臺灣博碩士論文加值系統

本文探討循環比例位移路徑( )下Sn/3.5Ag/0.75Cu BGA銲點試片拉/扭循環負荷之初始疲勞壽命預測。首先利用BGA錫球直立高度0.52mm修正Lee, T. K. 2007年碩士論文中位移-負荷數據，並繼續使用循環內涵時間黏塑性理論之材料參數與核心函數預測各 下之循環應力-應變曲線，利用等效非彈性應變 與等效應力 建立其關係式 。
本文(1)引入損傷等效非彈性應變 於彈性應變密度釋放率和損傷率關係式中之參數 ；(2)在內涵損傷時間定義下建立循環比例位移路徑之內涵損傷演化方程式，並提議損傷累積速率與循環圈數 有乘冪關係。由此可推導出損傷因子 ，並由循環負荷振幅隨 之下降數據獲得 及 並發現 為 、 及 的函數而 與 無關。在 之下Endochronic疲勞壽命預估公式為 ，其 與 無關，但 ，故 vs. 圖中預測結果為與 相關之曲線。此結果在不同範圍 下，可用多段直線表達Coffin-Manson之經驗式。

The purpose of this paper is to investigate the fatigue initiation life prediction of BGA (Sn/3.5Ag/0.75Cu) solder joint specimens under mixed mode cyclic proportional displacement path( ) .First, by using the BGA solder joint standoff 0.52mm to adjust the displacement-loading data of the master's thesis of Lee, T. K. in 2007. And continue with using the material parameters and kernel function of Endochronic cyclic viscoplasticity to simulate cyclic stress-strain curve under proportional displacement path. Then using the effective inelastic strain and effective stress , the relation was established.
This paper(1) aim to employ damage effective strain in parameter that depend on elastic strain energy density release rate and damage rate. (2)Using the definition of intrinsic damage time to establish evolution equation of intrinsic damage under cyclic proportional displacement path. This paper purpose the power form relation between damage accumulate rate and numbers of cycle N. Then damage factor can be derived from the relation, by cyclic loading amplitude vs. N data could compute and n. The results find that depend on , and , n is independence from . Endochronic fatigue life prediction under proportional displacement path , is independence from , but , therefore the result of figure vs. depend on , the result under the different scope of , Coffin-Manson relationship can be expressed by straight lines.

摘要 .................................................................................................................... I
Abstract............................................................................................................. II
誌謝 ................................................................................................................. IV
符號說明 .......................................................................................................... V
目錄 ................................................................................................................. IX
表目錄 ........................................................................................................... XII
圖目錄 .......................................................................................................... XIII
第一章 緒論 ..................................................................................................... 1
1-1 前言 ..................................................................................................... 1
1-2 研究動機 ............................................................................................. 2
1-3 文獻回顧 ............................................................................................. 2
第二章 含循環損傷內涵時間黏塑性本構方程式 ......................................... 6
2-1 f0 與材料參數�v IN�w
a �� ��,e�s 之決定 ........................................................ 7
2-2 循環穩態下增量式本構方程式 ....................................................... 11
2-3 循環比例位移路徑下內涵損傷演化方程式之建立與Endochronic
疲勞壽命預估公式 .................................................................................. 18
2-3-1 循環比例位移路徑下內涵損傷演化方程式之建立 ............ 18
2-3-2 循環比例位移路徑下之Endochronic 疲勞壽命預估公式 .. 24
第三章 Sn/3.5Ag/0.75Cu 銲點試片循環比例位移路徑下之負荷-位移修正
法 ..................................................................................................................... 26
3-1 本章介紹 ........................................................................................... 26
3-2 負荷-位移修正方法 ......................................................................... 27
第四章Sn/3.5Ag/0.75Cu 銲點試片循環比例位移路徑下內涵時間黏塑性理
論之計算結果與實驗比較 ............................................................................. 34
4-1 本章介紹 ........................................................................................... 34
4-2 以單剪試驗(��=90�� )為基準決定內涵時間黏塑性理論之材料參數
.................................................................................................................. 34
4-2-1 定溫下以位移振幅(da=10μm)為基準之核心函數 ........... 36
4-2-2 材料函數�v IN�w
a g e�s 之決定 ......................................................... 37
4-2-3 循環軸向位移(Φ=0�� )之計算結果與實驗之比較 ................ 40
4-2-4 材料函數
IN
κ(0�� ,e�sa ) 之決定 .................................................... 41
4-2-5 材料函數
IN
a κ(27��,e�s ) 、
IN
a κ(45��,e�s )、
IN
a κ(63��,e�s ) 之決定 .... 42
4-2-6 循環比例位移角度( Φ=27��, 63��)之計算結果與實驗之比較
........................................................................................................... 44
4-3 等效循環應力-應變關係式之建立 .................................................. 45
第五章 Sn/3.5Ag/0.75Cu 銲點試片在循環比例位移路徑下含損傷內涵時
間黏塑性理論與疲勞初始壽命預估 ............................................................. 50
5-1 本章介紹 ........................................................................................... 50
5-2 含循環損傷內涵時間黏塑性理論計算結果與實驗之比較 .... 50
5-2-1 含循環損傷剪向位移(Φ=90�� )計算結果與實驗之比較 ..... 51
5-2-2 含循環損傷軸向位移( Φ=0�� )計算結果與實驗之比較 ....... 52
5-2-3 含循環損傷比例位移角度( ��=45�� )計算結果與實驗之比較
........................................................................................................... 54
5-3 臨界循環損傷因子C D 之決定 .......................................................... 55
5-4 Sn/3.5Ag/0.75Cu 銲點試片疲勞初始壽命之預估 .......................... 57
5-4-1 A、n 之決定 ......................................................................... 57
5-4-2 k�S�v���w、n�S之決定 .................................................................. 59
5-4-3 材料參數B�� 與Endochronic 疲勞壽命預估公式 ................ 60
第六章 結論 ................................................................................................... 63
附表 ................................................................................................................. 65
附圖 ................................................................................................................. 69
參考文獻 ....................................................................................................... 121

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