Question 1 of 6: Thermoforming a square box - wall thinning at edges and corners

Question 1: Thermoforming a square box - wall thinning at edges and corners

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. A square box produced by straight (pure) vacuum forming of a thermoplastic sheet, in which the edges and corners are observed to thin excessively.

Find. (a) an annotated sketch of the pure vacuum-forming cycle with representative sheet and mould temperatures; (b) the mechanism that concentrates thinning at the edges and corners; (c) a production route that evens out the wall.

(a) Pure vacuum forming

The sheet is clamped in a frame and heated by radiant elements until it is well above its glass transition temperature but still below the melting range - for amorphous grades such as ABS, HIPS or PVC the forming window is roughly 150-180 °C, and the sheet sags visibly when it is ready. The mould is a single female tool vented by small holes (0.5-1 mm) at the corners and along the base. When the cavity is evacuated to about 10 kPa absolute, the pressure difference across the sheet is at most one atmosphere, so the forming pressure is limited to roughly 0.09 MPa - this is why vacuum forming demands a soft, highly extensible sheet. The mould itself is deliberately run cool, typically 60-80 °C, so that the part sets quickly; aluminium tooling with drilled water lines is normal for production, epoxy or plaster for prototypes.

(b) Why the edges and corners thin

Thinning is a kinematic consequence of the order in which the sheet touches cold steel. The first material to contact the mould - the rim and the base - is chilled below its forming temperature almost immediately and, because the coefficient of friction between a hot polymer and the tool is high, that material is then locked in place. It stops stretching. Everything that remains free must therefore supply all of the subsequent deformation, and the free material that has to travel farthest is the material destined for the deep corners.

The geometry makes the point quantitatively. For a box of side S = 300 mm and depth D = 150 mm, an element on the centre-line of a side wall is drawn from a half-width of 150 mm to a slant length of $\sqrt{150^{2}+150^{2}} = 212$ mm, a linear draw ratio of 1.41. An element headed for a corner is drawn to $\sqrt{150^{2}+150^{2}+150^{2}} = 260$ mm, a ratio of 1.73. The corner therefore stretches 22 % more than the side wall in one direction, and because a corner is stretched biaxially while a side wall is stretched essentially uniaxially, the area increase - and hence the thickness reduction - is far larger still. Corners of a straight-vacuum-formed box routinely finish at 20-30 % of the starting sheet thickness while the base remains at 90 %.

Two secondary effects sharpen the same trend. Polymer that has already touched the mould is cooler, hence stiffer, so deformation migrates to the hottest and thinnest region - a self-aggravating instability in any material whose flow stress falls with temperature. And a square box concentrates three-dimensional stretching at eight corner regions, so the local draw ratio there is set by the deepest diagonal in the part.

(c) A production method that reduces thinning

The remedy is to pre-distribute the material before it touches the cold cavity. In plug-assist forming a male plug - made from syntactic foam, filled PTFE or hardwood, all chosen for low conductivity, and held at roughly the sheet temperature - descends into the clamped sheet and carries material down into the cavity mechanically. Because the plug is not chilled, the sheet it touches is not frozen; the stretched material is delivered to the base and corners, and the vacuum then only has to complete the shape. Wall-thickness uniformity typically improves from 3:1 to better than 1.5:1. Plug travel, plug shape and the timing between plug entry and vacuum application are the three variables that are tuned on the shop floor.

Two alternatives achieve the same end by different means. Billow (bubble) pre-stretching inflates the hot sheet with low-pressure air into a free bubble before the mould closes, which biaxially and uniformly pre-thins the sheet without any tool contact at all, and is often combined with a plug. Pressure forming supplements the vacuum with 0.3-0.7 MPa of air on the free side, which shortens the forming time so much that less heat is lost to the mould before the shape is complete, and it also permits sharper detail. Zone heating - profiling the radiant elements so that the corner-bound material starts hotter - is a cheap partial fix. Finally, a design change is always available: increase the corner radii and reduce the draw ratio, since the depth-to-width ratio of a straight-vacuum-formed box should be kept below about 0.5.