PSI - Issue 60

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Chitresh Chandra et al. / Procedia Structural Integrity 60 (2024) 165–176 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

Appendix B. Analysis of Crack growth The corrected crack length ( a ) is computed by means of interpolation using the voltage difference output initial ( U i ) and final ( U f ) from DCPD and initial ( a i ) and final ( a f ) physical crack lengths measured using the stereo microscope and adopting the nine-point average as in the following expression: (Tang Z. et. al. 1993) =[ ( − ) ( − ) ( − ) ]+ (3) The crack tip opening is quantified by ∆V which is composed of an empirical component ∆V e and an experimental component ∆V c . ∆V c represents the deformation occurring during the dwell period and ∆V e exemplifies the instantaneous elastic part during the cyclic portion of the loading cycle. ∆V is expressed by means of the following expression (ASTM E2760 2019) = ∆ +∆ (4) Where ∆ V e is calculated by, ∆ = ℎ ( ) [ 2∆ 2 ′ ] (5) Subsequently, the corrected crack lengths were used for computing corrected crack growth rate and fracture mechanics parameters. The crack growth rate has been presented as a function of ΔK or (C t ) avg . For a side-grooved C(T) specimen under mode I loading, the ΔK is expressed by the following expression (Chandra C. et. al. 2022) ∆ = ∆ ( ) 1 2 1 2 ( ) (6) Where, f(a/W) is expressed by, f( W a )=[ 2+ Wa (1− Wa ) 3 2 ] (0.886 + 4.64 ( W a )−13.32( W a ) 2 +14.72( W a ) 3 −5.6( W a ) 4 ) (7) It has been inferred from literature that, for creep ductile materials, (C t ) avg is the most suitable parameter for associating CFCG crack growth rates under trapezoidal waveform with a dwell period t h and is expressed as following equation (ASTM E2760 2019) (C t ) avg = P max (ΔV c ) (BB N ) 1 2 Wt h ( f f ′ ) (8) where ( f’/f) is given by, ′ =[ 2+ 1 + 2(1 3 − ) ]+[ {4.64−26.64( )+44.16( ) 2 −22.4( ) 3 } {0.886+4.64( )−13.32( ) 2 +14.72( ) 3 −5.6( ) 4 } ] (9) The crack growth rate is derived by means of the secant technique, wherein slope of the line in between adjacent points on a vs N curve during the dwell period ( t h ) is derived as follows: (Saxena A. 2015) ( ) = ( +1 − ) ( +1 − ) (10) ( ) = 1 ℎ ( ) ` (11)