Our safety, comfort and peace of mind are heavily dependent upon our capability to prevent, predict or postpone the failure of components and structures on the basis of sound physical principles While the external loadings acting on a material or component are clearly important, There are other contributory factors including unfavourable materials microstructure, pre-existing defects and residual stresses Residual stresses can add to, or subtract from, the applied stresses and so when unexpected failure occurs it is often because residual stresses have combined critically with the applied stresses, or because together with the presence of undetected defects they have dangerously lowered the applied stress at which failure will occur Consequently it is important that the origins of residual stress are understood, opportunities for removing harmful or introducing beneficial residual stresses recognized, their evolution in-service predicted, their influence on failure processes understood and safe structural integrity assessments made, so as to either remove the part prior to failure, or to take corrective action to extend life This paper reviews the progress in these aspects in the light of the basic failure mechanisms

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Residual stress and its role in failure

The electric-field-induced strain in 93%(Bi0.5Na0.5)TiO3–7%BaTiO3 polycrystalline ceramic is shown to be the result of an electric-field-induced phase transformation from a pseudocubic to tetragonal symmetry. High-energy x-ray diffraction is used to illustrate the microstructural nature of the transformation. A combination of induced unit cell volumetric changes, domain texture, and anisotropic lattice strains are responsible for the observed macroscopic strain. This strain mechanism is not analogous to the high electric-field-induced strains observed in lead-based morphotropic phase boundary systems. Thus, systems which appear cubic under zero field should not be excluded from the search for lead-free piezoelectric compositions.

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Electric-field-induced phase transformation at a lead-free morphotropic phase boundary: Case study in a 93%(Bi0.5Na0.5)TiO3–7% BaTiO3 piezoelectric ceramic

The electromechanical coupling in ferroelectric materials is controlled by several coexisting structural phenomena which can include piezoelectric lattice strain, 180 degrees and non-180 degrees domain wall motion, and interphase boundary motion. The structural mechanisms that contribute to electromechanical coupling have not been readily measured in the past, particularly under the low-to-medium driving electric field amplitudes at which many piezoelectric materials are used. In this feature, results from in situ, high-energy, and time-resolved X-ray diffraction experiments are interpreted together with macroscopic piezoelectric coefficient measurements in order to better understand the contribution of these mechanisms to the electromechanical coupling of polycrystalline ferroelectric materials. The compositions investigated include 2 mol% La-doped PbZr0.60Ti0.40O3, 2 mol% La-doped PbZr0.52Ti0.48O3, 2 mol% La-doped PbZr0.40Ti0.60O3, undoped PbZr0.52Ti0.48O3, and 2 mol% Fe-doped PbZr0.47Ti0.53O3. In all compositions, a strong correlation is found between the field-amplitude-dependence of the macroscopic piezoelectric coefficient and the contribution of non-180 degrees domain wall motion determined from the diffraction data. The results show directly that the Rayleigh-like behavior of d(33) piezoelectric coefficient is predominantly due to a Rayleigh-like behavior of non-180 degrees domain wall motion. Furthermore, after separating contributions from lattice (atomic level) and domain wall motion (nanoscale level) to the measured macroscopic piezoelectric properties, we show that previously ignored intergranular interactions (microscopic level) account for a surprisingly large portion of the electromechanical coupling. These results demonstrate that electromechanical coupling in polycrystalline aggregates is substantially different from that observed in single crystalline materials. The construct of emergence is used to describe how averaged macrolevel phenomena are different from the material response observed in an isolated subcomponent of the material. Consequently, and due to its size-scale complexity, the description of grain-to-grain interactions is presently inaccessible in most ab initio and phenomenological approaches. Results presented here demonstrate the need to account for these interactions in order to completely describe macroscopic electromechanical properties of polycrystalline materials.

Origins of Electro-Mechanical Coupling in Polycrystalline Ferroelectrics During Subcoercive Electrical Loading

The origin of the electric field-induced strain in the polycrystalline ceramic 0.92Bi1/2Na1/2TiO3–0.06BaTiO3–0.02K1/2Na1/2NbO3 was investigated using in situ high-resolution X-ray and neutron diffraction techniques. The initially existing tetragonal phase with pseudocubic lattice undergoes a reversible phase transition to a significantly distorted rhombohedral phase under electric field, accompanied by a change in the oxygen octahedral tilting from a0a0c+ to a−a−a− and in the tilting angle. The polarization values for the tetragonal and rhombohedral phases were calculated based on the structural information from Rietveld refinements. The large recoverable electric field-induced strain is a consequence of a reversible electric field-induced phase transition from an almost nonpolar tetragonal phase to a ferroelectrically active rhombohedral phase.

