臺灣博碩士論文加值系統

本研究建立一個新的單元體模型(unit-cell model)描述雙相複合材料的彈性常數(包括彈性、體、剪切係數及泊松比)及熱膨脹係數，此單元體模型的預測結果與實驗數據及文獻上已有之理論模式進行比較，證實本單元體模型的可行性。
與多數均質單相材料比較，複合材料的彈性及熱膨脹性質的影響因素較為複雜，例如：複合材料內所含第二相的形狀、組成份、孔隙的大小與分佈、以及相界面的完整性等等，均嚴重影響複合材料的性質。除了材料微結構的複雜因素外，有關應力在複合材料內部傳遞的機制因未能清楚了解，導致無法獲得精確預測的複合材料彈性常數及熱膨脹係數，因此，本研究規劃以上下邊界的預測方法將彈性及熱膨脹性質可能的變化範圍予以涵蓋，模型主要的假設條件有：僅針對組成相具緊密結合之完全緻密複合材料，不考慮當複合材料如果受外力或受熱作用會導致相界面剝離的情況，這允許我們以巨觀角度進行探討，即假設複合材料所含的第二相大小是大於微觀結構尺寸，因此不需考慮原子級與差排力學等微觀情況，故可以直接用連續力學觀點進行複合材料性質模型的推導，同時假設所分析模型之大小是比第二相要大，因此複合材料性質可以用組成相的平均性質來表示。
本研究模型之目的是希望所獲得的預測結果可以涵蓋整個雙相複合材料性質的組成範圍，亦即可以包括所含第二相的含量從0到100體積百分率(vol.%)的複合材料，因為文獻上所能涵蓋整個組成範圍之實驗數據較不完整，所以本研究應用熱壓燒結準備一組NiAl的含量從0到100體積百分率之緻密化Al2O3-NiAl複合材料，分別以超音波技術及熱機械分析儀(TMA)量測其彈性常數及熱膨脹係數。
對於雙相複合材料，當第二相的含量逐漸地增加會使原本孤立狀之第二相產生互相連接，逐漸地使組成相形成各自連通之微觀結構，考慮此連通之微觀特性，本研究之單元體模型便假設所含之第二相的形狀為長條狀，並將雙相之間的應力與應變的隅合作用予以考慮。由模型預測得知雙相複合材料的彈性係數、泊松比以及熱膨脹係數均與組成相的彈性係數比值有密切關係，亦即第二相與基底相彈性係數的比值是這些性質的主要影響因素，所以有關影響某一溫度變化範圍之複合材料熱膨脹係數的結果，事實上是受彈性係數的比值的控制。
將Al2O3-NiAl複合材料的實驗數據及廣泛收集文獻上已有的雙相複合材料之實驗數據與本研究模型所獲得的預測結果進行比較，由實驗數據比較得知，證明本研究模型的預測具有合理的適用性。並與文獻上其他理論模式進行預測性質之比較，例如：用於預測彈性常數的Hashin-Shtrikman (H-S)模式、以及用於預測熱膨脹係數的Kerner 及 Schapery模式，經由比較結果顯示，當彈性係數的比值小於10時，本研究所建立的模型之預測值與其他理論模式有相似的精確預測功能，但是當彈性係數的比值大於20時，對於雙相複合材料之彈性及熱膨脹性質預測，本研究所建立的模型具有較佳的預測結果。

