A tensile elastic-plastic-viscoplastic constitutive equation is proposed, where the concepts of understress and overstress are introduced. The strain-rate dependence and the high-strain-rate dependence of stress are shown using the proposed constitutive equation. An equation is given describing propagation speed of an elastic-plastic-viscoplastic stress wave, and the strain dependence and strain-rate dependence of this speed. One-dimensional numerical analysis of a bar subjected to longitudinal impulsive loading under constant particle velocity loading conditions is carried out using the proposed constitutive equation. Results indicate the attenuation of the constant particle velocity with distance in the particle velocity-time plane, the existence of the strain plateau and changing of the plateau with time in the strain-distance plane, the existence of constant strain and the attenuation of constant strain with distance in the strain-time plane, and the maximum value of stress at the impact end and its decrement with time in the stress-time plane.

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The stress-induced failure in an aluminum conductor of a microelectronic package was investigated in terms of diffusion along the surface and grain boundary. The mechanism of grooving, which initiated and grew at elevated temperature along a grain boundary perpendicular to the stress, was proposed and the failure process was numerically simulated. The grooving process was found to be sensitive to thermal stress as well as diffusion ratio, F = (grain boundary diffusion) / (surface diffusion). The active grain boundary diffusion brought about a crack-like groove at the high magnitudes of F and/or stress, whereas the low magnitudes led to a V-shaped groove and marked thinning of the conductor.

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The numerical method which has been proposed by the present authors for wave propagation analysis in functionally gradient piezoelectric material (FGPM) plates is used to investigate SH waves in FGPM plates. The material properties of the plate change gradually with the thickness of the plate. To evaluate the properties of the energy transfer between the electrical and mechanical energies during acoustic wave propagation in dispersive media, an electromechanical coupling constant is defined on the basis of group velocities of the acoustic waves. Numerical examples are given for a hypothetical FGPM plate and a homogeneous plate. It is found that there are SH surface waves propagating on the softer surface of the FGPM plate. Furthermore, the electromechanical coupling constant based on group velocities is found to be more appropriate than that based on phase velocities for waves in dispersive media.

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The effects of the composition gradient in the radial direction on thermal stress have been analyzed for thick-walled tubes of functionally graded material (FGM) under uniform thermal loading. The combinations of aluminum and silicon carbide were assumed to be the same as in the plaster/corundum model. The distributions of the stress and strain components depended mainly on the composition gradient. Its qualitative estimation seems to make it possible to consider variations in the linear expansion coefficient and elastic modulus. The circumferential stress at the inner surface varied from tension to compression according to the increase in composition gradient accompanied by a decrease in the linear expansion coefficient and an increase in the elastic modulus. For generalized plane strain conditions (axial strain, ε_z=constant≠0), circumferential stress and radial stress are independent of axial strain. The optimum composition gradient generated by compressive circumferential stress at the inner surface is estimated.

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This paper deals with the strength of joints that combine adhesion and tap bolts. When an external load was applied to a combination joint, which was constructed by joining two hollow cylinders by adhesion and the clamping them together using a tap bolt with an initial clamping force, the stress distributions in the adhesives and the variation of the bolt axial force were analyzed using an axisymmetric theory of elasticity. In addition, a method for estimating the strength of the combination joint was proposed. Experiments were performed and the analytical results were consistent with the experimental results concerning the variation of the bolt axial force and the joint strength. It is seen that, as compared with the adhesive joint in which two tap bolts are used, as the length of the tap bolt increases, the strength of the combination joint increases. Furthermore, the strength in the case where rectangular T-shape flanges were used was examined by both analyses and experiments. The characteristics of the combination joint were elucidated.

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Experiments on the forming limit strains of several metal sheets are performed exclusively under the (quasi-) plane strain tension. As well known, sheet breaks generally due to localized necking (localized-type instability or bifurcation). All theories predicts that any sheet would break at the tensile strain comparable with its n-value (strain-hardening exponent) under such conditions. It is clarified here why there exist so many materials whose forming limit strains for plane strain tension are not coincident with their n-value. It is verified that the theoretical critical condition for localized necking is basically correct, in which the first-order derivative of the stress-strain relation (the strain-hardening characteristic) of the material plays the decisive role. The conventional n-th power law approximation of the strain-hardening characteristic is not reliable when its first-order derivative must be used. It is emphasized that the strain-hardening characteristic has to be formulated precisely up to its first order derivative when determining the forming limit strain.

