22-Mec-A4 Design and Manufacture of Machine Elements · Undated paper

Question 2 of 6: Press-formed part failing in stretching — forming-limit diagnosis

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Question 2: Press-formed part failing in stretching — forming-limit diagnosis (25 marks)

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.

(a) Diagnose with a grid-strain (circle-grid) analysis, supported by a fracture examination and a records audit. The measurement that settles the question is the strain state at the failure site, and the standard industrial method for obtaining it is to electrochemically etch a grid of small circles (typically 2.5 mm diameter) onto flat blanks, run them through the production die, and measure the ellipses that the circles have become. The major and minor engineering strains follow directly from the ellipse axes, $e_1 = (d_1-d_0)/d_0$ and $e_2 = (d_2-d_0)/d_0$, and plotting those pairs on the forming-limit diagram for that grade and thickness shows immediately whether the part is failing because it exceeds the forming-limit curve or for some other reason.

Three supporting checks make the diagnosis conclusive. First, examine the fracture: a split preceded by visible local necking is a genuine forming-limit failure, whereas a clean split with no neck points to an edge condition (a sheared or burred trim edge, where the FLC does not apply) or to a bend fracture over a sharp radius. Second, section the part and map the thickness; the thinnest section identifies where the strain localised, and comparing it with the theoretical value from the shape tells you how much metal never fed in. Third, audit the inputs — blank size and orientation to the rolling direction, lubricant type and coverage, blank-holder force, drawbead height and penetration, die and punch radii, and the material certificate ($n$, $\bar r$, thickness, yield strength) for the failing coil against a coil that ran well.

(b) The likely causes all push the strain path into the worst region of the FLD. The question states the two conditions that matter: the part is formed by almost pure stretching, and drawbeads are used. Drawbeads exist to lock the flange, and a locked flange means no metal is drawn in from outside the die opening. Every bit of surface area the part needs must therefore come from thinning the blank that is already under the punch. That drives the major strain $e_1$ up while the minor strain $e_2$ stays close to zero — and $e_2 \approx 0$ is plane strain, the lowest point of the forming-limit curve, denoted FLC₀. The part is being pushed vertically up the FLD at the one abscissa where the curve offers the least room.

Layered on top of that geometry are the usual contributing factors: a low strain-hardening exponent $n$ (the FLC₀ intercept scales roughly with $n$ and with sheet thickness, so a low-$n$ or thin coil lowers the whole curve), poor or unevenly applied lubrication (friction pins the sheet against the punch nose so the strain cannot spread, and a dry patch becomes the necking site), excessive blank-holder force or over-penetrating beads (more restraint than the part needs), and small punch or die-entry radii that concentrate bending strain on top of the membrane strain. Batch-to-batch scatter in coil properties explains why the same tool runs for months and then starts splitting.

(c) Two remedies that hold the part shape fixed, shown as two arrows on the FLD. Since the geometry cannot change, only the strain path and the curve itself are available.

1. Move the operating point downward — reduce the major strain at the critical site. Reduce the restraint so the same shape is made with less thinning: back off the blank-holder force, reduce the drawbead height or penetration (or open one bead entirely on the ends), enlarge the die-entry and punch radii, and improve the lubricant so the strain spreads over a larger area of sheet instead of concentrating at the punch nose. On the FLD this is a vertical arrow from the failing point down into the safe zone below the curve.
2. Move the operating point to the right — get off the plane-strain trough. Deliberately introduce some positive minor strain by relieving restraint in one direction only: open the beads along the two ends while keeping them along the sides, or re-cut the blank outline so the sheet can feed on one axis. The path shifts toward balanced biaxial stretching, where the FLC rises, so the same major strain is now safely under the curve. On the FLD this is a horizontal arrow away from the FLC₀ minimum.

A third arrow is available in principle — raising the curve itself with a thicker gauge or a higher-$n$ grade — and it is drawn upward as a shift of the whole FLC. It changes the material rather than the tooling, so it properly belongs to part (d).

(d) If the process window cannot be opened, change the material, the blank, or the sequence. In roughly increasing order of cost and disruption: switch to a more formable grade with higher $n$ and $\bar r$ (a DDQ/EDDQ or bake-hardenable steel in place of a plain commercial-quality one), which lifts the FLC bodily; increase the sheet thickness, which raises FLC₀ nearly in proportion; use a tailor-welded or tailor-rolled blank so that only the severely stretched region carries the thicker or more formable material; split the operation into a preform plus a restrike so the strain accumulates along a gentler path with an intermediate anneal if necessary; or change the process to one that supports the sheet hydrostatically — hydroforming, rubber-pad forming, or warm forming for aluminium and magnesium, where a modest temperature rise buys a large gain in the strain-rate sensitivity $m$ and hence in post-uniform elongation. Only if all of these fail is a shape change justified, and then the cheapest form of it is usually a shallow rib or emboss that redistributes strain without altering the visible surface.