Influence of domain switching zones on the fracture toughness of ferroelectrics
This paper considers the fracture process of ferroelectric materials, taking into account poling, re-poling and wake energy effects. The model is based on the energy balance method combined with a suitably simplified domain switching model. The macroscopic crack has a fracture plane perpendicular to the uniaxial mechanical loading direction, and a straight crack front parallel to the applied electric field. After formulation of the general energy balance of crack advance, specific values of dissipated and stored energy are related to material properties. Then, it is introduced a simplified description of hysteretic ferroelectric material behavior based on internal variables, which measure the relative frequences of a set of six representative domain orientations. Based on these internal variables, the author analyzes relevant processes which material undergoes near the crack tip: (i) poling by electric field; (ii) switch transformation under mechanical and electrical load, and (iii) partial re-transformation into a residually stressed state in the wake region. The resulting equations give explicit results on dissipated energy and residual wake zone energy. Then, numerical results are presented on fracture toughness as a function of the applied electric field. To this aim, the author uses approximate value for the size of dissipation zone based on the results for fine-grained barium titanate. The increase in fracture toughness with electric field is predicted, and the size of the process zone has a reasonable coincidence with experimental results.
scientific article; zbMATH DE number 1788080