State normalization and temperature window
Select thermoplastic crystallization for a semicrystalline polymer. Crystallinity X is bounded between its initial value and the user-supplied maximum Xmax. Kinetics are active only when the current nodal temperature lies strictly between the calibrated glass-transition and melting temperatures.
Equation detailsExplanation · variables · model connection · reference+
Expresses current absolute crystallinity as a fraction of the maximum crystallinity available to the selected thermoplastic grade.
Model connectionThe normalized state is used by both Nakamura branches and the bounded integration rule; the crystallinity history retains the absolute crystallinity X.
Theory basisNakamura nonisothermal crystallization
Equation detailsExplanation · variables · model connection · reference+
Combines Arrhenius temperature dependence with a calibrated undercooling function that vanishes at the melting temperature and is evaluated only inside the Tg–Tm process window.
Model connectionEvaluated at every active thermoplastic transport node using the current thermal iterate. Outside Tg<T<Tm, R15 sets the crystallization rate to zero.
Theory basisPEEK dual-mechanism crystallization model
Nakamura/Avrami evolution
Equation detailsExplanation · variables · model connection · reference+
Differentiates the Nakamura form of Avrami crystallization to obtain an instantaneous nonisothermal rate in the normalized state. Numerical floors protect the logarithm near ξ=0 and ξ=1.
Model connectionThe single-branch crystallization law uses its calibrated rate directly. The rate is then advanced using the irreversible bounded update.
Theory basisNakamura rate formulation
Equation detailsExplanation · variables · model connection · reference+
Blends two independently calibrated Nakamura branches to represent two-stage crystallization with one bounded weighting factor.
Model connectionThe dual-branch crystallization law. The same combined rate controls crystallinity growth, latent heat release, and the subsequent shrinkage state.
Theory basisVelisaris–Seferis dual-mechanism PEEK model
Equation detailsExplanation · variables · model connection · reference+
Integrates the normalized rate over the process step without consuming more than the remaining crystallizable fraction, then maps the state back to absolute crystallinity.
Model connectionApplied independently at every active thermoplastic node. The crystallization-rate history reports (Xⁿ⁺¹−Xⁿ)/Δt rather than the normalized branch rate.
Theory basisNonisothermal Nakamura state evolution
Latent heat and crystallization shrinkage
Equation detailsExplanation · variables · model connection · reference+
Converts absolute crystallinity growth and the calibrated heat of crystallization into a volumetric heat source.
Model connectionIncluded in the heat equation only when the crystallization-exotherm option is enabled and reported as crystallization heat generation.
Theory basisPEEK crystallization calorimetry basis
Equation detailsExplanation · variables · model connection · reference+
Maps crystallinity gained after the initial state into an anisotropic contraction in each ply material direction.
Model connectionStored in the process-shrinkage history, fitted through each ply, and optionally added to the laminate process resultants and local failure-stress recovery.
Theory basisProcess-shrinkage residual-stress framework
Material-grade calibration is required. PEEK and PEKK grade, molecular architecture, cooling history, prior melt state, reinforcement, and measurement method change the fitted kinetics. The pipeline is a model family, not a generic property card.
Required evidence
- DSC-derived crystallization rate and heat over relevant cooling/heating histories.
- Tg, Tm, and maximum crystallinity for the selected grade.
- Dilatometry or dimensional data for local crystallization shrinkage.
- Verification against nonisothermal process cycles before residual-stress use.
Theory references
- Nakamura et al., “Some aspects of nonisothermal crystallization of polymers. I,” Journal of Applied Polymer Science 16 (1972) 1077–1091.
- Velisaris and Seferis, “Crystallization kinetics of polyetheretherketone (PEEK) matrices,” Polymer Engineering & Science 26 (1986) 1574–1581.
- NASA composite process modeling reference for coupled heat generation, shrinkage, and residual response.
Workbench availability: released models, inputs and compatible study paths. The wider theory library includes reference formulations not available in every Workbench solve.