F. Guiu

CYCLIC FATIGUE OF CERAMICS

The fatigue behaviour of alumina, zirconia-toughened alumina (ZTA) and tetragonal zirconia (TZP) have been investigated using three different techniques. Direct push-pull testing has been used to generate both static and cyclic fatigue data. The results clearly show that all the materials studied are susceptible to both static and cyclic fatigue, and that the times to failure under cyclic loading are considerably shorter than under static loads. The fatigue failure origins have been identified and the influence of surface condition on fatigue life has been assessed. The slow propagation of cracks subject to cyclic tensile and compressive loads has been studied using compact tension specimens and tapered double cantilever beam specimens. These investigations have confirmed the existence of cyclic fatigue effects in coarse-grained alumina and have shown the crack increment per cycle (da/dN) to have a power-law dependence on the peak stress intensity factor. A technique, based on repeated indentation, has been used to investigate the propagation of sub-surface cracks subjected to cyclic loading in both fine-grained alumina and ZTA. The results of the investigation suggest that compressive or closure loads on the crack faces are factors which affect the cyclic fatigue crack growth in ceramics. Based on those observations, an explanation is proposed for the mechanical cyclic fatigue effects in the ceramics investigated.

Dislocations in polyethylene crystals: line energies and deformation modes

Abstract Explicit expressions are obtained for the line energy of straight dislocations in orthorhombic polyethylene crystals. It is found that the 〈0, 0, c〉 screw dislocation is the perfect dislocation with the lowest line energy whilst the 〈0, 0, c〉 edge has negative line tension and is therefore unstable. The possible dissociation of perfect dislocations into partials is discussed, and it is shown that both (110) and (310) twin dislocations can arise from such dissociations. Numerical calculations also show that homogeneous nucleation of 〈0, 0, c〉 dislocations, and twin dislocations, has a very high probability of occurrence under a stress of the order of the yield stress of polyethylene crystals. These results help to explain the readiness of polyethylene crystals to deform by c axis slip, twinning, and monoclinic transformation modes. The supression of c axis slip by irradiation and cross-linking is also explained by the very high line tension of the 〈0, 0, c〉 screw dislocations.

Thermal activation of ferroelectric switching

By applying the theory of thermally activated nucleation to the switching of ferroelectric domains, a method is developed to experimentally obtain the value of both the activation enthalpy, ΔH, and activation volume, V*, for the thermally activated process involved in ferroelectric switching. The method was applied to the switching of a soft lead zirconate titanate and values of ΔH=(0.16±0.02) eV and V*=(1.62±0.16)×10−25 m3 were obtained at the coercive field. These values imply that the energy, ΔU, required for the formation of switching nuclei is mainly supplied by the work done by the electric field. A comparison of these values with those obtained from theoretical considerations suggests that the switching is achieved by the sideways expansion of nuclei formed at the domain boundaries in the form of low amplitude and long wavelength fluctuations of the domain walls.

Low-temperature deformation and dislocation mobility in pure and Mg-doped LiF crystals

Abstract Two batches of LiF crystals, one essentially pure, and the other doped with 140 p.p.m. of Mg, were cooled from high temperature at different rates. The mechanical properties of these crystals were investigated in the temperature range 77 to 360 K. The results obtained are analysed and discussed in terms of the theory of interaction between dislocations and tetragonal defects for which improved expressions are derived. Good agreement is obtained between the predictions of the theory and experimental results. It is concluded that the thermally-activated deformation and low-temperature dislocation mobility are controlled by the interaction between dislocations and Mg2+ vacancy dipoles. The largest concentration of isolated Mg2+-vacancy dipoles is retained in the doped fast-cooled crystals which have the largest yield stress at low temperatures. It is estimated that in the doped slowly-cooled crystals one sixth of the total number of Mg2+ ions aggregate into complexes (containing more than 10 ions) w...

