PSI - Issue 70

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

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thereafter, ( ) is obtained as follows

( ) = ( )− 1 2

(12)

Now, a new SIF would be extracted for points subjected to an arbitrary Mode I 2D stress distribution, K(θ), along the semi-circular fracture front as ( ) = ∬ ( , ) ⋅ √ 2 3 2 2 [1+ ( )− 1 2 ⋅ (1− )] (13) The new non-dimensional SIF is shown as ( )= ( ) 0 √ = √2 2 √ ∬ ( , ) ⋅ √ 2 [1+ ( )− 1 2 ⋅ (1− )] (14) 3 = √2 2 √ ∬ ( , ) . √ 2 (15) 4 = √2 2 √ ∬ ( , ) .(1− ) (16) An explicit formula for predicting new SIF at various points along the semicircular crack front of any structure experiencing a Mode I arbitrary 2 D stress distribution on the crack surfaces is derived from approximate expressions for I1, I2, I3, and I4.The diverse 2 D normal stress present on the virtual crack surfaces of the unflawed structure is evaluated as a combination of uniform, linear, or quadratic forms. Consequently, the maximum allowable crack size when estimating the fatigue life of pressurized structures is considered less than ¼ of the wall thickness. Thus, the two-dimensional stress distribution on the semi-circular crack faces of the structure is given as ( , ) = 0 ∑ ∑ ≤ 2=0 ≤ 2 =0 .( ) .( ) (17) Where the stress distributions are estimated by using the curve fitting technique to identify the unknown coefficients, .Different stress distributions may act on crack surfaces depending on the applied loading conditions. A constant or uniform stress is expressed as σ(x, y) = A₀₀σ₀. For variations in depth, a 1 D linear distribution is given by σ(x, y) = A₁₀(x/a)σ₀, whereas a one - dimensional quadratic variation in width follows σ(x, y) = A₀₂(y/a)²σ₀. More complex loading can be described by a two-dimensional saddle- type distribution: σ(x, y) = A₁₁(x/a)(y/a)σ₀. A g eneral representation combining these stress types can be written as σ(x, y) = [A₁₀(x/a) + A₁₁(x/a)(y/a) + A₀₂(y/a)²]σ₀. To simplify the analysis, the rectangular coordinate system (x, y) is transformed into a polar- like system (s, φ), where s denotes the radial distance from the crack front and φ represents the angular position relative to the center of the semi circular crack by Ghajar, R., & Kaklar, J. A. (2015) et al. = ( − ) cos (18) =( − ) (19) 2 = ( − ) 2 + 2 − 2 ( − ) cos( − ) (20) J= | | (21)