Reference revision · 2026-09-27
Two model records track primary and secondary crystallization. Parallel is a weighted sum; series is a harmonic combination. Both follow the temperature histories at thermal nodes or use ply-average temperatures, according to the thermal case sampling setting.
Set up
- Open Models → Thermoplastic Crystallization. Copy either PEEK · Velisaris–Seferis parallel or series.
- Set the two exponents, contribution weight, initial conversions, maximum matrix crystallinity and five temperature/rate points. The supplied values are illustrative, not a validated PEEK-grade calibration.
- In Thermal → Initial conditions → Optional PEEK crystallization, select the model. This explicit case assignment applies one matrix formulation across all sampled nodes or plies. A material’s older Crystallization model link alone does not activate this case calculation.
- Run a transient thermal cycle. The existing moving-process velocity maps residence time to position.
- In the 2D thermal field dropdown choose PEEK matrix crystallinity, Relative crystallinity, Primary crystallization conversion or Secondary crystallization conversion. Move the cursor to inspect time and thickness sections. Expand calibration and assumptions for model provenance.
What the results mean
Primary and secondary conversions are dimensionless process progress, each from 0–100%. Relative crystallinity combines those processes. Matrix crystallinity is that combined value multiplied by the specified limiting matrix crystalline fraction; it is not the crystalline fraction of the entire fiber/resin composite.
Equations and temperature history
Each branch has qᵢ = qᵢ₀ + ∫Kᵢ(T)dt and αᵢ = 1 − exp(−qᵢⁿⁱ). Initial clocks reproduce the supplied initial conversions. At constant temperature, the usual Avrami coefficient is kᵢ = Kᵢⁿⁱ. Enter K in 1/s; do not enter k in s⁻ⁿ.
Parallel: α = wα₁ + (1−w)α₂. Series: α = 1/[w/α₁ + (1−w)/α₂]. With a positive weight and zero conversion in either branch, the series result is zero. Series does not impose a hard delayed start for the secondary clock. Matrix crystallinity is X = Xmax α.
The nonisothermal implementation uses Nakamura accumulation. K is linearly interpolated between the editable table points and is zero outside that window. Thermal segments split at every rate-table knot, so integration is exact for the saved piecewise-linear temperature history. Refine thermal output spacing to capture short heating pulses; plot smoothing cannot recover an unsaved peak.
Inputs
| Control | Function |
|---|---|
| Model family (model) | Parallel weighted sum or series harmonic combination of two Avrami conversions. |
| Primary Avrami exponent (—) | Published parallel PEEK fit exponent. Refit for the series variant or another material grade. |
| Secondary Avrami exponent (—) | Published parallel PEEK fit exponent; not a universal PEEK constant. |
| Primary contribution (%) | Illustrative fixed weight. Secondary weight is 100% minus this value. Calibrate both mechanisms together. |
| Initial primary conversion (%) | Initial relative conversion of the primary process, not absolute matrix crystallinity. |
| Initial secondary conversion (%) | Initial relative conversion of the secondary process. Initial states are mapped to equivalent accumulated kinetic clocks. |
| Maximum matrix crystallinity (%) | Illustrative limiting crystalline fraction of the matrix, not composite fiber-plus-resin mass. Use one consistent mass or volume basis from calibration. |
| Full melting temperature (°C) | Simplified instantaneous full-melt reset at/above this temperature. No partial melting kinetics. This is a CDS extension, not the original crystallization equation. |
| Kinetics temperature 1 (°C) | Illustrative temperature grid. Strictly increasing; outside the table growth pauses. Endpoint rates must be zero. |
| Primary K 1 (1/s) | Illustrative Nakamura rate K = k^(1/n). Enter fitted primary rates; interpolation is linear in K, with time in seconds. |
| Secondary K 1 (1/s) | Illustrative secondary Nakamura rate. These table rates are not published Seferis coefficients. |
| Kinetics temperature 2 (°C) | Illustrative temperature grid. Strictly increasing; outside the table growth pauses. Endpoint rates must be zero. |
| Primary K 2 (1/s) | Illustrative Nakamura rate K = k^(1/n). Enter fitted primary rates; interpolation is linear in K, with time in seconds. |
| Secondary K 2 (1/s) | Illustrative secondary Nakamura rate. These table rates are not published Seferis coefficients. |
| Kinetics temperature 3 (°C) | Illustrative temperature grid. Strictly increasing; outside the table growth pauses. Endpoint rates must be zero. |
| Primary K 3 (1/s) | Illustrative Nakamura rate K = k^(1/n). Enter fitted primary rates; interpolation is linear in K, with time in seconds. |
| Secondary K 3 (1/s) | Illustrative secondary Nakamura rate. These table rates are not published Seferis coefficients. |
| Kinetics temperature 4 (°C) | Illustrative temperature grid. Strictly increasing; outside the table growth pauses. Endpoint rates must be zero. |
| Primary K 4 (1/s) | Illustrative Nakamura rate K = k^(1/n). Enter fitted primary rates; interpolation is linear in K, with time in seconds. |
| Secondary K 4 (1/s) | Illustrative secondary Nakamura rate. These table rates are not published Seferis coefficients. |
| Kinetics temperature 5 (°C) | Illustrative temperature grid. Strictly increasing; outside the table growth pauses. Endpoint rates must be zero. |
| Primary K 5 (1/s) | Illustrative Nakamura rate K = k^(1/n). Enter fitted primary rates; interpolation is linear in K, with time in seconds. |
| Secondary K 5 (1/s) | Illustrative secondary Nakamura rate. These table rates are not published Seferis coefficients. |
| Source (source) | Velisaris & Seferis (1986), PEEK two-process crystallization. |
| Parameter basis (text) | Source-grounded formulation; this seed is not a validated PEEK material calibration. |
Calibration and scope
The original parallel PEEK exponents are 2.5 and 1.5. The seeded rate table, weight, maximum fraction and melting temperature are illustrative CDS inputs, not original Seferis fitted coefficients. The series record requires a separate fit. Calibrate against DSC data for the actual polymer grade, reinforcement and cooling-rate range.
This version postprocesses the solved temperature field. It does not feed latent heat, crystallization shrinkage or evolving stiffness into the solver, or modify the separate intimate-contact/healing calculation. It assumes one PEEK matrix throughout the thermal section. Pressure dependence, heterogeneous polymer assignments, high-rate correction and partial melting are outside this version.
Full melting resets both clocks instantaneously at the editable threshold; cooling permits renewed crystallization. This reset is a simplified CDS extension, not a fitted melting model. Below the rate window, crystallinity is retained.
Sources
- Velisaris & Seferis (1986): PEEK crystallization kinetics
- Kelly et al. (2020): parallel and series formulations, equations 6–7
- Pérez-Martín et al. (2022): dual-process and Nakamura nonisothermal formulation; PEKK study, not PEEK parameter calibration
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.