Issue 17

M. Paggi et alii, Frattura ed Integrità Strutturale, 17 (2011) 5-14; DOI: 10.3221/IGF-ESIS.17.01 8 Mode I problem. Similar considerations apply for Mode Mixity. For more details about the calibration of the model parameters using molecular dynamics simulations, the readers are referred to [2]. Figure 3 : Shape of the Mode I nonlocal CZM as a function of  . This nonlocal CZM has been implemented in the FE code FEAP [17] using zero-thickness interface elements, see [3] for more details about the computational aspects. The anelastic relative displacements N g and T g are the main input of the element subroutine and are obtained as the difference between the normal and tangential displacements of the nodes of the finite elements of the continuum opposite to the shared interface. The residual vector and the tangent stiffness matrix of the interface element are computed by linearizing the corresponding weak form using a Newton-Raphson algorithm. Due to the implicit form of the CZM in Eq. (1), since the damage variable D on the r.h.s. of Eq. (1) is a function of the unknown cohesive tractions through Eqs. (2) and (3), a nested Newton-Raphson iterative scheme is used in to compute the cohesive tractions. A quadratic convergence is achieved, as shown in Fig. 4 for a Mode I problem. Figure 4 : Quadratic convergence of the Newton-Raphson method used for the computation of the cohesive tractions, for three different values of / N c g w and for / 0 T c g u  . A PPLICATIONS TO POLYCRYSTALLINE MATERIALS he proposed nonlocal CZM for finite thickness interfaces is applied to the polycrystalline material microstructure of Copper analyzed in [1] and depicted in Fig. 5. From this input geometry, the grain size distribution, shown in Fig. 6(a), can be computed. The average grain diameter is 1 μm and its r.m.s. deviation is 0.26 μm. The interface thickness distribution is also computed and shown in Fig. 6(b). T