22-Mec-A4 Design and Manufacture of Machine Elements · May 2015

Question 2 of 6: Failure Modes and Tooling Geometry in Deep Drawing

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

Question 2: Failure Modes and Tooling Geometry in Deep Drawing (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.

Every deep-drawing failure is a competition between two quantities: the tensile stress that the cup wall must carry, and the strength of that wall. The wall is the weakest part of the cup because it has already been thinned and it is the only load path between the punch and the flange. Diagnosing a drawing failure therefore means asking when in the stroke the wall stress peaked relative to the wall strength, and the timing of the fracture is the diagnostic clue the question is built around.

i) (a) Fracture toward the end of the draw

Late fracture points to the material rather than the tooling. As the draw proceeds, the flange is progressively consumed and the last metal to be pulled in is the metal from the original blank periphery — the material that has travelled the furthest, undergone the largest circumferential compression, and therefore work hardened the most. Drawing that last, hardest ring of material through the die requires a higher radial pull than anything earlier in the stroke, and it is applied to a wall that has itself been thinned and hardened. If the blank material has a low strain-hardening reserve remaining, or the reduction is close to the limiting drawing ratio, the wall gives way just below the punch nose late in the stroke.

The remedies follow from the diagnosis: reduce the reduction taken in this operation by drawing a smaller blank or by splitting the job into a draw plus one or more redraws; introduce an intermediate anneal to restore ductility before the last stage; or select a material with a higher strain-hardening exponent and, more importantly, a higher normal anisotropy ratio, which raises the limiting drawing ratio directly. Reducing the blankholder force late in the stroke, where the flange area under the holder is small and the required restraint has fallen, also relieves the wall.

i) (b) Fracture earlier in the draw

Early fracture, by contrast, indicates that the wall stress was excessive from the outset, and that points at the process conditions and the tooling. The drawing force in fact peaks at roughly one third of the stroke, when the flange is still large and the resistance to drawing it in is highest; a wall that is going to fail from excessive restraint will fail there. The usual causes are an excessive blankholder force, which converts flange friction into extra wall tension; poor or absent lubrication at the blankholder and die faces; a punch or die corner radius that is too small, so the sheet is bent, straightened and locally thinned over a sharp corner; too large a drawing ratio for the material; and excessive clearance or a burred blank edge that concentrates the stress.

The remedies are correspondingly broad. Reduce the blankholder pressure to the lowest value that still suppresses wrinkling. Improve the lubricant, or apply a draw-bead-free polymer film for difficult materials. Increase the die corner radius and, separately, the punch nose radius. Open the punch-to-die clearance to roughly one to one and a tenth times the sheet thickness so that the wall is drawn rather than ironed. Reduce the blank diameter so the drawing ratio falls, and deburr or re-shear the blank edge. If the geometry is fixed, change to a material of higher ductility and higher normal anisotropy.

ii) Critique of "make the punch and die radii as large as possible"

The suggestion is right in its direction and wrong at its limit. Increasing the die corner radius from a sharp value does help: it lowers the bending and unbending work the sheet must absorb as it enters the die throat, reduces the localised thinning at that corner and lowers the peak drawing force, which allows a larger reduction. Increasing the punch nose radius likewise moves the highest tensile stress away from a sharp bend at the cup bottom.

But a radius cannot grow without limit. The blankholder can only restrain flange material that it actually contacts. As the die radius grows, the flange is lifted clear of the die face over an ever-longer arc, so an annular band of sheet near the die throat is left unsupported on both faces. That band is in circumferential compression and, being unsupported, it buckles: the part wrinkles in the wall just where the blankholder can no longer reach it. Exactly the same argument applies to the punch: too generous a nose radius reduces the area of the cup bottom that is supported by the punch face and lets the sheet stretch and thin over the nose instead of being drawn in from the flange. In addition, a very large die radius consumes blank material as it wraps the corner and shortens the effective flange, and it makes depth control and part geometry harder to hold.

The engineering conclusion is that both radii have an optimum rather than a maximum. Practice puts them in the range of about four to ten sheet thicknesses, with the smaller end used when wrinkling is the binding constraint and the larger end when fracture is.

iii) Is a blankholder always needed?

No, and the assertion should be rejected. The blankholder exists for one purpose: to prevent the flange from buckling into wrinkles under the circumferential compressive stress that develops as the flange diameter shrinks. Whether the flange buckles is a stability question, so it depends on the slenderness of the flange — that is, on how thick the sheet is compared with the unsupported radial width it must span.

Qualitatively, a blankholder can be dispensed with when the blank is thick relative to its diameter, so that the flange is stocky enough to carry the hoop compression without buckling; when the reduction is small, so that the hoop strain and therefore the compressive stress are modest; and when the die geometry itself provides support, as in a tractrix or conical die that guides the flange continuously rather than letting it span an unsupported arc. The customary shop rule of thumb captures the first two conditions together: no blankholder is needed if the difference between the blank and punch diameters is less than roughly five sheet thicknesses, which for a typical draw corresponds to a sheet thickness of more than about two percent of the blank diameter. Below that, the flange is slender, wrinkling governs, and a blankholder — or a draw ring with controlled restraint — is essential.