The Mechanical Response of a Cantilever Beam With an Embedded Crack With Non-Linear Crack Surface Closure Effects

Abstract

This study addresses the crack surfaces closure effects of a cracked cantilever beam subjected to transverse force applied at its free end under static loading. A crack closure method is developed as needed to account for crack surface contact in regions wherein the linear solutions predict physically inadmissible crack surface inter penetration. An efficient finite element algorithm is developed accordingly to solve the static problem of the beam containing a fully embedded sharp crack in a linear, elastic, homogeneous and isotropic system. Emphasis is placed on the comparison between the near-tip fracture characteristics estimates, e.g. the normalized energy release rate, Mode I and Mode II stress intensity factors (SIF), and mode mixity, with closure effects and those without closure effects reported elsewhere. The crack length, orientation, and crack center location appear as the studied model parameters of a beam of fixed beam aspect ratio. In addition, based on the study observations of pure Mode II crack, a case study on the beam with an embedded vertical crack in the compressive regime is reported to show the deformed profiles due to full crack surfaces closure during loading. The curvature profile of the cracked beam with and without closure effects are compared to those of the healthy beam for the application of closure effects in improving the results accuracy.