance test on a composite beam with metal facings and an adhesive core. In order to determine this shear modulus from such method ( Composite Beam Test Method), it is necessary to know the torsional rigidity of a three-layer composite beam. This was analyzed exactly, and a method to determine the complex shear modulus was presented herein using the result of analysis. An error analysis is essential in this method for reliable determination of characteristics of the extremely thin adhesive layer, and it was performed in the present paper. The test beam configuration which minimized the resultant error of the shear modulus were discussed theoretically based on the results of error analysis .Validity of the present method was verified by some torsional tests which were carried out on the symmetrical elastic beams bonded by two types of structural adhesives at several temperatures.

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