HARMONIC AND RANDOM VIBRATION DURABILITY INVESTIGATION FOR SAC305 (Sn3.0Ag0.5Cu) SOLDER JOINT

ABSTRACT Title of Dissertation: HARMONIC AND RANDOM VIBRATION DURABILITY INVESTIGATION FOR SAC305 (Sn3.0Ag0.5Cu) SOLDER INTERCONNECTS Yuxun Zhou, Doctor of Philosophy, 2008 Dissertation directed by: Professor Abhijit Dasgupta Department of Mechanical Engineering Vibration loading is commonly encountered during the service life of electronic products. However, compared to thermal cycling durability, vibration durability is more complex and has been less investigated. In surface mount technology, solder joints are the primary mechanical, thermal and electrical interconnects between the component and the PWB. So the reliability of solder joints is very crucial for most electronic assemblies. The vibration durability of Pb-free solder joints is the focus of this dissertation. The characteristics of the stress from vibration loading are low amplitude and high frequency, while those from cyclic thermal loading are high amplitude and low frequency. In this study, several exploratory vibration tests were conducted, using both narrow band and broad-band, step-stress excitation at several different isothermal and thermal cycling conditions. The effect of thermal pre-aging on solder joint vibration failures was also investigated. Some of the vibration durability results were analyzed in detail, to obtain quantitative insights into the vibration fatigue behavior of the SAC305 solder material. A time-domain approach was adopted to investigate the durability of solder interconnects under different kinds of vibration and quasi-static mechanical loading. First, the solder interconnects were subjected to narrow-band (harmonic) vibration loading. The test were conducted at the first natural frequency of the test board using constant-amplitude excitation and solder fatigue properties were extracted with the help of a time-domain analysis that is based on quasi-static finite element simulation. Compared to broad-band step-stress vibration durability tests, the advantage of the harmonic constant-amplitude test is less complexity in the model extraction process, hence, less uncertainty in the desired fatigue constants. Generalized strain-based S-N curves have been obtained for both SAC305 and Sn37Pb solder materials. The strain-life model constants show that SAC305 solder material has superior fatigue properties compared to Sn37Pb solder material under low-cycle fatigue loading, while the reverse is true for high-cycle fatigue loading. These results are consistent with test results from other researchers. In actual application, SAC305 assemblies almost always fail before Sn37Pb assemblies under comparable vibration excitation because of (i) higher solder strain at a given excitation level; and (ii) multiple failure modes such as copper trace cracking. Next, durability was investigated under step-stress, broad-band (random) excitation. These test results show that SAC305 interconnects are less durable than Sn37Pb interconnects under the random excitation used in this study, which agrees with the harmonic durability results. The random and harmonic durability results were quantitatively compared with each other in this study. Finite element simulation was used to investigate the stress-strain response in the interconnects. The output of this simulation is the strain transfer function due to the first flexural mode of the PWB. This transfer function is used to obtain the solder strain from the measured board strain. This fatigue assessment method demonstrated that the model constants obtained from the harmonic test overestimate the fatigue life under random excitation by an order of magnitude. The causes for this discrepancy were systematically explored in this study. The effects of cyclic loading and mean stress on the vibration durability were addressed and found to be minimal in this study. The stress-strain curves assumed for the solder material were found to have a very large effect on the durability constants, thus affecting the agreement between harmonic and random durability results. The transient response of the components on the test board under both harmonic and random excitation was also included in the strain transfer function with the help of dynamic implicit simulation, and found to have a much stronger effect on the vibration durability at the high frequencies used in broad-band excitation compared to the low frequency used in narrow-band test. Furthermore, the higher PWB vibration modes may play a strong role and may need to be included in the strain transfer-function. This study clearly reveals that the solder strain analysis for broad-band random excitation cannot be limited to the quasi-static strain transfer-function based on the first PWB flexural mode, that has been used in some earlier studies in the literature. The time-domain approach used in this study provided fundamental and comprehensive insights into the key factors that affect vibration durability under different types of excitation, thus leading to a generalized S-N modeling approach that works for both harmonic and random vibration loading

Causal meets Submodular: Subset Selection with Directed Information

We study causal subset selection with Directed Information as the measure of prediction causality. Two typical tasks, causal sensor placement and covariate selection, are correspondingly formulated into cardinality constrained directed information maximizations. To attack the NP-hard problems, we show that the first problem is submodular while not necessarily monotonic. And the second one is "nearly" submodular. To substantiate the idea of approximate submodularity, we introduce a novel quantity, namely submodularity index (SmI), for general set functions. Moreover, we show that based on SmI, greedy algorithm has performance guarantee for the maximization of possibly non-monotonic and non-submodular functions, justifying its usage for a much broader class of problems. We evaluate the theoretical results with several case studies, and also illustrate the application of the subset selection to causal structure learning

The impact of the government response on pandemic control in the long run — A dynamic empirical analysis based on COVID-19

