Issue 10

M. Paggi, Frattura ed Integrità Strutturale, 10 (2009) 43-55; DOI: 10.3221/IGF-ESIS.10.06 43 A dimensional analysis approach to fatigue in quasi-brittle materials Marco Paggi Politecnico di Torino, Dep. of Structural and Geotechnical Engineering, Corso Duca degli Abruzzi 24, 10129 Torino, Italy marco.paggi@polito.it R IASSUNTO . Nel presente lavoro si propone uno studio di analisi dimensionale del fenomeno della fatica nei materiali quasi-fragili. Esso costituisce una generalizzazione della metodologia pionieristica proposta da Barenblatt e Botvina e si prefigge di interpretare le deviazioni dalle leggi di potenza classiche usate per caratterizzare il comportamento a fatica dei materiali. In base a questo approccio teorico, gli effetti dovuti alla dimensione microstrutturale (correlabile al contenuto volumetrico di fibre nei calcestruzzi fibrorinforzati), alla dimensione delle fessure e alla scala strutturale sulla legge di Paris e sulle curve di Wöhler sono discussi in un contesto matematico unificato. Il modello teorico è confermato dal confronto con rilevanti risultati sperimentali disponibili in letteratura, usati per determinare i valori degli esponenti di autosimilarità incompleta. Le informazioni fornite da questa teoria possono essere particolarmente utili per guidare la progettazione di nuovi esperimenti, dal momento che viene chiarito il ruolo delle diverse variabili adimensionalizzate che governano il fenomeno della fatica. A BSTRACT . In this study, a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth is proposed in order to highlight and explain the deviations from the classical power-law equations used to characterize the fatigue behaviour of quasi-brittle materials. According to this theoretical approach, the microstructural-size (related to the volumetric content of fibres in fibre-reinforced concrete), the crack-size, and the size-scale effects on the Paris’ law and the Wöhler equation are presented within a unified mathematical framework. Relevant experimental results taken from the literature are used to confirm the theoretical trends and to determine the values of the incomplete self-similarity exponents. All these information are expected to be useful for the design of experiments, since the role of the different dimensionless numbers governing the phenomenon of fatigue is herein elucidated. K EYWORDS . Fatigue; Quasi-brittle materials; Fibre-reinforced concrete; Dimensional analysis; Incomplete self- similarity. I NTRODUCTION he assessment of the fatigue behaviour of quasi-brittle materials, such as plain or fibre-reinforced concrete (FRC), is particularly important from the engineering point of view. Concrete pavements for highways are in fact subjected to millions of cycles of repeated axial loads of high stress amplitude due to passing vehicles. Airport pavements are also subjected to a number of loading cycles during their design life, ranging from about several thousand to several hundred thousand. Concrete structures supporting dynamic machines may also fail due to repeated loadings causing complex stress states. To make the problem even more complex, very often failure is the result a steady decrease in the stiffness of the structural element, rather than by the propagation of a single macroscopic crack [1]. From the design point of view, the classical methods used to assess the fatigue performance of concrete are mainly empirical and are based on the cumulative fatigue damage approach, well-established for the analysis of the fatigue T