探討不同纖維排列下複合材料之機械行為

Abstract

本研究目的在於探討纖維複合材料在不同纖維排列情況下對其機械性質之影響，而主要探討的幾何排列分為下列三種，正方型排列(SEP)，對角線排列(SDP)，六角形排列(HP)。本論文將對此三種不同排列之纖維複合材料做以下探討，熱殘留應力對於不同纖維排列之複合材料其非線性機械行為之影響，以及不同纖維排列下複合材料之阻尼響應。在模擬纖維複合材料時，將取出一代表性單元體（Representative Volume Element, RVE）進行分析，進而推求出整體纖維複合材料之機械性質。在材料特性方面，纖維部份假設為線彈性且具低阻尼特性，而基材部份則假設為非線性且具高阻尼特性。在熱殘留應力對機械性質之非線性影響的分析裡，利用Paley以及Aboudi [1]所提出的微觀力學廣義網格法 (Generalized Method of Cells, GMC)，來做纖維以及基材的熱殘留應力分析。再經由數值上的運算，建構出含有熱殘留應力之纖維複合材料的應力應變關係。分析結果顯示，相較於對角線纖維排列，熱殘留應力對六角形及正方型纖維排列之機械性質之影響，來的輕微了許多。 對於不同纖維排列之複合材料對其阻尼影響的分析中，於代表性單元體上分別施以相對於材料主軸方向的單軸載重或是剪力，利用微觀力學廣義網格法，推求纖維複合材料主軸方向的應變能及其相對應的應變能消散量。藉由應變能消散概念，計算出纖維複合材料位於各材料主軸方向上的阻尼參數。從有限單元的分析方法，首先求出纖維複合材料所構成的桿或平板結構，分別在自由邊界 (free-free) 以及一端固定 (clamp-free)的情況下，其自由震動振動模態之變形﹔並結合材料主軸方向上之阻尼係數以及振動模態之變形，即可求得在不同纖維幾何排列下，對於不同結構的模態振動阻尼效應(Damping Capacity) 。由分析結果可觀察出，在由對角線排列所構成的桿或平板之複合材料結構上，在前三個振動的模態中，所求得之阻尼效應，分別大於另外兩種纖維排列。

This study aims to investigate the effect of fiber array on the mechanical responses of fiber composites. Basically three different fiber arrays, i.e., square edge packing (SEP), square diagonal packing (SDP), and hexagonal packing (HP), were considered in the analysis. The sensitivities of thermal residual stress on the nonlinear constitutive behaviors as well as the damping behaviors of the composites with different fiber arrays were the focus of the research. The representative volume element (RVE) containing fiber and matrix phase was employed to describe the overall mechanical behaviors of fiber composites. For the fiber phase, it was assumed to be a linear elastic material with low damping capacity, whereas the matrix was a nonlinear material with high damping capacity. The generalized method of cell (GMC) micromechanical model originally proposed by Paley and Aboudi [1] was extended to include the thermal-mechanical behavior, from which the thermal residual stress within the fiber and matrix phases was calculated. Through a numerical iteration, the constitutive relations of the composites in the presence of residual stress were established. Results show that for the composites with square edge packing, the mechanical behaviors are affected appreciably by the thermal residual stress. On the other hand, the composites with hexagonal packing and square diagonal packing are relatively less sensitive to the thermal residual stress. Regarding the damping behaviors of the composites, the RVE was subjected to a simple loading (either axial or pure-shear loading), and the corresponding damping properties of the fiber composites with respect to the material principal directions were calculated from the GMC analysis together with the energy dissipation concept. With the assistance of FEM analysis, the mode shapes of composite rod and plate structures with vibration under free and clamp boundary conditions were determined. In conjunction with the model shape and the damping properties, the damping capacity of the composite structures constructed based on unidirectional composites with different fiber arrays were calculated. It was found that, in both composite structures, the square diagonal packing always exhibits better damping performance rather than other two fiber arrangements at first three vibration modes.