An External Circular Crack in an Infinite Solid Under Axisymmetric Heat Flux Loading in the Framework of Fractional Thermoelasticity

In a real solid there are different types of defects. During sudden cooling, near cracks, there can appear high thermal stresses. In this paper, the time-fractional heat conduction equation is studied in an infinite space with an external circular crack with the interior radius R in the case of axial symmetry. The surfaces of a crack are exposed to the constant heat flux loading in a circular ring R<r<ρ. The stress intensity factor is calculated as a function of the order of time-derivative, time, and the size of a circular ring and is presented graphically.

Torsional Vibration of an External Circular Crack in a Transversely Isotropic Composite

The forced torsional vibratory motion of an external circular crack in a transversely isotropic composite is investigated by using the method of Hankel transforms. A pair of vibratory torques of equal amplitude is applied at infinity. The infinite integral involved is evaluated through a contour integration to be discontinuous in nature. An exact expression for the dynamic stress intensity factor is obtained in terms of the frequency factor and the anisotropic material constants. The maximum value of the normalized dynamic stress-intensity factor is shown to occur at different frequency factors for the sample fiber-reinforced and metal matrix composites. The distortion of the dynamic crack surface displacement from the associated static displacement depends also on the forcing frequency and the material anisotropy.