Details
| Original language | English |
|---|---|
| Pages (from-to) | 1634-1643 |
| Number of pages | 10 |
| Journal | Computational materials science |
| Volume | 50 |
| Issue number | 5 |
| Publication status | Published - 8 Jan 2011 |
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.
Keywords
- Finite elements, Finite thickness interfaces, Nonlinear and stochastic fracture mechanics, Nonlocal cohesive zone model, Polycrystalline materials
ASJC Scopus subject areas
- Computer Science(all)
- General Computer Science
- Chemistry(all)
- General Chemistry
- Materials Science(all)
- General Materials Science
- Engineering(all)
- Mechanics of Materials
- Physics and Astronomy(all)
- General Physics and Astronomy
- Mathematics(all)
- Computational Mathematics
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In: Computational materials science, Vol. 50, No. 5, 08.01.2011, p. 1634-1643.
Research output: Contribution to journal › Article › Research › peer review
}
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 -