Issue 33

C. Bagni et alii, Frattura ed Integrità Strutturale, 33 (2015) 105-110; DOI: 10.3221/IGF-ESIS.33.14 105 Focussed on characterization of crack tip fields Gradient-enriched linear-elastic tip stresses to perform the high- cycle fatigue assessment of notched plain concrete C. Bagni, H. Askes, L. Susmel Department of Civil and Structural Engineering, The University of Sheffield, Sheffield S1 3JD, United Kingdom c.bagni@sheffield.ac.uk , h.askes@sheffield.ac.uk , l.susmel@sheffield.ac.uk A BSTRACT . Gradient Elasticity (GE) allows the stress analysis to be performed by taking into account the size of the dominant source of microstructural heterogeneity via a suitable length scale parameter. This is done by simply assuming that the material under investigation obeys a linear-elastic constitutive law, albeit equipped with additional spatial strain gradients. From a practical point of view, the most important implication of this modus operandi is that gradient-enriched linear-elastic stresses at the notch tips are always finite, this holding true also in the presence of sharp stress risers (such as cracks). In the present investigation, the accuracy of two different GE based design strategies was checked against a number of experimental results generated by testing, under cyclic four-point bending, plain concrete samples containing different geometrical features. The high level of accuracy which was obtained by directly using gradient-enriched linear-elastic notch stresses strongly supports the idea that GE is a powerful tool suitable for designing notched concrete components against high-cycle fatigue. This result is very promising also because the required stress analysis can directly be performed by using standard Finite Element (FE) solvers. K EYWORDS . Concrete; Fatigue; Notch; Gradient elasticity. I NTRODUCTION n the civil infrastructure sector, concrete is the most commonly used material. This explains the reason why the problem of optimising the static assessment of concrete has been studied by the international scientific community for decades. The outcomes from this enormous amount of work allow modern concrete structures to be efficiently designed against static loading via the adoption of low safety factors. By so doing, slender concrete structures can safely be built by remarkably reducing the usage of natural resources, this having positive effects not only on sustainability, but also on carbon emissions. Owing to the fact that the magnitude of in-service local stresses increases as the size of concrete structural components decreases, slender concrete structures are obviously more susceptible to fatigue. Examination of the state of the art shows that, since the beginning of the 1900s [1, 2], much research work has been done to formalise efficient design methods suitable for estimating the fatigue damage extent in concrete components subjected to time- variable loading. Unfortunately, the experimental work carried out so far has resulted in design curves suitable for estimating the fatigue lifetime solely for those specific concrete mixtures that were tested. It has to be highlighted also that, apart from three isolated investigations [3-5], no effort has been made so far to devise and validate (through appropriate experimental investigations) specific techniques capable of modelling the detrimental effect of notches on the overall fatigue strength of plain concrete. In this setting, the aim of the present investigation is to check whether linear-elastic gradient-enriched notch tip stresses are successful in performing the high-cycle fatigue assessment of notched plain concrete. I