Atomic diffusion near an aluminum grain boundary is analyzed in order to investigate the basic mechanism of stress-induced migration(SM) in a thin wiring line in LSI. Molecular dynamics based on effective-medium theory(EMT) is applied to a model consisting of a surface and Σ=5[001]symmetrical tilt grain boundary with a bamboo-like structure. EMT is derived without any empirical knowledge and is known to be effective for analysis of an inhomogeneous atomic structure. Above the transition temperature from low- to high-temperature modes of SM, jump motion of atoms near the grain boundary occurs and the diffusion coefficients(DCs) which are estimated from the mean square displacement of atoms increase markedly. DC is largest in the region where the grain boundary intersects the surface. The magnitude of DC in the grain boundary region and its temperature dependence agree well with the results obtained by Plimpton and Wolf[Phys.Rev., B, Vol.41, No.5(1990), p.2712], who used several pair-wise interatomic potentials. It is proven that DC increases exponentially with tensile strain and decreases with compressive strain.

View full abstract

This paper describes the effect of temperature and interatomic force between a workpiece and tool on the atomic-scale cutting mechanism, by means of molecular dynamics simulation. The interatomic force between the workpiece and tool is assumed to be derived from the Morse potential function. Molecular dynamics cutting simulations were carried out using a rigid pin tool, with changing of the temperature and the value of Morse potential parameters γ₀, D and α. The increase in the potential parameters D and α resulted in the positive effect of surface roughness, but the increase in the parameter γ₀ and temperature resulted in the negative effect of surface roughness. Chip formation and side flow resulted due to the collision between the workpiece and tool, which lead to a temperature increase of the workpiece. The surface of workpieces observed experimentally in micro-scale cutting was similar to that in atomic-scale cutting by molecular dynamics simulation.

View full abstract

Topology of any one-dimensional complex can be represented by zero- and one-dimensional homology groups, which are isomorphic to the direct sum of additive groups. In this paper, a method is proposed to impose constraint on the topology of a frame treated as a one-dimensional complex by use of homology groups in the field of structural optimization. As the numerical examples, the total strain energy of the frame is minimized under topological constraints and constant weight. Useless members are eliminated from a ground structure by use of genetic algorithm. Any number of additive groups can be freely set up as a topological constraint because of generalized inverse matrices, and a rule of coding in the genetic algorithm is prescribed so that all strings(corresponding to chromosomes in biological systems)generated in the optimization process could satisfy the topological constraints. As the result it is found that loops in the topology of the optimum structure adjoin each other. The proposed method is also applied to the topology optimization of a square, flat panel board fixed on a rigid wall and loaded vertically on points distant from the wall.

View full abstract

A formulation is presented for interval analysis of eigenvalue problem on the basis of the finite element sensitivity analysis and representation of uncertainty involved in a structural system by a convex model. The first-order approximation obtained by the sensitivity analysis is employed to express the response change due to the uncertainty that is assumed to be confined in a convex hull. The maximum and minimum of responses, by which the interval is bracketed, are searched on the convex boundary by the Lagrange multiplier method. The validity of the present formulation is demonstrated by a numerical example of the axial buckling load of an elastic straight column in the case of spatially uncertain Young's modulus.

View full abstract

In particle or short-fiber reinforced composites, cracking of reinforcements is a significant damage mode because the cracked reinforcements lose load carrying capacity. This paper deals with elastic stress distributions and load carrying capacity of intact and cracked ellipsoidal inhomogeneities. Axisymmetric finite element analysis has been carried out on intact and cracked ellipsoidal inhomogeneities in an infinite body under uniaxial tension. For the intact inhomogeneity, as well known as Eshelby's solution(1957), the stress distribution is uniform in the inhomogeneity and nonuniform in the surrounding matrix. On the other hand, for the cracked inhomogeneity, the stress in the region near the crack surface is considerably released and the stress distribution becomes more complex. The average stress in the inhomogeneity represents its load carrying capacity, and the difference between the average stresses of the intact and cracked inhomogeneities indicates the loss of load carrying capacity due to cracking damage. The load carrying capacity of the cracked inhomogeneity is expressed in terms of the average stress of the intact inhomogeneity and some coefficients. The coefficients are given as functions of an aspect ratio for a variety of combinations of the elastic moduli of inhomogeneity and matrix. It is found that a cracked inhomogeneity with high aspect ratio maintains higher load carrying capacity than one with low aspect ratio.

View full abstract

In estimating reliability of a structural system, a limit-state function is needed to relate the structural state(failure or safety)to random variables of the system. However, it is not easy to obtain such an explicit function for complex structures. As a consequence, structural analysis must be performed repeatedly to check the structural state, which is very expensive. We develop an approximate limit-state function by using a neural network. Orthogonal factorial designs are selected as learning data for the network. An "active learning algorithm" is proposed to enable the network to determine important failure regions by itself and also to do further learning at those regions to achieve a good fitness with the real structural state there. The validity of the method is illustrated through numerical examples.

