PSI - Issue 41

Daniele Gaetano et al. / Procedia Structural Integrity 41 (2022) 439–451 Author name / Structural Integrity Procedia 00 (2019) 000–000

444

6

3. Numerical results This section is devoted to the numerical experiments carried out to assess the reliability of the proposed multiscale model, which adopts a hierarchical continuous/discontinuous multiscale model and an inter-element fracture approach in a combined way. In particular, two tests have been simulated, both involving transverse cracking in fiber-reinforced composite specimens. In the first experiment, a three-point bending test on a composite beam is simulated, here used to validate the proposed methodology under global pure Mode-I fracture conditions. The second experiment is devoted to the numerical simulation of a L-shaped composite panel subjected to global mixed-mode boundary conditions. 3.1. Three-point bending test on a composite beam The first case study considered here is a three-point bending test performed on a fiber-reinforced composite beam, already analyzed from both experimental and numerical points of view by Canal et al. (2012). Assuming a plane-strain state, different simulations have been performed on a notched beam (Fig. 3a) with a span s of 11.2 mm and a rectangular cross-section having a thickness t of 2 mm and a height h of 2.8 mm. The notch has a length of 1.4 mm and a diameter of about 130 μm. This composite structure is characterized by a periodic microstructure, made of 54% glass fibers with diameter of 15 μm, according to a hexagonal arrangement, so that the resulting homogenized material is also isotropic (at the macroscopic scale). As already explained in Section 2.1, matrix cracking is represented by a Diffuse Interface Model, whereas fiber/matrix debonding is described by a Single Interface Model. All the embedded microscopic interfaces are equipped with a phenomenological mixed-mode cohesive traction-separation law, characterized by two stiffness parameters, in normal and tangential directions (indicated as K n and K s , respectively) two strengths, in the normal and tangential directions (indicated as σ nc and σ sc , respectively), and two fracture energies (i.e., the Mode-I and Mode-II toughness, indicated as G I c and G II c ). In Tables 1 and 2, the elastic properties (i.e., the Young’s modulus E and the Poisson’s ratio ν ) of the micro constituents are reported, as well as all the parameters (i.e. stiffnesses, strengths, and fracture energies) of the embedded cohesive interfaces, including the (physical) fiber/matrix interfaces (capable to simulate fiber/matrix debonding), and the (mathematical) matrix/matrix interfaces (able to capture matrix cracking).

Fig. 3. Three-point bending test on a composite beam: (a) geometry configuration and boundary conditions of the macroscopic specimen; (b) geometry configuration of the Repeating Unit Cell.

Table 1. Elastic properties of the micro-constituents. Component Material

E (GPa)

ν (-) 0.35 0.20

Matrix

Epoxy Glass

3.50 74.0

Fiber

Table 2. Inelastic properties of the embedded cohesive interfaces. Interface K n = K s (N/mm 3 ) σ nc (MPa) σ sc (MPa)

G I c (N/m)

G II c (N/m)

Fiber/matrix Matrix/matrix

1.00×10 8 1.06×10 9

50 75

75 75

150 200

150 200