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Pure copper rectangular blocks are simply set in a multilayered manner without bonding and compressed up to 50% reduction in height per operation in the plane strain condition. When as-received copper (Cu-H) or precompressed dead-soft copper (Cu-O) is compressed, the interfaces of such multilayered blocks turn into extremely wavy surfaces, while those of virgin Cu-O blocks remain almost flat. This phenomenon may be a kind of diffuse-type instability depending on the work-hardening property (i. e., n-value) of the material. This phenomenon appears more markedly when an aluminum sheet is inserted between the interfaces. When the interface of the two layered blocks becomes saw-toothed, its waviness after compression is reduced to a comparable extent. Furthermore, when two blocks are designed in an hourglass or barrel-type, the interface remains a little wavy with no instability for both specimens with flat and saw-toothed interfaces. The saw-teeth of the interface surprisingly grow in height and width with compression particularly in the central portion of the interface of the barrel-type two-block specimen, inducing complete bonding of the blocks. Finally, when Cu-O severely precompressed up to 87. 5% (-2.1 in log strain) is tested as 8-layered blocks, the specimen fractures along a plane oblique to the compression axis before further deformation. This phenomenon may be a kind of localized (shear band) -type instability.

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Concerning the largely deformed shapes of a soft rubber sphere created by impact or compression, some interesting phenomena are observed which cannot be explained by the Hertz theory. To understand such phenomena, this paper presents a recently proposed theory and another new theory for estimating the contact stresses and deformations of a solid rubber sphere under diametral compression, placing an emphasis on press approach, radial extension of its contact areas, and lateral extension of its free surface.

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In this paper, experimental methods and results are presented for deformations of solid rubber spheres under diametral compression in a very wide range of forces from 0. 5 N to 5 000 N, for five rubber spheres of the same size and different stiffnesses. The experimental results show some phenomena of large deformations beyond the Hertz theory. By measuring the Young modulus of each rubber sphere, three displacements (approach, contact radius, and lateral extension) against force are calculated by the previous and new theories presented in Part I and are compared with the experimental data. The recent theory I and the new theory II are both compatible with the data. Profiles of compressed shapes of the rubber spheres are measured and compared with those predicted by theories I and II. It is concluded that the two theories, I and II are approximately valid for the compression of rubber spheres.

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The optical method of caustics is one of the most powerful techniques for evaluating stress intensity factors in static as well as dynamic fracture mechanics problems. In the method of transmitted caustics, optically anisotropic (birefringent) materials such as Araldite B and polycarbonate are often used. Double caustic curves appear for the tip of a crack in an optically anisotropic plate due to the birefringence. In this paper, a theory of caustics was developed for stationary cracks in birefringent materials under in-plane mixed-mode conditions. Completely analytical expressions were derived for the double caustic curves as well as for the double initial curves. The combined effects of optical anisotropy and mixed-mode state on the caustic curves and initial curves were investigated. A new procedure was also developed for the evaluation of mixed-mode stress intensity factors using the characteristic dimensions of the double caustic patterns.

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Plane bending fatigue tests were carried out on notched specimens of a glassfiber / epoxy laminate for a wide range of notch-root radii and stress amplitudes. Our attention was focussed on the damaged zone near the notch root of specimens. The process of fatigue damage was studied by measuring the luminance at a limited spot near the notch root. Closer observation by means of a scanning electron microscope revealed that the initiation of microcracks at the notch root was accompanied with the decrease of luminance near the notch root. The experiment shows that the number of cycles to failure is determined by both the maximum elastic stress at the notch root and the notch-root radius. On the basis of the concept of severity near the notch root, the experimental results can be clarified. Applying the fatigue failure criterion derived here, we can make an accurate estimate of the life of notched specimens of FRP.

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The software which enables us to classify six typically different fracture surface morphologies, such as striations, equiaxed dimples, elongated dimples, transgranular failures, intergranular failures, and cleavage failures, has been developed based upon computer image processing and pattern recognition. The texture analyses used here are the Fourier power spectrum, generalized co-occurrence matrices, and three-dimensional fracture surface topographies. Fourier power spectrum analyses are very powerful for recognizing striations and intergranular failures, whereas a generalized co-occurrence matrix and fracture surface area ratio are suitable for cleavage failures. We also point out that the membership values based upon a soft clustering method, a fuzzy C-means algorithm, allow the system an uncertain fracture surface. This increases the precision of recognition.

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