多層樑結構層間熱應力分析與應變能釋放率計算

Thermal Stress Analysis and Strain Energy Release Rate in a Multi-layer Beam

林志賢(Chin-Hsien Lin)

指導教授 ： 何旭川

元智大學/工程學院/機械工程學系/碩士(2006年)

https://doi.org/10.6838/YZU.2006.00306

摘要

多層材料的複合結構為半導體及微機電製程中常見的結構組成，當結構承受溫度變化各層材料由於熱膨脹係數不同產生熱應力，使結構翹曲變形甚而在界面出現裂縫。本文針對多層樑結構因溫度變化所產生之熱應力進行研究，分析雙層樑結構、三層樑結構中間區域軸向熱應力及自由邊(Free Edge)熱應力，並應用破壞力學理論推導出多層樑結構含界面裂縫之應變能釋放率。再將理論推導所得多層樑結構熱應力與應變能釋放率與ANSYS有限元素數值解比較，驗證理論推導的準確性。並藉由參數分析暸解各層材料之楊氏係數比、熱膨脹係數比與厚度比對熱應力與應變能釋放率之影響。

關鍵字

多層樑結構 ； 熱應力 ； 界面裂縫 ； 應變能釋放率

並列摘要

Multi-layer structures are common in electronic package especially for the micro devices manufactured Via the semi-conductor processes or MEMS processes. As the multi-layer structures subject to uniform temperature change, the thermal stresses are induced due to the mismatch of the coefficients of thermal expansion between the adjacent layers. In this investigation, the longitudinal thermal stresses in the middle region of a bi-layer beam and a tri-layer beam are derived basing on the Euler-Bernoulli beam theory. The strain energy release rate of a bi-layer beam and a tri-layer beam with interfacial crack are derived basing on the theory of fracture mechanics. The analytical expressions of the longitudinal thermal stress and strain energy release rate are validated by the finite element method. The effect of Young’s modulus, coefficients of thermal expansion and thickness between the adjacent layers on the thermal stress and strain energy release rate are presented through parametric study.

並列關鍵字

multi-layer beam ； thermal stress ； interfacial crack ； strain energy release rate

參考文獻

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