Reference revision · 2026-09-27
Epoxy contact can use cure-dependent resin viscosity. Flow stops at gel. The thermoplastic healing model must be disconnected for this epoxy calculation.
These two model records describe a thermoplastic bond line. Intimate contact predicts how much of the nominal surface actually touches; healing describes polymer interdiffusion across contact; coupled bonding accounts for the different times at which each area first touches.
Set up and run
- In Models → Interface Bonding, copy the Intimate Contact Model example. Set its interface depth, pressure source, surface coefficient and viscosity law for the tape.
- For healing and bonding, copy Interface Healing and Coupled Bonding Model and select the contact record inside it. Set welding-time coefficients and initial healing. Fully healed bond strength is optional.
- In the transient Thermal case → Initial conditions → Optional interface bonding, select the contact model for contact-only results, or select the bonding model for both calculations. You do not need both case links. If both are set they must reference the same contact model.
- Run the existing temperature and pressure schedule. Global pressure excludes rollers; Total uses one shared global-plus-roller pressure on both faces. Opposing roller pressures are not added. Time and length schedules use the existing travel-velocity conversion.
- In the 2D thermal dropdown select Intimate contact and bonding profile. Compare all three percentages or choose temperature, pressure, viscosity, welding time or scaled strength. Moving runs offer Time/Distance. Bonding CSV exports every saved quantity.
Meaning of the curves
Contact is the percentage of nominal area touching. Healing potential assumes contact existed from the beginning and is an upper reference, not the actual bond. Coupled bonding is the area-weighted healing of patches created at their own contact times. It cannot exceed contact. A 100% bonding index is model saturation, not a structural qualification or measured strength.
Equations
Contact exposure J = ∫ Pnet/η dt. The lumped asperity model uses Dcontact = min(1, [D0⁵ + Rc⁵ J]¹ᐟ⁵). For zero initial contact this is the Mantell–Springer form used by Tierney and Gillespie. Nonzero initial contact uses an equivalent prior exposure; it deliberately differs from adding D0 after the fifth root in the empirical contact formulation code.
Viscosity is η = A exp(B/(T[K]+C)). The supplied legacy contact fit has A=132.95 Pa·s, B=2969 K and C=−273.15 K, reproducing its empirical Celsius denominator. Do not reinterpret it as a kelvin Arrhenius fit. Use calibrated effective surface-flow viscosity.
Yang–Pitchumani healing uses H(t)=∫dt/tw(T), with tw=tw_ref exp(Ea/R [1/T−1/Tref]) and kelvin temperatures. A patch born at τ heals by min(1, [H(t)−H(τ)]¹ᐟ⁴). Existing initial contact can start with a specified healing level. The Butler coupling is Db(t)=D0 Dh_initial(t)+∫Dh(τ,t)dDcontact(τ).
The AS4/PEEK example welding time is 0.11 s at 400°C, activation energy 57.3 kJ/mol, and activation threshold 338°C. Coefficients for other materials must be measured or otherwise justified. Surface roughness and viscosity are independent of the void model’s permeability and pore-flow viscosity.
Controls
Intimate Contact Model
| Input | Example | Function |
|---|---|---|
| Model family | Intimate Contact Model model | Editable model coefficient; see equations above. |
| Initial intimate contact | 0 % | Initial fraction of interface already touching. Prior exposure is initialized as D0^5, preserving continuity under subsequent flow. |
| Surface roughness coefficient | 0.29 — | Lumped asperity coefficient Rc. AS4/PEEK example reported by Tierney and Gillespie; calibrate to tape surfaces. |
| Contact viscosity prefactor | 132.95 Pa·s | Empirical contact fit: eta=A exp(B/(T[K]+C)). Effective surface-flow viscosity, not necessarily neat resin viscosity. |
| Contact viscosity coefficient | 2969 K | Editable model coefficient; see equations above. |
| Contact viscosity offset | -273.15 K | The legacy empirical fit uses Celsius in the denominator. Offset −273.15 K reproduces it. This is separate from the kelvin Arrhenius healing law. |
| Contact activation temperature | 338 °C | AS4/PEEK example melt threshold. Contact growth stops at/below this value; existing contact persists. |
| Interface depth | 0.5 fraction | 0=lower face, 1=upper face. Set to the intended ply bond line. One selected interface per case; not an automatic distribution. |
| Interface pressure source | Total type | Total is the shared through-thickness pressure: global plus the largest active roller contribution. Opposing nip pressures are not added. Global excludes rollers. |
| Interface pressure convention | Gauge type | Gauge is net compression; absolute subtracts ambient once. Negative net pressure creates no new contact. |
| Interface ambient pressure | 0.1 MPa absolute | Editable model coefficient; see equations above. |