Anisotropic and cyclic mechanical properties of piezoelectrics—compression testing

Abstract The mechanical stressing of PZT produces irreversible deformation by the irreversible switching of 90° domains. This leads to highly anisotropic deformation behaviour for poled materials. The threshold stresses required to produce this switching are relatively small,

Growth of indentation cracks in poled and unpoled PZT

The growth behaviour of indentation cracks in both poled and unpoled PZT is examined by subjecting the cracks to static and cyclic loading in bending. An anomalous growth of the cracks not subjected to any direct stressing was observed during cyclic fatigue loading in both the poled and unpoled materials. In the poled PZT specimens the length of the radial indentation cracks was found to be strongly dependent on their orientation with respect to the poling direction, in agreement with previously reported observations. The growth behaviour of the cracks is discussed after having estimated the magnitude of their total stress intensity factor. It is argued that the apparent fracture toughness anisotropy with respect to the direction of poling is not entirely consistent with previously proposed interpretations, and an alternative explanation is suggested.

Fracture toughness anisotropy of PZT

Abstract Fracture toughness of a lead zirconate titanate (PZT) piezoelectric was measured using the indentation technique and the single edge notch bend (SENB) method. Values of fracture toughness, K Ic , show significant anisotropy in poled samples, with longest and shortest crack lengths in the directions parallel and perpendicular to the poling axis, respectively. The crack profiles below the indented surfaces have been studied for both the unpoled and the poled samples. This also revealed the shape and size of the plastically deformed zone underneath the indentation. The microstructural anisotropy and internal stresses caused by the poling, and the contribution of stresses introduced by the experimental method are considered in the discussion.

Toughening produced by crack‐tip‐stress‐induced domain reorientation in ferroelectric and/or ferroelastic materials

Abstract A calculation is carried out of the toughening produced by the crack-tip-stress-induced reorientation of domains in a ferroelectric and/or ferroelastic material. The calculation is based on obtaining the shielding stress intensity factor produced by the shear transformation of a zone surrounding the crack tip and extending over the crack surfaces. It is argued that the effective shear strain γe of the transformation is not uniform inside the transformation zone but is a function of the resolved shear stress of the crack tip, τ activating the domain reorientation. It is shown that the relation between γe and τ can be obtained experimentally from the compressive stress-strain curve of the material. An accurate calculation of the shielding stress intensity factor produced by such an inhomogeneous transformation zone requires the solution of a difficult problem which is not attempted. However, a simple overestimate is made, showing that the toughening which can be expected from the crack-tip-stress-induced reorientation of domains in a ferroelectric and/or ferroelastic material is less than 10% even in the most favourable conditions. This result is justified on physical grounds and it is argued that the small toughening predicted by the calculations arises because the crack tip stresses needed to drive the transformation increase proportionally with the transformation strain. This case is contrasted with the much greater toughening which is expected from the crack tip-stress-induced phase transformations which are largely driven by the chemical or bulk, free-energy change of the transformation.

Physical interpretation of fracture-toughening mechanisms

The basic idea behind the toughening of materials by the introduction of energy-absorbing or dissipating artefacts is critically re-examined. It is shown that energy dissipation by plastic deformation or other dissipative processes at the tip of a growing crack does not contribute to increasing the effective surface energy or the crack resistance of the material. Erroneous interpretations of toughening by the presence of fibres or by phase transformations occuring at the tip of a growing crack are discussed. It is argued that all processes which dissipate energy at the crack tip produce crack shielding and that this effect must be an important contribution to toughening. It is concluded that most of the features and properties embodied in methods of toughening can be explained by shielding effects and that the increase in toughness is due to a reduction in the local value of the crack extension force, or its equivalent stress intensity factor, and not to an increase in energy dissipated.

Cyclic deformation of Nb single crystals II. Influence of orientation on cyclic hardening, shape changes and stress asymmetry

Abstract Niobium single crystals with seven different orientations of the stress axis have been deformed cyclically in tension-compression at room temperature and at a constant strain rate of 6 × 10−4 s−1 over a range of total strain amplitudes between 0.3 × 10−3 and 6 × 10−3. The cyclic hardening behaviour has been found to be strongly dependent upon the crystal orientation. Those crystals whose c.s.s. curves exhibit four well-defined regions do not obey a cyclic equation of state, but for certain crystal orientations, the c.s.s. curves are flat and independent of the cyclic strain history. The magnitude of the crystal shape changes during cyclic deformation, varies with the crystal orientation, and for some orientations no changes in shape take place. These results are explained in terms of both the asymmetric slip and the observed active glide systems in tension and compression. The stress asymmetry was also found to vary in magnitude and sign with the orientation of the crystal axis in agreement with ...