A numerical method is presented to determine the dispersion relation of wave propagation in an anisotropic laminated plate. A phase velocity surface, phase slowness surface, phase wave surface, group velocity surface, group slowness surface and group wave surface are defined and obtained using Reyleigh's quotient. The six characteristic surfaces can be used to illustrate the characteristics of the wave propagation in the anisotropic laminated plate due to the point wave source in it. As an example, the characteristic surfaces are obtained for graphite /epoxy angle-ply laminated plates and a hybrid composite laminated plate which consists of carbon/epoxy and glass/epoxy layers. The results for the graphite/epoxy laminated plates are compared with those obtained by the other approximated theory.

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Interaction between delamination and local deformation on a metal-polymer laminated material subjected to tension under plane-strain conditions is investigated numerically using a finite element method. The metal modelled is an Al alloy assumed to be plastic and the polymer is a PET to be viscoplastic. The delamination process is modelled as the destruction of the adhesive between laminated materials under the specified stress criteria in which the allowable shearing stress along the interface and positive normal stress perpendicular to the interface are prescribed. The results show that delamination at the early deformation is mainly caused by stress concentration around the void which is modelled by diminishing the stiffness of the element satisfied with this criteria. Local deformation starts in the metal after delamination is rapidly propagated at the relatively large strain field. The failure process from delamination of adhesive obtained from numerical analyses is found to be in reasonable agreement with experimental observations.

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The finite three-point bending of a fiber-reinforced tapered beam is analyzed with in the framework of the ideal theory of fiber-reinforced composite materials. The beam is reinforced in its axial direction and simply supported at its ends. It is thickest at its center and tapered towards its ends. The analysis, which was made by the method previously proposed by the author, yields an integral equation with respect to the curvature radius of the uppermost fiber. This equation is difficult to solve mathematically. However, its solution is successfully obtained by resorting to the method of sections. Deformed configurations of the beam are shown in the figures.

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In ceramic materials, it is important to evaluate the strength degradation after proof testing because of slow crack growth (SCG) in test cycles. In this study, a theoretical analysis of the strength of ceramics subjected to cyclic loading after proof testing was performed. The variation in crack length due to SCG during proof testing was calculated, assuming that the time-dependent crack velocity can be expressed as a single power function of the stress intensity factor. The fatigue life was correlated with the evaluated crack length. The life distribution and the minimum life were formulated using the distribution function of crack length, to be determined empirically. Effects of factors associated with testing condition on the fatigue life were investigated by a numerical simulation.

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Fatigue tests of a sintered silicon nitride were conducted after proof testing. Specimens of square bar and ring types were employed in the tests. Truncated minimum life was observed in both types of specimen geometry, when the largest tensile stress in the specimen was controlled during a series of tests. The experimental life distribution was compared with a numerical simulation based on a theoretical analysis of the stable crack growth from an inherent flaw. The applicability of proof testing as a procedure for improving fatigue reliability was discussed together with the validity of the theoretical estimate.

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Small corrosion fatigue crack growth behavior was investigated using smooth high-tensile strength steel HT 50 plate specimens in a sodium chloride aqueous solution (oxygen diffusion-type corrosion) and an acid solution made by adding H₂SO₄ to the salt water (hydrogen evolution-type corrosion). At a constant effective stress intensity factor range, the crack growth rate of the surface cracks increases with increasing stress amplitude range. That is, the crack growth rate of a small-size surface crack is higher than that of a comparatively large-size surface crack. This experimental result is observed in both types of corrosion conditions : oxygen diffusion-type corrosion and hydrogen evolution-type corrosion, and this peculiar crack growth behavior becomes marked in the latter corrosive environment whose corrosive capability is stronger than that of the former.

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Fundamental investigations were made as to slip initiation phenomenon in copper electroplating foil under variable amplitude stress which consists of overstress and understress. The applicability of the foil to the fatigue gauge which detects fatigue damage was discussed. It was found that the modified Miner's rule does not hold for the slip initiation under two-level single block loading composed of overstress and understress. The cumulative cycle ratio in this case is dependent on load histories. Namely, fatigue damage of high-low loading is greater than that of low-high loading and that of two-level multiple loading is the greatest. It was also found that fatigue damage under two-level multiple loading increases as the cycle ratio of overstress to understress increases. This indicates that fatigue damage during understress applied after overstress is greater in the early period of the cycles. The deviation from modified Miner's rule, however, can be said to be small.

