Issue 17

M. Paggi et alii, Frattura ed Integrità Strutturale, 17 (2011) 5-14; DOI: 10.3221/IGF-ESIS.17.01 11 subjected to pure Mode I. In both cases, the final failure of the sample is characterized by a sudden stress drop in the stress-strain diagram, probably due to a snap-back instability, typical of cohesive solids. Figure 9 : Crack patterns (cohesive microcracks with dashed line and stress-free cracks with solid line) for different strain levels. Figure 10 : Homogenized stress-strain curve. The nonlocal CZM response (with stochastic distribution of interface properties) is compared with the prediction of the local CZM by Tvergaard with the same fracture energy for all the interfaces. The proposed nonlocal CZM is also able to capture the grain-size effects on the tensile strength. In polycrystalline materials, the tensile strength significantly depends on the grain size. An empirical correlation was proposed by Hall [18] and Petch [19], suggesting that the tensile strength is in general proportional to the inverse of the square root of the grain size at the microscale. To assess the capability of the proposed nonlocal CZM to capture this effect, we consider different material microstructures, replicas of that in Fig. 5, obtained by rescaling the diameters of the grains. Since the interface thicknesses depend on the grain size according to the power-law relation displayed in Fig. 2(b), the rescaled geometries are not self- similar. As a consequence, the distribution of the interface fracture parameters will also depend on the grain size. The Mode I fracture energy distributions corresponding to microstructures with average grain sizes of 0.1μm, 1μm and 10μm are shown in Fig. 11. The shapes of the CZM for the three cases are similar to that shown in Fig. 8. In particular, the maximum cohesive stress of the curves changes, whereas the critical separation remains the same. The average fracture  =0.100  =0.124  =0.115 Local CZM Nonlocal CZM - - Cohesive microcracks — Stress-free cracks