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A nonlocal cohesive zone model for studying crack propagation in mechanical systems with finite thickness interfaces

Paggi, Marco and Wriggers, Peter A nonlocal cohesive zone model for studying crack propagation in mechanical systems with finite thickness interfaces. In: Atti del XX Congresso Associazione Italiana di Meccanica Teorica e Applicata. Publi&Stampa Edizioni, pp. 1-10. ISBN 978-88-906340-0-0 (2011)

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Finite thickness regions between heterogeneous material constituents are often simplified as zerothickness interfaces. Then, the cohesive zone model (CZM) is employed, establishing a constitutive relation between tractions and displacement discontinuities. The shape of the CZM is usually chosen as simple as possible for numerical reasons, rather than being physically meaningful. Therefore, the reliability and the predictive capabilities of these models are a serious concern. In this contribution, the complex nonlinear damage phenomena occurring in finite thickness interface regions are modeled using damage mechanics. The derived nonlinear relation between cohesive tractions and anelastic displacements is then reinterpreted as a new nonlocal CZM. Depending on the ductility of the material, different shapes of the CZM can be recovered, from linear and bilinear softening curves, typical of brittle materials, to bell-shaped curves typical of ductile materials. It is also shown that the parameters of the damage law can be tuned according to molecular dynamics simulations. The implementation of the proposed nonlocal CZM in the finite element method is then presented. Special attention is given to the numerical treatment of the related nonlocality and to the computation of the tangent stiffness matrix to be used in the Newton-Raphson method for the solution of the nonlinear boundary value problem. The numerical model is applied to polycrystalline materials and it is shown that the nonlocal CZM is able to reproduce realistic statistical distributions of Mode I fracture energies, as a consequence of the interface thickness distribution. Finally, we demonstrate that the relation between interface thickness and grain size can also be used to explain the grain size effects on the material tensile strength, namely the Hall-Petch law and its inversion at the nanoscale.

Item Type: Book Section
Subjects: T Technology > TJ Mechanical engineering and machinery
Research Area: Computer Science and Applications
Depositing User: Prof Marco Paggi
Date Deposited: 16 Dec 2013 13:43
Last Modified: 09 Oct 2014 09:20
URI: http://eprints.imtlucca.it/id/eprint/2071

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