| Maximum bonding step | 1 s | Internal steps also resolve schedule events, temperature thresholds and contact/healing increments. |
| Maximum contact increment | 0.5 % | Maximum area gained per internal step. Reduce to check coupled bonding convergence. |
| Bonding integration tolerance | 0.000001 fraction | Controls midpoint step-doubling for pressure/viscosity and reciprocal welding-time integrals. |
| Parameter basis | AS4/PEEK example; Rc from Tierney–Gillespie, viscosity from empirical contact formulation; calibrate for the actual tape text | Editable model coefficient; see equations above. |
Interface Healing and Coupled Bonding Model
| Input | Example | Function |
|---|---|---|
| Model family | Interface Healing and Coupled Bonding Model model | Editable model coefficient; see equations above. |
| Intimate contact model | MOD-CONTACT-001 ref | Required linked contact model supplies surface flow, interface depth, pressure convention and integration settings. |
| Initial healing of existing contact | 0 % | Applies only to area already in contact initially. New areas start unhealed. |
| Reference welding time | 0.11 s | AS4/PEEK example: full-healing time at the reference temperature, reported in Tierney–Gillespie from Yang–Pitchumani. |
| Healing activation energy | 57300 J/mol | tw(T)=tw_ref exp(Ea/R [1/T−1/Tref]); both temperatures in kelvin. |
| Healing reference temperature | 400 °C | Editable model coefficient; see equations above. |
| Healing activation temperature | 338 °C | Healing pauses at/below this example PEEK melt threshold. Retains exposure on cooling and reheating; no crystallization kinetics. |
| Fully healed bond strength | Optional MPa | Optional calibrated strength. Blank reports dimensionless bonding only; no strength is invented. |
| Parameter basis | AS4/PEEK example; compatible thermoplastic surfaces only. Includes contact delay in healing; calibrate before strength prediction. text | Editable model coefficient; see equations above. |
Scope and convergence
This version postprocesses one selected interface from the solved temperature history. Net compressive pressure drives new contact. Established contact is retained on unloading, and healing may continue while hot even after a roller leaves. Cooling below a threshold pauses that mechanism; reheating resumes it. The model does not predict reopening, damage, degradation, crystallization, thermoset chemical bonding, or mismatched polymer compatibility. It does not change thermal conductivity, laminate thickness or mechanical properties.
Integration resolves schedule knots, roller pressure events, activation crossings and bounded contact/healing increments. Reduce maximum step, maximum contact increment and tolerance to check numerical convergence; refine saved thermal output for rapid heating. The simple lumped asperity law is implemented here, not the full Yang–Pitchumani fractal contact model.
References
- Tierney & Gillespie (2006): in-situ tow-placement strength development
- Yang & Pitchumani (2002): nonisothermal healing
- Butler, McCullough, Pitchumani & Gillespie (1998): coupled fusion bonding
- Bastien & Gillespie (1991): earlier nonisothermal healing work
Node, interface and ply sampling
In Thermal → Initial conditions → Material model sampling, choose All thermal nodes or Interfaces and ply averages, then rerun. All thermal nodes evaluates each linked void, interface and PEEK model at every thermal node. Reduced sampling evaluates contact/healing only at internal ply boundaries and evaluates voids/PEEK using each ply's thickness-averaged temperature.
An eight-ply laminate has seven internal interfaces and eight ply histories. The outer surfaces are excluded from the interface count. Ply numbering runs from the lower face to the upper face. The linked model coefficients, initial states and pressure source apply at every sampled location.
Select a material output in the temperature dropdown, then choose All interfaces or All ply results. Each location has a separate trace, a visibility checkbox and a value at the slicer time cursor. Moving runs support distance; Slice CSV exports all traces. With node calculations, the slicer can also show all thermal nodes. Cursor output retains the existing detailed plot; reduced PEEK results use the ply slicer and its time cursor.
Reduced mode averages temperature before running the nonlinear bulk model. In node mode, the ply slicer averages already calculated results, while interface traces interpolate node results. These operations can differ. Compare the two modes when temperature varies strongly across a ply. The thermal mesh, cure/reaction model and saved thermal output interval are unchanged.
Model defaults preserves older studies: void and interface models use their chosen depth; PEEK uses thermal nodes. Older saved runs need a new run with a sampling mode selected to produce material slices. PEEK rate coefficients remain illustrative and require calibration.