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This mini-project was inspired by Dennis Brands’ PhD on Forming simulations for unidirectional thermoplastic composites: Improving in-plane shear characterization and modeling; it’s a minimal, practice-oriented replication of key ideas.

Thesis: Forming simulations for unidirectional thermoplastic composites.

This mini-project implements rate–temperature shear and rheo-bending for molten PA6 with a solver-style hook. The current model is isotropic; UD anisotropy can be added Outputs: viscosity isotherms (η–γ̇), bending isotherms (M–κ̇), Fast vs Slow M–κ, and a solver-style material hook. No new rheological tests were conducted. Only the constitutive models and plotting workflow are illustrated by the curves used here, which are synthetic/representative and parameterized to fall within published PA6 melt ranges.

• η–γ̇: shear-thinning; 260 °C curve below 230 °C below 200 °C.
• M–κ̇: M increases with κ̇; hotter is lower.
• Fast vs Slow (M–κ): Fast > Slow at same κ.
• CLT vs molten: ratio ≈ 10²–10³ at 230 °C, κ̇≈0.5 s⁻¹.

• src/ – code (main.py, models, plotting)
• cases/ – parameters (materials_pa6.json)
• data/ – optional CSVs
• figs/ – generated plots
• form_cases/dome/ – material_hook.py (solver-style call)

Constitutive modelling + figures + a solver-ready hook.
No full contact forming simulation.

CLT vs molten: figs/CLT_vs_molten_ratio.txt

CLT vs molten (summary): see figs/CLT_vs_molten_ratio.txt.

Shear (Carreau–Yasuda, with anchored Arrhenius):
$$[\eta(\dot\gamma,T)=\eta_\infty + \big(\eta_0(T)-\eta_\infty\big),\Big[1+(\lambda,\dot\gamma)^a\Big]^{\frac{n-1}{a}},\quad$$ $$\eta_0(T)=\eta_{0,\mathrm{ref}}\exp!\Big(\frac{Q}{R}\big(\tfrac{1}{T}-\tfrac{1}{T_\mathrm{ref}}\big)\Big)]$$

Rheo-bending (viscous, rate- and temperature-dependent):
$$[M = K_b(T),\dot\kappa^{,m},\qquad$$ $$K_b(T)=K_{b0}\exp!\Big(\frac{Q_b}{R}\big(\tfrac{1}{T}-\tfrac{1}{T_\mathrm{ref}}\big)\Big),\qquad$$ $$D_\text{eq}=\frac{M}{\dot\kappa}]$$

CLT vs molten contrast (wrinkling relevance): compare room-T $$(D_\text{room})$$ to $$(D_\text{eq}(T,\dot\kappa))$$ at forming conditions.

• Experimental validation: Refit shear (Carreau–Yasuda) and rheo-bending parameters; substitute measured PA6 (or UD PA6/CF) data for synthetic curves.
• Anisotropy (IFRF-lite): Make bending orthotropic $$(K_b^L vs. K_b^T)$$ and extend shear to fiber-aligned viscosities $$(η_L, η_T)$$.
• Forming integration: Apply form_cases/dome/material_hook.py to a FE solver (UMAT/VUMAT/plugin) and evaluate it against a benchmark for dome-forming.
• Thermo-rheology: Reassess Arrhenius/WLF validity over a broader window; couple temperature fields (T(x,t)) and contact/heat transfer.