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Thermal transient fatigue tests of ten pipe models with SUS304 steel and 21/4Cr-1Mo steel dissimilar joints were performed. Transient temperature distributions and thermal stresses caused by sudden a temperature change of the internal fluid were analyzed using FEM. Using these data, we evaluated the potential margin of the allowable number of thermal transient cycles according to the ASME Code Case N-47 and the elevated temperature structural design guide by the Power Reactor and Nuclear Fuel Development Corporation. The results are as follows: (1) The sequence of crack initiation of various parts of the test models could be well predicted by the analysis. (2) The buttering boundary should be kept suffiently apart from any discontinuity caused by counter-bore machining. (3) A sufficient safety margin for initiation of a crack 1mm in depth is observed and compared with the result based on the design rule by PNC.

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Three-dimensional shape of a corrosion fatigue crack is investigated for a high-tensile strength steel, HT60, under plane bending in tap water. The crack accompanies a corrosion pit which is nearly a semi-sphere and is situated at the center of the crack on a specimen surface. The shape of the crack front is not a semi-ellipse but a circular arc. The ratio of the crack depth to crack length on the specimen surface is 0.286 (that is, a central angle subtending the arc is 120°). Crack opening due to dissolution of the crack surface is observed in all regions, except that near the crack front. The amount of opening and the area of dissolution depend on the applied stress amplitude, whereas the size of the corrosion pit is independent of it.

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An interferometric strain/displacement gage system was developed to measure the crack closure behavior of small fatigue cracks nucleated in smooth specimens by fatigue. Interference takes place between laser beams reflected by two Vickers indentations. Linear image sensors were used to detect the movement of interferometric fringes due to strain. The resolution in displacement of our system was ± 1nm for the gage length of 100μm. The system was first applied to a through-thickness fatigue crack at the center of a low-carbon steel plate. The profile of crack opening displacement agreed with the prediction based on the Dugdale model. The crack opening point of small surface cracks in fatigue specimens of aluminum alloy 2024-T3 was determined from the record of load versus displacement. Surface cracks smaller than about 100μm in length mostly showed faster growth rates than those given by the da/dN versus ΔK_eff relation for long cracks.

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It is necessary for determination of crack size and shape by means of D.C. potential drop technique to know electric potential distribution at the surface of cracked body beforehand. The potential distribution on a body with semi-elliptical surface-crack is investigated in this paper. The results obtained are summarized as follows. (i) Exact distribution is derived as Eqs. (1)∼(3) for semi-infinite body with a semi-elliptical surface-crack. As it requires numerial integral to evaluate the potential, a simple approximation method (Eqs. (14) and (15)) is proposed for convenience. It is confirmed by numerical analysis that the error of approximation is very small. (ii) We propose an easy method to make a cracked body with an arbitrary crack shape and size for the calibration of electric potential distribution. Plate specimens with a semi-elliptical surface-crack are made of a wood metal, and the potential distribution is examined experimentally. The values measured coincide the solution of infinite body (see (i)) except that the crack depth is nearly equal to the thickness of plate. It implies that specimen's back surface affects fairly little on the potential distribution at the front surface.

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The authors have developed an influence function method (IFM) to analyze effectively the stress intensity factor, K, for surface cracks subjected to arbitrarily distributed surface stresses. In the developed IFM the influence coefficients are calculated by boundary element method in order to save the computing time and the labor of generating the input data. Some examples show that the developed method gives accurate values of K and that it is effective especially for the analysis of the mixed mode cracks.

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In fracture problems, stress intensity factors obtained theoretically or by experimental analysis have been effectively utilized in analytical evaluation of the effect of cracks. Use of the caustics method to determine the stress intensity factors of two-dimensional cracks has been established theoretically and experimentally. However, relatively few experimental analysis concerning the three-dimensional crack by using caustics method have so far been conducted. In this paper, the distributions of stress intensity factors along the crack front of a three-dimensional elastic solid have been determined by using the method of reflected caustics in combination with the photoelastic stress freezing method. In order to make a comparison between two experimental results for stress intensity factors determined by the caustics and photoelasticity, two kinds of experimental models with three-dimensional surface cracks were used. There was satisfactory agreement between the results of two methods.

