2. Materials and Manufacturing
3. Experimental Methods
3.1. Material Characterization
3.2. Testing of Composite Cylinders
4. Modeling Techniques
5. Results and Discussion
5.1. Experimental Results
5.2. Load-Bearing Capacity: Calibration of SLIMC and NFLS Parameters
5.3. Predicted and Experimentally Observed Damage
Conflicts of Interest
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|Parameter||Meaning||Units||Value or Range||Comment for the Chosen Initial Value|
|TSIZE||Time step for automatic element deletion.||s||1E-10||Disabled by choosing a very small time step value for element deletion.|
|ERODS||Maximum effective strain for element failure. If lower than zero, the element fails when effective strain calculated from the full strain tensor exceeds ERODS.||mm/mm||−2.00||Chosen to be significantly higher than any directional strain at failure initiation.|
|SLIMT1||Factor to determine the minimum stress limit after stress maximum (fiber tension).||-||0.10||A recommended value |
|SLIMC1||Factor to determine the minimum stress limit after stress maximum (fiber compression).||-||0.1–1.0||See discussion in Section 4.|
|SLIMT2||Factor to determine the minimum stress limit after stress maximum (matrix tension).||-||0.10||A recommended value |
|SLIMC2||Factor to determine the minimum stress limit after stress maximum (matrix compression).||-||0.1–1.0||See discussion in Section 4.|
|SLIMS||Factor to determine the minimum stress limit after stress maximum (shear).||-||1.00||A recommended value |
|Property||Value or Range||Rationale|
|NFLS, MPa||9.00–18.00||NFLS can be bound by the following values:|
lower bound—the transverse strength of a typical unidirectional GFRP (~30 MPa), which would be a reasonable estimate in the case of interlaminar failure by adhesive mechanism (cracks formed at the interface between the epoxy in the interlaminar resin-rich region and fibers in the layer adjacent to it).
upper bound—the ultimate strength of bulk epoxy resin (~60 MPa), which would be a reasonable estimate in the case of interlaminar failure by cohesive mechanism.
In addition, a scaling factor of 0.30 was used to account for the mesh dependency observed for this delamination model (see the recommendation provided in  for meshes with element sizes between 2 and 3 mm).
A particular value from the specified range was chosen via calibration with experimental data, as will be discussed in Section 5.2.
|SFLS/NFLS, -||0.58||Assumed as SFLS = NFLS/ (von Mises criterion)|
|G_Ic, kJ/m2||0.24||Measured experimentally, see Table 3 in Section 5.1|
|G_IIc, kJ/m2||1.96||Measured experimentally, see Table 3 in Section 5.1|
|CN, MPa/mm||200,000.00||CN = Eepoxy/δRRR, where Eepoxy is the Young’s modulus of epoxy matrix (~3650 MPa) and δRRR is the thickness of the interlaminar resin-rich region (typically within 0.01 and 0.10 mm). Thus, the lower and upper bounds for CN correspond to 36,500 MPa/mm and 365,000 MPa/mm, accordingly. This averages to 200,000 MPa/mm as an estimate for the CN parameter.|
In addition, the condition for CN > CNmin must be ensured (see ), where CNmin = (1/2) × (NFLS2)/(G_Ic). This condition is satisfied for the listed set of parameters of the delamination model.
|CT2CN, -||0.37||CT2CN = CT/CN = Gepoxy/Eepoxy = 1/2 × (1 + νepoxy), where Gepoxy and νepoxy are the shear modulus and the Poisson’s ratio (~0.35) of epoxy resin, correspondingly.|
|Property||Value||Standard Deviation||Test Method|
|Longitudinal Young’s modulus (E1), MPa||20,800||1600||ASTM D 3039|
|Transverse Young’s modulus (E2), MPa||12,200||740||ASTM D 3039|
|Poisson’s ratio (nu21)||0.079||n/a||ASTM D 3039|
|Shear modulus (G12), MPa||2950||53.12||ASTM D 3518|
|Tensile strength in warp direction (Xt), MPa||397||22.64||ASTM D 3039|
|Compressive strength in warp direction (Xc), MPa||153||5.76||ASTM D 3410|
|Tensile strength in fill direction (Yt), MPa||240||14.59||ASTM D 3039|
|Compressive strength in fill direction (Yc), MPa||101||5.32||ASTM D 3410|
|Shear stress at onset of nonlinearity, MPa||25 (see Figure 11)||n/a||ASTM D 3518|
|Shear stress at 5% shear strain, MPa||33||1.87||ASTM D 3518|
|Mode I critical strain energy release rate (G_Ic), kJ/m2||0.24||0.02||ASTM D 5528-01|
|Mode II critical strain energy release rate (G_IIc), kJ/m2||1.96||0.50||End-notched flexure|
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