The Importance of Critical Aspect Ratio

The improvement in mechanical properties of a fiber filled thermoplastic composite is due to the ability of the fiber to withstand a higher proportion of the mechanical load than the matrix that it replaces. A critical aspect ratio (length to diameter ratio) has been identified for adequate load transference [34]. This critical aspect ratio relates to a single fiber embedded in, and completely wet by, the matrix. Fibers shorter than the critical aspect ratio will pull out of the matrix, therefore the full reinforcing effect of the fiber will not be utilized. At the critical aspect ratio, both the fiber and the matrix will fracture along the same failure plane. Further increases in fiber aspect ratio will not lend additional strength to the composite, since the failure will be the same as that experienced at the critical aspect ratio. The critical ratio is given by  

Ti = interfacial shear strength between the fiber and the matrix (strongly influenced by processing conditions and degree of adhesion between the fiber and the matrix) 

In actual practice, the fibers must overlap each other, even if all are oriented in the same direction, in order to provide homogeneity within the part. At any given failure plane, all the fibers will then be able to share the mechanical stress equally. In practice, maximum utilization of short fibers occurs when the fibers have an aspect ratio that is ten times the critical aspect ratio [35]. Under these conditions, uniaxially oriented short fibers can have tensile strengths equal to 95% of that of the continuous fiber uniaxially oriented composites. In randomly oriented fiber filled composites, the tensile strength is less than one third that of composites in which fibers are uniaxially oriented. 

An equation predicting the tensile strength of short fiber filled composites is  

For many fiber-polymer systems (L/D) is in the range 10 50. From this analysis, it is evident that fiber length is important to the development of maximum tensile properties in the composite. It is also apparent that changes in the composite tensile strength are monotonically dependent on fiber concentration. 

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CARBON FIBERS IN THERMOPLASTIC MATRICES 21.4.1 The importance of critical aspect ratio [101]... 

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