Fig. 1. Fracture modes for cracked plate under in-plane and out-of-plane loads: (a) tensile (mode-I), (b) In-plane shear (mode-II), (c) bending (mode-1), (d) out-of plane shear (mode-2) and (e) twisting (mode-3).

Fig. 2. Schematic of virtual crack extension.

Fig. 3. Typical FE mesh of crack tip region.

Fig. 4. Plate with center crack subjected to tension and moment loads.

Fig. 5. FE idealization of the rectangular plate (quarter symmetry).

Fig. 6. Variation of K_I and k₁ w.r. to Δa/a.

Fig. 7. Variation of K_I and k₁ w.r. to W/a.

Fig. 8. Variation of normalised K₁ with plate thickness.

Fig. 9. Plate with center crack subjected to combined tension and shear loads.

Fig. 10. Variation of k₂ w.r. to Δa/a and W/a.

Fig. 11. Variation of normalised K₂ with plate thickness.

SERR and SIF for a plate with center crack (tensile and moment loads)

Analytical solution: K_I = 25.59 [23] for W/a = 5, K_I = 25.07* k₁ = 84.85* (Kirchoff theory) k₁ = 55.75* (Reissner–Mindlin theory) * – Results for pure tension and moment loads for an infinite plate FI: 3 × 3 Gauss points for membrane, bending and shear SRI: 3 × 3 Gauss points for membrane and bending, 2 × 2 for shear.

SERR and SIF for a plate with center crack (tensile and moment loads)

Analytical solution: K_I = 25.59 [23] for W/a = 5, K_I = 25.07* k₁ = 84.85* (Kirchoff theory) k₁ = 55.75* (Reissner–Mindlin theory) * – Results for pure tension and moment loads for an infinite plate FI: 3 × 3 Gauss points for membrane, bending and shear SRI: 3 × 3 Gauss points for membrane and bending, 2 × 2 for shear.

SERR and SIF for a plate with center crack (tension and moment loads) comparison for different W/a and Δa/a values employing 9-noded element with assumed shear strain interpolations

SERR and SIF for a plate with center crack (tensile and moment loads) comparison for different W/a and Δa/a values employing 9-noded QPE with assumed shear strain fields

Analytical solution: K_I = 25.59 [23] for W/a = 5, K_I = 25.07* k₁ = 84.85* (Kirchoff tehory) k₁ = 55.75* (Reissner–Mindlin theory) * – Results for pure tension and moment loads for an infinite plate FI: 3 × 3 Gauss points for membrane, bending and shear.

SERR and SIF for a plate with center crack (tensile and shear loads)

Analytical solution: K_I = 25.59 [23] for W/a = 5, K_I = 25.07* k₂ = 84.85* (Kirchoff theory) * – Results for pure tension and shear loads for an infinite plate FI: 3 × 3 Gauss points for membrane, bending and shear SRI: 3 × 3 Gauss points for membrane and bending, 2 × 2 for shear.

SERR and SIF for a plate with center crack (tensile and shear loads)

Analytical solution: K_I = 25.59 [23] for W/a = 5, K_I = 25.07* k₂= 84.85* (Kirchoff theory) * – Results for pure tension and shear loads for an infinite plate FI: 3 × 3 Gauss points for membrane, bending and shear SRI: 3 × 3 Gauss points for membrane and bending, 2 × 2 for shear.

SERR and SIF for a plate with center crack (tension and shear loads) comparison for different W/a and Δa/a values employing 9-noded element with assumed shear strain interpolations

SERR and SIF for a plate with center crack (tensile and shear loads) comparison for different W/a and Δa/a values employing 9-noded QPE with assumed shear strain fields

Analytical solution: K_I = 25.59 [23] for W/a = 5, K_I = 25.07* k₂ = 84.85* (Kirchoff theory) * – Results for pure tension and shear loads for an infinite plate FI: 3 × 3 Gauss points for membrane, bending and Shear.