PSI - Issue 66

Aditya Khanna et al. / Procedia Structural Integrity 66 (2024) 370–380 Author name / Structural Integrity Procedia 00 (2025) 000–000

373

4

(a)

(b)

Load,

Load,

0

0

Back- face strain, −

Back-face strain, −

Fig. 1. Schematic demonstrating the (exaggerated) back-face strain increment at maximum load due to crack extension in the presence of (a) compressive residual stress field; (b) tensile residual stress field perpendicular to the crack path. Figure adapted from Lados et al. (2007). Note that the sign of the back face strain is reversed to follow the same convention as the load vs. crack mouth opening displacement curves. Calculating the residual strain increment does not require any additional data processing since the least-square fitting of the cyclic load-strain data for an open crack simultaneously provides the slope (open crack compliance) and the intercept (residual strain). Subsequently, one of two methods can be applied to estimate the residual Stress Intensity Factor (SIF). 2.1. Influence function method For an arbitrary residual stress field, Schindler et al. (1997) derived the following relationship between the stress intensity factor at the tip of the crack (or crack-like cut) and the derivative of the measured strain with respect to the crack (cut) length: res ( ) = ( ) res ( ) . (2) The influence function ( ) can be obtained by substituting any known solutions for SIF and back-face strain for the same applied loading into Eq. (2). For instance, ASTM E647 provides the SIF solution for a compact tension specimen under pin loading and Eq. (1) from Newman Jr. et al. (2011) provides the corresponding back-face strain solution. Olson and Hill (2012) provided another reference solution for the case of an edge crack loaded by uniform internal pressure. In any case, the influence function for a compact tension specimen has the following general dependance on the unbroken ligament width: ( ) = ( ⁄ ) ( ) 3 / 2 , (3) where several solutions for the dimensionless function ( ⁄ ) obtained using different modelling approaches have been compiled by Olson and Hill (2012). For 0.2 ≤ / 0.95 , i.e., crack lengths relevant to fatigue crack growth testing, a polynomial approximation for ( ) can be obtained using the results present by Olson and Hill, as follows: ( )=166.8 7 − 635.2 6 +1017 5 − 890.9 4 +467.7 3 − 152 2 +30 0.4206.