R-curve effect, influence of electric field and process zone in BaTiO₃ ceramics

Abstract

Double cantilever beam (DCB) specimens were used to measure fracture toughness and R-curve effect of coarse grained BaTiO₃ doped with 0.5 mol% TiO₂ and fine grained BaTiO₃ doped with 1.5 mol% La₂O₃ and 3.3 mol% TiO₂. The coarse grained BaTiO₃ had an average grain size of 20 μm compared to 0.4 μm for the fine grained material. Coarse grained BaTiO₃ showed increasing crack resistance with rising crack length for crack elongations up to 2 mm. The R-curve behaviour can be attributed to mechanisms shielding the crack tip from applied loads, such as ferroelastic domain switching in a process zone ahead of the crack tip, which was observed in situ. Since domain switching events left a pattern on the polished surface of the DCB specimen, it was possible to visualise the domain switching during crack propagation using Nomarski differential interference contrast. The method allowed to measure the size and shape of the process zone in unpoled and poled material. The maximum width of the process zone was 120 μm in both cases but the spatial distribution of switching events showed remarkable differences. An electrical DC field applied to the DCB samples while the cracks were propagating promoted crack growth in coarse grained, unpoled samples. In specimens poled perpendicularly to the crack, a rising toughness was found, if negative electric fields were applied. Fine grained samples were not affected by electrical fields of up to 1 kV/mm.

Introduction

Ferroelectric toughening has been observed in many investigations of BaTiO₃ and PZT ceramics.1, 2, 3, 4 Cook et al.¹ showed that in the ferroelectric state, BaTiO₃ has an R-curve effect and a higher fracture toughness than in the paraelectric state. Pohanka et al.² observed that the fracture toughness of ferroelectric BaTiO₃ increased with increasing grain size, while the fracture toughness for the cubic phase was independent of the grain size.

It is generally believed that domain wall movement under mechanical and electric fields is responsible for the toughening effect.1, 2 The domain wall movement under the influence of an electric field was observed in situ by Oh et al.⁵ who investigated thin sections of BaTiO₃ with polarised light. When applying an electric field to the specimens, a 90° switching of the domains was reported. The domains did not switch back, unless an electric field in the opposite direction was applied. Arlt⁶ described the domain pattern as a result of the minimisation of the strain energy and the domain wall energy. It was shown that the domain distribution in thin sections with a thickness smaller than the grain size, is different from the domain structure of a grain inside a three-dimensional body. Therefore the domain wall movement in thin sections, which is easily observable using polarized light⁵ does not correspond to the conditions in bulk specimens. Alternatively, the domain structure of barium titanate bulk ceramics was investigated using voltage-modulated atomic force microscopy.⁷ This method has a very high resolution compared with others like the etching of the surface of a specimen or the application of polarised light on thin sections. However, it is almost impossible to observe domain switching in situ with this method.

The proposed mechanism for ferroelastic toughening8, 9 is similar to the well known transformation toughening observed for ZrO₂. Domain switching in front of the crack tip is assumed to be induced by mechanical stresses. The transformed zone with altered domain configuration ahead of the crack is later on found in the wake, when the crack tip moves during further crack growth. The strain caused by domain switching leads to compressive stresses which close the crack and lead to an increase of fracture toughness. The effectiveness of ferroelastic toughening depends on the distribution of domain orientation, while stress-induced phase transition in ZrO₂ is coupled with a volume expansion and, thus, independent of orientation effects.¹⁰

The orientation dependence of ferroelastic toughening was mostly studied with poled or unpoled samples under the simultaneous action of mechanical and electric fields.3, 8, 11, 12, 13, 14 Since there are many possible configurations for the respective orientation of crack, poling direction and applied field, the results are not always easy to compare and have found various conflicting interpretations. However, stress-induced domain switching provides a likely explanation for many of the experimental observations.

One study should be emphasised which focuses on the orientation dependence of the toughening effect under purely mechanical load.¹⁵ This study clearly reveals that the plateau toughness is higher for unpoled samples than for specimens with poling direction perpendicular to the crack, since the domain orientation is already favourable for the considered poling direction. If the poling direction is chosen parallel to the crack plane, the plateau toughness depends on the specimen dimensions. It was found that increasing specimen dimensions lead to mechanical clamping, which hinders domain switching and, thus, ferroelastic toughening.

It is the objective of the current work to present a new method to visualise the process zone in ferroelectric bulk ceramics during crack propagation in situ and to correlate these results with experimental data on the fracture toughness and the R-curve behaviour for various poling states and microstructures.