In the present study, a unit cell model is proposed to predict the elastic constants (Poisson’s ratio, Young’s, bulk and shear moduli) and thermal expansion coefficient of two-phase composites. The feasibility of the present model is verified by comparing the model predictions with experimental model.
Comparing with many monolithic materials, many more factors can affect the elastic and thermal properties of two-phase composites. For examples, the shape of the second phase, composition, the size and distribution of pores, interface integrity, etc., can all affect the resulting properties of composites. Apart from these microstructural complexities, the transfer of stress within the composite is also unknown. Therefore, it is almost impossible to deliver a precise estimation on the elastic constants and thermal expansion coefficient of composites. Instead, a pair of upper and lower bounds to cover the possible variation on the elastic and thermal constants is proposed in the present study. We further assume that the model is applied only to the fully dense composites in which the components are strongly bonded. Therefore, it is not possible for the two components to separate at their interfaces when the composite is loaded or heated. The discussion also restricts itself to macro-composites, namely, to those in which the scale of the second phase is large to microstructure so that composite properties can be modeled by using continuum mechanics without resort to atomic and dislocation mechanics. Furthermore, the size of specimen is much larger than the size of second phase so that the properties are an appropriate average of those of the components in the composites.
The present model tend to offer predictions over the entire composition range of the two-phase composites, namely, the amount of the second phase varies from 0 to 100 vol.%. The experimental data for the composites with the composition covers the entire composition range are sparse. Therefore, the Al2O3-NiAl composites with the NiAl content varied from 0 to 100 vol.% are prepared by hot-pressing. The elastic constants of the composites are measured by employing an ultrasonic technique, the thermal expansion coefficient by using a thermal mechanical analyzer.
As the amount of second phase is large, the second phase particle tends to interconnect with each other to form an interpenetrating microstructure. To reflect such microstructural feature, a unit cell model with elongated second phase is proposed in the present study. The stress-strain coupling is also taken into account. The model prediction on elastic modulus and Poisson’s ratio shows strong dependence on the ratio of elastic modulus of matrix to that of second phase. The thermal expansion coefficient of composite also shows strong dependence of the elastic modulus ratio. It demonstrate that the thermal expansion of a composite as it is under a temperature change is in-fact an elastic problem.
The model predictions are compared with the experimental data of the Al2O3-NiAl composites. A comprehensive collection on the experimental data for other two-phase composites has also been conducted. The comparison between the model predictions and all available experimental data demonstrates the validation of the model. The model prediction is also compared with other theoretical models, for example, the Hashin-Shtrikman model for elastic constants and Kerner and Schapery models for thermal expansion coefficient. The model proposed in the present study shows similar precision on the properties of composites as the elastic modulus ratio is lower than 10. However, the elastic modulus ratio is higher than 20, the model proposed in the present study shows improved prediction on the properties of two-phase composites.

摘 要 i
Abstract iii
Contents v
List of Tables vii
List of Figures viii
Nomenclature xii
I. Introduction 1
1.1 Background 1
1.2 Motivation 3
1.3 Objectives 4
II. Literature Survey 5
2.1 Theoretical Models 5
2.1.1 Elastic Constants 5
2.1.2 Poisson’s Ratio 10
2.1.3 Thermal Expansion Coefficient 12
2.2 Mechanical Behavior of Materials 16
2.2.1 Generalized Hooke’s Law 16
2.2.2 Thermal Strain 18
2.2.3 Equations from Simple Parallel and Series Models 19
III. Preparation of a Model Composite 20
3.1 Preparation of Al2O3-NiAl 20
3.2 Elastic Constants of Al2O3-NiAl Composites 22
3.2.1 Ultrasonic Testing 22
3.2.2 Results and Discussion 22
3.3.3 Conclusions 23
3.3 Thermal Expansion Behavior of Al2O3-NiAl Composites 24
3.3.1 TMA Test 24
3.3.2 Results and Discussion 24
3.3.3 Conclusions 25
IV. A Universal Model for Elastic and Thermal Constants 29
4.1 Geometry 31
4.2 Elastic Constants of Composites 32
4.3 Poisson’s Ratio of Composites 34
4.4 Thermal Expansion Coefficient of Composites 38
V. Comparison 42
5.1 Features of the Present Model 42
5.1.1 Elastic Constants 43
5.1.2 Poisson’s Ratio 44
5.1.3 Thermal Expansion Coefficient 45
5.2 Comparison with Experimental Data 47
5.2.1 Elastic Constants 47
5.2.2 Poisson’s Ratio 47
5.2.3 Thermal Expansion Coefficient 48
VI. Conclusions 59
References 60
Appendix 68
A.1 Features of the Present Model 68
A.2 Comparison with other Experimental Data 68
Curriculum Vitae 83

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