臺灣博碩士論文加值系統

本文針對63Sn/37Pb銲錫材料，以Lemaitre的損傷理論結合內涵時間塑性理論(Theory of Endochronic plasticity)，探討在單軸循環負載下含疲勞損傷循環應力-應變反應。
在Mesoscale尺度下，取一具代表性之體積元素(Representative volume element－RVE)，定義損傷為RVE中任一面上所包含的缺陷面積與整個面積之比例。損傷時RVE內材料之有效彈性係數因缺陷面積擴大而下降。本文藉由疲勞損傷實驗所得應力-應變遲滯曲線進行分析，在定應變振幅下得到塑性應變範圍隨循環過程變化極小而視為定值，而應力表達須以損傷有效應力為之，符合Lemaitre提出的等效應變原理，因此含損傷增量式內涵時間之計算以損傷有效應力進行。
根據Lemaitre損傷演化律及本文假設循環負載下拉應力在最大值附近對循環損傷的貢獻最大，文中應力對各循環之損傷而言假設應力為最大拉應力，將材料參數S以指數型式表示，歸納出疲勞損傷在循環負載過程中的變化為指數型經驗式，提供63Sn/37Pb材料在循環負載作用時損傷情況的預測，並引入含損傷增量式內涵時間之計算中，假設同一循環的損傷為定值，其計算結果與實驗數據吻合，說明內涵時間塑性理論亦適用於損傷環境下的計算。

The paper is in accordance with 63Sn/37Pb material. The discussion of fatigue damage is under the condition of simple cyclic loading based on Lemaitre’s damage theory linking up with theory of Endochronic plasticity.
In Mesoscale, the damage is the rate of the defect area and the whole area in any cross section of Representative volume element — RVE. While being in damage, the elastic modulus reduces because of the expansion of the defect area. The analysis comes by the stress-strain hysteresis loop from fatigue damage experiment. Under the constant strain amplitude, the plastic strain range is regarded as a constant with small change in the process of cycles and the stress must be expressed in effective stress which agrees with the equivalence strain principle.
According to Lemaitre’s damage evolution law and the assumption of this paper that the cyclic loading maximum tensile stress has the most contribution to the cyclic damage and assume that the stress is the maximum stress .The material parameters S which are expressed in exponential form and generalize the variation in the process of cyclic loading is exponential experience equation which provide the expectation of cyclic damage of 63Sn/37Pb material and lead it into the calculation of damaged incremental form and assume that damage keeps constant during the same cycle. The results match the experimental data. It proves that the Endochronic plasticity theorem adopt the calculation of damage environment.

考試合格證明
摘要Ⅰ
誌謝Ⅱ
目錄Ⅲ
表目錄Ⅵ
圖目錄Ⅶ
符號說明Ⅹ
第一章 緒論1
1-1 前言1
1-1-1連接技術2
1-1-2 銲錫凸塊2
1-2 研究動機與目的2
1-3 文獻回顧3
1-3-1 損傷分析理論之文獻回顧3
1-3-2 內涵時間塑性理論之文獻回顧5
第二章 損傷理論與內涵時間塑性理論基礎7
2-1損傷在力學上的表示法7
2-1-1損傷下的有效應力觀念9
2-1-2等效應變原理10
2-1-3損傷下的彈性定律10
2-2疲勞損傷理論在循環負載之應用12
2-2-1 Lemaitre損傷演化律12
2-2-2塑性應變範圍13
2-2-3累積循環塑性應變14
2-2-4定應變振幅下之損傷演化方程式15
2-3 內涵時間塑性理論16
2-3-1增量式內涵時間本構模式18
2-3-2含損傷之增量式本構模式及計算20
第三章 含損傷增量式內涵時間理論分析與實驗之討論22
3-1 實驗方法22
3-2 實驗之修正23
3-2-1 修正過程23
3-3 疲勞損傷演化律之決定26
3-3-1疲勞損傷下彈性係數之變化26
3-3-2循環疲勞塑性應變範圍Δεp 26
3-3-3累積塑性應變P 27
3-3-3-1累積塑性應變P的計算27
3-3-3-2累積塑性應變P與循環圈數N之關係27
3-3-3-3疲勞損傷D與累積塑性應變P之關係28
3-3-4 材料參數S的決定29
3-3-5 疲勞損傷與循環圈數之關係30
3-4 定應變振幅下含損傷內涵時間增量式計算31
3-4-1鬆弛模數中材料參數之決定31
3-4-2定應變振幅下含損傷內涵時間增量式之計算
法及結果34
第四章 結論及未來研究方向36
4-1結論36
4-2未來發展及研究方向37
參考文獻72
自述

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