PSI - Issue 2_B

Moslem Shahverdi et al. / Procedia Structural Integrity 2 (2016) 1886–1893 Shahverdi et al./ Structural Integrity Procedia 00 (2016) 000–000

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The  parameter, the ratio of the equivalent upper arm bending stiffness over the equivalent joint stiffness, like the  parameter, is defined as bending stiffness rather than thickness ratio.

L

c

Lever

P g

c g

P.c+P g .c g

P(L+c)+P g (L+c g ) L

Center of gravity

L

P

Applied load

5.7

L=170

L=170

Saddle

Fulcrum

Specimen

13.4

Loading roller

Initial crack

a =50 0

2L

2h

7.7

Base

400

P(L-c)+P g (L-c g )

2L P(L+c)+P g (L+c g )

2L

Figure 2. Left: Schematic of mixed-mode bending apparatus; Right: Applied loads, dimensions in [mm] In the case of the asymmetric MMB specimen, as shown in Figure 2, the bending moments at the section surrounding the crack tip are: g g 1 c P P c M a L   and g g 2 ( ) ( ) 2 P L c P L c M a L     (10) Substitution of Eqs. (10) into Eqs. (7) leads to: g g g I (2 1)( )-( ) 2 (1 ) Pc P c P P L M a L        g g II ( ) ( ) 2 (1 ) P L c P L c M a L       (11) Substitution of Eqs. (11) into Eqs. (8) leads to: 2 g g g 2 I 2 eq [(2 1)( )-( ) ] 8 (1 ) ( ) Pc P c P P L G a BL EI         and 2 g 2 2 II 2 2 eq [ ( ) ( g )] (1 (1 ) ) 8 (1 ) ( ) P L c P L c G a BL EI              (12) Eqs. (12) are closed form equations for the calculation of G I and G II in which all the parameters are obtained directly from the experiments. 2.3. Finite element method 2D plane-strain non-linear models were developed in ANSYS to calculate the Modes I and II fracture components for different lever lengths. All layers of the laminates were modeled. The material properties are given in Table 1. The element PLANE182, a 4-node structural solid, was used to model different layers. A manual mesh with controlled mesh size was used. The aspect ratio of the elements in the vicinity of the crack tip was kept at 1/1. Table 1. Properties used for FE modeling Material data First combined mat Second combined mat Roving Veil Adhesive E11 (GPa) 12.8 15.1 38.9 3.2 4.6 E22 (GPa) 12.8 15.1 3.2 3.2 4.6 E33 (GPa) 3.2 3.2 3.2 3.2 4.6 G12 (GPa) 6.2 6.7 2.7 1.2 1.7 G23 (GPa) 1.4 1.4 1.4 1.2 1.7 G31 (GPa) 1.4 1.4 2.7 1.2 1.7  12 0.27 0.27 0.32 0.38 0.37  23 0.36 0.36 0.27 0.38 0.37  31 0.36 0.36 0.35 0.38 0.37 Fiber bridging along the crack faces was modeled by using a single layer of zero-thickness cohesive elements, INTER202, along the crack plane. INTER202 is a 2-D 4-node interface element with two degrees of freedom at each node. The cohesive element behavior is based on a traction-separation law that defines the stresses, σ br , at a particular location as a function of the opening displacement, δ . The traction-separation relationship is such that with