TY - JOUR

T1 - Stiffness and strength of hierarchical polycrystalline materials with imperfect interfaces

AU - Paggi, Marco

AU - Wriggers, Peter

N1 - Funding information: MP would like to thank the Alexander von Humboldt Foundation for supporting his research fellowship at the Institute of Continuum Mechanics, Leibniz University Hannover (Hannover, Germany) during the year 2010. The support of AIT, MIUR and DAAD to the Vigoni project (2011-2012) “3D Modelling of fracture in polycrystalline materials” is also gratefully acknowledged.

PY - 2012/1/11

Y1 - 2012/1/11

N2 - In this study we investigate the effect of imperfect (not perfectly bonded) interfaces on the stiffness and strength of hierarchical polycrystalline materials. As a case study we consider a honeycomb cellular polycrystal used for drilling and cutting tools. The conclusions of the analysis are, however, general and applicable to any material with structural hierarchy. Regarding the stiffness, generalized expressions for the Voigt and Reuss estimates of the bounds to the effective elastic modulus of heterogeneous materials are derived. The generalizations regard two aspects that are not included in the standard Reuss and Voigt estimates. The first novelty consists in considering finite thickness interfaces between the constituents undergoing damage up to final debonding. The second generalization consists of interfaces not perpendicular or parallel to the loading direction, i.e., when isostress or isostrain conditions are not satisfied. In this case, approximate expressions for the effective elastic modulus are obtained by performing a computational homogenization approach. In the second part of the paper, the homogenized response of a representative volume element (RVE) of the honeycomb cellular polycrystalline material with one or two levels of hierarchy is numerically investigated. This is put forward by using the cohesive zone model (CZM) for finite thickness interfaces recently proposed by the authors and implemented in the finite element program FEAP. From tensile tests we find that the interface nonlinearity significantly contributes to the deformability of the material. Increasing the number of hierarchical levels, the deformability increases. The RVE is tested in two different directions and, due to different orientations of the interfaces and Mixed Mode deformation, anisotropy in stiffness and strength is observed. Stiffness anisotropy is amplified by increasing the number of hierarchical levels. Finally, the interaction between interfaces at different hierarchical levels is numerically characterized. A condition for scale separation, which corresponds to the independence of the material tensile strength from the properties of the interfaces in the second level, is established. When this condition is fulfilled, the material microstructure at the second level can be efficiently replaced by an effective homogeneous continuum with a homogenized stressstrain response. From the engineering point of view, the proposed criterion of scale separation suggests how to design the optimal microstructure of a hierarchical level to maximize the material tensile strength. An interpretation of this phenomenon according to the concept of flaw tolerance is finally presented.

AB - In this study we investigate the effect of imperfect (not perfectly bonded) interfaces on the stiffness and strength of hierarchical polycrystalline materials. As a case study we consider a honeycomb cellular polycrystal used for drilling and cutting tools. The conclusions of the analysis are, however, general and applicable to any material with structural hierarchy. Regarding the stiffness, generalized expressions for the Voigt and Reuss estimates of the bounds to the effective elastic modulus of heterogeneous materials are derived. The generalizations regard two aspects that are not included in the standard Reuss and Voigt estimates. The first novelty consists in considering finite thickness interfaces between the constituents undergoing damage up to final debonding. The second generalization consists of interfaces not perpendicular or parallel to the loading direction, i.e., when isostress or isostrain conditions are not satisfied. In this case, approximate expressions for the effective elastic modulus are obtained by performing a computational homogenization approach. In the second part of the paper, the homogenized response of a representative volume element (RVE) of the honeycomb cellular polycrystalline material with one or two levels of hierarchy is numerically investigated. This is put forward by using the cohesive zone model (CZM) for finite thickness interfaces recently proposed by the authors and implemented in the finite element program FEAP. From tensile tests we find that the interface nonlinearity significantly contributes to the deformability of the material. Increasing the number of hierarchical levels, the deformability increases. The RVE is tested in two different directions and, due to different orientations of the interfaces and Mixed Mode deformation, anisotropy in stiffness and strength is observed. Stiffness anisotropy is amplified by increasing the number of hierarchical levels. Finally, the interaction between interfaces at different hierarchical levels is numerically characterized. A condition for scale separation, which corresponds to the independence of the material tensile strength from the properties of the interfaces in the second level, is established. When this condition is fulfilled, the material microstructure at the second level can be efficiently replaced by an effective homogeneous continuum with a homogenized stressstrain response. From the engineering point of view, the proposed criterion of scale separation suggests how to design the optimal microstructure of a hierarchical level to maximize the material tensile strength. An interpretation of this phenomenon according to the concept of flaw tolerance is finally presented.

KW - Cohesive zone model

KW - Effective properties

KW - Hierarchical materials

KW - Honeycomb cellular polycrystalline materials

KW - Imperfect interfaces

UR - http://www.scopus.com/inward/record.url?scp=84856719496&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2012.01.009

DO - 10.1016/j.jmps.2012.01.009

M3 - Article

AN - SCOPUS:84856719496

VL - 60

SP - 557

EP - 572

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

IS - 4

ER -