Figure 1.
Schematic of the composite plate with an edge crack.
Figure 2.
Crack-tip geometry showing the coordinate system and the J-integral contour.
Figure 3.
Local coordinate system defined ahead of the crack tip, illustrating the stress components (σx, σy, τxy, τyx), radial distance r, and angle θ.
Table 1.
The stresses σyy calculated by the theoretical analysis.
| rradius (mm) | J (N/mm2) | σyy theoretical (MPa) |
|---|---|---|
| 0.2 | 15.9 | 894.92 |
| 0.6 | 15.9 | 516.68 |
| 1 | 15.9 | 400.22 |
| 1.4 | 15.9 | 338.25 |
| 2 | 15.9 | 283.00 |
| 2.4 | 15.9 | 258.34 |
| 2.8 | 15.9 | 239.18 |
| 3 | 15.9 | 231.07 |
| 4 | 15.9 | 200.11 |
| 5 | 15.9 | 178.98 |
Figure 4.
Stress vs. distance r from notch tip at θ = 0° (theoretical method).
Figure 5.
Assembly of composite materials.
Figure 6.
The Von Mises stress contour plot of the composite plate without a hole, presented at different radial distances (r) from the crack tip.
Mechanical Properties of the Composite Material
| Property | Symbol | Value | Unit |
|---|---|---|---|
| Longitudinal Young’s modulus | E1 | 140000 | MPa |
| Transverse Young’s modulus | E2 = E3 | 9000 | MPa |
| In-plane shear modulus | G12 = G13 | 5000 | MPa |
| Out-of-plane shear modulus | G23 | 5000 | MPa |
| Poisson’s ratio | V12 = V13 | 0.30 | – |
| Poisson’s ratio | V23 | 0.40 | – |
| Density | ρ | 1.5 × 10−6 | kg/mm3 |
Table 2.
σyy vs. distance r from notch tip at θ = 0° (theoretical vs. numerical results).
| r (mm) | σyy theoretical (MPa) | σyy numerical (MPa) |
|---|---|---|
| 0.2 | 894.92 | 884.9 |
| 0.6 | 516.68 | 454.6 |
| 1 | 400.22 | 345.9 |
| 1.4 | 338.25 | 290.6 |
| 2 | 283.00 | 242.2 |
| 2.4 | 258.34 | 220.7 |
| 2.8 | 239.18 | 190.1 |
| 3 | 231.07 | 197.1 |
| 4 | 200.11 | 170.2 |
| 5 | 178.98 | 152 |
Figure 7.
Theoretical vs. numerical σyy stress as a function of r (mm) from the notch tip at θ = 0°.
Figure 8.
Dimensions of perforated plate.
Figure 9.
Perforated plate mesh.
Figure 10.
The Von Mises stress contour plot of the composite plate hole of varying radii (r) and distances (S) from the notch tip.
Table. 3.
Variation of stress σyy as a function different value of the distance (S) in the plate with a hole and without a hole.
| r (mm) | σyy (MPa) | σyy (MPa) | σyy (MPa) | σyy (MPa) | σyy (MPa) | σyy (MPa) |
|---|---|---|---|---|---|---|
| 0.2 | 885.1 | 885 | 846.3 | 831.7 | 811.5 | 884.9 |
| 0.6 | 455.4 | 455 | 454.6 | 442.2 | 427 | 454.6 |
| 1 | 387.2 | 371.1 | 364.5 | 333.7 | 333.4 | 345.9 |
| 1.4 | 281.8 | 279.9 | 251.6 | 242.6 | 229.8 | 290.6 |
| 2 | 237.7 | 228.3 | 228.1 | 226.5 | 218.8 | 241.9 |
| 2.4 | 202.5 | 201.4 | 200.9 | 199.5 | 199 | 204.2 |
| 2.8 | 189.1 | 186.9 | 186.1 | 185.5 | 184,7 | 190.1 |
| 3 | 190.6 | 187.4 | 179.5 | 179.1 | 177.7 | 196.9 |
| 4 | 169.4 | 162.9 | 157.3 | 155.7 | 154.9 | 170.2 |
| 5 | 150.7 | 144.4 | 142.1 | 140.3 | 139.3 | 152 |
Figure 11.
The plots of the stress σyy versus for different values of distance S (in the plate with one hole).
Figure 12.
Plots of the σyy stress for different average values of the distance S (in the plate with and without a hole).
Table 4.
Variation of the σyy stress as a function of different average distance (S) values in the composite laminate, with and without a hole.
| r (mm) | σyy (MPa) – Without Hole | σyy (MPa) – With Hole |
|---|---|---|
| 0.2 | 884.9 | 851.92 |
| 0.6 | 454.6 | 444.84 |
| 1.0 | 345.9 | 357.98 |
| 1.4 | 290.6 | 257.14 |
| 2.0 | 241.9 | 227.88 |
| 2.4 | 204.2 | 199.6 |
| 2.8 | 190.1 | 186.46 |
| 3.0 | 196.9 | 182.92 |
| 4.0 | 170.2 | 160.44 |
| 5.0 | 152 | 143.36 |
Figure 13.
J-integral plots for S = 35 mm (in the plate with and without hole).
Table 5.
Variation of the J-integral as a function of different average distance (S) values in the composite laminate, with and without a hole.
| r (mm) | J (N/mm2) S = 15 mm | J (N/mm2) S = 20 mm | J (N/mm2) S = 25 mm | J (N/mm2) S = 30 mm | J (N/mm2) S = 35 | J (N/mm2) Without holes |
|---|---|---|---|---|---|---|
| 0.2 | 17.85 | 17.84 | 18.78 | 19.41 | 20.01 | 17.86 |
| 0.6 | 14.29 | 14.27 | 14.25 | 14.39 | 14.46 | 14.22 |
| 1 | 15.05 | 15.31 | 14.85 | 14.51 | 14.75 | 13.80 |
| 1.4 | 13.78 | 13.88 | 13.80 | 13.94 | 13.88 | 13.67 |
| 2 | 14.01 | 13.92 | 13.90 | 13.71 | 13.64 | 13.57 |
| 2.4 | 14.19 | 14.10 | 13.92 | 13.72 | 13.66 | 13.59 |
| 2.8 | 14.45 | 14.09 | 13.90 | 13.88 | 13.72 | 13.59 |
| 3 | 14.61 | 14.12 | 13.93 | 13.88 | 13.62 | 13.52 |
| 4 | 15.41 | 15.35 | 14.27 | 13.99 | 13.86 | 13.49 |
| 5 | 16.46 | 15.06 | 14.62 | 14.24 | 13.98 | 13.48 |