雙尺度相場架構應用於微結構與等效性質之研究

Development of Two-Scale Phase Field Models with Applications to Microstructures and Their Effective Properties

陳宏志(Hung-Zhih Chen)

指導教授 ： 舒貽忠

國立臺灣大學/工學院/應用力學研究所/博士(2013年)

https://doi.org/10.6342/NTU.2013.00864

摘要

本文目的為建立適用於不同材料的多尺度模擬系統，並且能模擬特定條件下的微結構分佈，以及建立微結構與宏觀的連結關係，進而對材料整體的宏觀效應有進一步的理解。無論是形狀記憶合金或者鐵電材料，對於宏觀的材料特性都必須由微觀角度進行分析與研究，因此團隊過去以新式相場架構進行研究，並且成功的模擬出諸多情況下的微結構分佈。本文則是在於前人的基礎上，以多尺度的概念建立宏觀特性與微觀微結構的連帶關係，藉此分析薄膜元件受到溫度與壓力影響而發生的制動行為。另一個重點則是建立可用於非均質材料係數的相場架構，此相場架構建立於Eshelby的等效模型上，能正確的模擬材料微結構，更可以藉由等效架構與微結構計算出材料宏觀上的各式等效材料模數。
本文所建立的雙尺度相場架構與前人最大的不同點在於，本文的相場架構引入了溫度的影響，並且成功的模擬形狀記憶合金的超彈性行為。配合多尺度概念所模擬的薄膜元件制動行為，不僅反應了不同晶系與晶向對於薄膜元件制動量與反應速度的影響，更可以藉由模擬呈現不同薄膜的形變行為。
本文利用Hashin-Shtrikman的變分方式使得非均質問題的應力場等於均質材料等效應力場，除了麻田散鐵材料外本文也推導出鐵電材料的等效能量型式。不僅能夠模擬出材料的微結構，更可以計算出材料的等效材料模數。從結果可以發現消極化電場對於等效材料模數的影響非常顯著，因此不同晶域之間的介面寬度在後續研究中是值得注意的。

關鍵字

形狀記憶合金 ； 鐵電材料 ； 微結構模擬 ； 雙尺度相場模型 ； 薄膜模擬 ； 多尺度分析 ； 非均質材料 ； 等效材料模數 ； 消極化電場

並列摘要

The thesis aims to develop multiscale material models for microstructure simulations and their macroscopic properties under environmental loadings. The materials of current interest are shape-memory alloys and ferroelectrics which possess particular microstructures in response to external conditions. The simulations are based on multiscale phase-field models for analyzing shape-memory thin film devices under varying temperature and fixed pressure loading. In addition, phase-field models accounting for material inhomogeneity are established based on the Eshelby principle. It is applied to the calculation of effective properties of particular microstructure.
Specifically, in the case of shape-memory alloys, a two-scale phase-field model for describing the coexistence of austenite and martensite phases is developed. It accounts for the temperature effect so that the model can be applied to investigate the actuation behavior of shape-memory micropump. In addition, the macroscopic deformation of the thin-film device is predicted by introducing another length scale which is linked to the microscale through the calculation of accommodation strain.
Next, a vairational formulation based on the Hashin-Shtrikman principle is proposed for establishing phase-field models considering the effect of material inhomogeneity. The results show that both patterns and their overall properties are able to be simulated effectively. Besides, it is shown that a key factor influencing the effective constants of ferroelectrics is the depolarization field within the neighboring domains.

並列關鍵字

Shape-Memory Alloys ； Ferroelectrics ； Microstructure Simulations ； Two-Scale Phase-Field Model ； Thin Films ； Multiscale Analysis ； Nonhomogeneous Materials ； Effective Properties ； Depolarization Field

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