Abstract
Mode I steady crack growth is analyzed to determine the toughening due to domain switching in ferroelectric ceramics with electric field applied parallel to the crack front. A multi-axial, electromechanically coupled, incremental constitutive theory is applied to model the material behavior of the ferroelectric ceramic. The constitutive law is then implemented within the finite element method to study steady crack growth. The effects of electric field on the fracture toughness of both initially unpoled and poled materials are investigated. Results for the predicted fracture toughness, remanent strain and remanent polarization distributions, and domain switching zone shapes and sizes are presented. The effects of the plane-strain constraint and transverse stress are also established. Finally, the model predictions are discussed in comparison to recent experimental observations.
Highlights
This work is motivated by recent experimental and theoretical investigations on the effects of electric field on the fracture toughness of ferroelectrics
The goal of this paper is to investigate the influence of the electric field on the fracture behavior of ferroelectric materials when the electric field or the poling direction is applied parallel to the crack front
The model presented here differs from previous theoretical explanations of the effects of electric field and polarization on the fracture toughness of ferroelectrics in that an incremental, micro-electromechanically tested, phenomenological constitutive law has been applied instead of a discrete switching law
Summary
This work is motivated by recent experimental and theoretical investigations on the effects of electric field on the fracture toughness of ferroelectrics. Kreher [12] proposed a fracture model based on the balance of energy supplied by the driving forces and the total energy either dissipated by domain switching, stored in the crack wake region or consumed by the formation of new fracture surface. For these proposed theories either the details of the mechanical and electrical coupling behavior of the material is neglected or the calculation of the complicated crack tip electromechanical fields is avoided. The model to be presented in this work intends to amend these simplifications by applying a recently developed phenomenological constitutive law for ferroelectric switching within the finite element method to determine the details of the crack tip fields and the toughening due to domain switching during steady crack growth
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