View full abstract

As the main causes of strength reduction in welded joints subjected to cyclic thermal transients, attention was given to (1)metallurgical discontinuity in which different deformation responses of base metal and weld metal can result in nonuniform stress and strain across the weldment, (2)peak strain concentration at penetration beads of unfinished welded joints, and (3)degradation of weld metal due to precipitation of dissolved metal. In order to evaluate the first two factors, an elastic follow-up model was applied. Thermal transient strength test results verified that the elastic follow-up model ensures adequate life in elevated-temperature component weldments. The proposed method was proven to be adequate in Type 304 SS, and to have safety margin in FBR grade Type 316 SS.

View full abstract

Fatigue crack bending and propagation behaviors were studied under mixed-mode conditions, using annealed and fatigue slant precracks with a center-hole notch. The fatigue crack propagation directions were estimated from the maximum tangential stress criterion using the stress intensity factors{(K_I)_est(K_II)_est}evaluated from the discontinuous displacements(opening for Mode I, sliding for Mode II)along the precrack, and they were in good agreement with the measured ones. The fatigue crack propagation rates during bending were evaluated from the effective stress intensity factor K_eff using{(K_I)_est(K_II)_est}, in which a total critical displacement ahead of the crack tip under mixed-mode conditions was adopted as the fracture criterion based on the BCS crack theory. After the crack was bent, the subsequent fatigue crack propagated under the mode I behavior at the crack tip; therefore the(K_I)_est evaluated from the discontinuous displacements measured along a bent crack could be regarded as the K_eff controlling the fatigue crack propagation rate of the crack bent from a slant precrack.

View full abstract

This paper deals with the two-dimensional thermoelastic contact problem of a rolling rigid cylinder of specified shape, which induces of friction and heat generation in the contact region, moving with constant velocity in an elastic half-space containing a subsurface crack. In the present temperature analysis, the speed of the moving heat source is assumed to be much greater than the ratio of the thermal diffusivity and the contact length. The problem is solved using complex-variable techniques and is reduced to singular integral equations which are solved numerically. Numerical results of stress intensity factors are obtained for a relatively short crack. The effects of the frictional coefficient, the sliding/rolling ratio, the crack depth and the crack angle on the stress intensity factors are considered.

View full abstract

A direct measuring method of bridging stresses for polycrystalline ceramics has been developed. Bridging stresses are measured by the stable fracture of the double-edge-notched specimen using the bridging stabilizer developed in this study. The opening displacement of the fracture surfaces is evaluated from the deformation of the bridging stabilizer and the double-edge-notched specimen without the need for microscopic measurement. As an example of the application, the bridging stresses of polycrystalline alumina are measured under monotonic load. The bridging characteristics measured using the present method are compared with those obtained by the other methods. An approximate expression of the bridging stresses obtained in this study is presented.

View full abstract

In this paper, interference between an elliptical inclusion and cracks is considered. The problem is analyzed by the body force method, using a solution for point force doublets outside an elliptical inclusion in an infinite plate as a fundamental solution. Numerical results for the crack tip stress intensity factors are presented for a case of two cracks lying on the interface and for a case of a kinked crack a portion of which lies on the interface. Based on the numerical results, the effect of the geometry and elastic properties of the inclusion on the stress intensity factors are investigated.

View full abstract

Microcrack propagation behavior of Mod.9Cr-1Mo steel under high-temperature fatigue in vacuum and air conditions were periodically observed. Microcracks propagated in the direction normal to stress axis in vacuum while the microcracks propagated in the maximum shear direction in air condition. It was found that propagation rate in air was faster than that in vacuum until the crack grew 1 mm length due to oxidation effect which was insignificant for the crack larger than 1 mm. Acceleration of the crack propagation rate in the compression hold test was supposed to be caused by accumulation of tensile strain in the center of the specimen due to off-balance of strain distribution between tension and compression side.

View full abstract

The contour J-integral values were calculated using the three-dimensional elastic-plastic finite element method for semielliptical surface cracks originated at notch roots under tensile loading. Then these were compared with the J-integral values calculated using the conventional equation we proposed in earlier papers, which we refer to as J hereafter. The difference between the two was quite small at the deepest point A in the semielliptical surface crack, but was fairly large at the edge of a crack on the specimen surface, C. The conventional equation was modified by considering stress/strain gradients developed in the cross section at the notch root. The J-integral value calculated using the proposed equation, J′ was in quite good agreement with the contour J-integral value at both points, A and C in a semielliptical surface crack. The difference between the ratio J/J′ and 1.0 increased with increase in crack depth, depending upon the aspect ratio of the surface crack, magnitude of the applied stress and notch root radius. The parameter R_W was proposed, so that J/J′ could be expressed by a unique curve as a function of R_W over quite wide ranges of notch root radius, surface-crack shape and magnitude of stress. The application limit of the simple J-integral estimation proposed earlier was assessed using this curve. The crack growth rates obtained from fatigue tests of notched specimen were successfully plotted against J-integral range calculated using the modified conventional equation.

