本文是應用有限元素軟體ANSYS分析低溫共燒陶瓷製程中所產生的應力問題。探討燒結過程中所產生之燒結應力、降溫過程所產生之熱應力。陶瓷基板和銀之收縮值不匹配，以熱收縮係數處理燒結過程之密度變化及利用元素去除之技巧來處理超過破裂應力之情形和降溫過程中熱膨脹係數不匹配所產生殘留應力之分佈。

In this study, stress problems occurring in low tempera -ture cofired ceramic processes are analyzed by finite element package ANSYS. Sintering stresses of sintering processes and residue stresses in cooling processes are investigated. The thermal shrinkage coefficient are used to deal with the density variation due to the shrinkage mismatch between the green tape and silver paste in the sintering processes. Deleting the elements is used to treat the situation when the element stress exceeds its fracture stress. The residue stresses due to the mismatch of the thermal expansion coefficients in cooling processes are also discussed.

目錄……………………………………………………………………..Ⅰ
圖目錄…………………………………………………………………. Ⅲ
表目錄…………………………………………………………………. Ⅶ
摘要…………………………………………………..…………………Ⅷ
第一章 緒論……………………………………………………………..1
1-1前言…………………………………………………………………..1
1-2低溫共燒陶瓷的優點………………………………………………..3
1-3研究動機與本文之目的……………………………………………..4
1-4文獻回顧……………………………………………………………..5
第二章 基本理論與彈性係數之量測…………..………………………8
2-1熱傳遞理論……………………………………….………...………..8
2-2力學理論……………………………………………………………..9
2-3結構熱傳偶合分析模式………………………………..…………..11
2-4非線性分析理論………………………………………………..…..12
2-5彈性係數之量測…………………………………………………....16
第三章 有限元素模式之建立…………………………………………23
3-1材料性質之描述……………………………………………………23
3-1-1陶瓷基板(Green tape)材料性質之描述……………………23
3-1-2銀膏(Silver paste)材料性質之描述………………………24
3-2基本假設…………………………………………………………....25
3-2-1材質之假設……………………………………………………26
3-2-2模型之架構及幾何描述………………………………………28
3-3邊界條件及材質之假設……………………………………………28
3-3-1邊界條件及網格化……………………………………………29
3-3-2模擬材質之假設………………………………………………30第四章 模擬結果與討論………………………………………………44
4-1前言…………………………………………………………………44
4-2收縮值不配合分析之結果…………………………………………44
4-2-1尺寸變化情形…………………………………………………44
4-2-2燒結應力………………………………………………………45
4-3熱膨脹係數不匹配分析之結果………………………………........47第五章 結論與建議……………………………………………………64
5-1結論………………………………………………………………....64
5-2建議…………………………………………………………………65




