A simple and physically meaningful analytical model is developed for the evaluation of the interfacial stresses in a simple lap shear joint (LSJ). The emphasis is on the “peeling” stress, i.e., the stress acting in the through-thickness direction of the joint. The model is a modification and an extension of the model developed earlier for the shearing stress. Based on the developed model, we were able to explain a paradoxical situation due to the “transverse groove effect” (TGE). This effect has been detected by one of the authors of this paper (Reinikainen) from the finite-element-analysis (FEA) computations: deep enough transverse grooves deliberately introduced in the LSJ adherends (“pins”) resulted in an appreciable reduction in the magnitude, and in a significant improvement in the uniformity, of the distribution of the interfacial shearing stress. It was determined that the stress relief due to the grooves was caused by the favorable effect of the increased interfacial compliance, while the adverse effect of the increased axial compliance of the pins (also due the grooves) was relatively small in a particular LSJ design and was suppressed by the favorable impact of the TGE. We show that the peeling stress in the LSJ is considerably lower than the interfacial shearing stress and that the TGE is even stronger for the peeling stress than for the shearing stress. This is because the grooves affect the peeling stress not only directly, through the increased interfacial compliance, but also indirectly, through the lower gradient of the interfacial shearing stress in the longitudinal direction. We show that this gradient can be reduced considerably if the interfacial compliance is increased, especially in a small size joint. We would like to point out that, although reasonably satisfactory agreement between the analytical and the finite-element analysis (FEA) predictions was obtained, the objective of our analysis was not so much to develop a more or less accurate analytical or a FEA model, but rather to demonstrate that the peeling stress, whatever technique is employed to evaluate it, can be reduced considerably by introducing the transverse grooves. The results of this article can be used in the analyses and design of LSJs, both in electronic packaging and beyond.

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Structural analysis problems are traditionally solved using the Finite Element Method (FEM). However, when the structure of interest contains discontinuities such as cracks or re-entrant corners, a large number of elements are required to accurately reproduce the stress characteristics in the region of the discontinuities. As a result, the FEM method requires a large storage space and has a slow convergence speed. It has been shown that the Infinite Element Method (IEM) overcomes these limitations and provides a feasible means of solving various types of elasticity and singularity problems. Previous studies have generally focused on the use of IEM formulations based on low-order elements (2×2). By contrast, this study develops a high-order (3×3) IEM formulation. The solutions obtained using the proposed IEM method for various 2D elasto-static problems are compared with the results obtained using the traditional low-order IEM method and the analytical solutions presented in the literature. It is shown that the results obtained using the proposed method are more accurate than those obtained using the low-order IEM method and are in excellent agreement with the analytical solutions.

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When an isotropic and homogeneous solid sphere and/or infinitely long solid cylinder are suddenly subjected to an instantaneous uniform heating, a stress wave occurs at the moment thermal impact is applied. The stress wave proceeds radially inward to the center of a sphere and/or cylinder. The wave may accumulate at the center and give rise to very large stress magnitudes, even though the initial thermal stress is relatively small. This phenomenon is called the stress-focusing effect. In this study, the stress focusing effect in a solid sphere and solid cylinder under instantaneous uniform heating at the free surface is studied on the basis of the generalized thermoelastic theories, that is, the Lord-Shulman (L-S) and the Green-Lindsay (G-L) theories. The combined governing equations of both theories are solved by the numerical inversion of Laplace transform. Calculations have been performed to exhibit the radial distributions and time variations of the radial and hoop thermal stresses on the basis of the L-S theory. The effects of the thermomechanical coupling and the relaxation time on the stress focusing phenomena as well as the singularity of stresses are discussed.

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An analysis is carried out to investigate the dynamic characteristics of a rotating, thermally loaded circular saw that undergoes tensioning over a double annular domain. By using the plate bending theory, the governing equations for the in-plane behavior during rotation and under thermal load and plastic strain and those for the resulting out-of-plane behavior are derived. Then, the solution of in-plane forces is obtained and the modal analysis is carried out. The in-plane forces and natural frequencies are calculated numerically to investigate their dependence on tensioning conditions and to find suitable tensioning conditions for the stable operation of the saw.

