Vol. 14, No. 3, 2019

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Thermoelastic fracture initiation: the role of relaxation and convection

Louis M. Brock

Vol. 14 (2019), No. 3, 393–412

An isotropic, thermoelastic solid is at rest at uniform (absolute) temperature, and contains a semi-infinite, closed plane crack. Thermal relaxation governs, and crack surfaces are subject to convection. In-plane and compressive point forces, applied to each face of the crack initiate transient 3D extension. Wiener–Hopf equations are formulated in integral transform space from expressions whose inverses are dynamically similar and valid for short times. The solutions, upon inversion, are subjected to the dynamic energy release rate criteria, with kinetic energy included. A differential equation for crack edge contour is produced, and demonstrates that a certain type of point-force time variation can indeed cause a constant extension rate. Calculations for the pure compression case show that variation in crack growth rate with convection is not necessarily monotonic. A finite measure of crack edge thermal response for pure compression is provided by the temperature norm. Calculations indicate even greater sensitivity to thermal convection.

thermoelastic, relaxation, transient, fracture, discontinuity, convection
Received: 28 January 2019
Revised: 5 May 2019
Accepted: 11 May 2019
Published: 8 October 2019
Louis M. Brock
Department of Mechanical Engineering
University of Kentucky
151 Ralph G. Anderson Building
Lexington, KY 40506-0503
United States