Weakening of Crack-tip Singularity due to Buckling of Thin Bodies under Tension

Abstract: When thin sheets containing a crack is subjected to tensile loading in the direction perpendicular to the crack surface out of plane displacement will occur in areas surrounding the crack. By this the stress state in the vicinity of the crack tip is changed and leads to a weaker crack tip singularity than the r-1/2 by linear elastic fracture mechanics. During lab testing the buckling is artificially prevented thus the conditions for transfer of predicted fracture criteria to real structures are changed. The weaker singularity is used to formulate an adopted fracture mechanical theory. Approximation is made based on the assumption that the buckled area of the paper is unable to carrying any load and that region is approximated by the region under compressive load at plane stress conditions. The result is compared with experiments performed on large paper specimens that imply that the fracture toughness does not hold a constant value for small cracks. A post-buckling analysis was performed to closely study the change of the singularity. The analysis suggests that at an applied load at 100 times the buckling load the drop of the singularity for a crack length of 20% of the sheet width is about 2%, which does not cause any major deviations from the predictions of the linear theory. However by experimental data it is predicted that the crack growth will commence at an applied load approximately 2572 times the buckling load and the drop of the singularity would be considerable larger at such load magnitudes which will result in greater impact in comparison with the linear theory