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Fundamentals ... (cont.)
  Mechanical Considerations
  
    Maximum Applicable Forces (Compressive Load Limit, Tensile Load Limit) The mechanical strength values of PZT ceramic material (given in the literature) are often confused with the practical longterm load capacity of a PZT actuator. PZT ceramic material can withstand pressures up to a few hundred MPa (a few 10,000 psi) before it breaks mechanically. This value must not be approached in practical applications, because depolarization occurs at pressures on the order of 20% to 30% of the mechanical limit. For stacked actuators (which are a combination of several materials) additional limitations apply. Parameters such asaspect ratio, buckling, interaction at the interfaces, etc. must be considered. If the specified maximum compressive force" for a PZT is exceeded, mechanical damage to the ceramics as well as depolarization may occur.
The load capacity data listed for PI actuators are conservative values which allow long lifetime. Standard PI PZT stack actuators can withstand compressive forces to several 10,000 N (several tons).
Tensile loads of nonpreloaded PZTs are limited to 5 s 10% of the compressive load limit (maximum compressive force). PI offers a variety of piezo actuators with internal spring preload for extended tensile load capacity. Preloaded elements are highly recommended for dynamic applications. Shear forces must be isolated from the PZT ceramics by external measures (flexure guides, etc.).
Stiffness When calculating force generation, resonant frequency, system response, etc., piezo ceramic stiffness is an important parameter. In solid bodies stiffness depends on the Young's modulus of the material, i.e. the ratio of stress (force per unit area) to strain (change in length per unit length). Stiffness is generally described by the spring constant kT, relating the influence of an external force to the dimensional change of the body.
This narrow definition is of limited application for PZT ceramics because the cases of static, dynamic, largesignal and smallsignal operation with open and shorted electrodes must all be distinguished. The poling process of PZT ceramics leaves a remanent strain in the material which depends on the magnitude of polarization. The polarization is affected by both the drive voltage and external forces. When an external force is applied to poled PZT ceramics, the dimensional change depends on the stiffness of the ceramic material and the change of the remanent strain (caused by the polarization change). The equation L_{N} = F/k_{T} is only valid for small forces and smallsignal conditions. For larger forces, an additional term describing the influence of the polarization changes, must be superimposed on the stiffness (k_{T}).
Since piezo ceramics are active materials, they produce an electrical response (charge) when mechanically stressed (e.g. in dynamic operation). When the electric charge cannot be drained from the PZT, it generates a counterforce opposing the mechanical stress. (This is why a PZT element with open electrodes appears stiffer than one with shorted electrodes). Mechanical stressing of PZT actuators with open electrodes, e.g. open wire leads, should be avoided, because the resulting induced voltage might damage the stack electrically.

   

Fig. 18. Quasistatic characteristic mechanical stress/strain curves for piezo ceramic actuators and the derived stiffness values (note that displacement is negative because the applied force is compressive). Curve 1 is with the nominal operating voltage (voltage giving nominal maximum displacement) on the electrodes, Curve 2 is with the electrodes shorted (showing ceramics after depolarization)
