PSI - Issue 70

Varsha S et al. / Procedia Structural Integrity 70 (2025) 51–58

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stress distribution σ(x,y), the weight function m (x,y;P′) and the stress distribution σ(x,y) over the whole fracture surface area, the SIF at point P′ on the crack front can be determined ( ′ )=∬ ( , ) ⋅ ( , ; ′ ) (3) Multiple methods exist to enhance the mathematical execution of weight function integration . The writer describes the mathematical point load weighted function expression for elliptical cracks in infinite and semi-infinite bodies using Wang, X., & Glinka, G. (2009) ( , ; ′ )= √2 3/2 2 [1+∑ = 1 ( , ) (1 − (( )) ) ] (4) As illustrated in Fig. 1, the variable s denotes the smallest distance between the load point P(x,y) and the boundary of the crack front Γ, while ρ represents the distance connecting point P to point P′ under consideration. In Fig. 2, the parameters r and φ are used to represent the coordinates of the point using parametric polar expressions of point P(x,y); the corresponding crack front point is R(φ), and θ indicates the position of point P′. The general form of Eq. (4) employing only a single term, that is, n = 1, can effectively approximate the point load weight function with a considerable level of accuracy across various surface crack configurations, as shown ( , ; ′ )= √2 3/2 2 [1 + ( , ) (1 − (( )) )] (5) Where ( , ) contains the unknown coefficients. in the present work, SIF of semicircular cracks in an arbitrary structure subject to a Mode I stress distribution is introduced through a formula. The suggested formulation is confirmed for two cases, which involve cracked finite thickness plates. ( )=∬ 0 ⋅ √ 2 3 2 2 [1 + ( ) ⋅ (1 − )] (6) Where represents the surface area of the semi- circular crack. It has been noted that α in semi -circular fractures equals 1. Therefore, for any specified damaged material, the unknown coefficient M will solely rely on θ. To enhance the efficiency of the solution process, the following non-dimensional form will be considered ( )= ( ) 0 √ = √2 2 √ ∬ √ 2 [1 + ( ) ⋅ (1 − )] (7) Where stands for the non-dimensional SIF reference. The singular word and the phrase that accounts for the impacts of the crack configuration are combined to form this ( ) = ( ) 0√ = √2 2 √ + ( ) √2 2 √ ∬ √ 2 + ( ) √2 2 √ ∬ √ 2 (1− ) (8) which would be summarized as ( )= ( ) 0√ = 2 ( ) (9) 1 = √2 2 √ ∬ √ 2 (10) 2 = √2 2 √ ∬ (1− ) (11)