PSI - Issue 2_A

M. A. Kamaludin et al. / Procedia Structural Integrity 2 (2016) 227–234 M. A. Kamaludin et al. / Structural Integrity Procedia 00 (2016) 000–000

230

4

2 16 1 9    = = +  0 P EB x δ

  

16 ( )

2 Y xdx

C

x

=

φ

(1)

EB

where C is the specimen compliance, E is the Young’s modulus of the specimen material, Y is the shape factor and φ is the bracketed term, the latter two both depending on x. For an equivalent blunt notched specimen, the compliance expression is similar, however in this case the bracketed term is fixed as the crack does not extend. The compliance thus increases only due to creep: ( ) 16 2 16 1 9 0 2 b b x b x EB Y xdx P EB C b φ δ =     = = +  (2) where C b is the compliance for a blunt notched specimen (notch tip radius ρ ≈ 1000 μ m), x b is its crack length, and φ b is a constant depending on x b . By monitoring C(t) and C b (t), φ (x) can be determined, which is used to find x and a. Crack speeds can then be calculated by differentiating successive values of a. Numerical values of C b /C as related to x are provided in Table 1; the case with x b = 0.35 is provided.    

Table 1. Numerical and fitted values of C b /C for x b = 0.35. x=a/W C b /C (numerical) C b /C (fitted) Error (%) 0.25 1.326 1.338 0.9 0.30 1.161 1.161 0.0 0.35 1.000 0.995 0.5 0.40 0.847 0.842 0.6 0.45 0.706 0.701 0.6 0.50 0.576 0.573 0.6 0.55 0.459 0.456 0.7 0.60 0.357 0.352 1.4

For x > 0.25, the plot of Cb/C against the square of the (normalised) ligament (1-x) tends to a straight line, for which a fit may be utilised:

2 1

  

     

  

C

( ) p x q x    = − −  = − + 2 1 1 C C b

W a

1

  

q

=

b

(3)

C

p

where p and q are constants. The relevant values of p and q, together with φ b are provided for different values of x b in Table 2: