PSI - Issue 52

Chen Zhou et al. / Procedia Structural Integrity 52 (2024) 234–241 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

237

4

( ) ( ) c c zx xz

( 2) ( 2) f f zx xz  

1

1

−

 

−

(

)

2 E h e c c s

2 2 f E h e h h − − 2 f s c

H

=

+

(8)

2

2

f

2

2

2

   

   

h

( ) ( ) c c zx xz

2

( 2) ( 2) f f zx xz  

   

  

1

1

h

h

h

−

−

 

 

  

  

2

f

2 e + + 

c

c + −

c

(9)

H

E h

E h

e

h e

=

+ −

3

2 2 f

2

c c

s

f

s

f

s

2

12

2

3 2 

2

where zx  and xz  are the Poisson’s ratios; E denotes elastic modulus; h denotes the thickness; The upper and lower index f 1 , c , and f 2 denote the upper face sheet, core, and lower face sheet respectively. The specific derivation process can refer to the work of Kardomateas et al. (2013). a b

c

Fig. 2. The DCB-UBM specimen: (a) geometric model; (b) J-integral path; (c) finite element model.

The results are presented in Table 2. The change in ERR is small when the bending moment ratio (M R =M 1 /M 2 ) changes, but the change in PA is more pronounced. When the M R is set to -0.1, the PA reaches 14.5° and the mode Ⅰ fracture is dominant; when the M R is set to 0.05, the PA reaches - 67.3° and the mode Ⅱ fracture is dominant. The MCSDE solution is in good agreement with both the analytical solution and finite element method (FEM) solution, demonstrating the accuracy and reliability of the proposed MCSDE method.

Table 1. Material properties of the DCB-UBM sandwich specimen (Burlayenko et al. 2019) Constituents Material constants

E x = E z =16.5GPa; E y =3.8GPa; G xy = G xz =1.3GPa; G yz =6.6GPa; υ xy =0.05; υ xz = υ yz =0.25; ρ =1650kgm -3 E x = E y = E z =105MPa; G xy = G xz = G yz =78MPa; υ xy = υ xz = υ yz =0.325; ρ =100kgm -3

GFRP face sheet

PVC H100 foam core

Table 2. Calculations of the ERR and the PA with respect to the moment ratio M R .

M 1 (N • mm) M 2 (N • mm)

75.6

103.42 -1034.2

123.4 -123.4

104.13 1041.3

73.8 1476 0.05 0.342 0.342 0.340 -67.3 -70.71

Load

-1512.2

M R

-0.05 0.363 0.363 0.363

-0.1

-1.0

0.1

G Anal (N/mm) G FEM (N/mm) G MCSDE (N/mm)

0.369 0.368 0.367

0.377 0.376 0.376 -12.3 -17.16

0.370 0.369 0.369 -47.2 -51.87

ERR

ψ 1 (°) ψ 2 (°)

32.6

14.5

PA

30.26

11.31

Note: ψ 1 is calculated by the MCSDE method; ψ 2 is calculated by Burlayenko et al. (2019).