A Study on the Method of Elastic-Plastic-Creep Finite Element Analysis for a Solder Joint in a Surface Mounted Component

A model of a surface-mounted gull-wing-leaded device was proposed for elastic-plastic-creep finite element analysis. Stresses and strains of a solder joint und ercyclic thermal loads were analyzed. Plastic strain and creep strain were calculated, even for the temperature-change domain. The results of cyclic hysteresis behaviors were compared with those analyzed based upon the conventional model in which both the dependence of temperature on the yield stress of the solder and creep behavior in loading and unloading temperature cycling were ignored. It has been found that it is essential to consider these factors. The effects of the parameters such as temperature increments, strain rate and dwell time on the analytical results of stress were also studied.ガルウィング型リードを例に，はんだ接合部の熱応力解析における温度増分，温度勾配および等温保持時間などのパラメータが解析結果に与える影響について検討した．journal articl

Evaluation of Singular Stress Field at the End of the Interface of Dissimilar Materials Using Akin's Singular Element

A three-noded triangular element proposed by Akin, which has a stress singularity of O (γ^), was investigated. A singular element was incorporated into a general-purpose finite element program MARC, in order to analyze the two-dimensional stress field of joints made up of dissimilar materlals. A typical eight-noded isoparametric element was also used to analyze the same problem. Finally, by comparing the accuracy and efficiency of the two example problems, we have shown that Akin's singular element is very useful for the analysis of the stress field at the interface of dissimilar materials.半導体パッケージのような特異応力場が多数ある構造に対してAkinが提案した特異要素を使用することを提案し，一般の要素で密な分割を行った場合と結果の精度と労力について検討した．journal articl

Analytical and Experimental Hybrid Study on Thermal Fatigue Strength of Electronic Solder Joints : 2nd Report, Evaluation by Isothermal Mechanical Fatigue Tests

An isothermal mechanical fatigue test method and fatigue testing equipment were developed to investigate the low cycle fatigue strength of Sn-Pb eutectic solder joints. Based upon the results of finite element analysis, it is found that the rate of inelastic strain components (plastic strain and creep strain) in the solder joints can be accurately controlled by the displacement rate of the linearactuator of the test equipment. The isothermal mechanical fatigue tests were carried out by controlling the displacement at a very high displacement rate, and a very low displacement rate, respectively ; only plastic strain was generated in the solder joints at the high displacement rate, and only creep strain at the low rate. It is found that the low cycle fatigue life of Sn-Pb eutectic solder joints is not grealty affected by the ratio of inelastic components. Therefore, it can be said that the low cycle fatigue life can be estimated from the equivalent inelastic strain range, and the relationship of the cycles to failure and the strain range follows Coffin-Manson's law. In comparison of the mechanical fatigue strength results with the results of the cyclic thermal tests, it was found that the mechanical fatigue test method can be used as a good accelerated test method for the thermal fatigue strength of Sn-Pb eutectic solder joints.錫-鉛共晶はんだを対象として，機械的せん断疲労試験を行い熱サイクル温度試験の結果と比較した．解析・実験ハイブリット評価により，機械的試験の加速試験としての有効性を示した．journal articl

Analytical and Experimental Hybrid Study on Thermal Fatigue Strength of Electronic Solder Joints : 1st Report, Rationalization of Accelerated Thermal Cyclic Test and Evaluation of Thermal Fatigue

