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Many interesting ideas have emerged from research on electromagnetic eld interactions with di erent materials. Analyzing such interactions has extracted some essential proper- ties of the materials. For example, extracting constitutive parameters such as permittivity, permeability, and conductivity, clari es a material's behavior. In general, the electromag- netic eld interacts with materials either in the far- eld or near- eld of a source. This study focuses on the principle of near- eld microwave microscopy for detection purposes. Many studies have focused on the use of an electrically small resonator, such as a split-ring resonator (SRR) and a complementary split-ring resonator (CSRR), to act as a near- eld sensor for material characterization and detection. At the resonance frequency, the electric and magnetic energy densities are enhanced dramatically at certain locations in the resonator. Any disturbance of the eld around such a resonator with a material under test causes the resonance frequencies to exhibit a shift that is used as an indicator of the sensor sensitivity. In this thesis, a single CSRR is used as a sensing element for detecting cracks in metal surfaces. Many microwave techniques have been developed for crack detection. However, these techniques have at least one of the following drawbacks: working at high frequencies, measurement setup complexity and cost, and low sensitivity. The rst part of this thesis presents a new sensor based on the complementary split-ring resonator (CSRR) that is used to detect sub-millimeter surface cracks. The sensing mechanism is based on perturbing the electromagnetic eld around an electrically small resonator, thus initiating a shift in the resonance frequency. Investigation of the current distribution on a CSRR at the resonance frequency shows the critical location at which the enhanced energy is concentrated. In addition, the current distribution demonstrates the sensing element in the CSRR. The sensor is simple to fabricate and inexpensive, as it is etched-out in the ground plane of a microstrip-line using printed circuit board technology. The microstrip-line excites the CSRR by producing an electric eld perpendicular to the surface of the CSRR. The sensor exhibits a frequency shift of more than 240 MHz for a 200 m crack. In the second part of this thesis, the sensitivity of the sensor is increased by lling the same crack with a dielectric material such as silicon oil. While using CSRR to scan a block with 200 m wide and 2 mm depth dielectric lled crack, the resonance frequency of the sensor shifts 435 MHz more than a case scanning a solid aluminum. Finally, the total Inductance of a CSRR for miniaturizing purposes is increased using either lumped or distributed elements. In this thesis, the designs and the results are validated experimentally and numerically.

The interface crack branching phenomena, including thermal effects, has been investigated by using complex variable method and Stroh's dislocation theory, extended to thermo-elasticity in matrix notation. As one of the most catastrophic failure modes in structures like laminated and sandwich composites in aerospace and marine construction, thin film in electronic packaging, rotators in high speed engine of aircraft and reactor in nuclear power station, the study of interface crack branching has become a topic not only having theoretical importance, but also having practical significance. A unified approach is presented to address the thermoelastic interface crack problems in dissimilar anisotropic bimaterial composites, and a compact closed form solution is formulated by analytical continuation principle of complex analysis. Employing the contour integral method, an explicit solution to the interaction between the dislocations and the interface crack is obtained. By modeling the branched portion as a continuous distribution of the dislocations, the thermoelastic interface crack branching problem is then converted to a set of semi-coupled singular integral equations and solved by Gauss-Jacobi integration schemes. The influence of material property mismatches between the two constituents and the thermal loading effects on the interface crack branching are demonstrated by extensive numerical simulation. Some useful criteria for predicting the interface crack branching growth and guidance for optimal composites design are suggested. Further, a contact model to eliminate the overlapping between the two surfaces of an interface crack is also proposed and some new parameters which could influence the interpenetrating phenomena are also discovered. The technique to extend the current method to three dimensional problems is also outlined. Furthermore, the C++ source code has been implemented to manipulate the complicated complex operations for numerically solving the singular integral equations in complex matrix form.

