Extrusion Die Swell, Drawdown & Dimensional Control: Viscoelasticity & Land Length Physics

Extrusion profile manufacturing (e.g., pipes, window profiles, tubes) relies on precise dimensional control. Polymer melts are viscoelastic; as they emerge from the die, they experience die swell due to the relaxation of oriented polymer chains. Simultaneously, downstream pulling systems introduce drawdown, which stretches and thins the profile. Balancing die swell and drawdown requires precise calibration of die land length and cooling bath pull speeds. Indian pipe makers like Supreme Industries and Astral Pipes optimize these settings to meet strict dimensional tolerances.

• Explain the viscoelastic origin of die swell (extrudate swell) and its relationship to normal stress differences ($N_1$).
• Formulate the effect of die land length ($L/D$ ratio) on shear stress relaxation and die swell reduction.
• Calculate the drawdown ratio (DDR) and its effect on final extrudate dimensions.
• Design a die sizing adjustment profile to compensate for predictable die swell and drawdown.
• Reference extrusion quality standards such as IS 4985 (PVC pipes) and ISO 3126.

3.1 Viscoelastic Origin of Die Swell

As a polymer melt flows through a die, the shear field aligns and stretches the polymer chains. When the melt exits the die land:

1. The confining wall stresses are removed.
2. The polymer chains retract to their random coil state (elastic recovery).
3. This causes a contraction in the flow direction and an expansion in the transverse direction (die swell). Die swell ratio $B$ is:

$$B = \frac{D_{extrudate}}{D_{die}}$$

3.2 Role of Land Length ($L/D$) in Stress Relaxation

The longer the melt remains in a parallel channel (die land), the more time the polymer chains have to relax their elastic stress before exiting. Increasing the land length ($L/D$) reduces die swell:

$$B \propto \exp\left( -\frac{t_{res}}{\lambda_r} \right)$$

Where $t_{res}$ is the residence time in the die land ($t_{res} = L / v$) and $\lambda_r$ is the relaxation time of the melt. Typical land lengths range from $L = 10 D$ to $30 D$ depending on the polymer elasticity.

3.3 Drawdown Mechanics

Downstream puller systems (haul-offs) pull the extrudate at a speed $v_p$ greater than the die exit velocity $v_d$. This stretches the melt while it is still warm:

$$\text{Drawdown Ratio (DDR)} = \frac{v_p}{v_d} = \frac{A_{die}}{A_{final}}$$

Where $A_{die}$ is the die cross-sectional area and $A_{final}$ is the final solidified product cross-sectional area. Drawdown reduces profile dimensions, counteracting die swell.

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Problem: A HDPE pipe is extruded using a die with an outer diameter $D_d = 50.0$ mm and wall thickness $h_d = 4.0$ mm. The melt has a die swell ratio $B = 1.30$. The downstream puller is adjusted to pull the pipe at a speed that yields a Drawdown Ratio $\text{DDR} = 1.20$. Calculate:

1. The intermediate outer diameter of the extrudate after die swell but before drawdown.
2. The final outer diameter of the solidified pipe ($D_{final}$).

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Solution:

1. Calculate the intermediate diameter ($D_{swell}$) using the die swell ratio:

$$D_{swell} = B \times D_d = 1.30 \times 50.0 \text{ mm} = \textbf{65.0 mm}$$

1. Calculate the final diameter ($D_{final}$) incorporating drawdown. The cross-sectional dimensions scale inversely with the square root of the drawdown velocity ratio (for isotropic scaling):

$$D_{final} = \frac{D_{swell}}{\sqrt{\text{DDR}}} = \frac{65.0}{\sqrt{1.20}} = \frac{65.0}{1.0954} = \textbf{59.34 mm}$$

Interpretation: The extrusion die outputs melt at 50.0 mm. Viscoelastic expansion swells the profile to 65.0 mm, and downstream tension draws it down to a final product outer diameter of 59.34 mm. Sizing sleeves must be positioned to calibrate this final diameter to target specifications.

Supreme Industries (Gadegaon, Maharashtra) and Astral Pipes (Ahmedabad) manufacture chlorinated PVC (CPVC) and lead-free PVC pipes. Their extrusion lines utilize vacuum calibrator tanks with brass sizing sleeves to clamp the pipe outer diameter under vacuum, cooling the swollen extrudate to meet IS 4985 tolerances.

Indian toolrooms adjust land length configurations based on whether they process highly elastic LDPE (requiring $L/D \approx 25$) or low-elasticity PP ($L/D \approx 15$).

• Die Swell (Barus Effect): Transverse expansion of extrudate due to polymer chain relaxation.
• Land Length ($L$): The parallel portion of the die exit channel where stress relaxation occurs.
• Drawdown Ratio (DDR): Ratio of puller speed to die exit speed, resulting in profile thinning.
• Sizing Sleeve: A water-cooled sleeve located at the cooling tank entrance to calibrate pipe outer dimensions.
• IS 4985: Indian Standard code governing unplasticized PVC pipes for potable water supply.

1. IS 4985 — Bureau of Indian Standards (BIS) code for unplasticized PVC pipes for water supply
2. ISO 3126 — Plastics piping systems — Plastics components — Determination of dimensions
3. ASTM D2837 — Standard Test Method for Obtaining Hydrostatic Design Basis for Thermoplastic Pipe Materials
4. ISO 11443 — Plastics — Determination of the fluidity of plastics using capillary rheometers

1. Derive the relationship between melt residence time in the die land and the reduction of die swell using a single Maxwell relaxation model.
2. How does the molecular weight distribution (MWD) of polyethylene influence its die swell behavior? Compare narrow MWD metallocene PE with broad MWD unimodal PE.
3. Describe the defects associated with excessive drawdown (e.g., draw resonance, melt tear) and their mitigation.

Q1. Die swell in polymer melt extrusion is primarily a result of:

• C) Viscoelastic relaxation of oriented polymer chains upon exiting the die

Q2. Increasing the land length ($L/D$) of an extrusion die has what effect on die swell?

• B) Reduces die swell by increasing melt residence time to allow stress relaxation

Q3. The ratio of downstream puller speed to die exit velocity is called the:

• C) Drawdown Ratio (DDR)

Q4. Which sizing system is commonly used to freeze the outer dimensions of extruded PVC pipes under vacuum?

• A) Vacuum sizing sleeve and cooling bath

Q5. Which BIS standard governs unplasticized PVC pipes for water supply applications in India?

• B) IS 4985