探討球型顆粒對奈米複合材料拉伸強度的影響－利用線彈性破壞力學理論

Abstract

本研究致力於探討球型補強材料之顆粒尺寸、體積分率及分散性對含裂紋奈米複合材料拉伸強度的影響。透過有限元素法建立的一套微觀模型，配合線彈性破壞力學理論，可用於探討添加的顆粒對材料中裂紋破壞行為的影響，並從裂紋的應變能釋放率來預測補強材料顆粒對拉伸強度的影響。分析結果顯示，承受拉伸外力的奈米複合材料，其補強材料顆粒軸極區域是基材中裂紋較容易延伸破壞的地方，而在顆粒之側向則有一應力抑制區域可延緩裂紋的成長。隨著顆粒尺寸愈小可提升奈米複合材料的拉伸強度，局部群聚現象的出現則將導致拉伸強度明顯的下降。這些現象皆可由實驗文獻獲得相同的趨勢。而在補強材料體積分率的探討上，分析結果顯示隨著體積分率的增加將使拉伸強度降低，此部分實驗文獻中的現象眾說紛紜，無法確切指出含量與強度間的關係，故有待進一步的實驗來驗證。本研究中為了探討基材與補強材料介面裂紋的問題，整理了破壞力學書籍中較少提及的介面裂紋破壞力學理論，及其在有限元素上的計算方法。雖然文中僅有少部分的應用，然而基材與補強材料介面的剝離現象是很常見的破壞模式，期望介面破壞理論的整理能對未來這方面的延伸探討有所助益。

This research aims to investigate the effect of particle size, volume fraction and dispersion on the tensile strength of particulate nanocomposites with an initial crack. The finite element micromechanical model in conjunction with linear elastic fracture mechanics was used to study the particle effect on the fracture behavior. Calculating the strain energy release rates of the crack could be applied to estimate the tensile strength of particulate nanocomposites. It was shown that the crack in the matrix is more likely to extend at the pole region of the particle in the direction of the applied tension, and there is a stress shielding zone at the equator which can reduce the possibility of crack growth. The tensile strength of particulate composites can be improved with decreasing of particle size, and the local aggregation of particles results in a decrease of tensile strength. These analytical results demonstrate a good agreement with the experimental literature. The result also showed that the tensile strength decreased with increasing of volume fraction. However, various trends of the volume fraction effect on the composite strength had been demonstrated. It seems that there is no consistent conclusion in literature to determine the relation between volume fraction and strength. Hence, to verify the above result, further experimental research is needed. In this study, for the sake of investigating the particle/matrix interface crack problem, we summarized the fracture mechanics of the bimaterial interface crack and its calculating method by finite element analysis. Although there was less use of the calculating method in this research, we still expect that the summary can be helpful for the further investigation of the particle/matrix debonding.