PSI - Issue 14

Vamsi Krishna Rentala et al. / Procedia Structural Integrity 14 (2019) 597–604 Vamsi Krishna Rentala et al. / Structural Integrity Procedia 00 (2018) 000 – 000

599

3

B

specimen thickness, m

B N

specimen thickness between the roots of the side grooves, m

S

span length, m specimen width, m

W

a

crack size equal to a 90/95 , m

1.1. POD approaches for multiple cracks at a site-Theory

As per MIL-HDBK 1823A, POD(a) is defined as the fraction of targets of nominal size, a, expected to be found, given their existence. POD statistical analysis for qualitative or HIT/MISS type NDT data can be carried out using Berens approach of log-odds distribution function (Berens (1992)). The functional form of log-odds distribution function is as shown in Equation 1

    f a

i P e   1

(1)

    f a

e

 

  i a

f a

.ln    

(2)

By using a logit link function, binary logistic regression process can be performed between NDT response and the log(flaw size). The logit of a number P between 0 and 1 is given by Equation 3

P

  

  

Logit P

 ( ) log

(3)

P

1



As mentioned earlier, POD analysis of NDT data for an inspection site contains multiple flaws at a site, can be carried out using 2 different approaches, namely, maximum flaw size and sum of flaw sizes approaches. In order to use these 2 approaches, Equation 2 can be modified as       j f m a f a .     (4)      j f s a f a .     (5) The remaining fatigue cycles of a component to grow a crack from initial size to dysfunction size can be calculated using Equation 6      d a n d C K N 1 (6) C and n are the material constants which can be determined from the fatigue crack growth rate testing procedure. K Q is the stress intensity factor for particular specimen geometry at the crack tip. In the current study, NDT inspection data of fatigue cracks in a 3-point bend specimen were considered for demonstration. For a 3-point bend specimen, the K Q is calculated (ASTM E399-12e1 (2012)) from Equation 7        a Q 1 1.2. Remnant life calculations using Deterministic Fracture Mechanics Approach