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This paper deals with the electromagneto-elastic problem of a conductor with a finite crack under an impulsive electric current flow and a constant magnetic field. The crack disturbs the current flow and anti-plane shear stresses are caused by the interaction between the magnetic field and the disturbed current. Laplace and Fourier transforms are used to reduce the electromagnetoelastic problem to a Fredholm integral equation of the second kind in the Laplace transform plane. A numerical Laplace inversion 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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Dynamic crack opening displacement (DCOD) of a two-dimensional finite crack to the oblique incidence of an elastic plane wave is computed based on the elastodynamic theory for the fundamentals of ultrasonic wave scattering analysis. The formulations can be done through the Fredholm integral equations of the second kind. Infinite integration of the kernel is transformed to a finite one. Then, it is expanded into the Neumann series of the Bessel functions. This expansion enables us to estimate the kernel easily because the Bessel functions can be calculated by the recurrence relation of their order. The numerical results of the DCOD are plotted in three-dimensional graphic form and their frequency dependencies are shown in perspective.

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The grain-size dependence of the yield stress of polycrystalline metals in the range of normal grain sizes is known as the Hall-Petch relation. However, recent experiments by Armstrong et al. show that failure of this relation occurs in the range of ultrafine grain sizes. In the present paper, in order to elucidate the above phenomena over both ranges of grain sizes, we propose the dislocation pile-up model, Which consists of a crack, a dislocation-free zone and a slip band blocked at the grain boundary. Analyzing the above model by the method of the continuously distributed theory of dislocations, we obtain an analytical expression which gives the relationship between the macroscopic applied stress and the grain size D. It can be shown that the behaviors of the macroscopic yield stress vs. D^-1/2 explain the experimental results well over both ranges of grain sizes. The applicability of this model to the grain-size dependence of the fracture stress of engineering ceramics is discussed when the friction stress of the dislocation is reduced to zero.

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The elastic-plastic stress analysis was made by the finite element method. The surface crack growth rate, da/dN, was analyzed in terms of the elastic-plastic fracture mechanics parameters of the J-integral range, ΔJ and the strain intensity factor range, ΔKε, which were estimated in association with the stress and strain gradients produced in the cross section of the notched specimen. The low-cycle fatigue life for the crack propagation, N_c, was calculated by combining the cyclic stress-strain curve and the crack growth law expressed by the da/dN vs. ΔJ and da/dN vs. ΔKε relations. The calculation based on the fracture mechanics parameters determined from the stress-strain response at the notch root leads to a shorter life in the more sharply notched specimen under the lower stress condition. Meanwhile, the fracture mechanics parameters associated with the stress and strain gradients in the cross section of the notched specimen give a good estimation of the life prediction.

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The fracture process of cathodically charged, quenched and tempered SNCM439 steel specimens was studied from the viewpoint of fractographic analysis with a special emphasis on the characteristics of the morphology of crack propagation and the mechanistic condition of delayed fracture. The fracture initiated at an inclusion in the specimen, and the fracture appearance was initially radial quasi-cleavage, followed by quasi-cleavage, intergranular and microvoid coalescence. The brittle fracture condition of the delayed fracture could be formulated on the basis of Griffith's fracture criterion in the following. σ·d^0.44=2440 (σ: stress [MPa], d: depth of the crack origin [μm]) The life of the delayed fracture corresponded to hydrogen diffusion in order to attain the critical condition for crack initiation around the possible origin of inclusion.

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The path-independent T^* integral is valid for any material-constitutive model under quasi-static as well as dynamic conditions. The T^* integral has great potential as a unified crack-tip parameter for various types of fracture mechanics. A series of papers will be presented for research and development of the method of caustics for directly measuring the T^* integral. In this paper, finite element simulation aided by computerized symbolic manipulation was carried out for the formation process of a caustic pattern for an elastoplastic crack-tip in a compact, tension specimen. The computerized symbolic manipulation system (REDUCE) showed great ability to obtain precisely simulated caustic patterns. The relations between the T^* integral and the size of the caustic pattern were obtained for several cases.

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This paper is concerned with an analytical formulation and a numerical solution of the elasto/visco-plastic problems of multi-layered moderately thick shells of revolution under asymmetrical loads with application to a cylindrical shell. The analytical formulation is developed by extending the Reissner-Naghdi theory on elastic shells. It is assumed that the total strain rates are composed of an elastic part and a part due to visco-plasticity. The elastic strains are proportional to the stresses by Hooke's law. The visco-plastic strain rates are related to the stresses according to Perzyna's equation. As a numerical example, the elasto/visco-plastic deformation of a two-layered cylindrical shell composed of a titanium and a mild steel layer subjected to locally distributed loads is analyzed. Numerical computations are carried out for three cases of the ratio of the thickness of the titanium layer to the shell thickness. It is found from the computations that the stress distributions and the deformation vary significantly depending on the thickness ratio.

