改良相場法模擬鐵磁形狀記憶合金磁彈耦合微結構之研究

Abstract

鐵磁形狀記憶合金是一個同時具有鐵磁性以及鐵彈性的材料，由於內部微結構排列與演化使其具有多功能的特性，近年來廣泛的被研究。為了正確的使用這些材料，分析與模擬材料內部微結構是極重要的課題，因此從相場法著手進行分析。 本文(1)使用「新式相場法」以及「改良新式相場法」兩種數值模擬方法進行比較，其中發現「改良新式相場法」可以提高模擬效率以及使結果更穩定；(2)以本研究團隊所發展的理論為基礎，將「改良新式相場法」應用在鐵磁形狀記憶合金磁彈耦合中磁域微結構的演化，微觀磁學的部分使用著名的Landau Lifshitz Gilbert方程式來描述磁化向量的演化。最後在這些方程式的描述下，藉由能量最小原理搭配變分法來推導各種能量所造成的驅動力，並利用FFT(Fast Fourier Transform)的技術來計算消磁能以及應力場。4.2.1節中模擬結果與實驗[33]得到圖案相符，4.2.3節中展示材料受壓力後其兄弟晶翻轉的情形，4.2.4節驗證材料受磁場產生極大的應變；但是相對大的應力(blocking stress)會阻止此應變的產生，最後在4.2.5節中模擬了4.2.4節中的應變在適當磁場下的恢復性，證明材料在不同磁場下具有準塑性(quasi-plastic)或偽彈性(pseudo-elastic)的特性。

Ferromagnetic shape memory alloys (FSMA) are those possessing both ferromagnetic and ferroelastic orderings. Their unique properties are due to the formation of very fine scale magnetic and elastic domains. As a result, these materials have been extensively studied by understanding how and why these domains are formed and arranged. One of the power tools for investigating them is to use the phase-field simulations. Different from the “novel phase-field method” developed by the research group of Professor Shu, this thesis proposes a modification based on the new choice of phase-field variable [25]. It is shown that the modified method is more efficient and stable than the original approach. Second, we use this modified model, together with Landau-Lifshitz-Gilbert equation, to simulate the magnetoelastic couplings in FSMAs. First, the evolution equations are obtained by the vraiational argument and are solved numerically by Fast Fourier Transform (FFT). In Section 4.2.1, the simulated domain pattern is illustrated to agree well with the observed microstructure. Second in Section 4.2.3, it is shown that applied compressive stress can induce favorable magnetic domains. In addition, Section 4.2.4 demonstrates the effect of force and magnetic fields on the formation of magnetoelastic domains. It is found that magnetic-field-induced strain in FSMAs results from the process of variant rearrangement. Yet such rearrangement can be blocked by a relatively large compressive stress. Finally, it is demonstrated that FSMAs exhibit quasi-plastic or pseudo-elastic behavior depending on the strength of applied magnetic field.