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Fractal Modelling of Kinked Cracks and its Implications for their Fatigue Propagation in Concrete
Andrea Carpinteri, Andrea Spagnoli, Sabrina Vantadori, Danilo Viappiani

Last modified: 2013-03-11

Abstract


Threshold condition and rate of fatigue crack growth appear to besignificantly affected by the degree of deflection of cracks. In this paper, the reduction ofthe fatigue crack growth rate for a so-called ‘periodically-kinked crack’ as compared tothat for a straight counterpart is quantified via the Paris-Erdogan law modifiedaccording to some simple theoretical arguments. It is shown that such a reductionincreases as the value of the kinking angle increases. Then, a so-called ‘continuouslykinkedcrack’ (the kink length tends to zero) is considered and modelled as a self-similarinvasive fractal curve. Using the Richardson’s expression, the fractal dimension of thecrack is expressed as a function of the kinking angle. It is shown that the fatigue crackgrowth rate in the Paris range depends not only on the above fractal dimension and inturn on the kinking angle, but also on the crack length. Some experimental results relatedto concrete and showing a crack size effect on the fatigue crack growth rate are analysed.

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