Recently, some practical numerical analyses using simple programming process of Excel have been reported. In the analysis, each cell of the spreadsheet can be regarded as a nodal point, and calculations are performed by using equations written in those cells. Accordingly, a concrete image corresponding to the physical model can be drawn on the spreadsheet, and by doing classification based on colouring boundary and interior cells, writing and debugging are visually conducted with ease. In the present study, as an application of the useful method to thermal analysis on electronic equipment, visualization of programming and calculation processes by thermal network method have been shown by using the concrete example of a housing heated by solar radiation.

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A synchrotron radiation X-ray microtomography system called SP-μCT with a spatial resolution of about 1μm has been developed in SPring-8. Our research group first applied SP-μCT to the nondestructive evaluation of phase growth and fatigue crack propagation due to thermal cyclic loading in flip chip solder micro-bumps. The obtained CT images enabled us to evaluate the lifetime of the bumps to the initiation of fatigue cracks by estimating the increase in phase growth parameter. Additionally, a refraction-contrast imaging technique was used to visualize the crack propagation process of the fatigue cracks, and then the propagation lifetime was also estimated precisely. These results show the possibility that nondestructive inspection by synchrotron radiation X-ray microtomography system can be useful for the clarification of fatigue mechanism and the evaluation of fatigue lifetime in micro-joints.

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We developed a method for evaluating the life of solder joints for an electronic package with non-solder-mask-defined (NSMD) solder pads. Generally, the thermal-cycling life of a package with NSMD pads is longer than that of a package with solder-mask-defined (SMD) pads, which are usually used in packages. However, the fractural mechanism of joints on NSMD pads has not been sufficiently investigated. Therefore, we conducted mechanical fatigue tests on the joints of NSMD pads. We found that the crack propagation behavior in NSMD joints is different from that in SMD, and found that the difference of that behavior causes the life span of NSMD joints to be longer than that of SMD. In addition, we found that the life of a package with NSMD pads can be predicted from the strain in the solder bumps that is analyzed by using a finite element method, which compares the relationships between the strain and life span in the mechanical test data, although the relationship between the strain and life in NSMD joints is different from that in SMD.

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This paper presents the assessment of thermal fatigue life scatter of solder joints for chip components. Crack path simulation was carried out by using the finite element method. Fatigue life was evaluated based on Manson-Coffin's law and Miner's rule. Analysis was designed by using an orthogonal table and the response surface methodology was used to demonstrate the sensitivity analysis. The case study to evaluate the worst and best values of fatigue lives shows the large difference in fatigue life. Asymmetrical solder joints have the larger dispersion of fatigue life because the chip component has two solder joints influencing on each other. It means that the interaction between both solder joints affects the dispersion of thermal fatigue life.

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A new nondestructive inspection method for detecting delaminated bump joints was proposed by measuring local surface deformation of a chip in area-arrayed flip chip structures. The local deformation of a chip appears because of the mismatch of coefficient of thermal expansion among structural materials. Both lack and delamination of a bump change this local deformation drastically. Irregular bump joints can be detected easily by measuring the change of amplitude and period of this local deformation. In this paper, signal processing methods for minimizing the errors caused by various noises are discussed using a finite element method to improve the accuracy of this inspection method. Finally, a nondestructive inspection system that consists of the developed algorithm for defect detection and a laser measurement unit was developed for the practical inspection.

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The change of the electronic performance of NMOS transistors caused by mechanical stress was measured by applying a four-point bending method. The change rate of the transconductance of NMOS transistors increased to about 15%/100-MPa by decreasing the gate length from 400nm to 150nm. In addition, the local residual stress in the stacked chips mounted by a flip chip technology was measured by utilizing piezoresistive stress sensors with 2-μm long gauges. The amplitude of the residual stress in the top chip was almost constant of about 220MPa regardless of the bottom bump alignment. On the other hand, the amplitude of the residual stress in the bottom chip decreased to about 80MPa depending on the relative position of bumps between the top and bottom chips.

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This paper presents a fundamental method predicting the interfacial strength between a silicon and a resin with micro scale bonding structure. Scanning electron microscopy (SEM) observation of the interface with the application of mechanical force was carried out. The interface between the silicon and the resin consists of micro-scale bonding structures. Finite Element Analysis was performed to evaluate interfacial strength between the silicon and the resin. Interfacial bonding structures affect the stress singularity field near the edge of interface. By removing elements which satisfy the failure criteria, interfacial strength was evaluated for tensile and three point bending tests. The predicted critical force for the initiation of interfacial crack show good agreement with experimental results.

