Issue 17

M. Paggi et alii, Frattura ed Integrità Strutturale, 17 (2011) 5-14; DOI: 10.3221/IGF-ESIS.17.01 12 energy for the three cases is equal to 0.8974 N/mm, 0.1794 N/mm and 0.0361 N/mm, for d m =0.1μm, 1μm and 10μm, respectively. The r.m.s values are equal to 0.122 N/mm, 0.024 N/mm and 0.005 N/mm, respectively. Figure 11 : Distribution of interface fracture energies for three different average grain sizes. The peak stress of the stress-strain curves, obtained from tensile test simulations on the different cases, considering also d m =0.5μm, 2μm and 5μm in addition to 0.1μm, 1μm and 10μm, are shown in Fig. 12 vs. the grain diameter. The FE simulations lead to a peak stress which is a decreasing function of the grain size, in general agreement with the Hall-Petch relation that is superimposed to the same data in Fig. 12 by the dashed line. Therefore, the nonlocal CZM is fully able to reproduce the scaling of the tensile strength through the variation of fracture mechanics parameters connected to the variation of the interface thicknesses with the grain size. These numerical results imply that thicker interfaces are weaker than the thinner ones. Figure 12 : Numerically predicted vs. experimentally obtained peak stress vs. average grain size. C ONCLUSIONS n this paper, intergranular fracture in polycrystalline materials has been numerically investigated using finite elements. The main novelty with respect to previous contributions based on CZMs is represented by the use of a more sophisticated CZM whose properties (shape, fracture energy, peak stress) depend on the finite thickness of the interface. This is particularly suitable for polycrystalline materials in the micro-scale range, where the grain boundary thickness is not negligible and has an important role. The proposed nonlocal CZM is based on continuum damage I d m =10  m d m =1  m d m =0.1  m Hall-Petch law d m [  m] FE results