具非均質麻田散鐵薄膜基材系統之微結構模擬

Abstract

本文的目的在於建立一套能觀察二維非均質麻田散鐵薄膜於基材上微結構模擬的系統，對整體材料微結構的演化能有進一步的了解。過去，本研究團隊以新式相場法的架構進行研究，而本論文以此為根基，發展出一套能夠描述二維非均質麻田散鐵材料薄膜基材微結構演化的系統並且進行數值分析模擬。 本研究藉由能量極小原理搭配變分法推導出演化方程式，在週期性邊界上利用快速傅立葉轉換建立計算材料內應力之快速演算法，非週期性邊界則利用半隱性法取時間上的離散化。對於薄膜基材系統之數值模擬，(1) 我們首先驗證此方法計算應力場演算法之正確性，(2)調整係數將此與研究團隊發展的薄膜系統結果比較，(3) 改變模擬參數，觀察當薄膜與基材之係數不同時，能量最低時的微結構晶域分布圖，並將其與係數相同的結果比較並討論不同之處。在未來可為進行相關實驗或者進行類似模擬的研究員，提供相當程度的幫助。

This thesis aims to develop a model for microstructure simulation in a martensitic film/substrate system accounting for out-of-plane elastic inhomogeneity. The model is built on the novel phase-field approach developed by the present research team. But it differs from the consideration of elastic inhomogeneity between the film and substrate. The thesis derives the microstructure evolution equation based on the calculus of variation. The elastic stress field is solved by applying the Fourier Transform over the periodic boundary condition along the film. In addition, the semi-implicit method and central difference method are also used for non-periodic boundary conditions such as traction-free on the top of film and stationary at the bottom of substrate. The calculation of stress field is validated by the comparison with COMSOL simulation. In addition, the simulation results under the consideration of vanishing elastic constants of substrate agree with those in the case of free-standing film. Finally, our results indicate that the microstructure patterns accounting for elastic inhomogeneity between film and substrate are different from those based on the assumption of identical elastic moduli.