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To describe the directional effect of plastic pre-strain on creep an anisotropic creep constitutive equation was formulated on the basis of the representation theorem of rational continuum mechanics. Creep strain rate function was first assumed to be an isotropic tensor function and was written as a linear combination of tensor generators formed from deviatoric stress tensor and a second rank symmetric tensor in accordance with the polynomial representation theorem. From the general polynomial representation, a reduced constitutive relation was derived which only consisted of linear terms of the argument tensors. Special forms of a integrity basis and tensor generator were given to the reduced version which showed a similar form to the conventional kinematic hardening model. With the similar procedure, a simple evolution equation of the internal state variable tensor was also defined. The evolution equation was physically characterized so as to incorporate, in a natural way, a combined isotropic and kinematic hardening. The model was embodied by using the Bailey-Norton creep law. A comparison between predictions due to the proposed model and the experimental results for 316 Stainless Steel at an elevated temperature showed reasonable agreement with each other.

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High molecular materials are generally used for many important structural members of machines, in spite of the present circumstances where the ductile fracture characteristics have not been sufficiantly known. The present study has been directed to determin the plastic strain concentration facter at the edge of a round-hole notch under the uniaxial stress field. Plastic strain concentration factors at the edge of around-hole notch were measured by photoelastic stress analysis technique under different tension rate. Concentration factors were calculated from results obtained and the experimental result was compared with the theoretical values. Fairly good agreement was found between them.

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Modulation of elastic waves plays an important role in the analyses of dynamic behaviour and fracture of mechanical structures. The present article, following the preceding report, deals with scattering of dispersive waves by a notch on a rod by which geometrical inhomogeneity is introduced. The incident waves and the scattered waves caused by the notch are distorted with time during their propagation along the rod owing to dispersion. Unsteady frequency distribution is analysed by use of the FFT method to elucidate the wave interaction. Moreover, our interests are devoted to the simplified inverse scattering process in estimating the waveform of the incident waves and dimension of the notch from the information included in the scattered waves.

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Experimental schemes in order to study the strain-hardening properties of materials in large deformation regimes are discussed under the condition of simple deformation modes. Assuming the plastic incompressibility and an approximation of isotropic strain hardening in large deformations, the fundamental strain paths available are first shown with respect to a simple compression, a channel-die compression, and some sequential combinations in each of these modes. This indicates that some multiaxial nonproportional plastic strain paths and cyclic strain paths may be realized in several multidirectional combinations of the compressions. Finally, a brief discussion of the only published study available on multidirectional large deformation from the point of cyclic strain hardening is presented.

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The forming limit of sheet metals is examined in terms of the uniqueness of the solution. There are two cases indicating multiplicity, one is statically admissible and another is kinematically admissible. The multiplicities are considered to correspond to plastic instabilities. The necking plane is studied as the plane admitting the existence of velocity discontinuity, and in sheet forming it cannot take any mode except perpendicular necking. After statical instability appears, the strain path cannot be controlled as freely as we would like. Finally, localized necking occurs, when the process satisfies the condition of the second kinematical instability, the mode of which is consistent with the mode of perpendicular necking. Several strain paths are assumed, and their formabilities are discussed.

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Probabilistic data of load and strength are required to obtain the reliability index of a structure. In practice, the amount of field data is insufficient, and only experimental data can be available in the analysis of the reliability of a huge structure. The structure is often evaluated in linguistic values. If statistical data do exist regarding evaluation items, fuzzy values can be quantified using the fuzzy probability which is defined as the product of a fuzzy membership level and the probability density. On the other hand, the specialists possess not only strict knowledge, but also fuzzy knowledge. In this paper, the author proposes the fuzzy estimation method of the mean value and standard deviations of the load and/or strength utilizing the fuzzy rules of specialists and the statistical data. Further, this method is justified by comparison with the experimental data.

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The Structural effect of IC plastic packages on the residual stress of silicon chips was discussed experimentally. The residual stress was measured by stress-sensing chips which authors have developed. Concerning the package structure, two different types of package were selected. One was the SOJ-type package, which is widely used for the surface mount technology, and the other was the COL-type package, which is newly developed for the large chip mounting technology. It is found that the residual stress of the silicon chip is varied more than three times by not only composition of package material but also package structure. The residual stress of the silicon chip encapsulated in the COL-type package is mainly determined by resin material. But the residual stress of the silicon chip encapsulated in the SOJ-type package is varied by combination of resin and lead frame matarial.

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