Cracks at elliptical holes: Stress intensity factor and Finite Fracture Mechanics solution

• We model crack initiation at elliptical holes in plates under uniaxial tension.
• The instantaneous initiation of finite cracks is analysed by means of a coupled stress and energy criterion.
• We propose a new stress intensity factor with very good agreement to numerical results.
• Notch size effects are covered correctly.
• The Finite Fracture Mechanics solution renders a continuous transition from strength of materials to LEFM.

In this work crack initiation at elliptical holes in plates under uniaxial tension is studied by means of a closed form analytical Finite Fracture Mechanics approach. To allow for a detailed study of crack initiation, stress intensity factors available in literature are discussed and compared to extensive numerical results. Based on physical rationale, an improved stress intensity factor solution is proposed that shows a very good agreement with numerical results for a wide range of stress concentration factors of the ellipse and crack lengths. Using the exact solution of the stress field in the notched plate and the proposed stress intensity factor, an efficient Finite Fracture Mechanics solution is obtained. No empiric length parameters are introduced but only the strength and the fracture toughness are required for evaluation. The analysis comprises the case of a circular hole and the limiting cases of a crack tangential and normal to the loading direction. Typical notch size effects are covered by this coupled stress and energy approach. A continuous transition from strength of materials to Linear Elastic Fracture Mechanics can be rendered.