Computer simulations are about to replace experiments in various fields related to dynamic problems, such as crashworthiness of vehicles, vibration of nuclear reactors in earthquake, and ultrasonic wave propagation in cracked solid for nondestructive evaluation. For solving such large scale problems, parallel processing has become one of key technologies. In this paper, a parallel contact algorithm suitable for a domain decomposition technique is proposed, and implemented on a dynamic finite element analysis code based on an explicit time integration scheme. Parallel efficiency of the code is tested through sample analyses on a PC cluster.
In considering mechanical behavior of crystals, it is very important to know the elastic incompatible stresses near the dislocation, which plays an important role in elasto-plastic deformation. The authors proposed a finite element model of an edge dislocation, based on the mathematical model of dislocation. In this paper, a finite element model of an arbitrary inclined edge dislocation is proposed by the use of a discrepancy of displacement, and the stresses around an edge dislocation in an infinite region are obtained and compared with exact solutions. In this analysis, opening mode discrepancy of displacement and shear mode discrepancy of displacement are located along the same line, and the corresponding nodal points are connected with each other. Also, the problem with two edge dislocations is treated. The results coincide with exact ones.
The transient thermoelastic behavior of the functionally graded plate due to a thermal shock with temperature dependent properties is studied in this paper. The development of a micromechanical model for the functionally graded materials is presented and its application to thermoelastic analysis is discussed for the case of the W-Cu functionally graded material for the International Thermonuclear Experimental Reactor divertor plate. The divertor plate is made of a graded layer bonded between a homogeneous substrate and a homogeneous coating, and it is subjected to a cycle of heating and cooling on the coating surface of the material. The thermal and elastic properties of the material are dependent on the temperature and the position. Numerical calculations are carried out, and the results for the transient temperature and thermal stress distributions are displayed graphically.
This paper is concerned with the numerical treatment of one-spatial dimensional thermal and mechanical waves in nonlinear elastic solids subjected to impulsive heating. The formulation of the problem is based on the generalized theory of thermoelasticity proposed by Lord and Shulman. Presented is a set of generalized equations, which govern the propagation of plane, cylindrical, and spherical waves in nonlinear elastic solids. The system of equations is analyzed by the use of characteristics, yielding characteristics, and characteristic equations. Numerical calculations are carried out for the thermal and mechanical waves in nonlinear elastic plates subjected to the impulsive heating, and the results are presented in the graphical form.
In this paper, we describe a new FEM (finite element method)-BEM (boundary element method) analysis of molten metal under alternating currents. Nowadays, it is very important to calculate MHD (magneto-hydrodynamics) flows under an AC (alternating current) magnetic field in order to control the molten metal processing in a furnace by an electromagnetic force. Few previous researchs report on three-dimensional analysis for the circulating molten metal. Therefore, we attempt a three-dimensional calculation with the A-φ method using hybrid FEM-BEM, an improved method over the conventional FEM, and to capture the surface shape that influences the ALE method. The numerical analysis of an electromagnetic fluid using mercury is performed in order to observe the tangled physical parameters of an electromagnetic field in the vessel. To stabilize the meniscus shape, a DC magnetic field is imposed and the shape of the surface is held in three cases.
The point where the front of a 3-D crack intersects a free surface is called “corner point”. The ordinary elastic crack tip stress singularity of rλ is λ=−0.5. However, with regard to the stress singularity at the corner point there are several different theories. This paper concerns the detailed analysis of the stress singularity at the corner point for a through crack and a semi-circular crack under Mode II loading. According to the theories by Benthem and others, not only KII but also KIII has a non-zero value at a corner point which, however, contradicts the stress-free boundary condition of the free surface. The FEM analysis of the present study based on the careful meshing and accurate determination of singularity (λ) answers this paradox on the corner point singularity. The answer is that, although the value of KIII increases as the crack front approaches the corner point, the domain of non-zero value of KIII decreases to an infinitesimal value and accordingly the influence of KIII can be ignored at the corner point. Similarly, the domain of the singular stress field with λ≠−0.5 and λ=−0.6∼−0.5 also decreases as the crack front approaches the corner point. These conclusions should be considered when fracture criterion at a corner point under mixed-mode loadings is used.