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This paper is concerned with the theoretical treatment of transient thermoelastic problem involving a multilayered hollow cylinder with piecewise power law nonhomogeneity due to uniform heat supply. The thermal and thermoelastic constants of each layer are expressed as power functions of the radial coordinate, and their values continue on the interfaces. We obtain the exact solution for the one-dimensional temperature change in a transient state, and thermoelastic response under the state of plane strain. Some numerical results for the temperature change, the displacement and the stress distributions are shown in figures.

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In this study, the residual stresses in high-density polyethylene (HDPE) and a fiber reinforced polyethylene was measured using an x-ray stress measurement technique. There have been few reports published of residual stress investigations in polymeric materials by x-ray stress measurements based on conventional x-ray reflection methods. There are two problems associated with this measurement. Firstly, the diffraction peaks of the polymer appear in the low 2θ angle region and therefore the measurement accuracy for strains reduces. Secondly, the low 2θ angle region makes it extremely difficult to use the sin²ψ method. In the present study we tried to use a transmission method for measuring the residual stress in HDPE samples to resolve these problems. The HDPE sample is shaped into thin sheets which have the three kinds of crystallinity degrees. The measured data is fitted with a good linear regression line in a 2θ-sin²ψ diagram and the gradient of the regression line corresponded to the applied stress. On the other hand, the results of the residual stress measurement are deeply associated with degrees of the crystallinity in the HDPE material. The quantitative estimation of crystallinity degrees in the HDPE material was accomplished by a sink-float method. The residual stress distributions were discussed between micro-residual stresses in the crystal phase of HDPE with the amorphous phase of it. Finally, x-ray elastic constant (XEC) of HDPE was estimated and the residual stresses in the fiber reinforced polyethylene was also measured by use of this XEC parameter.

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Propagation characteristics of a flexural wave in a thin plate which surfaces are in imperfect contact with solid bodies are examined theoretically as well as numerically. To this purpose, a nonlinear interface model of solid-solid contact is incorporated in the Mindlin plate theory. The governing differential equations are derived for a plate in contact with rigid bodies on both surfaces, and the dispersion relation for infinitesimal amplitudes is obtained theoretically. The derived equations are solved by the finite difference method to examine the propagation of a flexural wave packet. The numerical results show that the interfacial stiffnesses influence the velocity and the broadening of the propagating wave packet, and the contact nonlinearity brings about harmonic generation. It is discussed how these features are influenced by the linear and nonlinear interface parameters, the wave amplitude and the propagation distance.

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Low pressure die casting is defined as a net shape casting technology in which the molten metal is injected at high speeds and pressure into a metallic die. The low pressure die casting process plays an increasingly important role in the foundry industry as a low-cost and high-efficiency precision forming technique. In the low pressure die casting process is that the permanent die and filling systems are placed over the furnace containing the molten alloy. The filling of the cavity is obtained by forcing the molten metal, by means of a pressurized gas, to rise into a ceramic tube having protuberance, which connects the die to the furnace. The ceramics tube, called stalk, has high temperature resistance and high corrosion resistance. However, attention should be paid to the thermal stress when the stalk having protuberance is dipped into the molten aluminum. It is important to reduce the risk of fracture that may happen due to the thermal stresses. In this paper, thermo-fluid analysis is performed to calculate surface heat transfer coefficient. The finite element method is applied to calculate the thermal stresses when the stalk having protuberance is dipped into the crucible with varying dipping speeds. It is found that the stalk with or without protuberance should be dipped into the crucible slowly to reduce the thermal stress.

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Coupled electrical-thermal and thermo-elastic-plastic analysis were performed to analyze the transient thermal and mechanical behaviors of resistance spot welding (RSW) process of the mild steel sheet metals with unequal thickness. The thermal histories of the whole process and temperature distributions in the sheet metals were obtained through the electrical-thermal analysis. Different from the temperature field distribution of RSW with the same thickness mild steel sheet metals, the research showed that the center of the weld nugget of RSW with unequal thickness mild steel sheets leaned to the thicker sheet. It accords with the practical RSW process of the sheet metals with unequal thickness. The residual plastic strain distributions and the deformations of the sheets after welding were obtained through the thermo-elastic-plastic analyses. Due to the asymmetry of the temperature field distribution in the sheet metals with unequal thickness, the edges of the two mild steel sheets warped to the thinner one. The warpage deformation of the two sheets with the thickness 1.0mm and 1.5mm was 5µm after RSW. Detailed studies showed that the warpage deformation of the asymmetric sheet structure was resulted from the changed residual plastic strain.

