以多階層狀結構理論模擬形狀記憶合金之相變研究

Abstract

本文建立一個有別於現象學角度的麻田散鐵模型，使用多階層狀微結構理論來探討形狀記憶合金之力熱耦合性質與其相變過程。本文以立方晶-正方晶固態對固態相變為例，考量高溫相為立方晶結構的沃斯田鐵與低溫相為正方晶結構的麻田散鐵。文中考量具應變諧和的多階層狀麻田散鐵微結構與沃斯田鐵兩相層狀結構，並利用層狀體積分率來描述晶相的組成與演化過程。 本文使用三種控制方式模擬相變過程，分別為應力控制、應變控制和溫度控制，其結果與實驗上大致相同。以應力、應變控制為例，高溫時可觀察出，施加的應力或應變釋放後會使材料恢復原狀，這符合記憶合金中的擬彈性特性。另外，當溫度超過相變溫度，會使在低溫變形的麻田散鐵材料恢復原狀，此現象稱為形狀記憶效應。由模擬的結果中可發現到應變諧和對遲滯的影響甚大，在不滿足諧和的情況下，遲滯會較為明顯。

Instead of choosing phenomenological models to describe thermoelastic martensitic phase transformation, the thesis develops a model based on multirank laminated microstructure to study it. Suppose the high temperature phase has a cubic symmetry and the low temperature phase possesses a tetragonal symmetry. A cubic-to-tetragonal solid-to-solid phase transformation is proposed to demonstrate this model. Here, the austenite phase alternates periodically with the martensite phase which consists of compatible tiny banded microstructure. The local volume fractions of low rank structure are used to describe different symmetry related variants and their magnitudes vary at the emerging of new phases. The evolution of variants is simulated under stress/strain/temperature control, and the results are qualitatively in agreement with experimental observations. For example, either stress or strain control will result in no permanent deformation at the removal of loads, giving rise to pseudoelastic behavior. In addition, at low temperature, the deformed martensitic material will recover its original shape when it is heated above the transformation temperature, giving rise to shape-memory behavior. Finally, the simulations results show that strain incompatibility plays an important role on the width of hysteresis. It grows as the incompatibility effect is enhanced.