PSI - Issue 52

Haseung Lee et al. / Procedia Structural Integrity 52 (2024) 252–258 Haseung Lee, Hyunbum Park / Structural Integrity Procedia 00 (2019) 000 – 000

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4

Fiber compressive failure: ℱ Matrix tensile failure:

( )=− 11 11 < 0,0 ℎ ℱ ( )= 22 2 2 + 12 2 2 22 ≥ 0,0 ℎ

(2)

(3)

Matrix compressive failure:

ℱ ( ) = 22 2 4 2 + 12 2 2 +[( 2 )

2 −1] 22 22 < 0,0 ℎ

(4)

In the equation above, damages occur if the damage index( ℱ , ℱ , ℱ , ℱ ) reaches 1. where is the three-dimensional stress component, is the tensile strength in the fiber direction, is the compressive strength in the fiber direction, is the tensile strength in the normal direction of the fiber, is the compressive strength in the normal direction of the fiber, is In plane shear strength, is transverse shear strength As shown in the above formula, the Hashin damage criterion distinguishes between tension and compression acting in the fiber direction and the fiber vertical direction. Afterwards, failure is determined based on the ratio of the material properties acting in each direction and the external stress. This study used Matzenmiller-Lubliner-Tayor (MLT) method by A. Matzenmiller, J. Lubliner and R. Taylor(1995) that progressive failure consists in linking failure criteria to stiffness degradation through damage variables. The compliance by the MLT method is represented as eq. (5), { 11 22 12 }= [ (1− 1 11 ) 1 − 12 11 0 − 12 1 (1− 1 22 ) 1 0 0 0 (1− 1 12 ) 12 ] { 11 22 12 } (5) where 11 , 22 and 12 is components of the strain tensor. 11 , 22 and 12 is components of the stress tensor, 1 , 2 and 12 is Young’s and shear moduli, 12 the Poisson’s ratio and 11 , 22 and 12 damage variables. These variables are often expressed from failure criteria. The damage variable can be expressed as the following equation for the Hashin failure criterion. 11 = ( ) (6) 22 = ( ) (7) 12 =1−(1− 11 )×(1− 12 ) (8) ( ̂) can be determined by Equations (1) and (2), and ( ̂) can be determined by Equations (3) and (4). where ̂ denotes the undamaged stress tensor. The finite element model basically consisted of 8-node hexahedral elements, and damage law is set to instantaneous damage and cohesive elements in the lamina interlayer is set consider delamination. The analysis was carried out with the boundary condition complying with the regulation of ASTM D3039 and D6641, and the virtual test analysis was done through the Marc nonlinear solver.