Crack repair using an elastic filler

Abstract

The effect of repairing a crack in an elastic body using an elastic filler is examined in terms of the stress intensity levels generated at the crack tip. The effect of the filler is to change the stress field singularity from order 1 / r 1 / 2 to 1 / r ( 1 - λ ) where r is the distance from the crack tip, and λ is the solution to a simple transcendental equation. The singularity power ( 1 - λ ) varies from 1 2 (the unfilled crack limit) to 1 (the fully repaired crack), depending primarily on the scaled shear modulus ratio γ r defined by G 2 / G 1 = γ r ε , where 2 π ε is the (small) crack angle, and the indices (1, 2) refer to base and filler material properties, respectively. The fully repaired limit is effectively reached for γ r ≈ 10 , so that fillers with surprisingly small shear modulus ratios can be effectively used to repair cracks. This fits in with observations in the mining industry, where materials with G 2 / G 1 of the order of 10 - 3 have been found to be effective for stabilizing the walls of tunnels. The results are also relevant for the repair of cracks in thin elastic sheets.