TY - JOUR

T1 - A nonlocal cohesive zone model for finite thickness interfaces - Part II

T2 - FE implementation and application to polycrystalline materials

AU - Paggi, Marco

AU - Wriggers, Peter

N1 - Funding information: The first author would like to thank the Alexander von Humboldt Foundation for supporting his research fellowship at the Institut für Kontinuumsmechanik, Leibniz Universität Hannover (Hannover, Germany) from February 1, 2010, to January 31, 2011.

PY - 2011/1/8

Y1 - 2011/1/8

N2 - 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.

AB - 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.

KW - Finite elements

KW - Finite thickness interfaces

KW - Nonlinear and stochastic fracture mechanics

KW - Nonlocal cohesive zone model

KW - Polycrystalline materials

UR - http://www.scopus.com/inward/record.url?scp=79952009643&partnerID=8YFLogxK

U2 - 10.1016/j.commatsci.2010.12.021

DO - 10.1016/j.commatsci.2010.12.021

M3 - Article

AN - SCOPUS:79952009643

VL - 50

SP - 1634

EP - 1643

JO - Computational materials science

JF - Computational materials science

SN - 0927-0256

IS - 5

ER -