Three-dimensional piezoelectric boundary elements
Abstract
The strong coupling between mechanical and electrical fields in piezoelectric ceramics makes them appropriate for use as actuation devices; as a result, they are an important part of the emerging technologies of smart materials and structures. These piezoceramics are very brittle and susceptible to fracture, especially under the severe loading conditions which may occur in service. A significant portion of the applications under investigation involve dynamic loading conditions. Once a crack is initiated in the piezoelectric medium, the mechanical and electrical fields can act to drive the crack growth. Failure of the actuator can result from a catastrophic fracture event or from the cumulative effects of cyclic fatigue. The presence of these cracks, or other types of material defects, alter the mechanical and electrical fields inside the body. Specifically, concentrations of stress and electric field are present near a flaw and can lead to material yielding or localized depoling, which in turn can affect the sensor/actuator performance or cause failure. Understanding these effects is critical to the success of these smart structures. The complex coupling behavior and the anisotropy of the material makes the use of numerical methods necessary for all but the simplest problems. To this end, a three-dimensional boundary element method program is developed to evaluate the effect of flaws on these piezoelectric materials. The program is based on the linear governing equations of piezoelectricity and relies on a numerically evaluated Green's function for solution. The boundary element method was selected as the evaluation tool due to its ability to model the interior domain exactly. Thus, for piezoelectric materials the coupling between mechanical and electrical fields is not approximated inside the body. Holes in infinite and finite piezoceramics are investigated, with the localized stresses and electric fields clearly developed. The accuracy of the piezoelectric boundary element method is demonstrated with two problems: a two-dimensional circular void and a three-dimensional spherical cavity, both inside infinite solids. Application of the program to a finite body with a centered, spherical void illustrates the complex nature of the mechanical and electrical coupling. Mode I fracture is also examined, combining the linear boundary element solution with the modified crack closure integral to determine strain energy release rates. Experimental research has shown that the strain, rather than the total, energy release rate is a better predictor of crack growth in piezoelectric materials. Solutions for a two-dimensional slit-like crack and for three-dimensional penny and elliptical cracks are presented. These solutions are developed using the insulated crack face electrical boundary condition. Although this boundary condition is used by most researchers, recent discussion indicates that it may not be an accurate model for the slender crack geometry. The boundary element method is used with the penny crack problem to investigate the effect of different electrical boundary conditions on the strain energy release rate. Use of a conductive crack face boundary condition, rather than an insulated one, acts to increase the strain energy release rate for the penny crack. These conductive strain energies are closer to the values determined using a permeable electrical boundary condition than to the original conductive boundary condition ones. It is shown that conclusions about structural integrity are strongly dependent on the choice of boundary conditions.
Degree
Ph.D.
Advisors
Farris, Purdue University.
Subject Area
Aerospace materials|Mechanical engineering
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