Stress-strain analyses for Sn-Pb cutectic solder joints in a thin single outline package (STOP), a ball grid array (BGA) assembly, and a leadless ceramic chip carrier (LCCC) were carried out for investigation of plastic-creep behavior, and of stress relaxation behavior due to accelerated thermal cycling tests or the operating conditions. the temperature dependence of plastic behavior (yield stress) and creep behavior (creep properties) were taken into account in all numerical analyses. The results of finite element analysis (FEA) show that in an accelerated terperature cycling test, long high-temperature and low-temperature dweel times do not contribute to an increase in the cyclic inelastic equivalent strain range in solder joints, although the creep behavior occurring during the dwell times under operating conditions is very important in estimation of the fatigue life of solder joints. Based upon the results of the strain analyses, an efficient temperature cycling test process for microelectronic solder joints was proposed, and cycling tests were carried out. The experimental results show that the thermal fatigue life of microelectronic Sn-Pb eutectic solder joints can be predicted by an associated fracture parameter of total equivalent inelastic strain range, and the fatigue life of solder joints follows Coffin-Manson's law.錫-鉛共晶はんだを対象として，熱サイクル加速試験の効率化と熱疲労強度評価を行った．はんだの非線形特性を考慮した解析・実験ハイブリット評価により，Coffin-Manson則に基づき熱疲労寿命を評価する手法を確立させた．journal articl

台灣農業資本結構與農業資金供需之研究

一、研究目的： （１）探討在經濟發展過程中，農業資本結構的變動趨勢以及農業部門的財務地位和 償債能力。 （２）農業發展已至資本集約的階段，資金需求殷切，然供給是否能妥善配合﹖論者 或謂資金需求大於資金供給，實際情況是否如此﹖本文擬從實證與理論著手驗證之。 二、資料來源： （１）台灣省政府農林廳「台灣農家記賬報告」。 （２）中國農民銀行調查研究室「台灣省專業兼辦農貸機構貸款數金額統計表」。 （３）中央銀行「金融機構業務概況年報」。 （４）行政院農發會「各類農業專案放款辦理情形」。 三、研究方法： （１）以「農業部門資產負債平衡表」為分析基礎，比較歷年的資本結構並剖析其變 動趨勢。同時採用「財務比率分析」計算各年之流動比率、負債淨值比率、淨值資產 比率及負債資產比率，比資明瞭農業部門的償債能力。 （２）就供給和需求雙方面的觀念，探討台灣農業資金運用之情況。以演繹法求算各 種模式下的農業資金需求，再以此和農業資金供給的時間序列資料相互比較，據以尋 求資金供需失衡之解答。 四、研究結果： 由「農業部門資產負債平衡表」的建立，可發現台灣農業部門的資本結構，其槓桿比 率偏低，顯示農家對資本的運用過於保守。鑑於農業部門高幅度的淨值成長趨勢，適 度提高供入資本的比率，當不致發生不利的財務風險。此外，資金的供給無法有效滿 足農民的需求，主要是由於農業資金融通的方式與條件尚存有難以克服之障礙，於是 產生多年來農業資金在總量上「供過於求」和在品質上「供不應求」的件衡局面

Akin特異要素による異材接合端部における特異応力場の評価

A three-noded triangular element proposed by Akin, which has a stress singularity of O (γ^), was investigated. A singular element was incorporated into a general-purpose finite element program MARC, in order to analyze the two-dimensional stress field of joints made up of dissimilar materlals. A typical eight-noded isoparametric element was also used to analyze the same problem. Finally, by comparing the accuracy and efficiency of the two example problems, we have shown that Akin's singular element is very useful for the analysis of the stress field at the interface of dissimilar materials.半導体パッケージのような特異応力場が多数ある構造に対してAkinが提案した特異要素を使用することを提案し，一般の要素で密な分割を行った場合と結果の精度と労力について検討した

表面実装部品はんだ接合部の弾塑性-クリープ有限要素解析法に関する研究

A model of a surface-mounted gull-wing-leaded device was proposed for elastic-plastic-creep finite element analysis. Stresses and strains of a solder joint und ercyclic thermal loads were analyzed. Plastic strain and creep strain were calculated, even for the temperature-change domain. The results of cyclic hysteresis behaviors were compared with those analyzed based upon the conventional model in which both the dependence of temperature on the yield stress of the solder and creep behavior in loading and unloading temperature cycling were ignored. It has been found that it is essential to consider these factors. The effects of the parameters such as temperature increments, strain rate and dwell time on the analytical results of stress were also studied.ガルウィング型リードを例に，はんだ接合部の熱応力解析における温度増分，温度勾配および等温保持時間などのパラメータが解析結果に与える影響について検討した