J-Integral Analysis of Crack Behavior in Composite Material Geometries Cover

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J-Integral Analysis of Crack Behavior in Composite Material Geometries

Fatigue of Aircraft Structures

By: Regad Abdelmalek , Kacimi Noureddine , Mebarki Hichem , Mohamed Ikhlef Chaouch , Djedai Hayette , Nehila Abdelhak , Damba Nadhir and Oudrane Abdellatif

Open Access

|Jul 2025

Figures & Tables

Schematic of the composite plate with an edge crack.

Crack-tip geometry showing the coordinate system and the J-integral contour.

Local coordinate system defined ahead of the crack tip, illustrating the stress components (σx, σy, τxy, τyx), radial distance r, and angle θ.

Stress vs. distance r from notch tip at θ = 0° (theoretical method).

Assembly of composite materials.

The Von Mises stress contour plot of the composite plate without a hole, presented at different radial distances (r) from the crack tip.

Theoretical vs. numerical σyy stress as a function of r (mm) from the notch tip at θ = 0°.

Dimensions of perforated plate.

Perforated plate mesh.

The Von Mises stress contour plot of the composite plate hole of varying radii (r) and distances (S) from the notch tip.

The plots of the stress σyy versus for different values of distance S (in the plate with one hole).

Plots of the σyy stress for different average values of the distance S (in the plate with and without a hole).

J-integral plots for S = 35 mm (in the plate with and without hole).

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)	σ_yy (MPa) – Without Hole	σ_yy (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

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

The stresses σyy calculated by the theoretical analysis_

r_radius (mm)	J (N/mm²)	σ_{yy 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

σyy vs_ distance r from notch tip at θ = 0° (theoretical vs_ numerical results)_

r (mm)	σ_yy theoretical (MPa)	σ_yy 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

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)	σ_yy (MPa)	σ_yy (MPa)	σ_yy (MPa)	σ_yy (MPa)	σ_yy (MPa)	σ_yy (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

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

DOI: https://doi.org/10.2478/fas-2025-0001 | Journal eISSN: 2300-7591 | Journal ISSN: 2081-7738

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Language: English

Published on: Jul 14, 2025

Published by: ŁUKASIEWICZ RESEARCH NETWORK – INSTITUTE OF AVIATION

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

composite materials,

fracture mechanics,

finite element analysis (FEA),

crack propagation,

stress distribution,

geometric discontinuity

Related subjects:

Introductions and overviews,

Engineering, other

© 2025 Regad Abdelmalek, Kacimi Noureddine, Mebarki Hichem, Mohamed Ikhlef Chaouch, Djedai Hayette, Nehila Abdelhak, Damba Nadhir, Oudrane Abdellatif, published by ŁUKASIEWICZ RESEARCH NETWORK – INSTITUTE OF AVIATION
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.