Mathematical study on the propagation of Griffith crack in a dry sandy strip subjected to punch pressure

Abstract

The present study investigates the features of a moving Griffith crack in a dry sandy infinitely long and finitely thick isotropic strip with moving parallel punches of constant load acting on both of its boundaries owing to plane wave propagation under point loading. Coupled singular integral equations and Cauchy-type singularities are used to formulate the present model, the Dirac delta function is employed to analyse the point load located at the moving crack edge, and the properties of Hilbert transformation are employed to obtain the closed-form expression of the stress intensity factor with constant point loading. For the sake of validation, the obtained results are matched with pre-established and standard results. Numerical simulations and graphical illustrations are performed to analyse the influences of the prevalent parameters, viz., sandiness parameter, punch pressure, distinct point load positions, length and speed of the crack corresponding to the plane wave on the stress intensity factor for the considered dry sandy isotropic material strip.

KEYWORDS:

• Hilbert transformation
• stress intensity factor
• dry sandy layer
• crack
• punch

Data availability statement

The data required to reproduce the findings of the present work are available to download from [56].

Acknowledgments

The authors convey their sincere thanks to University Grants Commission (UGC) New Delhi for providing Senior Research Fellowship to Mr. Ajeet Kumar Singh for carrying out this research work. The authors would like to express their gratitude to Indian Institute of Technology (Indian School of Mines) Dhanbad for providing the essential facilities for this research.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by University Grants Commission: [grant number (1070/(CSIR-UGC NET DEC.2016))].