探討粉體局部群聚效應對複合材料機械性質之影響

Abstract

本研究的目標在探討顆粒的區域群聚效應對含裂紋複合材料拉伸強度的影響。其中，顆粒尺寸、體積分率、介面層厚度及顆粒楊氏模數等因子的影響在文中皆有所討論。我們使用一個可用來表示顆粒分布結構的微觀有限元素模型研究顆粒群聚效應對複合材料破壞行為的影響。使用線彈性破壞力學計算應變能釋放率，然後透過與純基材模型比較得到的標準化拉伸強度來評估材料的破壞行為。所有的分析皆採用鑲埋式模型以節省程式運算的時間。由模擬結果發現當複合材料的裂紋缺陷發生在基材中，相同的體積分率下，增大補強顆粒尺寸會使得顆粒型複合材料的拉伸強度下降。此外當顆粒群聚發生時，越大的顆粒下降的幅度越明顯。同樣的趨勢也出現在不同體積分率的模型。相同顆粒尺寸下，提高體積分率並伴隨著顆粒群聚的惡化會明顯降低複合材料的拉伸強度。另一方面，補強顆粒對基材的楊氏模數比值對於複合材料的拉伸強度的影響很小。此外顆粒周圍介面層的存在會些微的降低複合材料的拉伸強度。當複合材料的裂紋缺陷發生在雙材料介面，在相同的顆粒尺寸且顆粒均勻分散的複合材料中，體積分率並不影響複合材料的拉伸強度。但隨著群聚程度的上升，複合材料的拉伸強度逐漸下降，體積分率越高的複合材料拉伸強度下降的幅度越大。比較裂紋在基材中與裂紋在雙材料介面模型的應變能釋放率可以發現，當裂紋長度遠小於顆粒直徑時，基材中的裂紋較雙材料介面的裂紋具有較高的應變能釋放率。另一方面，當裂紋長度與顆粒直徑接近時，基材中的裂紋與雙材料介面的裂紋具有相當接近的應變能釋放率。由前述的模擬結果可以發現，當顆粒發生群聚時會降低材料的拉伸強度。此結論與文獻中實驗觀察到的現象相符合。

This research aims to investigate the effect of local aggregation on tensile strength of particulate composites with an embedded crack. Particle size, volume fraction, interphase thickness and particle Young’s modulus were taken into account in the exploration. A micromechanical finite element model (FEM) accounting for the configuration of particle distribution was employed to study the particle aggregation effect on the fracture behavior of the composites. Basically, the concept of strain energy release rate anchored in the linear elastic fracture mechanics was adopted to evaluate the fracture behavior, from which the “normalized” tensile strength of the particulate composites with respective to the pure resin was determined. It is noted that all analysis was conduced based on the continuum mechanics approach in an attempt to efficiently save the computing cost. Results reveal that increasing particle size can deteriorate the tensile strength of the composites associated with the same volume fraction. Moreover, the declining behavior becomes more significant as particle aggregation taking place. Similar tendency was also observed in the composites with different volume fractions. The increase of particle volume fraction together with high extent of particle aggregation would dramatically decrease the tensile strength of composites. Basically the ratio of particle modulus to matrix modulus exhibits less influence on the normalized tensile strength of composites. In addition, the introduction of interface layer in the vicinity of particles also depicts little effect on the tensile strength of composites. When initial crack is embedded on the particle/matrix interface, the tensile strength of composite with good particle dispersion is not influenced by volume fraction. However, when the degree of aggregation increases, the rate of reduction in tensile strength is raising with the increment of particle volume fraction. Comparing the energy release rate of the composites with an embedded crack either in the matrix or on the interface revealed that when the crack size is much less than the particle diameter, the composites with crack in matrix demonstrates higher energy release rate than that with interfacial crack. On the other hand, when the crack size is compatible to that of particle size, the strain energy release rate calculated in both cases are quite close. In light of forgoing investigations, it is concluded that particle aggregation can considerably depreciate the tensile strength of composites, which is in a good agreement with experimental observations.