指導教授：吳文方臺灣大學：機械工程學研究所盧羿安Lu, Yi-AnYi-AnLu2014-11-292018-06-282014-11-292018-06-282014http://ntur.lib.ntu.edu.tw//handle/246246/263301電子封裝體的可靠度一直是工程師最關心的課題之一。傳統的電子封裝體壽命評估方式分為兩大派別：以有限元素法為例的數值分析法，以及使用加速試驗的實驗分析法。有限元素法主要由設計工程師所使用，其原理為利用有限元素分析所觀測到的物理現象來預測電子封裝體的失效時間。加速測驗則主要為可靠度工程師所使用，以加速因子的模型來連結環境因子與電子封裝體的疲勞壽命。本研究連結兩種不同的工程觀點與兩種不同的工程師，結合其各自的分析方式並提出一高效率且低成本的壽命預估模型。以往的研究多半將各設計參數視為一定值，忽略製造過程中可能產生的誤差與材料間自然的性質差異。若把這些參數不確定性納入有限元素模型，我們將可利用此模型替代加速測驗法中的實驗，在不需增加成本的情況下得到多筆可用的數據及更為準確的加速模型。本研究建構一塑膠球陣列之有限元素模型，並以實驗數據驗證其準確度。利用此模型，本研究進行兩種分析：傳統的定值分析，以及本研究所提出的隨機分析。比較兩種分析方法所得到的預測模型，我們發現本研究提出的隨機分析在可用的範圍與準確度都有較優良的表現。另外本研究探討參數不確定性對疲勞壽命所產生的影響，並發現基板之厚度與疲勞壽命的連結最為直接。最後，討論不同熱循環負載下的壽命分佈情形，以不同模型來預估壽命分佈之標準差、韋伯分佈參數等等代表性統計量，得到良好的成果。The reliability and fatigue life of electronic packages are of a major concern to engineers. Traditional prediction approaches include numerical methods such as the finite element method (FEM) and experimental methods such as accelerated life testing (ALT). FEM, used mainly by design engineers, aims to predict the fatigue life of a package by observing physical processes that lead to failure. On the other hand, ALT is usually carried out by reliability or quality engineers to correlate the fatigue life of an electronic assembly under different environmental conditions in the form of acceleration factors (AF). This study bridges the gap between two types of engineers and presents an efficient and cost effective way of fatigue life prediction. Previous studies are mostly of a deterministic nature, neglecting the variation of dimension and material properties that are present in real life. By introducing parameter uncertainties into FEM modeling, this study uses FEM as a substitute for ALT experiments, giving the possibility of performing a large number of tests for a more accurate AF model without the experimental cost. An FEM model of the plastic ball grid array (PBGA) with 316 solder balls is constructed and verified against literature data. The model is then used for both deterministic (traditional) and probabilistic analyses (the proposed method), the results of which are used to devise its respective AF models. The study shows that the probabilistic approach is a great improvement over its deterministic counterpart, with better accuracy and a wider range of use. The effects of parameter variation are discussed, with the height of the BT Substrate being of the most importance. The life distribution of each of the 6 test conditions are also investigated, with an attempt at prediction of the statistical terms such as standard deviation and Weibull parameters, which shows promising results.口試委員會審定書 # Acknowledgements i 中文摘要 ii ABSTRACT iii CONTENTS v LIST OF FIGURES viii LIST OF TABLES x Chapter 1 Introduction..1 1.1 Background and Motivation 1 1.2 Research Purpose 3 1.3 Research Procedure 3 Chapter 2 Literature Review and Theory 6 2.1 Literature Review 6 2.1.1 General Research 6 2.1.2 Finite Element Method 6 2.1.3 Fatigue Life Formula 7 2.1.4 Parameter Uncertainties 8 2.1.5 Accelerated Life Testing 9 2.2 Fatigue 9 2.3 Reliability 10 2.3.1 Continuous Probability Distributions 11 2.4 Accelerated Life Testing 14 2.4.1 Acceleration Factor Model 15 2.5 Probabilistic Design System 15 Chapter 3 Finite Element Analysis ……………………………………………….17 3.1 Finite Element Assumptions 17 3.2 ANSYS Parametric Design Language (APDL) 18 3.3 Modeling Techniques 18 3.3.1 Reduced Modeling 19 3.3.2 Sub-Modeling 19 3.4 Model Dimensions and Material Properties 20 3.4.1 Model Dimensions 20 3.4.2 Material Properties 21 3.4.3 Mesh 21 3.5 Boundary Conditions and Loading Conditions 21 3.5.1 Boundary Conditions 21 3.5.2 Loading Conditions 22 3.6 Results 22 3.6.1 Fatigue Life 23 3.6.2 Verification of Finite Element Model 23 Chapter 4 Deterministic Model 35 4.1 Thermal Profiles 35 4.2 Results of Finite Element Analysis 35 4.3 Accelerated Factor Model 36 4.3.1 The Norris-Landzberg Model 36 4.3.2 Samela Model 37 4.3.3 Formulation of AF Model 38 4.4 Results of Deterministic Fatigue Life Prediction 38 Chapter 5 Probabilistic Model 41 5.1 Variation of Geometric Parameters and Material Properties 41 5.2 Effects of Parameter Variation 42 5.2.1 Sensitivity Analysis 42 5.3 Fatigue Life Distributions 42 5.4 Formulation of Accelerated Factor Formula 43 5.5 Results of Probabilistic Fatigue Life Prediction 44 5.5.1 Probabilistic Fatigue Life Prediction using All PDS Results 44 5.5.2 Probabilistic Fatigue Life Prediction using Averaged PDS Results 44 5.6 Comparison between Deterministic and Probabilistic Models 45 5.7 Discussion of Fatigue Life Statistical Terms under Different Conditions 46 Chapter 6 Conclusions and Future Work 63 6.1.1 Conclusions 63 6.1.2 Future work 64 REFERENCES 652372005 bytesapplication/pdf論文公開時間：2014/08/26論文使用權限：同意有償授權(權利金給回饋學校)有限元素分析加速測驗電子封裝體參數不確定性thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/263301/1/ntu-103-R00522514-1.pdf