Issue 59

E.S.M.M. Soliman, Frattura ed Integrità Strutturale, 59 (2022) 471-485; DOI: 10.3221/IGF-ESIS.59.31

1 2

   

   

         2 z b

         2 z b

         2 a b

    z

2

2



E

cos

cos

sin

0

(20)

 m

 m

   

i









 

2 2 k

2 2 k

 2 2 k



 



 2 1

2 E kz c

k z

k F z

2 1

  

k

k

2 2 1





k

k

1

 z c

         i z c z



K

e

 2 2 lim

(21)

I z c

  z x iy

  1 i

  c b a where: Φ (z), ϕ (z) and ω (z) are complex stress functions, c is the half length of the ligament, 2b is width of the plate, a is the length of each edge crack, E k and F k are coefficients, K I is the stress intensity factor, α is an angle of inclination of the crack with the x axis, k is Kolosov constant. Empirical formulas for mode I SIF, for a finite cracked plate under tensile stress, σ , can be written as [24]: In case of single edge crack                      2 3 4 1.122 0.231 10.550 21.710 30.382 a a a a K a b b b b I (22)

In case of center crack

2

3

  a b

  a b

  a b

    

    

 1 0.5





0.370

0.044

  a



(23)

K

I

a



1

b

where: 2a is the length of crack, 2b is the width of plate In case of double edge crack having two symmetric edge cracks                        2 3 1.122 0.561 0.015 0.091 1 a a a b b b K a I a b where: a is the length of each edge crack, 2b is the width of plate

(24)

M ETHODOLOGY D plane strain models of single edge cracked plate (SECP), center cracked plate (CCP), and double edge cracked plate (DECP) under tensile stress, are executed in ANSYS, FEA to determine the numerical values of mode I stress intensity factor K I . The material of the plate is steel with properties Young’s modulus of elasticity (E) = 200GPa 2

476