圖目錄
圖1-1LTCC生產製程[19].……………………………………………...2
圖1-1LTCC生產流程圖[17]…..………………………………………...2
圖1-3多層陶瓷的共燒被動元件集成[19]…………………………….3
圖2-1控制體積[15].………………………………………………….18
圖2-2不同硬化法則之應力空間……………………………………...18
圖2-3等向硬化………………………………………………………...19
圖2-4動態硬化………………………………………………………...19
圖2-5陶瓷基版(green tape)試片………………………………….. 20
圖2-6拉伸試片尺寸圖………………………………………………...21
圖2-7INSTRON 5582萬能試驗機………………………………..……..21
圖2-8未燒結前陶瓷基板之應力應變關係…………………….……..22
圖3-1-1Green tape 之組成(未燒結前)[17]………..………………33
圖3-1-2陶瓷和銀之收縮值[11]...……………………………………34
圖3-2燒節製程之升降溫圖[18]……………………………………...34
圖3-3有限元素分析流程………………………………………….......35
圖3-4低溫共燒陶瓷堆疊體圖………………………………………...36
圖3-5堆疊體之三視圖………………………………………………...37
圖3-6對稱邊界之圖形………………………………………………...38
圖3-7網格化圖形.…………………………………………………….38
圖3-8模擬之溫度時間歷程圖………………………………….……..39
圖3-9應力分析流程……………………………………………….…..40
圖3-10(模式1-a)銀及陶瓷之收縮值………………………………..41
圖3-11(模式1-a)銀-陶瓷之塑流應力(1058K以下)……………….41
圖3-12(模式1-a)銀-陶瓷之塑流應力(1058K以上)………..………41
圖3-13(模式1-a)銀-陶瓷楊氏模數轉換過程…………..……..…….42
圖3-14(模式1-b)銀-陶瓷之收縮值……………………………..…...42
圖3-15(模式1-b)銀-陶瓷之塑流應力(298K)……………………….42
圖3-16(模式1-b)銀-陶瓷之塑流應力(1123K)………………..…….43
圖3-17(模式1-b)銀-陶瓷楊氏模數之轉換過程…………………….43
圖3-18銀-陶瓷之塑流應力.…………………………………………43
圖4-1外部陶瓷本體收縮值之表示……………………………….…..49
圖4-2內部銀本體收縮值之表示………………………………….…..49
圖4-3陶瓷X-方向之收縮值……………………………………….….50
圖4-4銀X-方向之收縮值……………………….……………….……50
圖4-5陶瓷Y-方向之收縮值………………………………………….50
圖4-6銀Y-方向之收縮值…………………………………………….51
圖4-7共燒過程最高溫之等效應力分佈……….……………………..52
圖4-8燒結過程中缺陷示意圖[16]…………………………………...52
圖4-9(模式1-a)銀板x方向之應力……………………………….....53
圖4-10(模式1-a)銀板x方向之應力…………………………….…..53
圖4-11(模式1-a)銀板x方向之應力…………………………….…..53
圖4-12(模式1-a)銀板y方向之應力.……………………………….54圖4-13(模式1-a)銀板y方向之應力…………………………………54
圖4-14(模式1-a)銀板y方向之應力………………………….……..54
圖4-15(模式1-a)陶瓷x方向之應力…………………………………55
圖4-16(模式1-a)陶瓷x方向之應力…………………………….…..55
圖4-17(模式1-a)陶瓷x方向之應力………………………………...55
圖4-18(模式1-a)陶瓷y方向之應力………………………………...55
圖4-19(模式1-a)陶瓷y方向之應力………………………………...56
圖4-20(模式1-a)陶瓷y方向之應力………………………………...56
圖4-21(模式1-b)應力過大處予以刪除之網格圖…………………...57
圖4-22(模式1-b)接點處x方向之應力………………………………57
圖4-23(模式1-b)接點處y方向之應力………………………………58
圖4-24銀板升降溫之等效應力態…………………………………….58
圖4-25熱疲勞破壞之裂縫[9]………………………………………...59
圖4-26銀板X-方向升降溫之應力………………………………….....59
圖4-27銀板Y-方向升降溫之應力……………………………………60
圖4-28銀板von Mises升降溫之應力……………………………….60
圖4-29接點X-方向升降溫之應力………………………………….....60
圖4-30接點Y-方向升降溫之應力…………………………………....61
圖4-31接點von Mises升降溫之應力……………………………….61
圖4-32陶瓷X-方向升降溫之應力……………………………………61
圖4-33陶瓷Y-方向升降溫之應力……………………………………62
圖4-34陶瓷von Mises升降溫之應力……………………………..…62
圖4-35銀板之塑性功………………………………………………….62
圖4-36銀接點處之塑性功…………………………………………….63









表目錄
表3-1陶瓷及銀膏之成分[2]………………………………………….31
表3-2陶瓷及銀之熱傳性質…………………………………………...31
表3-3裝體陶瓷及銀膏其尺寸描述…………………………………...28
表4-1LTCC之物理特性及收縮值[14]………………………………...51

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清華大學博士論文