DOCUMENTATION / FATIGUE MODELS
Fatigue Models — Formulas & Parameters
BondLife implements three stress-based fatigue models for bonded joints. All three consume FEA stress output from the adhesive layer, scaled linearly from the simulation load (FFEA) to the real applied load (Freal) before computing fatigue life.
Stress Quantities
The following stress quantities are extracted from the imported Abaqus .rpt file and used by all three models.
| Symbol | Name | Source / Definition |
|---|---|---|
| σVM | Von Mises stress | Abaqus S.Mises output field |
| σH | Hydrostatic stress | = −S.Pressure, or (σ11+σ22+σ33)/3 (plane-stress fallback) |
| I1 | First stress invariant | = σ11+σ22+σ33 = 3·σH |
| J2 | Second deviatoric invariant | = σVM²/3 (invariant form), or exact from stress components when available |
| k = Freal/FFEA | Load scale factor | Linear scaling: σ(Freal) = σ(FFEA) × k; I1 scales by k, J2 by k² |
The critical node is selected from the adhesive mid-plane using PCA-based thickness-direction detection, then the node with maximum principal stress (or maximum von Mises if S.Max.Prin is unavailable) is chosen within the critical-distance filter.
Antelo Model
Reference: Antelo et al. (2021), equation (6). Calibrated using ARCAN Mode I / II tests; validated against Mixed-Mode data.
Effective stress
σeff(F_FEA) = σVM + |σH|^γ / σVM
σeff(F_real) = σeff(F_FEA) × (F_real / F_FEA)
Note: the scaling is applied to σeff after computing the non-linear |σH|^γ/σVM term at F_FEA. Pre-scaling the raw stresses would produce a different result when γ ≠ 1.
Fatigue life (Wöhler S-N law)
Nf = (σeff / α)^(−1/β)
During calibration, α and β are fitted by log-log linear regression on (σeff, Nexp) from Mode I and II data; γ is optimised by golden-section search to minimise the RMSD objective.
| Parameter | Description | Notes |
|---|---|---|
| γ (gamma) | Hydrostatic exponent — weights the contribution of σH relative to σVM. | 1–5; Araldite 2015 calibration: ≈ 2.23. Optimised from ARCAN data. |
| α (alpha) | S-N intercept (MPa). Stress magnitude at Nf = 1 in the log-linear fit. | Fitted from ARCAN calibration dataset. Must be positive. |
| β (beta) | S-N slope. Stored as a positive number; applied as −1/β in the Nf formula, giving the expected negative slope. | Negative physical slope: a larger |β| means a flatter S-N curve. Fitted from calibration. |
Cavdar Model
Reference: Cavdar et al. Invariant-based equivalent stress combining deviatoric (J2) and hydrostatic (I1) contributions.
Equivalent stress
τeq = √(J2 + c·I1²)
Fatigue life
Nf = A · τeq^(−m)
| Parameter | Description | Notes |
|---|---|---|
| A | Fatigue strength coefficient (cycles·MPa^m). Scales the magnitude of the S-N curve. | Must be non-zero. Fitted from joint fatigue data. |
| m | Wöhler exponent. Controls the rate of life reduction with increasing equivalent stress. | Must be non-zero. Larger m → steeper S-N slope. |
| c | Hydrostatic weight factor. Controls how much the mean (hydrostatic) stress component contributes to τeq. | c = 0 → pure deviatoric (von Mises-like); c > 0 → hydrostatic stress accelerates damage. |
Sousa Model
Reference: Sousa PhD thesis. Same invariant-based equivalent stress form as Cavdar, parameterised as a characteristic stress ratio.
Equivalent stress
τeq = √(J2 + c·I1²)
Fatigue life
Nf = (τeq / A)^(−k)
| Parameter | Description | Notes |
|---|---|---|
| A | Characteristic equivalent stress (MPa). The value of τeq at Nf = 1 cycle; sets the horizontal position of the S-N curve. | Must be positive. Structurally equivalent to α in the Antelo formulation. |
| k | Wöhler exponent (S-N slope). Applied as the negative power −k, so higher τeq → lower Nf. | Must be non-zero. Analogous to m in Cavdar or 1/|β| in Antelo. |
| c | Hydrostatic weight factor. Same physical meaning as c in the Cavdar model. | c = 0 reduces τeq to √J2, the pure deviatoric measure. |
Model Selection Guidance
Use Antelo when ARCAN calibration data are available (Mode I + II + Mixed tests) — it produces the most validated parameter set for Araldite-class adhesives. Use Cavdar or Sousa when calibrating directly from joint-level fatigue data (TAST, butt joint, SLJ) without ARCAN tests.
Not sure where to start? See the end-user FAQ for the same guidance in plain-language form, or the developer docs for the fatigue-engine implementation and calibration pipeline.