Modeling of fracture in ferroelectric ceramics

The energy release rates for dielectric, piezoelectric and ferroelectric strips are analyzed. Energy minimization is used to determine the electromechanical fields in the strip. Once these fields are computed conservation of energy is used to determine the energy release rates. Three different sets of assumptions are used to treat the void space and solid material. First, an impermeable void space assumption is analyzed with small deformation assumed to be valid in the solid. Next, the void space is assumed to have finite dielectric permittivity and aside from changes in the position of its boundary the solid is treated with small deformation theory. Finally, a large deformation formulation is used for the solid along with a permeable void space. By minimizing the energy of the system we are able to show that mechanical tractions act on the crack surfaces as a result of the finite dielectric permittivity of free space. Lastly, a piezoelectric strip with remanent polarization is analyzed and it is shown that the energy release rate for a poled piezoelectric is not equal to that of a material with identical elastic, dielectric and piezoelectric properties but no remanent polarization.