Issue 52

B. Paermentier et alii, Frattura ed Integrità Strutturale, 52 (2020) 105-112; DOI: 10.3221/IGF-ESIS.52.09 107 Void growth can be written as a function of the rate of plastic volume change, pl kk   .   1 pl growth kk f f      (4) Void nucleation is defined in a strain-controlled nucleation function that considers a normal distribution for the nucleation strain. Consequently, the void nucleation rate can be written as: 2 2 1 exp 2 pl pl N N nucleation N N f f s s                     π ε ε (5) where N f defines the void volume fraction of nucleated voids, N  and N s indicate the mean value and standard deviation of the nucleation strain respectively, pl  indicates the equivalent plastic strain, and pl   defines the equivalent plastic strain rate. Finally, the initial void volume fraction 0 f indicates the presence of initial voids and is a measure for the relative density of the material. Multiple studies have reported on the use of the GTN damage parameters for X70 and X100 grade pipeline steels [9, 10, 11, 12]. In this investigation, the GTN damage parameters, listed in Tab. 1 , were considered as typical material constants which were obtained from literature. Material ଵ ଶ ଴ ஼ ி ே ே ே X70 1.5 1.0 0.000401 0.001517 0.5 0.067143 0.8 0.1 X100 1.5 1.0 0.00015 0.02 0.18 0.005 0.3 0.1 Table 1: GTN damage parameters for X70 and X100. Figure 1: True stress-strain curve for X70 and X100 grade steels. M ATERIAL P ROPERTIES he mechanical properties of the investigated X70 and X100 grade steels were obtained from the literature [2, 3]. The flow curves – as presented in Fig. 1 – describe the plasticity based on the true stress-strain relations. Two different isotropic hardening laws were used to define the material behaviour in the post-necking region. For X70 grade steel, 0 200 400 600 800 1000 1200 0 0.2 0.4 0.6 0.8 1 True Stress [MPa] True Plastic Strain [-] X70 X100 T