Probabilistic modelling of the size effect on ductility of a C-Mn steel

Abstract
Tensile tests were performed on homothetic different sized axisymmetrical notched tensile specimens (NT), at 100°C. A strong size effect was observed on the ductility : The average strain at fracture, as well as the scatter of results, decrease with the size of the specimen. Two statistical methods are proposed to model this size effect. The first modelling is a continuous approach based on mechanics of porous material, on a distribution of Manganese Sulphide volume fraction in a representative volume elements (R.V.E.) and on the weakest link theory. The second one is a discrete approach based on a Monte Carlo randomisation of critical growth rate of voids in finite element calculation. These two models are in agreement with the experimentation. In both cases, the size and scatter effects are obtained by the dispersion of the chosen intrinsic variable, as well as by the relative dimensions of the R.V.E. and of the whole specimen. The discrete approach shows a larger variation of the scatter than the continuous one. In particular, the saturation for large volume seems to be better described by the discrete approach. However, in the continuous approach, the introduction of an upper bound in the statistical description of the Manganese Sulphide fraction leads to an accurate description of the saturation effect.