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| Fracture mechanics of cracked elliptical hole based on surface elasticity theory |
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Abstract Mode III fracture characteristics of a nano-sized cracked elliptical hole is investigated. Based on the surface elasticity theory and the conformal mapping technique, closed form solutions of the stress fields around the defects (crack and elliptical hole) and the stress intensity factor at crack tip are presented by using the complex potential function. The present solution is fairly general such that many existing and new results can be regarded as special degenerated cases. By applying the analytical solutions to typical examples, effects of the size of defects, the shape ratio of elliptical hole and the relative size of crack on the stress intensity factor are discussed. The results show that the stress intensity factor is size-dependent significantly when considering the surface effect of the defects at the nanometer scale. The size effect of the defects decreases with the increase of the defects size, and gradually approaches the classical elastic theory. The variation of the stress intensity factor with shape ratio of the elliptical hole is related to the surface constant of the defects. With the increase of the elliptical hole shape ratio, the dimensionless stress intensity factor increases slightly and then decreases for the case of classical elastic theory and positive surface constant. When the surface constant is negative, the dimensionless stress intensity factor monotonously decreases to a stable value. The effect of the surface effect of defects depends on the shape ratio of the elliptical hole, and the very high shape ratio shields the contribution of the surface effect. With the relative size of the crack increases, the dimensionless stress intensity factor increases first to the maximum and then decreases. The surface effect is weak when the relative size of the crack is very small, whereas the surface effect is obvious when the relative size of the crack is large.
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Received: 06 September 2018
Published: 22 February 2019
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2019, Vol. 40 