Purpose: Although the outbreak of Corona Virus Disease 2019 (COVID-19) occurred on a global scale, governments from different countries adopted different policies and achieved different anti-epidemic effects. The purpose of this study is to investigate whether and how the government response would affect the transmission scale of COVID-19 on the dynamic perspective. Methodology: This paper uses an dynamic generalized moment method to research relationship between the government response and COVID-19 case fatality rate by using panel data from the eight countries, including China, United States, Canada, Australia, Italy, France, Japan, and South Korea. Findings: We have the following findings: 1. Government responses have a significant impact on the scale of COVID-19 transmission. 2. The rate of increase of government responses on the growth rate of COVID-19 case fatality rate has the characteristics of cyclicity and repeatability, that is, with the increase in the growth rate of government responses, the COVID-19 case fatality rate shows the following cyclical motion law: increasing first, reaching the maximum point, and then declining, and finally reaching the minimum point and then rising; ultimately, its convergence becomes 0. The cyclical fluctuations of COVID-19 in the long term may be caused by the decline in the level of government response, the mutation of the virus, and the violation of restrictive policies by some citizens. 3. The government response has a lag in controlling the spread of COVID-19. Originality/value: Since there is a lack of literature on the impact of government responses on the development of COVID-19 from a long-term and dynamic perspective. This paper fills this gap in empirical research. We provide and expand new empirical evidence based on the current literature. This paper provides the basis for government decision-making and will help to formulate the response to other major public health events that may occur in the future

The impact of penalty and subsidy mechanisms on the decisions of the government, businesses, and consumers during COVID-19 — Tripartite evolutionary game theory analysis

Purpose: Based on the fact that punishment and subsidy mechanisms affect the anti-epidemic incentives of major participants in a society, the issue of this paper is how the penalty and subsidy mechanisms affect the decisions of governments, businesses, and consumers during Corona Virus Disease 2019 (COVID-19). Design/Methodology/approach: This paper proposes a tripartite evolutionary game theory, involving governments, businesses, and consumers, to analyze the evolutionary stable strategies and the impact of penalty and subsidy mechanism on their strategy selection during COVID-19. We then uses numerical analysis to simulate the strategy formation process of governments, businesses, and consumers for the results of tripartite evolutionary game theory. Findings: This paper suggests that there are four evolutionary stable strategies corresponding to the actual anti-epidemic situations. We find that different subsidy and penalty mechanisms lead to different evolutionary stable strategies. High penalties for businesses and consumers can prompt them to choose active prevention strategies no matter what the subsidy mechanism is. For the government, the penalty mechanism is better than the subsidy mechanism, because the excessive subsidy mechanism will raise the government expenditure. The punishment mechanism is more effective than the subsidy mechanism in realizing the tripartite joint prevention of the COVID-19. Therefore, the implementation of strict punishment mechanism should be a major government measure under COVID-19. Originality/value: Our paper extends the existing theoretical work. We use political economy to make the preference hypothesis, and we explicitly state the effect of subsidy and penalty mechanisms on the decision making of participants and compare their applicability. This is the work that the existing literature did not complete before. Our findings can provide an important theoretical and decision-making basis for COVID-19 prevention and control

Candidate Regulators of Dyslipidemia in Chromosome 1 Substitution Lines Using Liver Co-Expression Profiling Analysis

Dyslipidemia is a major risk factor for cardiovascular disease. Although many genetic factors have been unveiled, a large fraction of the phenotypic variance still needs further investigation. Chromosome 1 (Chr 1) harbors multiple gene loci that regulate blood lipid levels, and identifying functional genes in these loci has proved challenging. We constructed a mouse population, Chr 1 substitution lines (C1SLs), where only Chr 1 differs from the recipient strain C57BL/6J (B6), while the remaining chromosomes are unchanged. Therefore, any phenotypic variance between C1SLs and B6 can be attributed to the differences in Chr 1. In this study, we assayed plasma lipid and glucose levels in 13 C1SLs and their recipient strain B6. Through weighted gene co-expression network analysis of liver transcriptome and "guilty-by-association" study, eight associated modules of plasma lipid and glucose were identified. Further joint analysis of human genome wide association studies revealed 48 candidate genes. In addition, 38 genes located on Chr 1 were also uncovered, and 13 of which have been functionally validated in mouse models. These results suggest that C1SLs are ideal mouse models to identify functional genes on Chr 1 associated with complex traits, like dyslipidemia, by using gene co-expression network analysis

SugarMate: Non-intrusive blood glucose monitoring with smartphones

Inferring abnormal glucose events such as hyperglycemia and hypoglycemia is crucial for the health of both diabetic patients and non-diabetic people. However, regular blood glucose monitoring can be invasive and inconvenient in everyday life. We present SugarMate, a first smartphone-based blood glucose inference system as a temporary alternative to continuous blood glucose monitors (CGM) when they are uncomfortable or inconvenient to wear. In addition to the records of food, drug and insulin intake, it leverages smartphone sensors to measure physical activities and sleep quality automatically. Provided with the imbalanced and often limited measurements, a challenge of SugarMate is the inference of blood glucose levels at a fine-grained time resolution. We propose Md3RNN, an efficient learning paradigm to make full use of the available blood glucose information. Specifically, the newly designed grouped input layers, together with the adoption of a deep RNN model, offer an opportunity to build blood glucose models for the general public based on limited personal measurements from single-user and grouped-users perspectives. Evaluations on 112 users demonstrate that Md3RNN yields an average accuracy of 82.14%, significantly outperforming previous learning methods those are either shallow, generically structured, or oblivious to grouped behaviors. Also, a user study with the 112 participants shows that SugarMate is acceptable for practical usage.</jats:p