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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 nine-parameters Gurson-Tvergaard damage law has been used. The damage parameters depend on the micro-structural characteristics and have to be calculated, measured or opportunely tuned. This can be done, as proposed by the author, by using an opportunely tuned GT 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 FEM 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.