14.6 Sheet Metal Forming: Shearing, Bending & Deep Drawing

Shearing Operations

Shearing separates sheet metal by subjecting it to shear stress between a punch and a die until fracture propagates.

Blanking versus piercing

This distinction generates more objective items than any other point in the topic.

The reasoning behind the clearance rule follows from where the fracture surface forms. In blanking, the blank must match the die opening, so the die is made to size and the punch is made smaller by the clearance. In piercing, the hole must match the punch, so the punch is made to size and the die opening is made larger.

Other shearing operations

Cut edge quality

A sheared edge has four distinct zones from top to bottom: rollover, a smooth burnished band, a rough fracture zone, and a burr on the exit side. Correct clearance makes the fracture lines from punch and die meet cleanly. Too little clearance produces secondary shear and a ragged double burnish; too much produces excessive rollover and a large burr.

Clearance and force

Clearance per side is typically

$c = 0.0032\,t\sqrt{\tau}$

with $t$ in mm and $\tau$ the shear strength in MPa, or as a practical rule 2 to 10% of thickness per side.

The cutting force is

$F = L\,t\,\tau$

where $L$ is the total length of the cut perimeter. For a circular blank of diameter $d$, $L = \pi d$.

Worked example. Blanking a 50 mm disc from 2 mm sheet with shear strength 300 MPa:

$F = \pi(50)(2)(300) = 94{,}248 \text{ N} \approx 94 \text{ kN}$

Reducing the force

Press capacity is often the constraint, and two techniques reduce peak force:

• Shear on the punch or die — grinding an angle so the cut is progressive rather than simultaneous. This reduces peak force but not the total work done.
• Stepped punches in a multi-hole tool, so that the punches enter at different times.

Bending

Bend allowance

The length of the neutral axis through the bend determines the developed blank length:

$L_b = \theta\left(R + k\,t\right)$

with $\theta$ in radians, $R$ the inside bend radius and $k$ the location of the neutral axis, taken as 0.33 for $R < 2t$ and 0.5 for $R \geq 2t$. The neutral axis shifts towards the inside surface for sharp bends because the compressed inner fibres are constrained.

Bending force

For V-bending in a die of opening $W$:

$F = \frac{k_{bf}\,\sigma_{ut}\,w\,t^2}{W}$

with $k_{bf}$ about 1.33 for V-bending and 0.33 for edge (wiping) bending.

Spring-back

The outer fibres of a bend are in tension and the inner in compression, and both recover elastically when the load is released, so the bend opens out. The spring-back factor is

$K_s = \frac{\theta_{\text{final}}}{\theta_{\text{die}}}$

Spring-back is greater for higher yield strength, larger bend radius relative to thickness, and lower elastic modulus. Compensation methods:

1. Over-bending past the required angle by the anticipated recovery.
2. Bottoming, where the punch compresses the bend zone at the end of the stroke.
3. Coining, applying very high localised pressure to yield the material through the full thickness.
4. Stretch forming, applying tension so the whole section yields.

Minimum bend radius

Bending is limited by cracking of the outer fibres. The minimum radius, expressed as a multiple of thickness, correlates with the material's tensile reduction in area $r$:

$\frac{R_{\min}}{t} = \frac{50}{r} - 1$

A material with 50% reduction in area can be bent to a radius equal to its thickness. Bending across the rolling direction is easier than along it, because the elongated grain structure makes the sheet anisotropic.

Deep Drawing

Deep drawing converts a flat blank into a cup or box. It is not a stretching operation — the material flows inward from the flange to form the wall, which is why the flange must be free to draw in.

The forces at work

The circumferential compression in the flange is what causes wrinkling, the characteristic deep-drawing failure. A blank holder suppresses it by clamping the flange. The blank holder force must be carefully set: too little and the flange wrinkles, too much and the flange cannot draw in, so the wall tears at the punch radius.

Limiting drawing ratio

The drawing ratio is

$DR = \frac{D_{\text{blank}}}{D_{\text{punch}}}$

The wall must transmit the entire drawing force, so it fails once that force exceeds the wall's strength. This sets the limiting drawing ratio, theoretically $e = 2.72$ for a frictionless ideal, and practically about 2.0 for a single draw. Deeper cups require redrawing through successive smaller dies, with annealing between stages if cold work accumulates.

The percentage reduction is

$\text{Reduction} = \frac{D_b - D_p}{D_b}\times100$

typically limited to about 50% on the first draw, 30% on the second and 16% on the third.

Drawing force

$F = \pi\,D_p\,t\,\sigma_{ut}\left(\frac{D_b}{D_p} - 0.7\right)$

The blank holder force is typically about 30 to 40% of the drawing force.

Blank size

For a cylindrical cup of diameter $d$ and height $h$, equating surface areas gives

$D_b = \sqrt{d^2 + 4dh}$

and with a corner radius $r$ the expression is adjusted accordingly.

Anisotropy and earing

Rolled sheet has directional properties. The normal anisotropy ratio $\bar{r}$ compares width strain to thickness strain; a high $\bar r$ means the sheet resists thinning and draws well, so it raises the limiting drawing ratio. Planar anisotropy causes earing — wavy peaks and troughs around the rim of the drawn cup — which must be trimmed off as scrap. Steel developed specifically for drawing, such as interstitial-free grades, is processed to maximise $\bar r$ and minimise planar variation.

Defects Summary

Presses and Tooling

Mechanical presses deliver their rated force only near the bottom of the stroke, which suits shearing where the work is done in a short distance. Deep drawing needs force throughout a long stroke, which is why hydraulic presses dominate that application.