An approach to predict fatigue delamination propagation in curved composite laminates under non-constant mixed-mode conditions: experiments and simulation correlation
Abstract
Carbon-fibre reinforced polymer (CFRP) laminates are the backbone of modern aerospace structures—but predicting their failure under fatigue remains a challenge, especially in curved components where delamination by unfolding occurs. This study introduces a Virtual Crack Closure Technique (VCCT)-based simulation combined with a Paris–Erdogan power-law approach to accurately predict fatigue-driven delamination under non-constant mixed-mode conditions. Implemented as a custom Abaqus subroutine, the method accounts for load ratios and mode mixity, ensuring strong correlation with experimental data. Validation came through four-point bending tests on L-shaped CFRP beams, with Digital Image Correlation (DIC) tracking delamination growth. The results? A robust predictive tool that enhances structural integrity analysis, supports sustainable design optimization, and informs maintenance and repair strategies—all while improving safety and durability in next-generation aircraft.
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1Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or CINEA. Neither the European Union nor the granting authority can be held responsible for them. An approach to predict fatigue delamination propagation in curved composite laminates under non-constant mixed-mode conditions: experiments and simulation correlation EASN International Conference on Innovation in aviation & Space towards sustainability today and tomorrow Session title: Simulation and experimental validation of sustainable aircraft structures and their manufacturing processes 14-17/10/2025, Madrid (Spain), Carlos Mallor (ITA)
2EASN International Conference | 14-17/10/2025 | Madrid (Spain) Predicting fatigue-driven delamination in curved composite laminates under non-constant mixed-mode conditions using a VCCT-based approach 1Introduction
3 •Material and structural discontinuities → interlaminar stresses •Delaminations pose a complex problem •Difficult to model and predict Background: Delamination in Composite Materials Sources of delaminations at geometric and material discontinuities Raju IS, O’Brien Fracture mechanics concepts, stress fields, strain energy release rates, delamination initiation and growth criteria. Shear & normal stresses Front Spar of the torsion box of a horizontal stabilizer of an Aircraft •Demo case: Spar •Primary structure component ensuring structural integrity and damage tolerance
5EASN International Conference | 14-17/10/2025 | Madrid (Spain) Predicting fatigue-driven delamination in curved composite laminates under non-constant mixed-mode conditions using a VCCT-based approach 2 Methodology
6 Fatigue Delamination Growth (FDG) methodology: Static & Fatigue •Delamination = propagation of existing delamination cracks •Modelling: Linear Elastic Fracture Mechanics (LEFM) + Paris Law & Model for non-constant mixed-mode + BK model U MIX MODE FATIGUE Finite Element Method (FEM) + Virtual Crack Closure Technique (VCCT) to compute (𝐆) Mode I: opening Mode II Sliding: in plane shear. Mode III Tearing: out-ofplane shear. φ=Τ 𝐺𝐼𝐼 + 𝐺𝐼𝐼𝐼 𝐺𝑇 oStatic case oFatigue case 𝐺𝑇= 𝐺𝐼+ 𝐺𝐼𝐼 + 𝐺𝐼𝐼𝐼
7 Paris’ law fatigue delamination growth rate Paris’ law variants: 𝑓 𝐺 in composites can be based on: 𝚫G as the arithmetic difference DCB Mode I (φ= 𝟎) Fatigue For 𝚫G arithmetic-based: C = 615.3, n = 9.030 For 𝚫G arithmetic-based: C = 0.003, n = 4.0 Delamination growth rate, da /dN [mm/cycle] – ΔG [N/mm] Delamination growth rate, da /dN [mm/cycle] – ΔG [N/mm] Non-constant mixed-mode ENF Mode II (φ= 𝟏) Fatigue 𝑑𝑎 𝑑𝑁 = 𝐶 ⋅ 𝐺𝑚𝑎𝑥 − 𝐺𝑚𝑖𝑛 𝑛
8 Fatigue delamination under non-constant mixed-mode Non-monotonic model with respect to the mode mix The fatigue delamination growth rate 𝒅𝒂/𝒅𝑵 can be generalised to account for the mode mix Two parabolic equations are suggested to model the material parameters C and n. Considering pure mode I, c1 = log CI and n1 = nI. Including the mode II and mixed-mode parameters, the equations become: where Cm and nm are the extra mixed-mode parameters that must be determined by curve fitting (experimentally derived factors). blanco et al. 2004 log𝐶 = 𝑐1+ 𝑐2 𝐺II 𝐺𝑇 + 𝑐3 𝐺II 𝐺𝑇 2 𝑛 = 𝑛1+ 𝑛2 𝐺II 𝐺𝑇 + 𝑛3 𝐺II 𝐺𝑇 2 log𝐶 = log𝐶I+log𝐶m 𝐺II 𝐺𝑇 +log 𝐶II 𝐶I𝐶m 𝐺II 𝐺𝑇 2 𝑛 = 𝑛I+ 𝑛m 𝐺II 𝐺𝑇 + 𝑛II − 𝑛I− 𝑛m 𝐺II 𝐺𝑇 2 Adapted from: vallejo et al. 2019 Interpolate material data C and n for the local mode-mixity and load ratio 𝑓φ, 𝑅 𝑑𝑎 𝑑𝑁 =𝐶⋅ 𝐺𝑚𝑎𝑥 − 𝐺𝑚𝑖𝑛 𝑛
10 EASN International Conference | 14-17/10/2025 | Madrid (Spain) Predicting fatigue-driven delamination in curved composite laminates under non-constant mixed-mode conditions using a VCCT-based approach 3 Results and Discussion
11 Exp. test configuration: 4-point bending (4PB) Mixed-mode on L-angle specimen. Delamination under Unfolding conditions (curvature of the spar) IMA21E TAPE (epoxy resin matrix M21E/IMA-12K carbon fibres) Stacking UD20: [0]20 = [(0)10 / T / (0)10] Delamination length a0=15mm off-centred Fatigue loading: Applied fatigue displacement δ= 1 mm Central front Displ controlled