PSI - Issue 35

E.A. Dizman et al. / Procedia Structural Integrity 35 (2022) 91–97 Author name / Structural Integrity Procedia 00 (2021) 000–000

95

5

to potential extensions which might require element level interventions. A brick element with quadratic displacement interpolation with reduced integration is implemented through UEL subroutine. Two examples are considered in the following subsections.

4.1. Simple Shear Tests

As shown in Figure 3, two simple shear tests are considered in which the fibers are parallel and perpendicular to the loading direction, respectively. The associated model parameters are given in Table 2. Using a single element discretization with proper displacement boundary conditions, a homogeneous plane strain state is imposed.

Table 2: Model Parameters

Model Parameter

Value

E f

171420 MPa

F

E m 2 ( = E m 3 )

8930 MPa

62.3

τ y

0.0

µ

0.32 5100

S1

S2

ν 12 G 12

Fig. 3: Simple shear tests (Dimensions are 1 by 1)

Analytical solutions for these two shear tests for rate independent crystal plasticity without hardening are given in Tan and Liu (2020). The rate independent limit is approximated here by using a very small m value, i.e. m = 0.0005 and the resulting comparison of analytical and finite element solutions are shown in Figure 4. The agreement between the crystal plasticity inspired finite element predictions and the analytical solution confirms the accuracy of the model.

150

70

60

50

)

)

100

12

12

40

30

50

20

Shear Stress (

Shear Stress (

10

FEA Analytical

FEA Analytical

0

0

0

1

2

3

4

5

6

7

8

9 10

0

1

2

3

4

5

6

7

8

9 10

Shear Strain ( )

Shear Strain ( )

Fig. 4: Left: Comparison of finite element predictions and analytical solution for 0 ◦ degree simple shear; Right: The same comparison for 90 ◦ degree simple shear.

4.2. Shear Test of Composite Laminate

After validating the accuracy of the model, it is tested with a problem where the strain and stress distributions are non-homogeneous. The geometry and the boundary conditions shown in Figure 5 are taken from Tan and Falzon (2021) which is the geometry of a cross-ply test specimen composed of four plies with di ff erent fiber orientations. Due to limitations of the current version of the implementation, a single ply with a thickness of t = 3 . 36 mm is considered under two di ff erent loading scenarios. In the first case, the specimen is loaded by a transverse displacement of 9 mm at the free end resulting in shear dominated state of stress. In the second case, both a transverse displacement of 9 mm and a tensile displacement of 1.5 mm are applied at the free end leading to a combined state of stress. The model parameters are given in Table 3.