In the present study, the relation between the plastic and the elastic stress intensity factors, Kp and Ke, for various V-shaped notch problems is studied by using the finite element analysis. Detailed results for mode I under plane stress and plane strain conditions are investigated. Based on the numerical results, it is found that there is a one-to-one correspondence between Kp and Ke, even when the load is so large that the condition of the small scale yielding is not satisfied. Also, it is found that the values of Kp1-λe/Ke1-λp for various notch problems depend only on the notch opening angle γ and hardening exponent n. This enables one to evaluate the factor Kp for various notch problems without any plastic stress analysis.
A theoretical method for estimating the elastic-plastic stress singularity at the interface edge of bonded power-law materials is proposed, based on the iterative approach developed in this study. It is found that the elastic-plastic stress singularity depends on the bonding angle and the larger hardening exponent of the composed materials. The smaller the hardening exponent is, the stronger the stress singularity becomes. Moreover, the elastic plastic stress singularity disappears when the bonding angle is smaller than 45°. The singularity coincides with that of an interface crack when the bonding angle approaches to 180°. Through the comparison with numerical results obtained by the elastic-plastic boundary element analysis, it is proved that the iterative method proposed in this study is accurate enough and very efficient.
The penetration of a viscous lubricating oil into a three-dimensional surface crack under a rolling contact stress was calculated. The finite element method was applied to solve the Reynolds equation coupled with the elastic deformation of the crack. The process of penetration is roughly the same as in the two-dimensional model. The lubricating oil begin to flow into the crack when the contact pressure passes the crack mouth. The lubricating oil enters the crack tip and increases the stress intensity factor when nondimensional viscosity β=ηvE2/(ap03) is small. The crack is not open when β is large, because the contact pressure passes before the lubricating oil flows into the crack. The critical value of β was calculated. The penetration of the lubricating oil in the three-dimensional model is not easy as compared with the two-dimensional model.
In 1995, the great Hanshin-Awaji earthquake caused a large amount of destruction and structural failures. One example, whose mechanism is not fully clear, is the fracture of a bridge bearing of a Nielsen type bridge that does not occur under the ordinary static or dynamic loading conditions. The fracture probably resulted from very high stress due to an unexpected dynamic mechanism. In this paper, the 3-dimensional dynamic behavior of a Nielsen type bridge was analyzed by assuming a collision between the upper and the lower parts of the bearing, which might have occurred in the great Hanshin-Awaji earthquake. The numerical results show that an impact due to a relative velocity of 5∼6m/s between the upper and the lower parts of the bearing generates a stress sufficient to cause a fracture in the upper bearing. The observed features of the actual fracture surface was also simulated fairly closely.
Stress intensity factors due to surface crack propagation were analyzed by using the influence function method and inherent strain analysis of the residual stress fields caused by welding. The initial residual stress in a plate welded-butt joint was calculated by using inherent strain analysis, and the redistribution of residual stress and the stress intensity factor due to crack propagation were analyzed as changes in the structure's shape. Stress intensity factor was also calculated by using an influence function database. The stress intensity factor in the residual stress fields due to crack propagation obtained by using inherent strain analysis completely agreed with that obtained by using the influence function method. The results of the crack propagation analysis were compared with the experimental results of a fatigue test. It was validated that both the inherent strain analysis and the influence function method were efficient for analyzing stress intensity factors in residual stress fields caused by welding.
