The Coffin-Manson equations of Sn/Ag/Cu and Sn/Pb solder joints are presented in this thesis. The experimental results of CSP thermal cycle fatigue test and ball shear test are used to formulate Coffin-Manson equations. The maximum amplitude of equivalent plastic shear strain corresponding to these two experiments are employed. The MARC finite element package is used to calculate the plastic shear strain. Different published fatigue experiment results have been used to show the accuracy and the feasibility of these proposed equations. The 3-D finite element models of the BGA type¡¦s CSP and VCSEL assembly are employed to simulate the thermal cycling fatigue. Results indicate that the fatigue lifes of solder predicted by using the proposed equations have good agreement with those measured from experimental tests.

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With electronic packaging towards the development of lead free process, the research on the portable electronic devices subject to impact load is emphasized gradually. At present, for drop test and cyclic bending test, most of the failure modes lie on the modes of "fracturing in IMC layer" or "fracturing on IMC/solder boundary". The purpose of this work is to use 3D numerical analysis software ANSYS/LS_DYNA, that were found out a proper numerical model, to further analyze the impact fracture of lead-free solder. From the numerical results, the strain rate of solder joint ranges from 103 s-1 to 104 s-1 under an impact velocity of 2 m/s. At this strain rate, the mechanical properties of solder joint could be effectively investigated. When IMC strength is smaller than 300MPa, the main failure mode is fracturing of IMC; whilst, IMC strength is greater than 300MPa, the failure mode becomes fracturing of bulk solder, but the failure mode of fracturing of IMC and a partial solder requires a model with more fine meshes to simulate. Different velocities did not affect the numerical results significantly, because the material parameters of a solder ball is strongly dependent on strain rate. Also, we found that the impact test in reality does not present a shear-dominant mode alone even when the impact angle is 0¢X. While using simulation to carry out the dynamic experiment, it can be observed that the course of solder joint suffering the damage provides a good reference and contrast for the experimental work in the future.

With the electronic packaging towards the rapid development of lead free process, the related research on the portable electronic devices subject to impact load is emphasized urgently. At present, the failure modes of fracturing in IMC layer and fracturing on IMC/solder boundary are mostly encountered due to drop test and cyclic bending test respectively. The purpose of this work is to use 3D numerical analysis software ANSYS/LS_DYNA, that were found to be a suitable numerical model for further analyzing the impact fracture of lead-free solder. The relationship between simulation and ball impact test system was compared and the effects of variable parameters on solder balls subjected to impact loading was investigated. Also, the transient deformation and fracturing of solder joints subjected to the impact load were studied numerically and experimentally. Then, the transient response and the failure modes of the solder joint due to impact load were predicted by varied strain rate tests. From the numerical results, the strain rate mechanical properties of solder joint due to high can be effectively obtained. The difference of IMC strength caused three kinds of failure modes of the solder ball, however the failure mode of fracturing in IMC and a party of solder requires a model to simulate with more refined meshes. Different velocities affected the numerical results significantly. The higher the velocity of impact test applied, the lower the impact loading received. That is mainly attributed to the material parameters adopted of a solder ball is strongly dependent on the strain rate considered. Also, it is found that the impact test in reality does not result in a shear-dominant failure mode. While using dynamic simulation instead of the experiment, the damage process of solder joint can be observed. That provides a good reference and contrast for the experimental work in the future.

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This work uses different size of strain gages (Gage Grid Length: 10mm, 1mm, 0.2mm) to measure the stress distributions of metal (Al 6061-T6) and composite (laminates of [0/+45/90/-45]2S and [0/90]4S layers ) with a central circular hole and a crack. Both the SCF (Stress Concentration Factor) and SIF (Stress Intensity Factor) are found to consider the stress scatteredness of experimental data in contrast to micro- mechanics. To understand the strain gage size effect is our main purpose in measuring both types of materials. The size effect of strain gage we find appears obviously in the measuring position with stress changing significantly. We find that the size of strain gage is bigger; the error of stress is higher. Analyzing the stress scattering around a central circular hole, we obtain the experimental result that the stress will first reduce drastically from central circular hole edge and then keep uniform. In analysis of the stress scattering around the crack tip, we observe that first stress rises quickly from the specimen¡¦s free edge to the top of crack tip with a maximum value, and the stress keeps a nominal value in the specimen central part. Comparing the empirical result of SCF and SIF, we find that the data of 0.2mm of strain gage close to the theoretical solution, while those of 1mm and 10mm strain gages appear inexact in measuring and calculating SCF and SIF.

