The elasto-plastic damage behaviors of functionally graded materials (FGM) subjected to thermal loading are analyzed by the finite element method using continuum damage mechanics. Lemaitre's damage model is employed to analyze the damage behavior of a FGM disk subjected to thermal shock and a FGM coating subjected to thermal cycle. The effect of FGM on the thermal damage is discussed through some numerical examples for industrial materials. Numerical results reveal the validity of the present method for the development and the evaluation of new FGMs.
This paper describes an analytical formulation and a numerical solution of the elastic dynamic problems of fluid-saturated porous moderately thick shells of revolution. The equations of motion and relations between the strains and displacements are derived from the Reissner-Naghdi shell theory. As the constitutive relations, the consolidation theory of Biot for models of fluid-solid mixtures is employed. The fundamental equations derived are numerically solved by the finite difference method. As a numerical example, the simply supported cylindrical shell under a semi-sinusoidal internal load with respect to time is analyzed, and the variations of pore pressure, displacements and internal forces with time are discussed.
In this paper, stress wave propagation in transversely isotropic fluid-saturated porous media is studied based on Biot's theory with considering of the fluid viscosity. The analytical expressions for speeds and attenuation of plane waves are obtained and the complex characteristic equations and existence condition for general Rayleigh waves are also derived. The propagation characteristic of plane waves and Rayleigh waves in transversely isotropic fluid-saturated porous media is analyzed numerically. The effects of the fluid viscosity and the anisotropy of solid skeleton on the characteristic of stress wave propagation are discussed in detail.
In our previous study, the micromechanical modeling of an intelligent material containing TiNi fibers was performed and the stress intensity factor KI at the tip of the crack in the material was expressed in terms of the magnitude of the shape memory shrinkage of the fibers and the thermal expansion strain in the material. In this study, the value of KI at the tip of the crack in the TiNi/epoxy material is calculated numerically by using analytical expressions obtained in our first report. As a result, we find that the KI value decreases with increasing shrink strain of the fibers, and this tendency agrees with that of the experimental result obtained by Shimamoto etal.(Trans. Jpn. Soc. Mech. Eng., Vol. 65, No. 634 (1999), pp. 1282-1286). Moreover, there exists an optimal value of the shrink strain of the fibers to make the KI value zero. The change in KI with temperature during the heating process from the reference temperature to the inverse austenitic finishing temperature of TiNi fiber is also consistent with the experimental result. These results can be explained by the changes in the shrink strain, the thermal expansion strain, and the elastic moduli of TiNi fiber with temperature. These results may be useful in designing intelligent materials containing TiNi fibers from the viewpoint of crack closure.
Stress singularities at the bond edge of a bimaterial bonded structure with hourglass-shape and straight sides under an axisymmetric deformation are analyzed. The bonded materials are assumed to be transversely isotropic to the axis of deformation. One of the two materials is piezoelectric and the other one is either a dissimilar piezoelectric or a usual elastic material. The analysis assumes perfect bonding and is based on a general solution consisting of three quasi-harmonic functions. The eigenfunction expansion method is used to determine the singularities. The discussions are given for the difference of the stress singularities between the cases where the electro-mechanical coupling effect is considered or not. Moreover, the difference between the axisymmetric deformation and the plane strain deformation are made clear. Finally, the theoretical results are compared with the numerical ones and good agreement between them is demonstrated.
The plane elasticity solution is presented in this paper for the crack problem of a layered medium. A functionally graded interfacial region is assumed to exist as a distinct nonhomogeneous transitional layer with the exponentially varying elastic property between the dissimilar homogeneous surface layer and the substrate. The surface layer contains a crack perpendicular to the surface. Fourier transforms are used to formulate the problem in terms of a singular integral equation. The main results presented are the variations of the stress intensity factors as functions of geometric and material parameters of the layered medium.
In this study, the interfacial crack-kinking behavior of a bimaterial specimen, which consists of epoxy and aluminum, was investigated. From the magnitudes of the separated J integrals, it is found that the compliant material (epoxy) provides considerably larger fracture energy to the interfacial crack tip. All kinked fractures occurred at loading angle equal to or larger than 120°. This reason was explained by the direction of the global shearing mode. It was found that, for the kinked fractures from their initial crack tips, the average value of the separated J integral for the epoxy sides was close to the fracture toughness of the homogeneous epoxy Jic. Contrary to this, for all interfacial fractures, all values of the separated J integral for the epoxy sides were lower than Jic.
The inverse method applied successfully to several basic structures is extended to estimate dynamic stress intensity-time history for one point bend specimens. The response functions of the specimens are estimated by de-convolving the specimen response measured near the crack tip with the measured impact force. Two methods of deconvolution were used, e. g., a simple statistical method and a CG-FFT iteration method. The ill-posed nature of the deconvolution is removed successfully by the CG-FFT method and then the excellent estimation is obtained.
First, the separated dynamic J integral and the separated dynamic energy release rate useful for dynamic interfacial fracture mechanics are presented. The path independent separated dynamic J integrals have the physical significance of energy flows into an interfacial crack tip from adjacent individual material sides. Second, new definitions of the stress intensity factors for dynamically propagating interface cracks are derived, which are consistent with the dynamic stress intensity factors for cracks in homogeneous materials. Based on this, an explicit relationship between the dynamic J integral and the stress intensity factors is also derived. Then, using this relation, to extract mixed-mode stress intensity factors in dynamic interfacial crack problems, the component separation method is developed. This method is more advantageous than the M1 integral method often used for interfacial crack problems, since the present method requires no auxiliary solution field that is sometimes not possible to construct. Finally, to demonstrate the applicability of the separated dynamic J integral and the component separation method, interfacial cracks subject to impact loading as well as dynamically propagating interfacial cracks are solved using a moving finite element method. Several useful points are elucidated from the numerical simulation results.
The method of arbitrary lines (MAL) constitutes a general dimensional reduction methodology for elliptic boundary value problems (BVP) in arbitrary two- and three-dimensional domains by solving systems of one-dimensional boundary value ordinary differential equations (ODEs). It has been already applied to two-dimensional problem, and the good results have been reported. In this work, we consider the extension of the MAL to three-dimensional elasto-plastic stress analysis. We first give the MAL formulation of three-dimensional elasto-plastic problems. Although the MAL formulation is derived from the principle of three-dimensional increment virtual work as well as the finite element method (FEM), the MAL is different from FEM in that displacement increment and virtual displacement increment are expressed continuous functions along one direction and shape-functions along other two directions. Substituting displacement increment and virtual displacement increment into the principle of three-dimensional increment virtual work, we have a system of ODEs. The three-dimensional elasto-plastic analysis of BGA model, which was a method of the solder joints of electronic component, was carried out. As results, it was confirmed that to solve 3D elasto-plastic problem at the good accuracy was possible by the MAL.
Crush of square hollow columns subjected to dynamic axial loading is numerically studied. The column is thin-walled, and various cross-sectional shapes from a right square to an exact circle are treated, changing the corner radius. For calculation, the public domain version of the dynamic explicit finite element code DYNA3D is utilized. Two modes of buckling take place, i. e., an in-phase bilateral cyclic folding mode like an accordion and an out-of-phase bilateral cyclic folding mode. In the former mode, the crush strength attains a large value and is more advantageous in order to obtain a large capacity of energy absorption. The crush strength becomes greater for a larger corner radius. Hence, surprisingly enough, the circular hollow column (which is lighter than a right square one by 21.5%) attains the greatest crush strength among other cross-sectional shapes (50% or more than the right square column does). It is greater also for a faster impact speed and a thicker column wall. The buckling takes place more easily in the in-phase bilateral cyclic mode when the cross-section is closer to a circle. All circular hollow cylinders analyzed here have buckled in this mode. The impact speed higher than a certain value also leads the in-phase bilateral cyclic mode of buckling. Typical experiments are also carried out to confirm the calculation reliability.
We developed a method for estimating the bonding strength of bonded areas of various sizes. We compared the debonding forces estimated by the stress-singularity-parameters approach (SSPA) with those measured by a shear debonding test of photoresist patterns on Cu substrates. This comparison showed that SSPA cannot be used to estimate the bonding strength of bonded areas of a wide range of sizes. We therefore developed a new method (based on the energy release rate) for estimating the bonding strength. This method uses a finite element approach and places “energy release elements (EREs)” (which mathematically represent the energy release due to debonding) between the two materials. The characteristics of EREs are represented by two parameters determined by two experimental measurements. We used this method to estimate the shear debonding strength of photoresist patterns on Cu substrates and found that the estimated values for the debonding strength agree well with the measured results.
Dynamic creep test and its analysis were performed for Si-Ti-C-O ceramic fiber bonded body under bend loading at 1400°C. Creep displacement under cyclic loading with mean stress σm1=196MPa and stress amplitude σa=49MPa is quite similar to the one under constant static load of σ0=196MPa, while the dynamic creep displacement under loading condition at σm1=245MPa and σa=49MPa is much larger than static creep displacement at σ0=245MPa. SEM observations revealed that the failure of matrix material was caused around the neutral plane of the specimen by cyclic shear stressing in the dynamic creep process at σm1=245MPa and σa=49MPa. Finite element method analysis was performed for the dynamic creep process, where the gradual attenuation of shear modulus G12 with progress of dynamic creep was assumed. The calculation described qualitatively well the dynamic creep deformation behavior of this material. The normal stress distribution of the specimen and the shear stress distribution in the neutral plane along the specimen axis were presented on the basis of the FEM calculation.
A mathematical model is proposed in order to elucidate the mechanism that the fatigue strength of external threads increases by reducing the lead on a thread system such as a bolt and nut. The model is constructed from the concept that a local strain proportional to the reducing degree of the lead, although the local strain is at first produced in the bolt thread farthest from the bearing surface of the nut, is induced in each thread root with an increase of applied load. The fatigue life predicted from the mathematical model shows good agreement with the experimental fatigue life of cadmium-plated external threads with the reduced lead on the material having strength as high as 1270MPa. The model can provide useful suggestions for the design of fasteners for aerospace, which are required to satisfy severe requirements of fatigue strengths and dimensions.
Phase-shifting methods are advantageous for analyzing phases of fringe patterns obtained by interferometry. Conventional phase-shifting methods usually use three or four images obtained by phase-shifting. If only one camera is used for three or four images, the fringe images are recorded with phase-shifting disruption so that the brightness does not change during the camera exposure time. The stopping procedure obstructs the speed of the measurement system. We proposed a new method that takes four images for phase analysis without disrupting phase-shifting. The method is called the integrated phase-shifting method (IPSM), and is suitable for real-time phase analysis. In this method, four images are recorded continuously with full-exposure time during phase-shifting. In this paper, the development of a real-time phase analysis circuit using this theory and an application to nanometer-order displacement distribution measurement of a micro-accelerometer manufactured by micro-machining techniques are shown.