PSI - Issue 60

D. Sen et al. / Procedia Structural Integrity 60 (2024) 44–59 Deeprodyuti Sen/ Structural Integrity Procedia 00 (2024) 000 – 000

47

4

Figure 1: Idealized Flaw tip hydride representation used in process zone model in Scarth and Smith (2002)

The condition for DHC initiation from a blunt flaw as given in Scarth and Smith (2002) is as follows,

T C v v p p  

(1)

H C

The critical value, v c , proposed by Scarth and Smith (2002), is calculated from the threshold SIF associated with the onset of DHC and is given by the following equation,

2

K

v



IH

c

' E p E

c

(2)

'

E



2

1





In this work, a two dimensional process zone model proposed by Scarth and Smith (2002) is implemented numerically. Coupled closed-form equations are solved in an iterative manner to calculate the critical hydride length and threshold peak stress for DHC initiation. The salient steps in the process-zone model are as follows:- a. Cubic polynomial equation is fitted to the stress distribution ahead of the flaw tip:-

2

3

o   x     x

o   x     x

o   x     x

( ) A

x A A  

A

A







(3)

0

1

2

3

b. Solutions for the stress intensity factor for a crack at a planar surface of a semi-infinite solid under stress distributions of increasing powers of distance ‘ x ’ from the surface are given by Stallybrass (1972). These solutions were modified by Scarth (2002) to account for finite thickness and the curvature of the blunt notch. The stress intensity factor for the j th stress term is given in the form given by the following equation:-

j

o     s   x

  1/2 s 

j j j j K A g f  

(4)

where j = 0,1,2,3