Impact of Torsional Load on a Penny-Shaped Crack in an Elastic Layer Sandwiched Between Two Elastic Half-Space

Abstract

Sudden impact of torsional load on a penny-shaped crack in an elastic layer sandwiched between two elastic half-spaces has been analyzed in this paper. The axi-symmetric mixed boundary value problem is reduced to the problem of solving a pair of dual integral equations by using Hankel and Laplace transforms. The problem is further reduced to Fredholm integral equation of second kind which is solved numerically. Taking numerical inversion of Laplace transform, stress intensity factor at the tip of the crack is calculated and plotted for different values of the parameters.

Axisymmetric Torsion of an Elastic Layer Sandwiched between Two Elastic Half-Spaces with Two Interfaced Cracks

“…The only non-zero components of stress are given by (1) where u θ = u θ (r, z) and Gi is the shear modulus of the material. As the torsion of the homogeneous material is static, the displacement u θ (r, z) must satisfy (2) By means of Hankel's transformation, integral and its inverse given in [19],…”

“…15is reduced to the second Fredholm integral equation. Using the following formula we obtain the following Abel-type equation: (19) Now, we invert the above equation by applying the Abel transform formula to get (20) Using the following relationships we get the second Fredholm integral equation of the second kind (22) with the kernel To get a non-dimensionalized equation, from Eqs. (18) to (22), let us change the variables as follows (23) Next, we multiply the above two equations of the system by , respectively, and using the following substitutions 24we obtain the following equations:…”

Linear interface crack under harmonic shear: Effects of crack's faces closure and friction

“…Interfacial crack under impact loading was considered in [37][38][39][40][41][42]. Comparison of two hypersingular time domain boundary element methods for 2-D cracks under transient dynamic loading was done by Wuensche et al [37].…”

A mixed boundary value problem of a cracked elastic medium under torsion

“…The same method was used by Dhawan [24] for solving the problem of a rigid disc attached to an elastic half-space with an internal crack. By using Hankel and Laplace transforms and taking numerical inversion of the Laplace transform, Basu and Mandal [25] treated the torsional load on a penny-shaped crack in an elastic layer sandwiched between two elastic half-spaces. With the aid of the Hankel integral transformation method, in this paper we investigate the problem of a penny-shaped crack in the interior of a homogeneous elastic medium under axisymmetric torsion applied to a rigid disc glued inside.…”