Numerical aspects of the nonlocal cohesive zone model (CZM) presented in Part I are discussed in this companion paper. They include the FE implementation of the proposed nonlocal CZM in the framework of zero-thickness interface elements and the numerical treatment of the related nonlocality. In particular, a Newton-Raphson method, combined with a series expansion to obtain tentative values for the cohesive tractions, is used to efficiently compute the tangent stiffness matrix and the residual vector of the interface elements. Then, numerical applications to polycrystalline materials are proposed, focusing on the constitutive modelling of the finite thickness interfaces between the grains. It will be shown that the parameters of the nonlocal CZM (shape, peak stress, fracture energy) depend on the thickness of the interface. The CZM is able to produce statistical distributions of Mode I fracture energies consistent with those assumed a priori in stochastic fracture mechanics studies. The statistical variability of fracture parameters, originating from the natural variability of the interface thicknesses, has an important influence on the crack patterns observed from simulated tensile tests. Finally, we show that the relation between interface thickness and grain size can be used to explain the grain-size effects on the material tensile strength. In particular, considering a sublinear relation between the interface thickness and the grain diameter at the microscale, the nonlocal CZM is able to recover the Hall-Petch law. Therefore, the proposed model suggests that an inverse relation between the interface thickness and the grain size would lead to an inversion of the Hall-Petch law as well. This new interpretation seems to be confirmed by experimental data at the nanoscale, where the inversion of the Hall-Petch law coincides with the anomalous increase of the interface thickness by reducing the grain size.
A nonlocal cohesive zone model for finite thickness interfaces - Part II: FE implementation and application to polycrystalline materials
Paggi M;
2011-01-01
Abstract
Numerical aspects of the nonlocal cohesive zone model (CZM) presented in Part I are discussed in this companion paper. They include the FE implementation of the proposed nonlocal CZM in the framework of zero-thickness interface elements and the numerical treatment of the related nonlocality. In particular, a Newton-Raphson method, combined with a series expansion to obtain tentative values for the cohesive tractions, is used to efficiently compute the tangent stiffness matrix and the residual vector of the interface elements. Then, numerical applications to polycrystalline materials are proposed, focusing on the constitutive modelling of the finite thickness interfaces between the grains. It will be shown that the parameters of the nonlocal CZM (shape, peak stress, fracture energy) depend on the thickness of the interface. The CZM is able to produce statistical distributions of Mode I fracture energies consistent with those assumed a priori in stochastic fracture mechanics studies. The statistical variability of fracture parameters, originating from the natural variability of the interface thicknesses, has an important influence on the crack patterns observed from simulated tensile tests. Finally, we show that the relation between interface thickness and grain size can be used to explain the grain-size effects on the material tensile strength. In particular, considering a sublinear relation between the interface thickness and the grain diameter at the microscale, the nonlocal CZM is able to recover the Hall-Petch law. Therefore, the proposed model suggests that an inverse relation between the interface thickness and the grain size would lead to an inversion of the Hall-Petch law as well. This new interpretation seems to be confirmed by experimental data at the nanoscale, where the inversion of the Hall-Petch law coincides with the anomalous increase of the interface thickness by reducing the grain size.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
