Susmit Kumar

Crack propagation in piezoelectric materials under combined mechanical and electrical loadings

A finite element technique is used to study the stress distributions at the crack tip of a piezoelectric ceramic because of the mechanical and/or electrical loads. The stress distributions at the crack tip are found to be in conformity with those predicted theoretically by Sosa and Pak. For combined mechanical and electrical loads, the stress intensity factor at the crack tip is observed to increase with an increase in the electrical to mechanical load ratio for a negative applied electric field (electric field opposite to the direction of poling) which is in agreement with the experimental findings of Wang and Singh. For the positively applied electric field, compressive stresses are found to develop around the crack tip for high electrical to mechanical load ratios. For combined mechanical and electrical loads, the stress distributions at the crack tip under applied stress is found to be significantly different from those under applied strain. It is shown that a negative applied electric field with a tensile strain perpendicular to the crack surface increases the crack propagation.

Energy Release rate and crack propagation in piezoelectric materials. Part I: Mechanical/electrical load

Abstract A finite element technique is used to study the angular distribution of the energy release rates for crack propagation in a piezoelectric ceramic because of a mechanical or electrical load. Comparisons are made between the energy release rate and the maximum stress criteria for the crack propagation. Substantial differences are found in the mode of crack propagation based on these two criteria. Significant differences in the energy release rate are found between applied stress and applied strain, and between applied electric displacement and applied electric field. For applied electrical loads, oblique crack propagation, experimentally seen by McHenry and Koepke, is explained by the energy release rates.

Energy release rate and crack propagation in piezoelectric materials. Part II : Combined mechanical and electrical loads

Abstract A finite element technique is used to study the angular distributions of the energy release rates and stresses for the crack propagation in a piezoelectric ceramic because of the applied stress and applied electric field. The change in total energy is compared with the theoretical values of the energy release rates given by Pak. This change in the total energy is higher in the case of a positive applied electric field than in the case of a negative applied electric field. For high negative applied clectric fields, the strain energy of the specimen becomes negative although a remotely applied stress is tensile in nature and under these conditions, crack closure occurs.

Simulation of material microstructure using a 3D voronoi tesselation: Calculation of effective thermal expansion coefficient of polycrystalline materials

Abstract The three-dimensional Poisson-Voronoi model is used to simulate a topologically equivalent material microstructure. A finite element package has been written to use this model to calculate the effective thermal expansion coefficient of the polycrystalline aggregate using the single crystal thermoelastic properties. The results have been found to be close to the experimental values and the values calculated from the Hashins exact equation for hexagonal, tetragonal and trigonal materials.

Influence of applied electric field and mechanical boundary condition on the stress distribution at the crack tip in piezoelectric materials

A finite element technique is used to study the stress distributions at the crack tip of a piezoelectric ceramic subject to the applied electric fields. Under a negative applied electric field (electric field opposite to the direction of poling), the assumption of crack surfaces to be free of surface traction as the mechanical boundary condition is found to be invalid. It is shown that the stress distributions at the crack tip under the negative applied electric field are different for the closed crack mechanical boundary condition than those for the traction-free crack surface mechanical boundary condition.

Effect of the mechanical boundary condition at the crack surfaces on the stress distribution at the crack tip in piezoelectric materials

Abstract A finite element technique is used to study the stress distributions at the crack tip of a piezoelectric ceramic because of the combined mechanical and electrical loads. For high electrical to mechanical load ratios, the assumption of crack surfaces to be free of surface traction as the mechanical boundary condition is not valid for two cases of combined electrical and mechanical loadings—(i) applied stress and negative applied electric field (electric field opposite to the direction of poling) and (ii) applied strain and positive applied electric field. The stress distributions at the crack tip for these loading conditions under the assumption of closed crack mechanical boundary condition are found to be different from those under the assumption of crack surfaces to be free of surface traction.

Three-dimensional finite element modeling of residual thermal stresses in graphite/aluminum composites

Abstract Residual thermal stresses in graphite/aluminum fiber-reinforced metal—matrix composites is studied using three-dimensional finite element modeling and assuming the anisotropic thermal expansion coefficient of graphite fiber. The finite element results are compared with the two-cylinder model results of Vedula et al. and the experimental results of Tsai et al . During cooling from the processing temperature, the anisotropy of the graphite fiber results in the increase of the temperature range over which the elastic deformation of the matrix occurs. The effect of fiber volume fraction on the distribution of hoop and radial stresses at the fiber—matrix interface is also investigated. In the square and hexagonal array arrangements of fibers, the possible sites for the crack initiation are the points where the fiber—matrix interface intersects the lines joining the fiber center to its first nearest neighbors.

A Monte Carlo Study of Size and Angular Properties of a Three-Dimensional Poisson-Delaunay Cell

On the basis of simulation of 1.2×106 three-dimensional Poisson-Delaunay cells, the statistical properties of their size and angular parameters have been studied. The moments of the volume, face area, and edge length distributions are found to be equal to those obtained from the exact expressions of Miles and of Moller. The volume, surface area, and face area distributions can be described by the two-parameter gamma distribution. The normal distribution can be used to describe the distributions of the total edge length of a cell and the perimeter of a face. The edge length distribution has also been studied. The distribution of the angle in a face is found to be in accordance with its theoretical distribution.

The creep response of uni-directional fiber-reinforced ceramic composites: a theoretical study

Abstract Both the finite-element technique and the elastic-viscoelastic correspondence principle (in conjunction with the Hashin and Aboudi methods of calculating the effective elastic properties) methods have been used to calculate the effective creep properties of SCS6 (fiber)/SiC (matrix) composites and the results have been compared. In the finite-element technique, three different arrangements of fibers were used to study the effects of fiber arrangements on the creep properties of the composite. Effects of the fiber volume fraction on the creep behavior of composite were also studied. No significant difference was found in the longitudinal compliance, S11 (i.e. the compliance along the fiber axis), calculated from the five models. But, it was found that the fiber arrangement plays an important role in the transverse compliance, S22, and transverse shear compliance, S44. For S22, the correspondence principle method based on Aboudi method and the square array of fibers in the finite-element technique gave the upper and lower bounds, respectively. For S44, the square array of fibers in the finite-element technique and the correspondence principle method based on Hashin (for low volume fraction of fiber)/Aboudi (for high volume fraction of fiber) method gave the upper and lower bounds, respectively. The effects of fiber arrangements on S22 and S44 are explained by the strain energy and the energy dissipation due to creep.

Effects of coating properties on crack propagation in nicalon-fiber/SiC-matrix composites

A finite element technique has been used to study the effects of coating properties on the propagation of cracks which terminate perpendicular to the fiber coating or coating/matrix interfaces. Four types of coatings are considered for Nicalon/SiC composites. The hoop and tangential stresses and the energy release rates are analyzed for the various coatings. Although the change in the thickness of coatings has a very small effect on the stress ratio (ratio of hoop stresses along the crack and at the interface) and energy release rate ratio (ratio of energy release rates for the crack penetration and crack deflection), the magnitudes of the stresses and energy release rates change substantially. The finite element results for Nicalon/SiC composites with a carbon coating are in agreement with previous experimental findings.