PSI - Issue 61

Onur Ali Batmaz et al. / Procedia Structural Integrity 61 (2024) 305–314 Onur Ali Batmaz et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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2.2. Damage modelling Two distinct types of damage were observed in the experiments: transverse matrix damage within the embedded 90° composite plies and delamination failure at 0°/90° interfaces. Detailed descriptions of the corresponding damage modelling methodologies are provided in the following sections. 2.2.1. Matrix cracking To simulate the initiation and evolution of matrix damage within the composite plies, a continuum damage model (CDM)-based orthotropic constitutive material description is implemented into ABAQUS via a VUMAT subroutine. Figure 2(a) illustrates the bilinear relation between equivalent stress (σ eq ) and equivalent displacement (δ eq ) that an integration point obeys during complete failure. The material response is assumed to be linear until damage initiation (point A), which is predicted by the LaRC05 matrix failure index relation given as, (1) where η and η are internal friction parameters that contribute to the damage initiation by either strengthening or weakening the material, depending on the sign of the normal traction acting on the corresponding fracture plane. Previous study by Pinho et al. (2013) on composites with similar fiber and resin systems have reported a value of 0.082 for η . The friction parameter in the transverse direction, η , is calculated using the relation η = −1/ tan(2 0 ) , where 0 represents the fracture angle observed in pure transverse compression tests. In the literature, this angle has been consistently reported as 53° (Catalanotti, 2019; Pinho et al., 2013). The traction components acting on the fracture plane ( , , ) are obtained by stress transformation relations given in Equation 2,3, and 4 where θ is the possible fracture angle searched within the interval of [0,180). (2)

(3)

(4)

Table 1 Material properties used in simulations.

Density

ρ = 1780 kg/m 3

Elastic properties

E 1 = 135 GPa, E 2 = E 3 = 9.2 GPa, ν 12 = ν 13 = 0.3, ν 23 = 0.45, G 12 = G 13 = 5.5 GPa, G 12 = 4.5 GPa Y T = Z T = 60 MPa, Y C = Z C = 205 MPa, S L = 62 MPa T o,I = 87.6 MPa, T o,II = T o,III = 83.7 MPa G I,c = 260 N/m, G II,c = G III,c = 840 N/m

Ply strength

Interface strength Fracture toughness Penalty stiffness

K N = 2.88×10

14 N/m 3 , K

S = 8.14×10

13 N/m 3

Mixed-mode parameter

η = 1.45