Micromechanical modeling of an intelligent material containing TiNi fibers is performed by taking into consideration the existence of crack-bridging fibers given a tensile transformation strain. The total amount of shape memory shrinkage of the fiber corresponds to the transformation strain and this shrinkage strain is replaced with the eigenstrain of the fiber. Moreover, the thermal expansion strain due to the mismatch between the thermal expansion coefficients of a fiber and a matrix is also considered in the model. By analyzing the model, stress and strain fields in the composite, the total potential energy of the system is derived. Moreover, from the resultant total potential energy, the stress intensity factor at the tip of a crack in the composite is derived and expressed successfully in terms of the shrinkage strain of fibers and the thermal expansion strain in the material.
In this study, we analyze a two-dimensional electroelastic problem of an infinite piezoelectric body with two circular piezoelectric inhomogeneities, one of which contains a crack. We formulate the stress intensity factor (SIF) analytically and investigate the effect of interaction between inhomogeneities and a crack on the SIF numerically. We consider that the body is subjected to anti-plane shear mechanical loads and in-plane electrical loads at infinity. The SIF is formulated by regarding the crack as distributed screw dislocation. The distribution function of screw dislocation is obtained as the solution of a singular integral equation of the first kind. Some numerical results are shown to investigate the effect of the interaction between two inmonogeneities and the crack on the SIF.
In this paper, we study a two-dimensional electroelastic problem of two interface cracks between matrix and an inhomogeneity subjected to anti-plane shear stress and in-plane electric displacement. We formulate the stress intensity factor (SIF) and electric displacement intensity factor (EDIF) analytically. The SIF and EDIF are formulated by the potential functions representing the electroelastic field. These potential functions are obtained as the solutions of the Hilbert problems. The non-dimensional SIF and EDIF can be expressed by the product of two simple functions: one is the function of the non-dimensional lengths of the cracks, the other is the function of the non-dimensional material properties and the loads at infinity. The behavior of these functions, which characterize the effects of crack lengths, material properties and the loads at infinity on the SIF and EDIF, is examined for some cases.
Electronic devices, which are composed of materials of different thermal expansion coefficients, are subject to thermal deformation because of thermal cycling, and the strain induced by mismatching due to deformation leads to fatigue failure. To avoid strain concentration, the finite element method plays an important role in packaging design. However, non-linear behavior due to different thermal expansion coefficients and creep behavior of the solder bump make accurate prediction of failure difficult. Consequently, it is essential to estimate the results of analysis obtained by the finite element method. In this study, we measure real-time thermal displacement and strain distribution under thermal cyclic loading test by the Fourier transform Moiré method with the carrier pattern technique, and then extract creep behavior, residual strain, and also the effect of multicyclic loading, which are not predicted by the finite element method. To evaluate not only the behavior of the cross section but also that of whole devices, we measure out-of-plane displacement by means of the Moiré interferometry.
BGA (ball-grid array) is an advanced electronic packaging technology that has increasingly become more important and demanding in microelectronic industry. However, no effective technique is available to inspect the performances of the welding points and its co-planarity. The moiré fringe method is often employed to measure the three-dimensional (3D) shape of the welding spot on BGA, and a high-resolution CCD camera is utilised to capture the deformation stripe image. In order to gain high measuring accuracy, a frequency-shift moiré fringe technique is proposed in this paper, in which three light-sources are deployed to create the fringe. The system parameters are designed to ensure the BGA ball height within exactly one grade moiré fringe. By using zero-maximum equation transformation, the measuring range can be segregated into eight subsets. Equal-step interpolation and indexed table approaches are also introduced to greatly improve the measurement speed, so it may be useful for industrial on-line application. Finally, the predicted results based on the simulated images are presented, demonstrating that its measuring accuracy can be achieved to 5 micron.
The anisotropies of sheet metals originate from the texture developed by a cold rolling process. In the texture, the crystal grains assume a partial direction, and so the strength of the texture is different from that of the surrounding material. When the sheet metals are deformed with changes of the strain path, the difference in strength produces a new texture and defines a new anisotropic principal axis. Therefore, it is supposed that the principal axis of anisotropies does not behave like the material fiber printed on the sheet metals. To confirm the above assumption, a measuring method of revolution angles of principal axes is proposed by using a laser speckle surface strain meter. The revolution angle is measured by investigating the distribution of r-values with respect to the tensile directions. Finally, a dynamical revolution model of the principal axes is derived and its parameters are identified.
