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Compressive strength of fibre composites with random fibre waviness. (English) Zbl 1102.74015

The authors examine the compressive strength of unidirectional long fiber composites for plastic microbuckling for a random two-dimensional distribution of fiber waveness. The effect of physical size of waveness is addressed by using the couple stress theory with fiber bending resistance scaling with the fiber diameter. By using the Monte Carlo method, the authors predict the statistical distribution of compressive strength. Then, by use of the finite element method, the authors generate an assembly of fiber waveness profiles from an assumed spectral density. The predicted average strength agrees reasonably well with the practical values, confirming the hypothesis that microbuckles can be initiated by fiber misalignment. The authors find that the probability distribution of strength is well matched by a Weibull fit and can be determined in terms of Weibull parameters upon the spectral density of the waveness. For the practical range of fiber distribution considered, the strength depends mainly upon the root mean square amplitude of fiber misalingment. Then, the authors propose an engineering model for predicting the compressive strength. The authors examine a specimen containing randomly distributed waveness to locate the regions of high-fiber misalingment. The strength of each of these weak regions is estimated from a look-up table derived from calculations of some idealized waveness. The strength of composite is given by the failure stress associated with the weakest such patch.

MSC:

74E30 Composite and mixture properties
74E35 Random structure in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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