A method of the estimation of approximate stress intensity factor for a semi-elliptical crack at notch root was proposed. The stress distribution in the vicinity of notch root was divided into two components: uniform and linear components. The linear component was correlated with the notch root radius ρ. The stress intensity factors for these two stress components were calculated using the equations which were made on the basis of numerical results for a semi-elliptical crack at the surface of a semi-infinite body.
First, the accuracy of the proposed method was checked by comparing the present values with the accurate numerical results for a semi-elliptical crack at the inner wall of a pressurized hollow cylinder with an infinite outer radius. And then, the method was applied to a semi-elliptical crack in a pressurized hollow cylinder with a finite outer radius and to a semi-elliptical crack at notch root of CT specimen.
The following closed form formula is proposed for the estimation of stress intensity factors for a semi-elliptical crack at notch root in other problems.
KI, D=KIT+KIB
KIT=σ1√πbFIT(λ), λ=b/a
FIT(λ)=1.122-0.230λ-0.901λ2+0.949λ3-0.280λ4
KIB=(σ2-σ1)√πbFIB(λ)
FIB(λ)=0.443-0.310λ-0.104λ2+0.206λ3-0.061λ4
where σ2 is the maximum stress at notch root and σ1 is that at the point corresponding to the deepest point of the elliptical crack front.
