Question 3 of 6: Extrusion die design and flat-rolling defects

Question 3: Extrusion die design and flat-rolling defects

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Figure ex1 shows three sections of equal area: (a) an I-section with thin flanges and a thin web, (b) a channel whose two legs turn inward at the bottom into re-entrant lips, and (c) a thin split ring. Figure ex2 shows a heavy, unbalanced section carrying two small hollow holes and a labelled sharp inside corner. Figure Ro1 shows a rolled strip with wavy edges; Figure Ro2 shows a rolled strip cracked at both edges.

Find. (a) The section requiring the greatest extrusion force, with justification; (b) the consequence of leaving the ex2 section unbalanced, plus its other extrusion problems; (c) the mechanism behind each rolling defect.

(a) Which equal-area section takes the most force

Approach. Extrusion pressure is not a function of area alone. For a given reduction, the pressure is written p = Y_avg (a + b ln R) and is then multiplied by a shape factor that grows with the ratio of the section perimeter to the perimeter of a circle of equal area. The reason is physical: the perimeter is the length of the die land, so it sets the sliding-friction area, and a long, convoluted perimeter also forces the metal to undergo redundant (non-useful) shear as it turns into the thin outlying features.

Scaling the three outlines off the printed figure and normalising every one to the same area gives the complexity factor K_c = P/P_circle:

Answer: section (b), the channel with the inward-turned lips, requires the greatest force, with the I-section (a) an extremely close second and the split ring (c) clearly the easiest of the three.

The numbers put (a) and (b) within 1 % of each other — far inside the accuracy of dimensions scaled off a sketch — so the perimeter argument alone cannot separate them, and the tie is broken on a feature the perimeter does not capture. Section (b) is the only one of the three with a re-entrant profile: the lips turn back inward, so metal must flow into a deep, narrow pocket whose mouth is narrower than the space behind it, and the die must carry an unsupported tongue between the two lips. Filling a re-entrant pocket demands additional redundant shear and a higher local pressure, and the cantilevered die tongue deflects under that pressure, which the operator compensates for with still more pressure. Section (a) has the same thin walls but every feature opens outward, so metal reaches it by a direct radial flow.

The split ring (c) is the counter-intuitive result worth stating explicitly: it looks the most delicate, but a uniform thin annulus has a comparatively modest perimeter for its area, no re-entrant features and no sharp corners, so it is the least demanding of the three. Thinness by itself does not raise the extrusion force — convolution and re-entrancy do.

(b) The unbalanced section of Figure ex2

An unbalanced section is one whose thick and thin regions are distributed asymmetrically about the extrusion axis. Metal leaves a die land at a velocity that depends on the local channel thickness and friction, so a thick region wants to run faster than a thin one.

If the imbalance is not addressed, the extrudate leaves the die distorted rather than straight. The faster-flowing heavy side elongates more than the light side, and because the two are joined they cannot separate — the profile therefore curves, bows and twists as it emerges, and it develops longitudinal residual stress even where it looks straight. The consequences on the run-out table are a product that will not stay within straightness tolerance, that whips against the puller and the die, that distorts again during subsequent ageing or heat treatment as the residual stresses relax, and that may tear along the thick/thin junction where the velocity mismatch is greatest. The extrudate can also drag against one side of the die and score its surface. The cure is to balance the flow rather than the geometry: lengthen the die land on the thick regions and shorten it on the thin ones (choke and relief), feed the thin sections preferentially with feeder plates or a pocket die, and where possible redesign the section toward uniform wall thickness.

The other extrusion problems visible in this design are:

• The labelled sharp inside corner. A sharp re-entrant corner in the die is a stress raiser in the die steel itself and is where die cracking begins; it also stagnates the metal flow locally and prints a longitudinal surface defect or a hot tear onto the extrudate. Generous internal radii — typically at least 0.8 mm, more on heavy sections — are the standard fix.
• The two enclosed holes. Hollow features cannot be produced by a simple flat die: they require a mandrel or a porthole/bridge die in which the metal splits around the mandrel legs and rewelds downstream. That imposes a higher pressure, restricts the process to alloys that weld well in the solid state (the 6xxx series, not the high-strength 2xxx and 7xxx), and puts a longitudinal weld seam in the finished part.
• Very unequal wall thicknesses, including a thin section next to a heavy one. Besides the velocity mismatch, the thin section cools faster on exit, so the two regions contract differentially and the profile distorts a second time after it has left the press.
• A large circumscribing circle with material concentrated to one side, which puts the section’s centroid away from the billet axis; the die must then be positioned off-centre or the flow will be starved on the far side.

(c) Flat-rolling defects

(i) Figure Ro1 — wavy edges. Under the separating force the work rolls bend elastically, deflecting away from each other at mid-span, so the roll gap is thicker at the centre than at the edges. The strip edges are therefore reduced more than the centre, and greater reduction means greater elongation. The edges cannot elongate freely because they are attached to the shorter centre, so they are held in longitudinal compression — and a thin plate in longitudinal compression buckles. The waves are that buckle, frozen into the strip. The remedies all attack the roll-gap profile: grind a positive camber onto the rolls, use backup rolls or roll-bending jacks to counteract the deflection, run with roll crown control, or simply take a lighter pass so the separating force and hence the deflection are smaller.

(ii) Figure Ro2 — edge cracking. This is the mirror-image fault. When the roll gap is thicker at the edges than at the centre — over-cambered rolls, or barrelled rolls, or a strip that has been over-crowned upstream — the centre of the strip is reduced more and elongates more, and it drags the under-reduced edges along with it. The edges are then in longitudinal tension, and since a rolled edge is also the coldest, most work-hardened and least ductile part of the strip (and often carries pre-existing edge damage from an earlier pass or from the slab), that tension opens transverse cracks in from each edge, exactly as drawn. Edge cracking is aggravated by low rolling temperature, by rolling material with poor edge ductility, and by the free-surface bulging (barrelling) of the edges, which superimposes a secondary tensile hoop stress on the edge surface. The remedies are to correct the roll-gap profile, to keep the edges hot (edge heaters), to edge-roll or trim the strip before the heavy passes, and to reduce the pass reduction.