ELASTOTHERMODYNAMIC DAMPING ANALYSIS OF A GRIFFITH CRACK USING FEM

Abstract

Elastothermodynamic (ETD) damping is one of the many damping mechanisms present in a real material. A temperature field is setup inside the material due to well-known thermoelastic effect. ETD is due to irreversible heat flow caused by this temperature field. ETD is quite small in homogeneous, isotropic materials. Nevertheless, ETD may be significant for heterogeneous materials. Cracks, voids and other inclusions further supplement this. During their life span, many materials develop flaws inside them. The damping properties of many composite material structures are greatly influenced by the presence of flaws. As such it is important to study the ETD behavior of materials in presence of cracks. In the present work, ETD behavior of a Griffith crack under mode-I loading has been investigated. It was not possible to obtain exact mathematical solution for the problem since it leads to intractable difficulties. Therefore, FEM technique has been employed in the present study. Exact expression for the hydrostatic field, 6kk has been used in the associated heat conduction equation to obtain the temperature field. Finally, the results are also compared with the analytical solutions available in the literature. The present study reveals that, for higher frequencies, the energy dissipation is largely concentrated in a small region near the crack tip. However the contribution from the rest of the plate is also significant and can not be ignored. At higher frequencies, the energy dissipation is more evenly distributed in the whole plate. The peak damping is observed at a much frequency for the full plate region as compared to the corresponding frequency for a small region near the crack tip.