Issue 29

R. Serpieri et alii, Frattura ed Integrità Strutturale, 29 (2014) 284-292; DOI: 10.3221/IGF-ESIS.29.24 285 which is often accompanied by dilatancy, in turn associated with the interlocking effect created by the asperities of the fracture surface. Therefore, in order to formulate models that properly account for the underlying physics of the problem it is essential to capture the distinct types of dissipation due to fracture and friction, the influence of the geometry of the asperities on the interlocking effect. Several interface models accounting for damage-friction coupling have been proposed in literature, see e.g. Del Piero and Raous [1] and references therein. Some of them are based on nonassociative softening plasticity, as for the multidissipative interface model proposed by Cocchetti et al. [2] and the contributions given by Bolzon and Cocchetti [3] and by Červenka et al. [4] in the field of concrete dams analysis, and by Giambanco et al. [5]. A different strategy was followed by Alfano and Sacco [6], Alfano et al. [7] and, more recently, Sacco and Toti [8], where interface damage and friction have been combined in a cohesive zone model based on a simplified micromechanical formulation. The main idea was to consider a representative area at a micromechanical scale, which is assumed to be additively decomposed into an undamaged and a fully damaged part; moreover, it is supposed that friction occurs only on the latter. The evolution of damage is assumed to depend on the elastic energy in the undamaged part while the frictional behaviour is governed by a Coulomb law. To simulate dilatancy and interlocking this approach was adopted by Serpieri and Alfano [9], within a multi-scale framework in which, at a small scale, the asperities of the interface are represented in the form of a periodic arrangement of distinct inclined planes, denominated Representative Interface Area (RIA). On each of these planes the interaction is governed by the formulation proposed in Alfano and Sacco (2006). The above formulation by Serpieri and Alfano was recently revisited by Serpieri et al. [10], where it was shown that use of a single damage variable, combined with the choice of having a threshold damage function only depending on the damage variable itself and an equivalent displacement norm, requires coincidence of fracture energies in modes I and II to preserve thermodynamic consistency. Furthermore, it was shown that the enhancement of the model to account for friction and interlocking, based on the formulation proposed by Serpieri and Alfano [9], results in retrieving the experimental evidence that the measured fracture energy in mode II is typically quite higher than in mode I. For mixed- mode loading, with positive (opening) mode I, the proposed model predicts an increase of the total fracture energy with increasing mode II loading component. Both facts are well supported by good agreement between experimental and numerical results. In this paper the model formulated in Refs. [9, 10] is revisited and applied to the study of the pull-put test of a ribbed steel bar from concrete specimen, in which the interface model is used to simulate the interaction between steel and concrete within a two-dimensional axisymmetric simulation. The ‘bond-slip’ interaction between steel and concrete has been widely investigated in the last decades, both theoretically and experimentally [11-14]. Many studies have revealed the significant role played by complex mechanisms including the progressive development of primary transversal and secondary inclined cracks [15], the influence of stress triaxiality on the formation of inclined struts in the concrete surrounding the steel bar [16], the fact that with increasing confinement the failure mode changes from being more brittle (splitting) to more ductile (pull out) [17]. All these studies also revealed that, for ribbed bars (the only ones nowadays used), interlocking is the predominant mechanism of stress transfer between concrete and steel with respect to adhesion and friction (the latter intended as the theoretical friction that would be obtained if the fracture surfaces were flat). All these complex mechanisms are influenced by aspects that are not limited to the point-wise interaction between concrete and steel at the interface but include other structural details. For this reason, all the models developed somehow depend on details such as the diameter of the bars, the type of confinement, the cyclic nature of loading, among many others, and typically include a number of corrective coefficients that need to be empirically determined and are of difficult, if not impossible, physical interpretation for the practicing engineer. Hence, the aim of this paper is to show that very accurate prediction of the bond-slip interaction between concrete and steel bars can be achieved through a physically well justified model, developed within a general and thermodynamically consistent framework in which each contribution to the overall energy dissipation on the interface is accounted for with a simplified, yet effective multiscale description of the microscale. To show the effectiveness of the formulation, the model is validated by simulating the pull-out test of a steel bar from a concrete specimen and comparing the numerical results with the experimental ones reported by Shima [18]. These have been chosen as benchmark test data because the relatively large dimensions of the concrete specimen, as well as the insertion of a clay sleeve with very small adherence in an initial part at the loaded end of the steel bar, prevents the formation of splitting cracks and results in rather negligible concrete damage or plasticity, except in a thin region immediately adjacent to the steel bar and its ribs, whose progressive damage is indeed incorporated in the cohesive-zone model. Therefore, the nonlinear response up to failure during the test is predominantly the result of the interface interaction, which is the focus of this investigation and is simulated by the proposed cohesive-zone model. This makes calibration of the model easier and gives more confidence in the robustness of the validation.