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This article presents the analysis of functionally graded hollow circular cylinders with finite length under axisymmetric dynamic loads. It is assumed that the functionally graded cylinder is comprised of metal-phase and ceramic-phase whereas material properties are graded in the thickness direction of the cylinder according to power law distribution. Two-dimensional finite element method in conjunction with the Newmark method is used to solve the system of time-dependent coupled equations that govern the dynamic responses. By introducing especial elements, it is possible to distribute the material properties through the thickness of cylinder exactly according to the power law distribution. Dynamic loads applied on the cylinder are axisymmetric in the hoop direction and can vary in the radial and axial directions. As examples, the transient responses of functionally graded cylinders which are excited in radial direction by increasingly and suddenly internal pressure and line load are calculated, and the characteristics of waves are discussed. The results in the present study are obtained for thick cylinder and cylindrical shell and compared with the results for isotropic cylinders.

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Janssen's bin effect has a great impact to a wide range of engineering applications and theoretical developments which relate to granular materials. The problem of storage silo under uniform vertical pressure exerting on horizontal cross section was investigated in two-dimensional system of equilibrium. Two choices of vertical plane where a ratio of radial stress to normal stress is constant are considered based on Janssen's approach as well as Jaky's approach. Exact stress solutions based on both approaches are generalized in cylindrical coordinates and are validated with boundary conditions at the top layer and at the great depth of silo. Despite of similar solutions obtained at the great depth, it was found that a constant coefficient of lateral pressure must be applied to the center line as suggested by Jaky, implying storage silo is stable in at-rest state. Then, the arch shapes formation in granular materials stored in silo was analyzed by quasi-statics under Jaky's approach. It was found that stacks of arch appear in variable shapes for different depths but tend to curve like catenary shape at the great depth.

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This paper is concerned with theoretical treatment of transient thermal stress problem involving a laminated composite hollow sphere with an interlayer of functionally graded material. The thermal and thermoelastic constants of the interlayer are expressed as power function of the radial coordinate variable. We obtain the exact solution for the one-dimensional temperature change, and thermal stresses of a hollow sphere. The numerical calculations are carried out for functionally graded materials composed of alumina and aluminum alloy. Some numerical results for the temperature change, the displacement and the stress distributions are shown. Furthermore, the influence of the thickness of the interlayer is investigated.

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Linear and nonlinear stress propagations in the problem of two-dimensional symmetrical sand pile were investigated. The hyperbolic-type differential equations were formulated under the criterion of self-weight loading. This study shows that the admissible stress solution can be obtained from a wave-like equation by combining the differential equilibrium equations and the local stress conditions with the boundary conditions. Unlike linear stress propagation which appears in straight line, nonlinear stress propagation appears in smooth curves of principal stress directions which are regarded as nests of major and minor arches formed in granular media. The spatial distribution of safety factor against sliding under each closure is also presented and discussed.

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In this paper, the evaluation of the strength of the VGCF/Aluminum composites which have high thermal conductivity is reported. VGCF (Vapor Growth Carbon Fiber) is a kind of the Carbon nanotube (CNT) which has very high thermal conductivity as well as CNT. The composites are made by spark plasma sintering. The stress-strain curves of the composites are obtained by the tensile tests and show that the composites have brittle behavior. The brittleness of the composites increases with increase in the volume fraction of VGCF. A numerical simulation based on the micromechanics is conducted to estimate nonlinear behavior in the elastic deformation and plastic deformation of the stress-strain relations of the composites. The theories of Eshelby, Mori-Tanaka, Weibull, and Ramberg-Osgood are employed for the numerical simulation. The simulations give some information of the microstructural change in the composite related to the volume fraction of VGCF.

