Interaction of Cracks and Domain Structures in Thin Ferroelectric Films

The fracture behavior of ferroelectric materials is a complex problem that has been addressed in numerous experimental and theoretical studies. Several factors have been identified to play an important role, such as the applied electric field, the medium inside the crack, the electrical conditions on the crack faces, and polarization switching at or near the crack tip. In this investigation, a phase field model for ferroelectric domain evolution is used to calculate crack tip driving forces for mode-I cracks in barium titanate thin films. The driving forces are obtained by employing the theory of configurational forces, which is equivalent to considering the J-integral. Simulations are done for permeable, impermeable, semi-permeable, and energetically consistent crack face conditions with both air and water as crack medium. The finite element calculations are performed for films with thicknesses varying from 5 to 30 nm. The results show that the impermeable, semi-permeable and energetically consistent conditions lead to similar crack tip driving forces if air is used as crack medium. In the absence of mechanical loading, strong electric fields result in a closing crack tip driving force, while the use of water as crack medium leads to opposite driving forces. It can be confirmed that polarization switching at the crack tip has a significant effect on the driving force.