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Alumina's spray coating is material including a lot of pores (cracks) and cracks interference exists in the alumina's spray coating, therefore the crack's interference leads to decrease the fracture strength. There are some reports to analyze by using the elastic analysis for two or more cracks. Moreover, there are some standards about union condition of the cracks. However in ceramics including alumina, the study of quantifying an internal spread of the crack when interfering and presuming static fracture strength with judgment of the crack interference after the stable crack propagation is hardly known. In this report, after the alumina's spray coating single layer is taken out, Vickers indentation crack is introduced, 4-point bending test is performed and R-curve is acquired. As a result, the fracture strength characteristic of the alumina's spray coating single layer is clarified. Then, three judgments of the crack interference with the R-curve are proposed. Moreover, correction methods of crack shape when the cracks interfere are proposed. The validities of the proposals are verified with bending tests after two Vickers indentation cracks have been introduced.

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There are some reports to analyze by using the elastic analysis for two or more cracks. Moreover, there are some standards about union condition of the cracks. However in ceramics including alumina, the study of quantifying an internal spread of the crack when interfering and presuming static fracture strength with judgment of the crack interference after the stable crack propagation is hardly known. In this report, in order to predict fracture strength, crack shape just before brittle fracture in alumina's spray coating single layer is predicted with methods proposed in former report. And statistics method with consideration of fracture toughness scattering is used. In order to predict the crack shape before brittle fracture, image processing software is developed, therefore efficient data processing become possible. Moreover, the proposed fracture strength presumption is done in the standpoint of the safe design and has aimed to presume accuracy good on the safety side. The fracture strengths predicted with the proposed method are almost equal to experimental results obtained by 4-point bending tests. Then flowchart of fracture strength safety design using the proposed method is proposed.

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A modified extended Tersoff interatomic potential function is proposed in order to simulate the environment-assisted crack propagation behavior. Firstly, the physical properties of Si, O_2, H_2, SiO_2, and H_2O are calculated by this modified function. It is confirmed that these calculated values agree with the measured values very well. Next, the potential surface of H_2O molecular transporting process to the crack tip of SiO_2 material is calculated by the same function. The relationship between the velocity of crack propagation "v" and stress intensity factor "K" is calculated based on this surface. The results agree with the experimental results well. From this simulation, it is clarified that the crack velocity is controlled by H_2O transporting process in the both region I and II of "v-K curve". In the region I, H_2O molecules have physically limited access to the crack tip due to the small opening of the crack. This works as energy barrier in transporting H_2O molecules. Due to the relatively large crack opening, in the region II, H_2O molecules have free access to the crack tip without energy barrier. This difference makes a bend in "v-K curve" between region I and II.

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This paper describes the effects of an enclosure and an inlet size of an electronic casing on the cooling fan performance. A performance of air-cooling fans is defined by their P-Q (pressure difference-flow rate) curves. Recent studies report that the P-Q curve of cooling fans depends on their operational environments. It is impossible for accurate CFD (Computational Fluid Dynamics) analyses to be performed on the thermal design of the electronic equipments, including fans. In this study, we measured the fan performance in the enclosure and explored the effects from the inlet size and an inlet shape while changing the number of revolutions of the test fan. Especially, a static pressure difference between forward and backward of the fan installed into the enclosure model was investigated and a total pressure difference which was calculated from a predicted dynamical pressure was also inspected. From experiments, we understood that a level of the fan performance change was decided by the size of the inlet area, and it was independent from the shape of the inlet and the working revolution of the fan.

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Cyclic deformation is applied on an amorphous nano-block of cis-1,4 polybutadiene (PB), which has 1000 random coil chains and the average length of [-CH_2-CH=CH-CH_2-]^<75>, by molecular dynamics simulation. As same as the previous polyethylene (PE) simulation, the bond stretch (BS) and van der Waals (VDW) dominate the hysteresis of the stress-strain curve; however, the bending (BE) shows negative stress despite of the elongation, leading subtle "strain softening" in the later stage of PB loading. We have carefully analyzed BS and BE stresses by focusing on the conformation of -CH=CH- and -CH_2-CH_2- dihedral angles, revealing that the negative BE stress emerges on the trans -CH=CH- segments normal to the loading axis. Here, the BE angles of the segments does not close but open by the tensile loading; the angles open in the lateral direction due to the tension in each molecular chain. But this generates the negative stress in the loading axis since the lateral contraction of BE is parallel to the loading axis. We have also revealed that there is a remarkable polarization in the BS stress; the cis -CH=CH- feels compression while the trans -CH=CH- does tension. On the other hand, the BS in the -CH_2-CH_2- shows tension in the gauche conformation and compression in the trans one, as if they balanced out the polarization of BS in the -CH=CH-. The connection of cis -CH=CH- and gauche -CH_2-CH_2- leads curled structure, while the other combination does straight one. Finally we have visualized the chain morphology by the conformation and evaluated the local density at each nodes, revealing that the former combination aggregates in the amorphous structure and doesn't dissolve under cyclic loading.