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The interaction problem of solid-fluid systems can be simulated by using unified constitutive models. One such model is the three-element solid model and it is useful for analyzing the dynamics concerning the deformation of the interaction problem. The model is also applied to analyze vibration absorption problems in systems. In this study, the dynamics of a solid-fluid system is numerically analyzed to investigate the absorption problem by using the three-element solid model. The monolithic approach of FEM using the model is applied to simulate the vibration phenomena of an elastic vessel filled with a viscous fluid. The FEM using the three-element solid model is formulated by the dynamic explicit method that is digitized by the central difference method in its time scale. Here, the behavior of the fluid is represented by neglecting the Young's modulus in the constitutive model. Some material properties are applied to represent the behavior of the vessel and the fluid, and the simulated results are evaluated based on the response variation of the power spectral density for design sensitivity. Then it is known that the dominant factor of the absorber can be analyzed by the monolithic approach of FEM using the three-element solid model. An absorber system based on the analysis of the interaction problem can be optimized by tuning its eigenfrequency.

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In stress-strain relationship on the compression process of low-density porous materials, nonlinear deformation is observed with the plateau region where much strain is occurred without stress increasing. This phenomena is useful to design the shock absorber in various machines,
however it also causes difficulties in the deformation analysis of the materials because of its nonlinearities. In this paper, some types of uniaxial compression testings are conducted for inspecting the nonlinear-deformation behavior of the materials in compression process. Here, we use a kind of polystyrene foam as a typical porous material with closed cellular structure. In the results of uniaxial compression testings with some constant rates, it is shown that the plateau stress, which is the stress level of the plateau region, has the strain-rate dependency. In the compression testing which transmits compression rates for the mechanical inspection of the dependency, it is revealed that the dependency relates to the behavior of well-known overstress phenomena. Therefore, the viscoplastic constitutive equation presented by Perzyna is adopted to simulate the uniaxial compression process for the representation of the dependency. Compared results of testings and simulation, it is indicated that the overstress phenomenon in the compression process of the material can be simulated by using the viscoplastic constitutive equation, and this technique has the ability to inspect the dynamic deformation process of the machines in which are implanted the materials.

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Effect of solution treatment temperature on trigger stress for stress induced martensitic transformation (SIMT) in Ti-10V-2Fe-3Al alloy has been investigated. The Ti-10V-2Fe-3Al tensile specimens were solution treated at 700-900°C and quenched to room temperature in water. All specimens, except the one solution treated at 700°C, experienced the SIMT when subjected to tensile deformation. The trigger stress was observed to initially decrease with the solution temperature increasing from 720°C to 760°C. However, it increased with the temperature increasing from 760°C to 900°C. Optical microstructure shows that with increasing solution temperature from 700°C to 740°C, β grain size of Ti-1023 alloy kept invariable. However, recrystallization was observed when solution treated at 760°C. The recrystallized β grains grew larger and larger with increasing solution treatment temperature from 760°C to 900°C. In addition, the volume fraction of primary alpha phase (α_p) always decreased with increasing ST temperature from 700°C to 780°C. The microstructure was composed of only β single phase when solution treated from 830°C to 900°C. Energy dispersive spectrometry (EDS) analysis indicates that the molybdenum equivalency (Mo_eq) of β matrix steeply decreased initially as solution temperature increased from 700 °C to 760°C. However, it almost kept invariable with solution treatment temperature increasing from 760°C to 900°C. This evolution in trigger stress was attributed to the variations of volume fraction of primary α phase, chemical composition of β phase and the β grain size with different solution treatment temperatures.

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In order to develop the rotary driving element with SMA thin strip, the torsional deformation and fatigue properties of a TiNi SMA thin strip were investigated. The results obtained are summarized as follows. (1) In the SMA thin strip subjected to torsion, the MT appears along the edge of the strip due to elongation of the edge of the strip and grows to the central part. (2) The number of cycles to failure decreases with an increase in the maximum angle of twist in torsion fatigue. The fatigue life in pulsating torsion is longer than that in alternating torsion by five times. The fatigue limit exists in a certain value of disspated work of the strip in each cycle. (3) Based on the two-way motion of a lifting model by using two kinds of SMA thin strip, it is confirmed that the two-way driving element with a small and simple mechanism can be developed by using the SMA thin strips.

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The propagation of transverse surface waves in a functionally graded material carrying a piezoelectric layer is investigated analytically. The material properties in the substrate change gradually with the depth coordinate. We here assume that all material properties of the substrate have the same exponential function distribution along the depth direction. The dispersion equations relating phase velocity to the material gradient in the substrate for the existence of the waves are obtained in a simple mathematic form for class 6mm piezoelectric materials. It is demonstrated that the material gradient in the elastic substrate significantly affects the phase velocity and cut-off frequency of long waves but has only negligible effects on short waves. The effects of the material gradient on the penetration depth and electromechanical coupling factor, which are two parameters of practical interest, are also calculated and plotted. The significant influence of the material gradient on the wave propagation behavior provides a potential factor for designing acoustic wave devices.