This paper describes an experimental investigation on the ultrasonic nondestructive evaluation of small cracks in the size range of 0.25 to 3mm. The cracks treated are 0.1mm-wide EDM slits (as open cracks) and closed fatigue cracks situated vertically on the back surface of the stainless steel specimens. In order to develop a method for the enhancement of sensitivity of ultrasonic evaluation of small cracks, firstly, the investigating feature and capability of usual ultrasonic techniques, specially, the normal incidence, small-angle incidence and large-angle incidence techniques of longitudinal wave and the large-angle shear wave beam technique are examined based on the open cracks. Then, the effect of incident beam angle of the longitudinal as well as the shear waves on the crack corner echo response is investigated by using a single probe transducer. Finally, the principle of a new angle-beam approach is proposed, where the use of shear wave with incidence around 50° upon the specimen back wall is emphasized. Highly sensitive feature of the present angle-beam approach is realized, especially for small closed cracks, when compared with the above techniques.
In this paper, as a new measurement method to estimate the structure change of weld metal, the simplified ultrasonic CT system, which uses the information of three directions, that is, 90°, +45° and −45° about inspection plane is developed. Use of simplified ultrasonic CT system has two merits: Firstly, the measurement time is very short comparing with general CT. Secondly, it can detect sensitively very infinitesimal defect in vertical or slant direction about inspection plane because the obtained image is not C scan image but CT image calculated from three directions. From these merits, this method can be considered as a very effective method for the evaluation of material condition. In order to compare the performance of simplified ultrasonic CT, the CT image obtained from several specimens with several simple defects was compared with the D scan image obtained by TOFD (Time of Flight Diffraction) method. We can see simple defects more clearly by new proposed method. Experimental results on several kinds of specimen, having welded joint by electron beam welding, welded joint by electron beam welding and fatigue crack showed that the obtained C scan or CT image has better resolution than the D scan image by TOFD method and shows similar image to actual shape.
To obtain fundamental data on superplasticity of fine-grained α+β titanium alloys obtained through protium treatment, superplasticity tensile tests were carried out in vacuum. Changes in the microstructure after the tensile test were observed using an optical and scanning electron microscope. The experimental results are as follows: A fine-grained material having a grain size of 1µm to 3µm exhibits a significant elongation of over 8000% at a testing temperature of 1123K and a strain rate of 1×10-3s-1. The m-value of the fine-grained material is much higher than that of a coarse-grained material, with the maximum m-values being 0.80 and 0.64, respectively. These results indicate that it is not easy for necking to occur in fine-grained material. In the observation of the structure after the superplastic-tensile test, a coarse-grained material did not exhibit grain growth, but the fine-grained material did.
The inelastic behavior of shape memory alloy under multi-axial loading conditions was investigated by applying combined loads of axial force and torque to the thin-walled tube specimen made of Cu-based shape memory alloy. In this paper, unique behaviors revealed by the experiments which are not observed in the uniaxial experiments, are shown and discussed. These include the path dependency created by the change in microstructure (especially when variants operate simultaneously). The results obtained here manifest the significance of constitutive equations formulated on the basis of the semi-microscopic approach in the 1st paper.
