Specular Reflection by Contacting Crack Faces

Abstract

<p>Non-linear relations are postulated between the transmitted tractions and the crack opening displacements across contacting rough crack faces. For the opening mode these relations take into account that a crack easily opens, but that the resistance to crack closure increases rapidly as the rough crack faces come in contact. For the sliding mode they account for initial elastic resistance as well as for frictional sliding resistance, with a maximum transmissible sliding traction whose magnitude strongly depends on the averaged contact pressure on the crack faces. For an incident pulse the nonlinear ordinary differential equations for crack-opening-displacements have been solved numerically. A Kirchhoff-type approximation to the representation integral has been used to compute the specular reflection. Results of para- metrical studies are presented.</p>