【正文】 astic to the plastic region. It corresponds to the moment when the σ(ε) curve bees almost a straight line. The value of fN was changed within certain limits in order to obtain the convergence of the σ(ε) values determined numerically and experimentally at that stage. The typical value used for steel grades fN = was critical value fc corresponds to the void volume fraction at which the void coalescence starts,revealing the decrease in the material strength visible in the σ(ε) curve. The critical value fc was changed within certain limits in order to obtain the convergence of the σ(ε) values determined numerically and experimentally and to define the beginning of the void growth corresponding to a decrease in the material strength. The determined value, . fc = was also pared with the values obtained by Richelsen and Tvergaard (1994)。 they related the value of fc to f0.The critical value fF corresponds to the void volume fraction at the plete loss of the material order to minimize the softening effect and perform calculations for a full range of deformations for all the analyzed elements with a notch depth ranging from up to , it was assumed that the maximum value, fF = , was the optimal one.The Tvergaard coefficients were established as: q1 = , q2 = , and q3 = . The mean void nucleation (initiation) strain for the inclusionrelated voids was εN = , and the standard deviation of the strain was sN = .The length scaleThe characteristic length, which is a minimum volume of material over which the fracture criterion needs to be satisfied to predict ductile crack initiation, is not easy to determine. All the methods for the determination of the length scale are subjective in nature. For example, Panontin et al. (1995) claim that this parameter can be related to the steel grain size, whereas according to Rousselier (1987), it is dependent on the diameter of dimples or the inclusiontoinclusion distance in the fracture surface. It is not yet clear what the exact correlations are. Other researchers such as Norris et al. (1978) suggest backcalibration of data obtained through FEM analyses and testing of sharp cracked specimens. Although some of the procedures were efficient, in a wider context, they turned out to be of no practical use. The most suitable approach in the case of ductile fracture is that proposed by Hancock and Mackenzie (1976).They assume that the characteristic length is related to some physical and microstructural coalescence of inclusion colonies in the presence of shear is responsible for void formation. As shown in Fig. 2, the size of a cluster of inclusion colonies represents the characteristic this analysis, the mean dimensions of an inclusion colony were determined by averaging the dimensions of the measured plateaus and valleys on the castellated fracture surface. The measurement was performed using the Chauvenet criterion. All atypical values were rejected. The measurement was repeated twenty times. The characteristic length L ranged from to mm, with the mean value of L being mm.The measurement of the plateaulike structures is similar to that performed for the dimples. Both are subjective in character. The length scale is very difficult to determine precisely to be used in micromechanical models, therefore further research on the subject is essential. However, predicting ductile fracture hardly ever requires measuring the characteristic length, L, because most defects are relatively smooth and the stress/strain gradients are low.Extensive research was conducted also to test another method. The characteristic length, L, was estimated in a microstructural analysis basing on the average spacing between the voids nucleated from large inclusions. The mean distance between large voids was mm.Numerical simulations of a standard static tension test were performed to check the influence of the mesh size on the experimental results. The dimensions of the cell localized near to the crack plane were equal to D D/2, where D was equal to the characteristic length being mm and mm.During the analysis of the forceelongation curves, it was observed that the simulation results were much more consistent with the results of the strength tests when D = mm than when D = mm.The process zone was very small when the cell dimensions, D, interpreted as the characteristic length L,defined by the mean spacing between the voids nucleated from large inclusions, were mm. This led to a smooth decrease in the material strength. When the cell dimensions, D, interpreted as the characteristic length L, defined by the dimensions of the plateaus and valleys formed from coalescing inclusion colonies leading to fracture, were mm, the results of the simulations were much more consistent with the experimental data.The characteristic length, L, was a fundamental parameter used in the numerical simulations for determining the mesh size. In this way, the minimum size of the finite element mesh for steel S235JR was specified as mm.Determining the SMCS model parameters for S235JR steelThe key parameters of the SMCS model, . critical strain and stress triaxiality, were determined for notched cylindrical specimens made of S235JR steel, using tensile tests and numerical cylindrical specimens had a diameter of mm and a notch radius of , or mm (Fig. 3).The objective was to determine the stress state at different values of stress triaxiality, ranging from σm/σeq= for R = through σm/σeq = for R = up to σm/σeq = for R = experiment involved measuring the load F and the displacement of points distributed symmetrically along the notch length l. The initial length of the extensometer l0s was mm (Fig. 4).The ductile fracture with localized plastic deformation shown in Fig. 5 results from the coalescence of voids. A macroscopic view reveals that the cracks are perpendicular to the maximum normal stress (the tensile axis). The folds in the central fracture region were attribut