Delamination Growth Under Fatigue Loading

What Is It?

Delamination growth under fatigue loading is the propagation of an existing delamination crack at a ply interface due to cyclic loading. Under each load cycle, the energy release rate at the delamination front fluctuates. If the energy release rate exceeds a threshold, the delamination grows incrementally each cycle. Over many cycles, this accumulation can extend the delamination significantly. Predicting the growth rate is essential for assessing whether the no-growth or slow-growth damage tolerance philosophy is satisfied for a given structure and loading spectrum.

Why It Matters

Delamination growth under fatigue is a primary concern for composite structural durability. An existing delamination — whether from manufacturing, impact or service loading — can grow under cyclic loads, reducing residual strength and potentially leading to failure. The growth rate determines the inspection interval: if growth is slow, long intervals are acceptable; if growth is fast, frequent inspection or repair is needed. Unpredictable or unstable growth is particularly concerning because it can lead to sudden loss of residual strength between inspections.

Delamination growth under fatigue determines inspection intervals and structural durability. Understanding the growth rate, the threshold below which no growth occurs and the uncertainty in the prediction is essential for a defensible damage tolerance assessment.

Cyclic Energy Release Rate

The energy release rate G is the energy available for crack growth per unit new crack area. Under fatigue, the relevant quantity is the cyclic variation of G — typically characterised by the maximum G (G_max), the minimum G (G_min) and the range ΔG = G_max − G_min. The growth rate depends on the cyclic G, not on the static G. The ratio R = G_min/G_max (or equivalently the load ratio) also influences the growth behaviour, analogous to metallic fatigue crack growth where R-ratio effects are well documented.

Cyclic energy release rate:

G_max = maximum energy release rate in a cycle
G_min = minimum energy release rate in a cycle
ΔG   = G_max − G_min  (range)
R    = G_min / G_max  (R-ratio)

G_th = threshold below which no growth occurs
G_c  = critical energy release rate (static fracture toughness)

Growth occurs when G_max > G_th
Unstable (static) fracture when G_max → G_c

Interface Damage and Crack Growth

Delamination growth occurs at the interface between two plies. The interface properties — the resin-rich interlayer, the fibre orientation of the adjacent plies and the bonding quality — determine the fracture behaviour. The crack grows through the interface, and the growth resistance depends on the mode mix (opening, shearing or a combination). Fibre bridging across the delamination plane can increase the apparent fracture resistance during growth, particularly in Mode I. This bridging is a test artefact that must be accounted for when extracting material properties for analysis.

• Growth occurs at the ply interface — resin-rich interlayer dominates behaviour
• Adjacent ply orientations affect the mode mix at the crack front
• Fibre bridging in Mode I can increase apparent resistance — a test artefact to be accounted for
• The interface fracture properties are obtained from DCB (Mode I), ENF (Mode II) and MMB (mixed-mode) tests
• Bridging effects make the R-curve different from the initiation value — use initiation values for conservative growth prediction

Mixed-Mode Loading

In real structures, delamination growth almost always occurs under mixed-mode loading — a combination of opening (Mode I) and shearing (Mode II). The mode mix at the delamination front depends on the loading, the laminate and the delamination shape. The growth rate under mixed-mode loading is not simply a weighted average of the pure-mode rates — it depends on the actual mixed-mode fracture behaviour. A mixed-mode failure criterion (e.g. the B-K criterion or a power-law interaction) is used to characterise the mixed-mode fracture envelope.

Mixed-mode fracture:

G_I   = Mode I (opening) energy release rate
G_II  = Mode II (shearing) energy release rate
G_T   = G_I + G_II  (total)
β     = G_II / G_T  (mode mix ratio, 0 to 1)

Mixed-mode fracture criterion (B-K form):
  G_c(β) = G_Ic + (G_IIc − G_Ic) × β^η

where η is a mixed-mode exponent
obtained from MMB tests.

Fatigue growth under mixed mode:
  da/dN = f(G_max, β, R, ...)

The growth rate depends on both the
total G and the mode mix β.