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This research is about improvement of the diagnostic accuracy of the fatigue crack monitoring via the statistical diagnostic method. Our research group proposes an unsupervised damage diagnostic method named SI-F method which diagnoses the damage from detecting the change of correlation between sensors caused by the initiation or propagation of the damage via the statistical evaluation. By the method, correlation between sensors is identified by using the response surface and the change of them is statistically investigated with the F-test. To identify the crack length by the method, identification about the relation between the crack length and the F₀ statistic is required. Then in this research, to evaluate effect of the regression error, the noise magnitude and the fluctuation of the external force to the relation, numerical simulation was conducted. For the simulation, two sets of data, one with constant load and one with variable load, are generated and compared. And the applicability of the result of the simulation is experimentally investigated. Finally, the results indicate that the F₀ affected by the regression error and the noise magnitude but not affected by the external force.

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To evaluate the crash safety of automobiles, various collision tests are performed by the auto industry. In the offset frontal collision test and the side collision test, the target is an aluminum honeycomb material which has thinning cell walls. In this study, based on the analyses of the shock absorption mechanism, a new crushing strength formula is proposed. First, load-displacement curves obtained from compression tests in quasi-static condition showed an almost linear relation between a thinning rate of cell walls and a crushing strength. Second, based on Wierzbicki's theory, a new formula was proposed, which can estimate a crushing strength of a honeycomb material with thinning wall. In addition, a correcting equation which considered an elastic deformation was also proposed. Third, parametric analyses were carried out with a FE model which can simulate a delamination between cell walls. The results obtained from the theory and FEM almost corresponded to each other for a wide range of the thinning rate. Fourth, impact tests were carried out, in which the weight was dropped freely at the speed used for the automobile tests. Those results almost agreed well with the sum of the theoretical crush strength and the inside air pressure.

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In this paper, an analytical method is presented to investigate dynamic characteristics in a functionally graded thick hollow cylinder under thermal shock loading. Thermo-mechanical properties of functionally graded (FG) thick hollow cylinder are assumed to be temperature independent and vary continuously in the radial direction. Dynamic thermo-elastic equation of the problem is analytically solved by employing the Laplace transform and series solution. The dynamic thermo-elastic stresses in a functionally graded thick hollow cylinder subjected to axisymmetric thermal shock loading are obtained and presented in closed forms at Laplace domain. The results are obtained in time domain using the fast Laplace inverse transform method. The dynamic behaviors of thermo-elastic stresses are illustrated and discussed for various grading patterns of thermo-mechanical properties in several points across the thickness of FG cylinder and cylinder thickness parameter. The presented analytical method furnishes a ground to study the time histories of radial and hoop stresses in FG cylinders with different thickness and various exponents of volume fraction. The presented results show good agreement with published data in previous literatures.

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When underwater vehicle moves at high speed, the local cavity is formed due to the drop of pressure. While the vehicle crossing the water free surface, the local cavity will collapse, and the water around the cavity will impact the hull of vehicle severely, causing dramatically change of pressure and posing a great challenge to the vehicle structure. Considering the interaction of water, water vapor and air, the simulation of the cavity collapse procedure during the vehicle crossing water free surface has been studied by a viscous flow solver with homogeneous multiphase flow model and modified Rayleigh-Plesset equations. And the structure response under the fluid load has been also calculated, considering the interaction between fluid and structure.

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This paper presents experimental investigations and computational analyses on the elastic moduli of aluminum alloy foams under compressive and tensile loading and flexural vibration conditions. Experimental investigations confirm that the flexural moduli are significantly greater than the corresponding compressive/tensile Young’s moduli. Our analyses based on experimental results suggest this to be due to the difference in cell deformation mechanisms between uniaxial loading and flexural vibration conditions. Two dimensional finite element models with square-cell structure are proposed to clarify these phenomena. Their elastic moduli and cell-deformation mechanism under compression loading and flexural vibration conditions are observed. The results successfully clarify the effect of cell-edge bending in the discrepancy in stiffness.

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