View full abstract

The general condition for a logarithmic stress singularities obtained by the author in a previous study is applied to a semi-infinite plate consisting of two-bonded wedges. When the eigenvalue is a multiple root, logarithmic stress singularities then may occur. The results of analysis show that the logarithmic singularities in the stress field may be of order(log γ)², log γ or γ^λ-1 log γ, depending on the combination of materials and the vertex angle of the wedges.

View full abstract

In this paper we propose a new homogenization method for composite materials in order to predict effective dynamic viscoelastic material properties in the frequency domain. The loss tangent, which is the ratio of storage modulus to loss modulus, is an important design variable for products made of viscoelastic materials. The proposed procedure, by which it is possible to compute the effective loss tangent of composite materials with periodic structure, is implemented in a homogenization analysis system based on the general purpose finite element analysis code, ABAQUS. The results of the numerical analysis are very close to experimental results which are obtained by using a rubber composite containing a stiff rubber and a soft rubber.

View full abstract

Effective creep compliance of carbon-fiber-reinforced composites is evaluated for applications of composites at elevated temperatures. A homogenization theory with two-scale asymptotic expansion in the Laplace domain is used to solve viscoelastic problems of composites. Effective constitutive equations and microscopic disturbed displacements are derived from the homogenization theory. A hexagonal array of fibers is employed for the microstructure of the composite and a hexagonal unit cell is placed in the microscopic field to represent a boundary value problem. In numerical calculations, a carbon-fiber-reinforced composite with thermoplastic matrix is considered at the glass transition temperature of the matrix. The matrix is viscoelastic and is represented using the generalized Maxwell model at the glass transition temperature, and fibers are considered as a transversely isotropic elastic medium. The effective creep compliance of the composite is determined by numerically solving a set of equations for macro- and microscopic fields.

View full abstract

An exact matrix formulation for analyzing wave fields generated by harmonic line loads in anisotropic media is presented. In this formulation, a Fourier transform with respect to spatial coordinates is employed. An efficient technique to evaluate the inverse integral is implemented. Using this technique, the inverse integration in one direction is carried out analytically and the displacement is subsequently expressed explicitly as a one-dimensional integration. A quadrature scheme and complex path is then used to evaluate the integration to obtain the displacement in the spatial domain for both pure elastic materials and materials with dissipation. Numerical examples are presented to demonstrate the validity of the present method, and wave fields for the displacement are investigated for isotropic and anisotropic media.

View full abstract

Bio-active ceramics which have the capability for bonding to bone have been developed as one of the most effective implant materials. Because these materials consist of brittle hydroxyapatite, their mechanical reliability and workability are much lower than those of metal. Therefore, hydroxyapatite ceramics are used as coating materials. During or after the coating process, cracking and tearing often occur in the coating layer of the implant. These defects are caused by the residual stress in the vicinity of the coating interface. It is important to evaluate the residual stress in this region. The purpose of work is to present a method for measuring simultaneously and nondestructively three-dimensional distribution of residual stress in both the hydroxyapatite coating layer and the titanium substrate, using polychromatic X-rays. From this method, the steep stress gradient in the coating layer and the increase in tensile residual stress on the surface of the substrate were confirmed.

View full abstract

Elasto-plastic constitutive equations which take into account yield-vertex effects are important in the study of localization instabilities of plastic deformations. However, they have never been discussed thermomechanically. In this paper, a method of deriving the above equations is proposed which is based on the second law of thermodynamics and the principle of maximal entropy production rate. Elastic strain as a strain measure which is conjugate to the objective stress rate is separated from total strain so that the Clausius-Duhem inequality, in which the Gibbs function is introduced as an elastic potential, can be always satisfied. The strain rate and stress rate are expressed by the same objective rate in the rate form of the elastic constitutive equation obtained. The plastic constitutive equation is derived using the principle of maximal dissipation rate. Since this equation is regarded as a flow rule in which the complementary dissipation function assumes the role of a plastic potential, it is indicated that the yield-vertex can exist on the dissipation surface. Furthermore, the spin which should be used in the objective stress rate is selected by taking into account not only usual requirements but also thermomechanical ones.

View full abstract

Uniaxial tension tests under various environmental temperatures are carried out for 5 kinds of polymers: high-density polyethylene(HDPE), poly(vinylidene fluoride)(PVdF), polyoxymethylene(POM), polyamideimide(PAI) and polyether-etherketone(PEEK). As temperature increases, yield stress decreases and yield strain, except in the case of PAI, increases in all of the materials tested. HDPE, PVdF and POM are strongly influenced by environmental temperature, but PAI and PEEK are weakly influenced. The authors previously proposed a spherical model based on intermolecular force(Lennard-Jones type), for understanding the influence of hydrostatic pressure, environmental temperature and strain rate on elastic modulus. In this paper, this model is extended to explain the yield behavior and to propose an experimental equation of yield stress and strain. We found that this equation is useful for describing yield stress under various environmental temperatures.

View full abstract