Fatigue Growth Data Representation

Fatigue delamination growth is typically characterised using a Paris-law-type relationship between the growth rate per cycle (da/dN) and the cyclic energy release rate. The data are obtained from fracture mechanics tests — DCB for Mode I, ENF for Mode II, MMB for mixed mode — conducted under cyclic loading. The resulting da/dN vs ΔG (or G_max) curve has three regions: a threshold region near G_th where growth is very slow, a power-law region where growth follows the Paris law, and a fast-growth region near G_c where growth accelerates toward static fracture.

Crack Growth Modelling

In finite element analysis, delamination growth under fatigue can be modelled using cohesive zone elements with a fatigue damage law or using VCCT with a Paris-law growth criterion. The cohesive approach degrades the interface stiffness under cyclic loading according to a fatigue damage accumulation law. The VCCT approach computes G at the crack front each cycle and advances the crack front according to the Paris law. Both approaches require the fatigue fracture properties (C, m, G_th) for the relevant mode mix.

• Cohesive zone + fatigue damage law: degrades interface stiffness under cyclic loading
• VCCT + Paris law: computes G at crack front, advances front per da/dN = C(ΔG)^m
• Both require fatigue fracture properties: C, m, G_th for the relevant mode mix
• Mixed-mode growth requires a mixed-mode Paris law or a mode-mix-dependent formulation
• Cycle-counting for variable-amplitude loading may be needed for spectrum loading

Uncertainty in Growth Prediction

Delamination growth predictions carry significant uncertainty. The sources include scatter in the fatigue fracture data (C and m can vary substantially between specimens), uncertainty in the mode mix at the crack front, fibre bridging effects that make the growth resistance dependent on crack length, and the effect of the R-ratio. The threshold G_th is particularly difficult to establish — it requires many cycles to confirm no growth, and small changes in G_th can dramatically change the predicted growth over a service life. This uncertainty means that growth predictions should be used with appropriate margins.

Delamination growth predictions carry significant uncertainty from data scatter, mode mix uncertainty, bridging effects and R-ratio. The threshold G_th is particularly difficult to establish. Use appropriate margins and do not treat growth predictions as precise — they are indicative and must be supported by test evidence.

No-Growth Demonstration

For the no-growth damage tolerance philosophy, the key task is to demonstrate that the energy release rate at the delamination front remains below the threshold G_th for the entire design fatigue spectrum. This is done by computing G for the critical damage size and the design loads, comparing against G_th (with appropriate margin), and confirming by fatigue test that no growth occurs. If G exceeds G_th for some load cases, the structure must either be redesigned, the damage category redefined or a slow-growth assessment conducted.

No-growth demonstration: show G_max < G_th (with margin) for the design spectrum at the critical damage size. Confirm by fatigue test that no growth occurs. If G exceeds G_th, redesign, redefine damage or perform slow-growth assessment.

Cross-Links

Delamination growth under fatigue connects to several related chapters. The Fatigue & Durability chapter addresses the broader framework of fatigue assessment for composites, including S-N behaviour and fatigue life prediction. The Experimental Mechanics chapter covers the fracture tests (DCB, ENF, MMB) that provide the fatigue fracture data. The Test & Analysis Correlation chapter addresses correlating growth predictions against structural fatigue tests.

• Fatigue & Durability — composite fatigue framework
• Experimental Mechanics — fracture mechanics testing
• Test & Analysis Correlation — structural fatigue correlation

Key Takeaways

• Delamination growth under fatigue is driven by the cyclic energy release rate at the crack front
• Mixed-mode loading is the norm in real structures — growth depends on both total G and mode mix
• Paris-law-type da/dN vs ΔG curves characterise growth; three regions: threshold, power-law, fast-growth
• Fatigue fracture properties (C, m, G_th) must be obtained from DCB, ENF and MMB fatigue tests
• Significant uncertainty exists from data scatter, mode mix, bridging and R-ratio — use appropriate margins
• No-growth demonstration: show G_max < G_th with margin for the design spectrum
• Growth predictions must be supported by test evidence — they are indicative, not precise