Aggregate strength, gradation, and shape play a vital role in controlling asphalt mixture performance. Many studies have demonstrated the effects of these factors on asphalt mixture performance in terms of resistance to fatigue cracking and rutting. This study introduces numerical and analytical approaches supported with imaging techniques for studying the interrelated effects of aggregate strength, gradation, and shape on resistance of asphalt mixtures to fracture. The numerical approach relies on the discrete element method (DEM). The main advantage of this approach is the ability to account for the interaction between the internal structure distribution and aggregate properties in the analysis of asphalt mixture response and performance. The analytical approach combines aggregate strength variability and internal force distribution in an asphalt mixture to predict the probability of aggregate fracture. The numerical and analytical approaches were calibrated and verified using laboratory tests on various aggregate types and mixtures. Consequently these approaches were used to: (1) determine the resistance of various mixture types with different aggregate properties to fracture, (2) study the effects of aggregate strength variability on fracture, (3) quantify the influence of blending different types of aggregate on mixture strength, (4) develop a mathematical expression for calculating the probability of aggregate fracture within asphalt mixture, and (5) relate cracking patterns (cohesive: aggregate - aggregate and matrix - matrix, and adhesive: aggregate - matrix) in an asphalt mixture to internal structure distribution and aggregate properties. The results of this dissertation established numerical and analytical techniques that are useful for developing a virtual testing environment of asphalt mixtures. Such a virtual testing environment would be capable of relating the microscopic response of asphalt mixtures to the properties of the mixture constituents and internal structure distribution. The virtual testing environment would be an inexpensive mean to evaluate the influence of changing different material and design factors on the mixture response.

Solder joints are the most fragile parts in electronic package. The properties of joints made of lead-free material are harder and crisper than those of lead-contained material. They tend to break due to dynamic loading by absorbing the impact energy and result in malfunction. Thus, how to improve the reliability of contact joints made of lead-free material in dynamic loading has become an important topic for research. This work is based on JEDEC Standard JESD22 - B111 ¡§Board Level Drop Test Method of Components for Handheld Electronic Products,¡¨ and JESD22 ¡V B110 ¡§Subassembly Mechanical Shock¡¨. The setup of drop test apparatuses was used to conduct dropping tests with the impact of acceleration 1500 G, in order to acquire the reliability of SnAgCu, SnCu, and SnAg alloy, which would be compared with 63Sn37Pb. The specimens would be red-dyed for an analysis under SEM to examine the distribution of the breakage. The results were analyzed by Weibull distribution to predict Mean Time to Failure (MTTF), it is revealed that MTTF of solder joints made of Sn0.7Cu, Sn2.6Ag0.5Cu, and Sn3.0Ag0.5Cu (MTTF=355.32, 295.82, 289.54 cycles respectively) are longer than that made of 63Sn37Pb (MTTF=152.52 cycles). Notably, MTTF of alloy Sn0.7Cu is 2.3 times of solder joints of SnPb. Alloy Sn3.0Ag0.5Cu has the shortest MTTF among the three, which is also 1.89 times of alloy SnPb. That is to say, under impact of 1500G, solder joints made of Sn0.7Cu, Sn2.6Ag0.5Cu, and Sn3.0Ag0.5Cu possess greater resistance to shock than alloy 63Sn37Pb, which is in common by used at present. In addition, the breakage of solder joints mainly generated on Intermetallic Compound (IMC) and around the four corners, distributed from the periphery to the central area. Especially, those on the corners receive greater stresses due to edge effect.

This study is the method of using the mechanical type to cut the substrate of the glass , under the circumstances that the glass surface is cut directly, probably produced 10¡ã20% of the depth of crack that is the thickness of glass, and then pulled the glass and split by mechanical stress , use the ANSYS and finite element method carry on relevant research and compare, survey the perfect cutting parameter to increase the yield in the future. This study is in order to find out the surface fracture stress distribution status after cutting and take advantage with the finite element method ,and compare with the result of median crack when glass substrate after cutting .It discuss with change parameter of the cutting pressure and Cutting depth ,than to compare with finite element method, it regard as discussing the quality after cutting to reduce the risk of surface defect.

To calculate the characteristics of electronic parts is divided by 1.Chip. 2.Assembly, i.e. package. 3. PCB (Printed Circuit Board). Analizing the electrical characteristics of package needs consideration from all system can distinguish the influence of function. Although the analysis method may be change but we can get the characteristics results from the parameters of circuit element (i.e. Resistance, Inductance, Capacitance). Different measurement or modeling technology can prove that the list data is correct. That moisture in plastic packages can cause cracking or delamination during the surface mount assembly process. During this process, the packages are heated to 220-240¢J. At these temperatures, any moisture present in the plastic vaporizes and exerts stresses in the package, which can cause delamination between the mold compound and the leadframe or die. The mismatch in thermal expansion coefficients of the package¡¦s components also induces stresses. If these combined stresses are greater than the fracture strength of the plastic, cracks will form. The susceptibility of a package to cracking depends on: 1.amount of absorbed moisture, 2.die size, 3.package design, 4.mold compound characteristics, 5.solder reflow temperature profile. Widely, flip chip technology is defined as mounting the chip to a substrate with any kind of materials and methods, as long as the chip surface (active area) is facing to the substrate. The advantages of FC-BGA is¡G1.Efficient use of PCB area. 2.Area array access for high I/O device. 3.Allow for finer pitches. 4.Fewer joints. 5.Better performance of high frequency application. 6.FC is and will be lowest cost.