In the printed wiring board manufacturing sector, methods have been developed to improve the circuit packaging density. The multi-layer printed wiring board manufacturing process is receiving particular attention. In the current manufacture of these boards, the method frequently used is to laminate the core with insulating resin, namely a build-up process. Etching is generally used to form the holes connecting the circuits of these boards. However, a problem has emerged in that the strength of the substrate decreases due to the insulating resin part as the multi-layers are progressively formed. Thus, it becomes necessary to use FRP for the insulation layer part. Since it is very difficult to etch composites, lasers have been proposed for a new way to drill holes in such materials. By appropriate adjustment of the laser penetration energy, the holes are drilled only in the insulation part, and a technique is proposed to stop the holes using the copper foil forming the circuit. AFRP has been considered a suitable FRP for such laser processing. In the present study, attempts were made to experimentally produce multi-layer boards using AFRP and GFRP for the build-up insulation layer, and the characteristics of blind via holes drilling with a small power laser were investigated.
To increase the fatigue limit of the Carburized gears, the following five techniques need to be developed: 1) Reduce abnormal surface structure. 2) Obtain a fine grain size. 3) Decrease the retained Austenite structure. 4) Increase hardness under the surface. 5) Improve the residual stress distribution under the surface. For this purpose, the authors conducted a study by using DSG1 steel gears on the new compound surface refining method consisting of Vacuum Carburizing, Contour Induction Hardening and Double Shot Peening. The result of the study showed that the fatigue limit of the gears processed by the new compound surface refining method achieved 150% better than that of the single processed Vacuum Carburized gears. Furthermore, the authors analyzed the correlation between the fatigue limit and the yield stress, the maximum compressive residual stress & the mean grain size of gears systematically, the consequence of which was the fatigue limit given with an equation.
Shape optimization for two types of specimens in opening mode and a cantilevered beam in mixed mode was accomplished by the linear elastic fracture mechanics and the growth-strain method. Linear elastic fracture mechanics was used to evaluate the stress intensity factors and fatigue lives. And the growth-strain method was used to optimize a shape. From the results, it was found that the optimized shapes of two types of specimens and a cantilevered beam greatly prolong their fatigue lives, and the growth-strain method is an appropriate technique for shape optimization of a structure having a crack.
In this paper, a logarithmic expression to describe the residual strength degradation process is developed in order to fatigue test results for normalized carbon steel. The definition and expression of fatigue damage due to symmetrical stress with a constant amplitude are also given. The expression of fatigue damage can also explain the nonlinear properties of fatigue damage. Furthermore, the fatigue damage of structures under random stress is analyzed, and an iterative formula to describe the fatigue damage process is deduced. Finally, an approximate method for evaluating the fatigue life of structures under repeated random stress blocking is presented through various calculation examples.
This paper presents the experimental and theoretical results of the effect of mean curvature on the response and collapse of thin-walled tubes subjected to cyclic bending. To highlight the influence of mean curvature effect, three different curvature ratios (minimum curvature/maximum curvature) were experimentally investigated in this study. It was found that the response and collapse of thin-walled tubes subjected to cyclic bending are strongly influenced by the magnitude of the mean curvature. In addition, the ordinary differential constitutive equations of endochronic theory were used to investigate the response of thin-walled tube subjected to cyclic bending. Furthermore, a theoretical formulation was proposed so that it can be used for simulating the relationship among the controlled curvature range, curvature ratio and the number of cycles to produce buckling for thin-walled tubes subjected to cyclic bending. The theoretical simulations were compared with the experimental tested data. Good agreement between the experimental and theoretical results has been achieved.
This paper presents a method for quantifying probability of brittle fracture in low alloy steels. The proposed method shows how the probability of brittle fracture varies with stress intensity factor, temperature, deformation characteristics and microstructural parameters of low-alloyed steel. Application of this method on Ni-Cr steel demonstrated very good agreement of predicted temperature dependence of scatter in brittle fracture toughness with experimental results. The method enables also to calculate characteristic distance as a radial dimension from the crack tip where microcrack initiation is most probable. The characteristic distance of investigated Ni-Cr steel was found to decrease with increasing temperature. Microstructural mechanisms of initiation and propagation of brittle fracture were identified from results of fractography analysis. The proposed procedure represents a foundation for systematic control of relationship between stress-strain behaviors, toughness and reliability of steel engineering parts.