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This paper describes a a numerical algorithm to improve the poor performance of a four-node linear tetrahedral element. For this purpose a novel finite volume method utilizing an arbitrary median-meshed polyhedral (AMP) cell is developed. The AMP cells are constructed uniquely by connecting the median points of unstructured tetrahedra: the edge mid-points; the face centers; the volume centroids. These cells are used as control volumes to descretize the equations of the conservation laws by the finite volume method and to solve constitutive equations. The derivation of the equation of motion to accelerate computational nodes is detailed. The present method is implemented in a general-purpose explicit Lagrangian program, which is applied to solve Taylor impact problems in order to evaluate the performance of the AMP cells. Test cases of the three different materials as Aluminum, Copper and Steel are selected. The deformed shapes of the test pieces obtained by the analyses show good agreements with the ones by the experiments even if the computational nodes are distributed nonuniformly. Computational results are also compared about plastic strains obtained by the eight-node hexahedral elements of the same computer program.

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Changes of the strength and the Mg_2Si precipitates in Boron-added Al-Mg-Si alloy, which is attempted to be used as casks in a nuclear power plant, during the long-time duration at the temperatures at 230℃ or 250℃ for 10000hr at maximum. β'-Mg_2Si with rod-like morphology was precipitated after the heat treated. The relationship between the strength and the Larson-Millar parameter (L.M.P.) is represented by liner function when the duration time is longer than 13hr (230℃) or 11hr (250℃); whereas the relationship between the inverse square root of the mean diameter (d^<-0.5>) along long axis of the β'-Mg 2Si precipitates and L.M.P. is also expressed by liner function. The strength change of the B-added alloy is explained using the Ashby's theory concerning precipitation hardening, just similar as that of the Al-Mg-Si alloys without B.

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Spherical indentation testing is a minimally invasive technique that can be used instead of highly invasive techniques such as tensile to measure the deformation behavior of various materials. Due to this characteristic, it is useful for evaluating the mechanics of human tissues because in vivo measurements can be performed easily. However, the large deformations that are caused by indentations lead to significant errors in the results evaluation by the Hertz theory, which is reliable in the case of the small deformation conditions. In this paper, spherical indentation testing is studied to evaluate the dimension and rigidity of soft materials such as biological soft tissues. Here, the Hertz theory is functionally expanded to evaluate indentations for soft materials, which undergo large deformations. In the expansions, the technique used for evaluating the thickness of finite specimens is first explained by alalyzing the experimental results of indentations. Then, the Young's modulus of soft materials with finite thickness is theoretically derived by defining an equivalent indentation strain for the analysis of the indentation process. The expansions are examined to evaluate its reliability by applying them to measure the thickness and Young's modulus of sheets of polyurethane resin.

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In friction-type joints where vibratory load is carried only by friction, the effect of contact pressure on fretting fatigue strength differs from that observed in conventional pad-type load-carrying tests. In this study, in order to clarify the effect and the mechanism of contact pressure in friction-type tests, we performed fatigue tests measuring changes in strain distribution with repetition and finite element (FE) analyses focusing on the shifting of actual contact edges. It was found that fatigue limits decreased as contact pressure decreased, and the minimum limits were observed at certain contact pressure. We clarified that the reduction in fatigue strength that occurred with decreasing contact pressure was caused by increasing stress concentration due to shifting of the actual contact edge, and decreasing compressive mean stress. The actual contact edges were confirmed to be positioned inside the contact surface under low contact-pressure conditions, and to move inwardly from the initial edge with the repetition of cycles under high relative-slip-range conditions. We also showed that fatigue limits can be explained well considering the shifting of the actual contact edge using the local reference stresses (mean stress and principal stress amplitude) specially defined in this study.

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Fatigue crack growth under mixed mode loading conditions is simulated using S-FEM. By using S-FEM technique, only local mesh should be re-meshed and it becomes easy to simulate crack growth. By combining with re-meshing technique, local mesh is re-meshed automatically, and curved crack path is modeled easily. Fully automatic crack growth simulation system in 3-dimensional problem is developed. At first, a basic slant surface crack problem is solved, and it is shown that surface crack grows under pure mode I conditions, which is similar in 2-dimensional problem. It is also shown that this system is available for complicated structure, for example, surface crack at inner surface of pipe. Finally, interaction effect of two surface cracks is evaluated.

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Geometry of propagating crack front and crack opening displacement were observed in situ in thermal stress cleaving of thin soda-lime glass plates using the interference fringe method. The crack front inclines to the propgaating direction advancing more at the heated surface due to the temperature gradient in the thickness. Mode I stress intensity factor was estimated from measured COD and its distribution along the curved crack front was found to be almost uniform. The uniform distribution was also confirmed from three-dimensional thermal stress FEM analysis. When a crack length at the middle plane of the plate thickness is used, two-dimensional analysis gives good approximation of K_1 attained at the propagating crack front.

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