Issue 24

G. Cricrì, Frattura ed Integrità Strutturale, 24 (2013) 161-174; DOI: 10.3221/IGF-ESIS.24.17 161 A consistent use of the Gurson-Tvergaard-Needleman damage model for the R-curve calculation Gabriele Cricrì Department of Mechanical Engineering, University of Salerno, Italy gcricri@unisa.it A BSTRACT . The scope of the present work is to point out a consistent simulation procedure for the quasi-static fracture processes, starting from the micro-structural characteristics of the material. To this aim, a local nine- parameters Gurson-Tvergaard-Needleman (GTN) damage law has been used. The damage parameters depend on the micro-structural characteristics and must be calculated, measured or opportunely tuned. This can be done, as proposed by the author, by using an opportunely tuned GTN model for the representative volume element simulations, in order to enrich the original damage model by considering also the defect size distribution. Once determined all the material parameters, an MT fracture test has been simulated by a FE code, to calculate the R-curve in an aeronautical Al-based alloy. The simulation procedure produced results in a very good agreement with the experimental data. K EYWORDS . GTN model; Ductile fracture; Cell calibration; R-curve. I NTRODUCTION luminium alloys are widely used in aircraft structures, transportation industries and civil engineering due to their relative lightness and versatility. In particular, the fuselage skin, which thickness ranges from 1 to 3 mm, is often made of aluminium alloys capable of fully ductile behaviour. Thus, in order to better take advantage from the material metallurgical characteristics, the damage tolerance design concept is often used in the aircraft structures sizing. Following this approach, the presence of macroscopic cracks during the ordinary service life can be tolerated, as long as they are under control. For this reason, in this field the study of both the static and the dynamic response of cracked panels in ductile regime, in terms of residual strength it assumes a relevance that can hardly be overestimated [1]. The so- called R-curve, that represents the critical stress intensity factor versus the crack length for a given structure, is a widely used tool to design by following the above criteria. Unfortunately the R-curve behaviour depends both from material and geometrical properties and then it changes as the test set-up changes [2, 3]. A reliable calculation model of the R-curve is, for this reasons, very important for the design purposes, in order to drastically decrease the amount of the very expensive physical tests. From a micro-mechanical point of view, ductile failure is typically characterized by three coupled stages: nucleation, growth and coalescence of voids, which are induced in the metal alloy matrix by the presence of a variety of microscopic defects. In order to consider the effects of these voids evolution on the stress-carrying capability of a mechanical continuum during simulations, damage mechanics models are often used. Many models for ductile fracture growth have been proposed in the past [4 - 11] and, for their relative simplicity and efficiency the Gurson-Tvergaard-Needleman (GTN) model and many of its variants are proposed by several authors and also included in some public FE codes, like WARP3D [12]. These kinds of models for ductile fracture include the micro-mechanical effects of void nucleation, growth, and coalescence of micro-voids in the constitutive equation used to describe the mechanical continuum. The coalescence mechanism, in particular, induces a strain softening at the large-scale material response. Therefore, the A