In the ¡Krst chapter, separation of variables is used to derive the explicit particular solutions for a class of singularly perturbed di¤erential equations with constant coe¢ cients on a rectangular domain. Although only the Dirichlet boundary condition is taken into account; it can be similarly extended to other boundary conditions. Based on these results, the behavior of the solutions and their derivatives can be easily illustrated. Moreover, we have proposed a model with exact solution, which can be used to explore the behavior of layer and to test numerical methods. Hence, these analytic solutions are very important to the study in this ¡Keld. In the second chapter, we study the model of Shi¤ et al. [20]. It is a biharmonic equation on the rectangular domain [¡ a; a]£ [0; b] with clamped boundary condition. We compute its most accurate numerical solution by boundary approximation method (BAM), which is a special version of spectral method or collocation method. Its convergence unfortunately is not as good as the usual spectral method with exponential decay rate. We discover that the slowdown is due to the very mild singularity at two corners not considered by BAM. We further simplify the basis functions and their partial derivatives. Using these functions we can construct several models useful for testing numerical methods. We also explore how the stress intensity factor depends on the sizes of domain a and b, and the load ¸ by reducing the original problem with three parameters lambda, a, b to that with only one parameter t.

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<p>The demands the automotive gear designer has to considerduring the gear design process have changed. To design a gearthat will not fail is still a challenging task, but now lownoise is also a main objective. Both customers and legalregulations demand noise reduction of gears. Moreover, thequality of the product is more in focus than ever before. Inaddition, the gear design process itself must be inexpensiveand quick. One can say that the gear designer faces a newdesign environment. The objective of this thesis is tocontribute to the answer to some of the questions raised inthis new design environment.</p><p>In order to respond to the new design situation, the geardesigner must consider new phenomena of gears that werepreviously not a matter of concern. One such phenomenon is anew gear failure type, Tooth Interior Fatigue Fracture (TIFF).As the gear teeth are made more slender in an attempt to reducethe stiffness variation during the mesh cycle, therebypotentially reducing the noise, the risk of TIFF is increased.The phenomenon of TIFF is explored in detail (paper III-VI)through fractographic analysis, numerical crack initiationanalysis using FEM, determination of residual stress by meansof neutron diffraction measurements, testing for determiningmaterial fatigue properties, fracture mechanical FE-analysis,sensitivity analysis and the development of an engineeringdesign method. The main findings of the analysis of TIFF arethat TIFF cracks initiate in the tooth interior, TIFF occursmainly in case hardened idlers, the fracture surface has acharacteristic plateau at approximately the mid-height of thetooth and the risk of TIFF is more pronounced in slender gearteeth.</p><p>Along with the more optimised gear design, there is atendency for the gear to be less robust. Low robustness, i.e.,great variation in performance of the product, implies a highincidence of rejects, malfunction and/or bad-will, all of whichmay have a negative effect on company earnings. As the use ofoptimisation decreases the safety margins, greater attentionhas to be paid to guaranteeing the products' robustness.Moreover, in order to be cost-effective, the qualities of thegear must be verified early in the design process, implying anextended use of simulations. In this thesis, two robustnessanalyses are presented in which the analysing tool issimulation. The first one considers robust tooth root bendingfatigue strength as the gear is exposed to mounting errors, thesecond one considers robust noise characteristics of a gearexposed to manufacturing errors, varying torque and wear. Bothof these case studies address the problem of robustness ofgears and demonstrate how it can be estimated by use ofsimulations. The main result from the former robustnessanalysis is that wide gears are more sensitive to mountingerrors, while the latter analysis showed that to achieve robustnoise characteristics of a gear it should have large helixangles, and some profile- and lead crowning should beintroduced. The transverse contact ratio is a trade-off factorin the sense that both low average noise levels and low scatterin noise due to perturbations cannot be achieved.</p><p><b>Keywords</b>: robust design, Taguchi method, gear, idler,simulations, Finite Element Method, Tooth Interior FatigueFracture, TIFF</p>