AbstractsPhysics

The behaviour of a free-standing thin film differs from that of a film surface-bonded or embedded due to the boundary constraints. A general dearth of analytical models, in regard to prediction of the operational competence of a constrained Piezoelectric thin film, prevails. In conventional design of miniaturized thin film devices, several non classical effects, for instance the effect of boundary constraints, are not considered. To warrant the design and performance optimisation of thin film sensors, such effect must be taken into account in a forethoughtful manner. This thesis is an attempt to achieve such optimisation through modeling of thin films. The coupled problem of a film on a substrate is solved semi-analytically in theoretical cases; and by finite element analysis in realistic cases for damage identification in the host structure. We first propose a two-dimensional analytical model of a constrained Piezoelectric thin film embedded in a host. Analytical expressions of capacitance and voltage across the electrodes are obtained by assuming first order shear deformation across the film thickness. The bonding layer between the film and the substrate, which is assumed to be an equivalent single layer including electrodes, insulation layer, adhesive layer etc., is modeled by taking into account its viscoelastic property. Residual stress is incorporated in the constitutive model through equivalent residual strain. Simulations on 10 m thick PVDF and 100 mPZT films are conducted. They illustrate the dependence of voltage response and capacitance on the applied stress, as well as on the residual stress. A maximum percentage variation in capacitance, as compared to the conventional estimate, is about 2% in a PVDF film and +75% to-65% in a PZT film for various combinations of tensile stresses applied at the ends of the film. Effect of residual stress is also exemplified via comparative response of a 1 m PZT film deposited on Pt/Ti/Si(0 0 1), with and without residual stress. For this case, an almost +50% increase in the voltage and an equivalent drop in the capacitance is observed. Next, we look into the voltage response profile of this model by employing it as a sensor to identify a finite mode I and mode II sub-surface cracks in a finite size host. To model the embedded crack, additional perturbation functions in the displacement field due to linear elastic crack tips in an infinite solid under plane strain condition are introduced to accommodate the stress free conditions at its surfaces. The film model requires the interfacial displacement and traction conditions, which are obtained from the analysis of the host. The combined analysis of the film and crack models brings forth the voltage gradient along the film span as a direct indicator of the location of crack in the axial direction, whereas the voltage magnitude represents the size of the crack. Following this analysis, a quasi three-dimensional(3-D) model of a Piezoelectric thin film surface-bonded to the host structure is proposed. With due consideration…