Issue 29

M. Marino et alii, Frattura ed Integrità Strutturale, 29 (2014) 241-250; DOI: 10.3221/IGF-ESIS.29.21 249 As already observed, the Huang’s failure criteria gives more accurate results. As long as one of the constituents attains its ultimate stress state, the lamina is considered to fail and its contribution to the overall stiffness matrix of the laminate is reduced. When this micromechanical approach is considered for the evaluation of the failure load, the progressive failure process in the laminate can be more properly understood, and the corresponding failure mode can be straight identified. Therefore, the evaluation of localized stress distributions occurring in the composite constituents seems to be extremely important for predicting the onset of damage mechanisms in the laminated plate. Accordingly, a refined method accounting for localization mechanisms in matrix and fibers, as the one proposed by Huang [14], should be preferred if the aim is the prediction and the analysis of the progressive damaging occurring in bolted FRP joints. Addressing the Huang’s criterion, Fig. 5 shows, for different values of  , the evolution of the failure mechanisms within the plate, from the damage onset up to the global failure. Proposed results, obtained by a post-processing procedure that involves a slave partition with respect to the finite-element mesh, highlight that damage occurs, as expected, close to the contact zone. In this figure, the spatial distributions of the equivalent material stiffness for the laminate along the fiber direction (denoted as D AA ) are also provided at different damage levels, aiming to show the damage evolution in terms of material degradation (namely, in the figure blue color indicates the lowest value of the equivalent material stiffness and thereby the damaged region). It is worth pointing out that the proposed model allows to discriminate the constituent within each layer experiencing damage. In the analyzed cases, since the plane stress assumption and the mono-directional plying pattern, damage initiation occurs simultaneously in each FRP layer, or in the CSM layers, or in both. Moreover, the numerical simulations predict a main occurrence of the bearing failure in matrix, in agreement with the experimental results discussed in [10]. Finally, it is worth noting also that the procedure is able to predict the onset of different damage mechanisms, as experienced for 90    , where a tensile matrix failure is shown in the direction orthogonal to the pin displacement, suggesting the onset of a net-tension failure mechanism together with the bearing one. C ONCLUSIONS n this paper, a progressive damage model based on a finite-element incremental approach has been proposed, in order to simulate failure mechanisms occurring in bolted joints between fiber-reinforced composite elements. Two available failure criteria (namely, by Rotem and Huang, and differently accounting for micro-structural material features) are employed, and unilateral frictionless contact conditions at the pin-plate interface are included. The model has been applied to study a pin-plate system. Proposed numerical results predict a bearing failure mechanism fully in agreement with the experimental evidence discussed in [10]. Results in terms of the failure load can be successfully compared with experimental data in a quantitative way only when localization mechanisms in matrix and fibers are suitably accounted for within the formulation of the failure criterion, such as in the Huang’s criterion. Nevertheless, some significant discrepancies among numerical results and experiments can be highlighted for small values of the angle between the fiber direction and the load one. In order to overcome such a drawback, and as a perspective application, future works will address the development of an ad hoc failure criterion. Proposed approach opens towards the possibility of simulating progressive damage mechanisms occurring in bolted joints between fiber-reinforced composite structural elements, allowing to provide useful contributions towards the definition of guidelines for design and analysis of FRP bolted joints. A CKNOWLEDGEMENT his work was partially supported by the Italian Civil Protection Department [RELUIS-DPC 2014-18, CUP: E84G14000480007] and it was developed within the framework of the Lagrange Laboratory, a European research group comprising CNRS, CNR, the Universities of Rome “Tor Vergata”, Calabria, Cassino, Pavia and Salerno, Ecole Polytechnique, University of Montpellier II, ENPC, LCPC and ENTPE. R EFERENCES [1] Kelly, G., Hallstro ̈ m, S., Pin-bearing strength of carbon fibre/epoxy laminates: effects of bolt-hole clearance, Composites Part B: Engineering, 35 (2004) 331–343. I T