二維麻田散鐵多晶薄膜微結構模擬

Abstract

本團隊提出一套以能量低點拘束理論來建立麻田散鐵微結構演化的理論架構，本理論以演化過程中能量逐步趨小的方式進行收斂，藉由能量最小原理觀察在能量最低點的微結構排列方式。在模擬上，使用快速傅立葉轉換計算應力場。 我們設計了簡單的二維兩晶粒薄膜模型，其中一晶粒以θ 角的轉量有別於另外一晶粒，觀察晶粒界面間的諧和關係。此外，對形狀記憶合金，我們在模型中施以外加應變，再執行模擬，並且對施加的應變和模擬結果內變數繪製成圖，查看外加應變對於微結構造成的影響， 亦持續觀察在單晶和多晶之間的分別。 在多晶中，晶粒的微結構會隨著θ 角轉量而旋轉，理論上其轉動的量也是θ，但是模擬結果中顯示晶粒彼此界面上缺乏諧和性，雖然如此，內部微結構的演化結果造成宏觀來看整塊模型沒有變形，並且處於能量最小的情況。 外加應變和內變數繪製成遲滯曲線圖，我們比較了單晶和多晶在不同厚度的結果，發現受到厚度的影響不大；而其他條件一樣時，多晶的狀況越複雜，需要越大的應變來驅使內變數轉換，也就是遲滯曲線圖轉換較晚。

Our team proposed a framework based on constrained theory, to establish evolution of microstructure in martensitic polycrystalline films. In this theory, the evolution converges by energy restraining gradually. We observed the arrangement of the microstructure of the bottom energy. We study the microstructure according to the arrangement as well as its evolutionary process of polycrystalline, and compute the stress with fast algorithm (FFT). We design a simple model which is two-dimensional two crystals film, and give one angle θ degree rotation to distinguish from another, we observe the compatibility of the grain boundary. In addition, we carry on the numerical simulation in another case, the thin film model is exerted by each kind of strain. We draw up with the strain and the result of simulation, and keep observing the difference between the single crystal and poly crystal micro structure. In poly crystal, the grain micro structure change depend on the θ degree rotation, but the grain boundary lack for compatibility, for all this, there is no strain of hole model attribute to the evolution of micro structure inside, under the bottom energy. The exerted strain and the variant can be drawn up the hysteresis loop. We have compared the single crystal and the poly crystals in the different thickness, and find the the influence of thickness is not conspicuous. And in the same other conditions, the crystals are more complex, more exerted strain is needed to urge the switch.