Die swell of an extruded rectangular bar, and sharkskin: 22-Mec-A4 Design and Manufacture of Machine Elements, May 2018, Q3

Question 3: Die swell of an extruded rectangular bar, and sharkskin

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Given. A thermoplastic extruded through a rectangular die opening, and a round thermoplastic bar whose surface has the regular ridged texture known as sharkskin.

Find. The shape actually produced by the rectangular die, superimposed on the die opening (1a); two die-design changes that recover the intended rectangle (2a); the cause of the sharkskin surface (1b); and a cure (2b).

(a)(1a) The extruded shape

Figure 3.1 - Die opening (dashed) with the extrudate superimposed: swollen overall, with convex bulged faces and rounded corners.

The extrudate is larger than the die opening in every direction - die swell, with a swell ratio of typically 1.1 to 1.5 for a well-designed land and more for a short one - and it is no longer rectangular. The faces bulge outwards and the corners round off, so a rectangular hole delivers a barrelled, almost elliptical section. The reason is that recovery of the stored elastic strain is not uniform around the perimeter: a corner has free surface on two sides and a much lower local constraint, so it relaxes and contracts inwards while the mid-face material, constrained on only one side, expands outwards. The effect grows with extrusion rate, with molecular weight, and with shortness of the die land, and it falls as the melt temperature rises.

(a)(2a) Two die-design changes

Figure 3.2 - Compensated (inverse) die profile: faces cut concave and corners extended, so that after swell and relaxation the product is rectangular.

Change 1 - inverse-compensated die profile. Cut the die opening to the inverse of the observed distortion: make the faces concave and extend and sharpen the corners, so that the swelling restores a true rectangle. This is standard practice for profile dies and is normally arrived at by one or two iterations of trial extrusion and die correction.

Change 2 - lengthen the die land (and streamline the approach). Increasing the parallel land length increases the melt residence time under simple shear, so more of the elastic strain stored in the converging entry relaxes before the material leaves the die. A land length of 10-20 times the section thickness substantially reduces swell; a gradual conical or streamlined approach in place of a sharp shoulder reduces the strain that is stored in the first place. Process levers - raising melt temperature or reducing haul-off rate - work in the same direction, and a modest draw-down applied to the extrudate at the take-off gives the final size control.

(b)(1b) Why the surface looks like sharkskin

Figure 3.3 - Sharkskin: the surface layer is nearly stationary in the land and must accelerate abruptly at the exit, tearing periodically into regular transverse ridges.

Sharkskin is a surface-layer failure that occurs at the die exit, not in the bulk. Inside the land the velocity profile has its maximum on the axis and nearly zero at the wall; the instant the melt leaves the lip that boundary condition disappears and the skin must accelerate to the plug velocity of the free extrudate over a very short distance. The resulting tensile strain rate in the surface layer exceeds the melt strength, the skin tears, relaxes, is dragged forward, and tears again - which is why the defect appears as regular transverse ridges rather than as random roughness. In some polymers, notably LLDPE, the same threshold is accompanied by a local stick-slip at the die lip. Sharkskin appears at a lower throughput than gross melt fracture and is a distinct phenomenon from it.

(b)(2b) Eliminating it

The direct cure is to soften the skin at the point where it has to accelerate: heat the die lip locally, using a separately controlled band heater on the last 10-20 mm of the die, so that the surface layer is hotter and weaker than the bulk. Reducing the extrusion rate achieves the same result by lowering the strain rate, at a direct cost in output. In production the most economical answer is a polymer processing aid: 400-1000 ppm of a fluoroelastomer coats the die land, allows the skin to slip rather than tear, and removes sharkskin without any loss of rate. Lengthening the land, rounding the exit lip and selecting a narrower molecular-weight distribution all help. Note that raising the bulk melt temperature alone can worsen the extrudate by reducing melt strength, so the die-lip heating is preferred to a general temperature rise.

Question 3 - summary
Item	Answer
(1a) Extrudate shape	Swollen, faces bulged convex, corners rounded (barrelled section); swell ratio typically 1.1-1.5
(2a) Die change 1	Inverse-compensated die: concave faces, extended and sharpened corners
(2a) Die change 2	Longer parallel land (10-20 x section thickness) with a streamlined approach
(1b) Cause of sharkskin	Abrupt acceleration of the near-stationary surface layer at the die exit; tensile strain rate exceeds melt strength, so the skin tears periodically
(2b) Cure	Heat the die lip locally; reduce rate; add a fluoropolymer processing aid; lengthen the land

Topic. Viscoelastic extrudate behaviour: die swell, sharkskin and profile-die correction.

Key relations. Swell ratio $s = D_{\text{extrudate}}/D_{\text{die}}$, decreasing with land length $L/D$ and increasing with shear rate; apparent wall shear rate $\dot{\gamma} = 4Q/(\pi R^{3})$. Sharkskin onset is governed by the exit strain rate, gross melt fracture by the entry shear stress.

Why this works. Everything in this question follows from one property: a polymer melt stores elastic strain, and whether that strain relaxes inside the die or outside it decides both the shape and the surface of the product.

Common pitfall. Cutting the die to the finished dimensions of the profile. A profile die never has the shape of the profile; and treating sharkskin as contamination or as a mould-release problem, when it is a rate-and-temperature defect.

Source. Kalpakjian and Schmid, 8th ed., Section 19.2 (extrusion, die swell, extrudate defects); Groover, 7th ed., Section 13.2.