In the present study, the buckling behavior of beams is analyzed by a plane strain finite element. The displacement-type finite element formulation is based on elasticity and has no any other simplification and assumption except that the beam is of moderate depth. Also all the displacement boundary conditions can be imposed exactly. These are the advantages that beam theories of conventional approach, which simulate beams with neutral plane behaviors, do not have. Therefore the present analyses should be able to obtain buckling load and buckling mode more accurately than conventional method. Numerical values of buckling loads of the present approach will be compared with previously published results of the Euler-Bernoulli beam theory and the Timoshenko beam theory, and further with the high order beam theory to reveal their differences. The effects of the geometry ratio, the distribution of axial loads and the displacement boundary conditions on buckling of beams are also discussed.

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During the bending of flange plate used for dapped girders some highway bridge fabricators are experiencing cracking of the flange plate particularly when heat is used in assisting the bending process. Due to the extreme strains experienced during the fabrication process, investigating this problem requires the use of a finite element analysis. The fabrication process was broken down into two parts, first the heating of the plate through the use of either a furnace or an acetylene torch (thermal), and the second was the bending process (structural). The five different temperatures collected during the thermal analysis were a uniform temperature of 75oF, a 1100oF uniform temperature as a result of furnace heating, both five and ten minutes of air-cooling after the plate had reached a uniform temperature of 1100oF, and the temperature gradient after heating the flange plate to a surface temperature of 1200oF though the use of an acetylene torch. After the thermal analysis was completed, the resulting temperatures were imported into the structural model. The plate thicknesses analyzed were one, one and a half, and two inches, assuming both 50 and 70 ksi yield strengths. To achieve a 90 degree six-inch radius bend the plate was bent in five separate locations. The result of this analysis showed that with the introduction of temperature gradients into thefabrication process, the strains along the plate??s extreme fibers increased. The model further showed that for both a one and a half and two-inch thick plate the extreme fiber strains exceeded ten percent, which further adds to the increased risk of the flange plate cracking during fabrication. The highest residual stresses through the plate??s thickness occurred during cold bending. The residual stresses through the plate??s thickness decreased when the fabrication process was carried out at elevated temperatures. When steel exceeds a strain of 10 to 16 percent during the fabrication process, the plate becomes susceptible to cracking. This strain limit was exceeded for plate thicknesses of one and a half and two inches.

Compaction of soil is essential in the construction of highways, airports, buildings, and bridges. Typically compaction is controlled by measuring the dry density and the water content of the compacted soil and checking that target values have been achieved. There is a current trend towards measuring the soil modulus instead or in addition to density. The reasons are that the density measurements are made using nuclear density meter, an undesirable tool in today??s political environment and that pavement design uses moduli as an input parameter. Although there are many apparatus available to measure soil modulus in the field such as Falling Weight Deflectometer, Dynamic Cone Penetrometer and Seismic Pavement Analyzer, a light weight and easy to use device which can measure the soil modulus fast and accurately is in great need. Briaud Compaction Device (BCD) is a portable device which can measure a soil modulus in several seconds. The principle of the BCD is to use the bending of a plate resting on the ground surface as an indicator of the modulus of the soil below. Numerical simulations show that within a certain range, the soil modulus is simply related to the plate bending. Strain gauges are glued on the top of the plate of BCD and a double half Wheatstone bridge is used to measure the strain. BCD tests were done in parallel with plate tests of the same size. A good correlation was found between the ratio of the plate pressure over the bending strain measured with a BCD and the reload soil modulus obtained from the plate test. This correlation can be incorporated into the BCD processor to display the soil modulus directly. To transit from dry density based compaction control to modulus based compaction control, BCD tests were also performed in the laboratory on top of a soil sample compacted inside the Proctor mold followed by plate tests. That way, a soil modulus versus water content curve is developed which parallels the approach for the dry density versus water content. The soil modulus versus water content curve can be used to provide the target values for compaction control in the field.