A Microstructural Model for Micro-Cracking in Piezoceramics


Article Preview

Piezoelectric ceramics are employed in several applications for their capability to couple mechanical and electrical fields, which can be advantageously exploited for the implementation of smart functionalities. The electromechanical coupling, which can be employed for fast accurate micro-positioning devices, makes such materials suitable for application in micro electro-mechanical systems (MEMS). However, due to their brittleness, piezoceramics can develop damage leading to initiation of micro-cracks, affecting the performance of the material in general and the micro-devices in particular. For such reasons, the development of accurate and robust numerical tools is an important asset for the design of such systems. The most popular numerical method for the analysis of micro-mechanical multi-physics problems, still in a continuum mechanics setting, is the Finite Element Method (FEM). Here we propose an alternative integral formulation for the grain-scale analysis of degradation and failure in polycrystalline piezoceramics. The formulation is developed for 3D aggregates and inter-granular failure is modelled through generalised cohesive laws.



Edited by:

Luis Rodríguez-Tembleque, Jaime Domínguez and Ferri M.H. Aliabadi




I. Benedetti et al., "A Microstructural Model for Micro-Cracking in Piezoceramics", Key Engineering Materials, Vol. 774, pp. 479-485, 2018

Online since:

August 2018




* - Corresponding Author

[1] Staszewski W, Boller C, Tomlinson GR (eds) Health monitoring of aerospace structures: smart sensor technologies and signal processing. John Wiley & Sons, (2004).

[2] Benedetti I, Aliabadi MH, Milazzo A. A fast BEM for the analysis of damaged structures with bonded piezoelectric sensors. Computer Methods in Applied Mechanics and Engineering, 199(9-12), 490-501, (2010).

DOI: https://doi.org/10.1016/j.cma.2009.09.007

[3] Suo Z, Kuo C-M, Barnett DM, Willis JR. Fracture mechanics for piezoelectric ceramics. Journal of the Mechanics and Physics of Solids, 40(4), 739-765, (1992).

DOI: https://doi.org/10.1016/0022-5096(92)90002-j

[4] Nemat-Nasser S, Hori M. Micromechanics: Overall Properties of Heterogeneous Materials, North Holland, (1999).

[5] Espinosa HD, Zavattieri PD. A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part I: Theory and numerical implementation. Mechanics of Materials, 35(3-6), 333-364, (2003).

DOI: https://doi.org/10.1016/s0167-6636(02)00285-5

[6] Simonovski I, Cizelj L. Cohesive zone modeling of intergranular cracking in polycrystalline aggregates. Nuclear Engineering and Design, 283, 139-147, (2015).

DOI: https://doi.org/10.1016/j.nucengdes.2014.09.041

[7] Verhoosel CV, Gutiérrez MA.. Modelling inter-and transgranular fracture in piezoelectric polycrystals. Engineering Fracture Mechanics, 76(6), 742-760, (2009).

DOI: https://doi.org/10.1016/j.engfracmech.2008.07.004

[8] Gulizzi V, Milazzo A, Benedetti I. Fundamental solutions for general anisotropic multi-field materials based on spherical harmonics expansions. International Journal of Solids and Structures, 100, 169-186, (2016).

DOI: https://doi.org/10.1016/j.ijsolstr.2016.08.014

[9] Aliabadi MH. The boundary element method, applications in solids and structures, Vol.2, John Wiley & Sons, (2002).

[10] Pan E. A bem analysis of fracture mechanics in 2d anisotropic piezoelectric solids. Engineering Analysis with Boundary Elements, 23(1):67-76, (1999).

DOI: https://doi.org/10.1016/s0955-7997(98)00062-9

[11] Davì G, Milazzo A. Multidomain boundary integral formulation for piezoelectric materials fracture mechanics. International Journal of Solids and Structures, 38(40):7065-7078, (2001).

DOI: https://doi.org/10.1016/s0020-7683(00)00416-9

[12] Sfantos GK, Aliabadi MH. A boundary cohesive grain element formulation for modelling intergranular microfracture in polycrystalline brittle materials. International Journal of Numerical Methods in Engineering, 69(8), 1590-1626, (2007).

DOI: https://doi.org/10.1002/nme.1831

[13] Geraci G, Aliabadi MH. Micromechanical boundary element modelling of transgranular and intergranular cohesive cracking in polycrystalline materials. Engineering Fracture Mechanics, 176, 351-374, (2017).

DOI: https://doi.org/10.1016/j.engfracmech.2017.03.016

[14] Benedetti I, Aliabadi MH. A three-dimensional grain-boundary formulation for microstructural modeling of polycrystalline materials. Computational Materials Science, 67, 249-260, (2013).

DOI: https://doi.org/10.1016/j.commatsci.2012.08.006

[15] Benedetti I, Gulizzi V, Mallardo V. A grain boundary formulation for crystal plasticity. International Journal of Plasticity, 83, 202-224, (2016).

DOI: https://doi.org/10.1016/j.ijplas.2016.04.010

[16] Benedetti I, Aliabadi MH. A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials. Computer Methods in Applied Mechanics and Engineering, 265, 36-62, (2013).

DOI: https://doi.org/10.1016/j.cma.2013.05.023

[17] Gulizzi V, Milazzo A, Benedetti I. An enhanced grain-boundary framework for computational homogenization and micro-cracking simulations of polycrystalline materials. Computational Mechanics, 56(4), 631-651, (2015).

DOI: https://doi.org/10.1007/s00466-015-1192-8

[18] Gulizzi V, Rycroft CH, Benedetti I. Modelling intergranular and transgranular micro-cracking in polycrystalline materials. Computer Methods in Applied Mechanics and Engineering, 329, 168-194, (2018).

DOI: https://doi.org/10.1016/j.cma.2017.10.005

[19] Benedetti I, Gulizzi V, Milazzo A. Grain-boundary modelling of hydrogen assisted intergranular stress corrosion cracking. Mechanics of Materials, 117, 137-151, (2018).

DOI: https://doi.org/10.1016/j.mechmat.2017.11.001

[20] Sfantos GK, Aliabadi MH. Multi-scale boundary element modelling of material degradation and fracture. Computer Methods in Applied Mechanics and Engineering, 196(7), 1310-1329, (2007).

DOI: https://doi.org/10.1016/j.cma.2006.09.004

[21] Benedetti I, Aliabadi MH. Multiscale modeling of polycrystalline materials: A boundary element approach to material degradation and fracture. Computer Methods in Applied Mechanics and Engineering, 289, 429-453, (2014).

DOI: https://doi.org/10.1016/j.cma.2015.02.018

[22] Froehlich A, Brueckner-Foit A, Weyer S. Effective properties of piezoelectric polycrystals. In Smart Structures and Materials 2000: Active Materials: Behavior and Mechanics, Vol. 3992, 279-288, International Society for Optics and Photonics, (2000).

DOI: https://doi.org/10.1117/12.388212

[23] Olson T, Avellaneda M. Effective dielectric and elastic constants of piezoelectric polycrystals. Journal of Applied Physics, 71, 4455-4464, (1992).

DOI: https://doi.org/10.1063/1.350788

Fetching data from Crossref.
This may take some time to load.