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The use of BGA (Ball Grid Array) interconnects utilizing the lead-free solder joint has grown rapidly because of its small volume and diversity of application. Thus, it requires the continuous quantification and refinement of lead-free solder joint reliability. The lead-free solder creep and cyclically applied mechanical loads cause metal fatigue on the lead-free solder joint which inevitably leads to an electrical discontinuity. In the field application, BGA solder joints experience mechanical loads during temperature changes caused by power up/down events as the result of the CTE (Coefficient of Thermal Expansion) mismatch between the substrate and the Si die. In this paper, extremely small resistance changes at joint area corresponding to through-cracks generated by thermal fatigue were measured. In this way, the failure was defined in terms of anomalous changes in electrical resistance of the joint. Furthermore the reliability of BGA solder joints in thermal cycling is evaluated by using the modified coffin-Manson criterion which may define and distinguish failure. Any change in circuit resistance according to the accumulated damage induced by the thermal cycling in the joint was recorded and evaluated in order to quantitate reliability of solder joint.

Structural hierarchies are universal design paradigms of biological materials, e.g., several materials in nature used for carrying mechanical load or impact protection such as bone, nacre, dentin show structural design at multiple length scales from the nanoscale to the macroscale. Another example is the case of diatoms, microscopic mineralized algae with intricately patterned silica-based exoskeletons, with substructure from the nanometer to micrometer length scale. Previous studies on silica nano-honeycomb structures inspired from these diatom substructures at the nanoscale have shown a great improvement in plasticity, ductility and toughness through these designs over macroscopic silica, though along with a substantial reduction in stiffness. Here, we extend the study of these structural designs to the micron length scale by introducing additional hierarchy levels to implement a multilevel composite design. To facilitate our computational experiments we first develop a mesoscale particle-spring model description of the mechanics of bulk silica/nano-honeycomb silica composites. Our mesoscale description is directly derived from constitutive material behavior found through atomistic simulations at the nanoscale with the first principles-based ReaxFF force field, but is capable of describing deformation and failure of silica materials at tens of micrometer length scales. We create several models of randomly-dispersed fiber-composite materials with a small volume fraction of the nano-honeycomb phase, and analyze the fracture mechanics using J-integral and R-curve studies. Our simulations show a dominance of quasi-brittle fracture behavior in all cases considered. For particular materials with a small volume fraction of the nano-honeycomb phase dispersed as fibers within a bulk silica matrix, we find a large improvement (≈4.4 times) in toughness over bulk silica, while retaining the high stiffness (to 70%) of the material. The increase in toughness is observed to arise primarily from crack path deflection and crack bridging by the nano-honeycomb fibers. The first structural hierarchy at the nanometer scale (nano-honeycomb silica) provides large improvements in ductility and toughness at the cost of a large reduction in stiffness. The second structural hierarchy at the micron length scale (bulk silica/nano-honeycomb composite) recovers the stiffness of bulk silica while substantially improving its toughness. The results reported here provide direct evidence that structural hierarchies present a powerful design paradigm to obtain heightened levels of stiffness and toughness from multiscale engineering a single brittle — and by itself a functionally inferior material — without the need to introduce organic (e.g., protein) phases. Our model sets the stage for the direct simulation of multiple hierarchical levels to describe deformation and failure of complex biological composites.

The quasi-static and dynamic compression responses and failure of fiber-reinforced syntactic foams were investigated. The role of fiber volume fraction on the compression response of syntactic foams was examined in terms of mechanical behavior and energy absorption under both quasi-static and dynamic conditions. Results showed that the mechanical behavior and energy absorption of the reinforced specimens increased with increasing fiber volume fraction. The syntactic foams exhibited distinct strain rate sensitivity; and their yield strength and elastic modulus increased by 41.1% and 85.1%, respectively, as strain rate increased from 0.0011 s${}^{\mathrm{\text{-1}}}$ to 1070 s${}^{\mathrm{\text{-1}}}$. The deformation and failure processes of the syntactic foams were also examined, and the underlying mechanisms were discussed.

This paper proposes a theoretical approach to predict the failure behavior of laminated carbon fiber reinforced polymer (CFRP) under combined thermal and mechanical loadings. Two types of CFRP Laminates, i.e., CCF300/BA9916 and T700/BA9916, are investigated, and TGA tests in both nitrogen and oxidation environments at different heating rates are carried out to obtain the thermal decomposition kinetic parameters of polymer matrix and carbon fiber. Based on the thermal decomposition behavior and a multi-level structure model, the thermal physical properties, mechanical properties and thermal deformations of the laminated composites at high temperatures are obtained. Then substituting thermally degraded properties into constitutive equations of composite materials as macroscopic defects, the damage mode and failure strength of the laminated composite under thermo-mechanical loadings is obtained. Predicted elastic properties and failure strength are compared with experimental results as well as previous models. Effects of heating rates and heating environments through rigorous physical model are considered in the present work. It is found that the heating rate significantly affects the thermal and mechanical properties, the higher the heating rate, the less degraded are the thermo-mechanical properties and failure strength at a given temperature. Young’s modulus and failure strength of T700/BA9916 are higher than those of CCF300/BA9916 at high temperatures, due to the higher volume fraction of carbon fibers, which are less weakened in thermal environment.

This research focuses on generating the plastic collapse load boundaries of a cylindrical vessel with a radial nozzle via employing three different plastic collapse load techniques. The three plastic collapse load techniques employed are the plastic work curvature (PWC) criterion, the plastic work (PW) criterion, and the twice-elastic-slope (TES) method. Mathematical based determination of plastic collapse loads is presented and employed concerning both the PWC and the PW criteria. A validation study is initially conducted on a pressurized 90-degree pipe bend structure subjected to in-plane closing bending via finite element analyses along with an elaborate explanation of the mathematical approaches for determining the plastic collapse loads via the PWC and the PW criteria. Outcomes of the validation study revealed very good outcomes for the three techniques. Accordingly, the aforementioned three techniques are utilized to determine the plastic collapse load boundaries of a pressurized cylindrical vessel/nozzle structure subjected to in-plane (IP) and out-of-plane (OP) bending loadings applied on the nozzle one at a time. The TES method revealed considerate limitations when applied within the medium to the high internal pressure spectra. It is shown that both the PWC and the PW criteria outperform the TES method in computing the plastic collapse loads. The vessel/nozzle structure revealed relatively higher plastic collapse moment boundaries under IP bending as compared to OP bending. Conclusively, methodical steps are devised for determining the plastic collapse loads via the PWC and the PW criteria for the ease of systematic application on pressurized structures in general.

In order to explore the integral safety degree, probable failure type and failure mechanism of high dam, the combination of overloading and strength reduction method is adopted to simulate the progressive failure and potential destabilization pattern of dam-foundation system. By using finite element method, the overloading of dam-foundation system is carried out firstly and then keeping the load combination unchanged, by reducing rock material strength parameters step by step. The general safety degree of dam-foundation system is obtained. The method mentioned above has been used in Guangzhao roller compacted concrete (RCC) gravity dam, the finite element calculation results show that integrated safety degree of GuangZhao RCC Gravity Dam is greater than 3.0 and the safety degree of the dam foundation surface which is the weakest position of the dam-foundation system is greater than 2.0. The research results indicate that the safety coefficient can satisfy the engineering requirement and the method is efficient and accurate in high dam safety evaluation.