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Field-induced phase transition in Bi1/2Na1/2TiO3- based lead-free piezoelectric ceramics

Piezoelectric actuators transform electrical energy into mechanical energy, and because of their compactness, quick response time and accurate displacement, they are sought after in many applications. Polycrystalline piezoelectric ceramics are technologically more appealing than single crystals due to their simpler and less expensive processing, but have yet to display electrostrain values that exceed 1%. Here we report a material design strategy wherein the efficient switching of ferroelectric–ferroelastic domains by an electric field is exploited to achieve a high electrostrain value of 1.3% in a pseudo-ternary ferroelectric alloy system, BiFeO3–PbTiO3–LaFeO3. Detailed structural investigations reveal that this electrostrain is associated with a combination of several factors: a large spontaneous lattice strain of the piezoelectric phase, domain miniaturization, a low-symmetry ferroelectric phase and a very large reverse switching of the non-180° domains. This insight for the design of a new class of polycrystalline piezoceramics with high electrostrains may be useful to develop alternatives to costly single-crystal actuators.

Electrostrain in excess of 1% in polycrystalline piezoelectrics

The lattice parameters and crystallographic texture in La, Sr-doped soft lead zirconate titanate ceramics were examined using high-energy synchrotron x-ray diffraction. The preferred orientations in poled tetragonal and rhombohedral ceramics near the morphotropic phase boundary, caused by ferroelectric domain switching, were determined by monitoring the (002)∕(200) and (111)∕(111¯) intensity ratios, respectively. The lattice strains were also monitored using the {111} and {200} plane spacings in tetragonal and rhombohedral ceramics, respectively. The diffraction experiments were carried out in transmission, enabling the true “bulk” state to be characterized. It was observed that for the tetragonal phase both the lattice spacing d{111} and the intensity ratio R{200} varied linearly as a function of sin2Ψ,Ψ being the angle between the plane normal and the macroscopic polar axis. Similar observations were made for d{200} and R{111} in rhombohedral ceramics. The results are interpreted in terms of the remanen...

A high energy synchrotron x-ray study of crystallographic texture and lattice strain in soft lead zirconate titanate ceramics

Analysis of elastic strain and crystallographic texture in poled rhombohedral PZT ceramics

This paper presents micromechanics based analysis of elastic strain and changes in the texture of poled polycrystalline ferroelectric PZT ceramics for direct comparison with synchrotron X-ray measurements. The grains are modelled as spherical inclusions, to which transformation strains are assigned depending on the fractions of different ferroelectric domains. Eshelby's inclusion problem with the classical self-consistent method is applied to evaluate the elastic state of the grains. In particular, the elongation due to lattice elastic strain is calculated as a function of inclination Ψ relative to the polar axis. The ratio of diffraction peak intensities, corresponding to the domain fractions, is also expressed as a function of Ψ . This analysis identifies the special character of the { 1 1 1 } reflection, for which the lattice strain along 〈 1 1 1 〉 in the stress free state is independent of ferroelectric domain population and hence unaffected by poling. The elongation due to the lattice strain parallel to 〈 1 1 1 〉 and peak intensity ratio are expressed in terms of the overall macroscopic strain of a poled specimen, each having a cos 2 Ψ dependence.

Micromechanics of residual stress and texture development due to poling in polycrystalline ferroelectric ceramics

Biodiesel production by a renewable catalyst from calcined Turbo jourdani (Gastropoda: Turbinidae) shells

The texture and lattice elastic strain due to electrical poling of tetragonal PZT (lead zirconate titanate) ceramics have been measured using high energy synchrotron X-ray diffraction. It is shown that XRD peak intensity ratios associated with crystal planes of the form { 0 0 2 } , { 1 1 2 } and { 2 0 2 } exhibit a linear dependence on cos ⁡ 2 Ψ , where Ψ represents the orientation angle between the plane normal and the macroscopic poling axis. The observed dependence of texture and lattice strain on the grain orientation can be understood on the basis that the macroscopic strain due to poling is the average of the poling strains of all the individual grains.

B. Cherdhirunkorn

Papers

A high energy synchrotron x-ray study of crystallographic texture and lattice strain in soft lead zirconate titanate ceramics

Analysis of elastic strain and crystallographic texture in poled rhombohedral PZT ceramics

Micromechanics of residual stress and texture development due to poling in polycrystalline ferroelectric ceramics

Biodiesel production by a renewable catalyst from calcined Turbo jourdani (Gastropoda: Turbinidae) shells

Texture of poled tetragonal PZT detected by synchrotron X-ray diffraction and micromechanics analysis