本文欲以循序漸進的方法發展一個可吻合高溫 FSS 超塑性材料之關鍵行為：「於不同應變率拉伸條件下具不同應力-應變關係」的組成律模型及FEM分析模式。案例分析使用二類超塑性材料：1400oC之3Y-TZP基陶瓷及400oC的AZ31B-H24鎂合金。FEM分析時假設二類材料皆為均質、均向性，材料進入塑性後的應力增量-應變增量之關係以3-D彈-塑力學性理論，結合von Mises諧和流法則及均向性硬化準則來運算材料的塑性流演化行為。本文先對二類超塑性材料的單軸拉伸試驗進行FEM模擬，驗證本文對各自材料所提出的組成律模型之可靠性、及FEM分析模式對超塑性大變形力學分析的適用性。
二類研究材料的組成律模型建構方法：3Y-TZP基陶瓷取其單軸固定速率拉伸實驗的應力-應變曲線上斜率變化明顯之點，以片段直線連接，得到一個簡化的組成律模型；另外，本文以曲線擬合方法分析AZ31B-H24鎂合金之不同固定真實應變率拉伸的單軸實驗應力-應變曲線，提出一個以應變、應變率為函數的應力流方程式之組成律模型。
本文將二類研究材料之組成律模型導入上述的FEM彈塑性分析模式，模擬各自的單軸拉伸試驗，分析結果顯示二類材料的FEA與實驗結果之應力-應變曲線及試體最終的變形形狀，皆具有相當不錯的吻合效果，顯示本文所提出的FEM分析模式對超塑性材料大變形力學分析之適用性，且驗證了本文所提出的AZ31B-H24鎂合金組成律模型可結合現行二種超塑性材料模型(黏塑性及彈塑性材料模型)之優點，即組成律模型可以吻合AZ31B-H24鎂合金(高溫FSS超塑性材料)之關鍵行為：「於不同應變率拉伸條件下具不同應力-應變關係」。
再者，本文藉此分析模式預測AZ31B-H24鎂合金單軸固定速率拉伸案例，分析結果可符合此案例為『應變率不斷減小的連續變形歷程』之物理行為；最後，本文對AZ31B-H24鎂合金的吹製成型試驗進行模擬，分析結果顯示，FEA與實驗記錄結果的吹脹高度、試體變形皆具有相當不錯的吻合性，驗證了本文所提出的AZ31B-H24鎂合金組成律模型及FEM分析模式對於超塑性成型力學之分析之實用性，可作為此類材料日後不論在應用數值分析或解析理論之研究，抑或供予超塑性成型工業針對製程改良、力學分析、破壞預測等，提供一個實用的參考。

This research developed constitutive laws as well as an FE model for the purpose of simulating the strain-rate dependent stress-strain characteristics of superplastic FSS materials. The materials used for FE case studies were codoped 3Y-TZP ceramics at 1400°C as well as an AZ31B-H24 mg alloy at 400°C. Two kinds of analyzed materials were assumed to be homogeneous and isotropic for FE simulations, and the incremental stress-strain relationships were formulated using a 3-D elastic-plastic model, which simulated the elastic response using Hooke’s law and the work hardening response using the flow rule associated with the von-Mises yield criterion combined with the isotropic hardening rule. The FE simulations on the uniaxial tensile tests of two kinds of materials were performed for the purpose of verifying the reliability of proposed constitutive laws of each material.
The methods used to develop the constitutive laws of two kinds of materials are described as follows: (1). The simplified constitutive laws of codoped 3Y-TZP ceramics were developed based on piecewise linear connections at the turning points of different deformation stages on the experimental stress-strain curves. (2). The constitutive law developed by curve fitting the tensile tests data of an AZ31B-H24 mg alloy was expressed as a flow stress function of strain and strain rate.
Both kinds of constitutive laws were embedded into the above mentioned elastic-plastic FE model to simulate both tensile tests. The results show that the stress-strain characteristics and the final deformed shapes in the FEA agree well with the experiments for both kinds of materials. These results show that the proposed FE model is suitable to simulate the mechanical behavior of superplastic materials, and the presented constitutive law of AZ31B-H24 mg alloy is reliable to describe the strain-rate dependent stress-strain characteristics, which combines advantages of viscoplastic and elastic-plastic constitutive models for superplastic materials.
In addition, the FE verification on a free bulge forming experiment of the AZ31B-H24 mg alloy show that the proposed FE model is practicable for mechanical analysis on superplastic forming problems. This research offers a selective numerical method for advanced analyses on superplastic materials.

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