What Is the Extruder Die Swell Ratio Calculator (Tanner Elastic Recovery)?
Die swell (also called extrudate swell or the Barus effect) is the phenomenon where a polymer extrudate emerges from a die with a cross-sectional area significantly larger than the die opening.
It is caused by the elastic recovery of macromolecular coils that were stretched and oriented inside the die channel.
How Does the Extruder Die Swell Ratio Calculator (Tanner Elastic Recovery) Work?
Inside the die, shear stress stretches polymer chains, storing elastic strain energy manifested as a first normal stress difference N₁ = 2·G·γr².
Upon exiting the rigid die restraint, normal stresses relax instantly, causing the extrudate to contract axially and expand radially.
Extruder Die Swell Ratio Calculator (Tanner Elastic Recovery) Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Tanner’s nonlinear viscoelastic formulation linking first normal stress difference to post-die elastic expansion.
How to Use the Extruder Die Swell Ratio Calculator (Tanner Elastic Recovery)
- Enter the wall shear stress inside the die land.
- Input the melt elastic shear modulus.
- Use the resulting swell ratio B to undersize the extrusion die tooling so the final cooled product meets design tolerances.
Step-by-Step Example Calculation
Low-Density Polyethylene Extrusion Die
Input Values:
Understanding Your Result
B = d / d₀ indicates diameter expansion (e.g. B = 1.25 means the strand expands 25% larger than the die orifice).
Factors That Affect the Result
- Die land length: Increasing die land length (L/D ratio > 10) allows stretched chains time to relax before exiting, cutting die swell in half.
- Extrusion speed: Higher throughput increases wall shear stress, magnifying die swell.
When Should You Use This Calculator?
- Designing extrusion dies for tubing, profiles, blown film, and wire coating.
- Blow molding parison programming calculations.
Assumptions & Limitations
- Valid for circular capillary dies without drawdown pulling tension.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Tanner’s standard nonlinear viscoelastic rheology equation.