PLASTIC WORKING OF METALS
STRUCTURE
Yieldable structural forces between the particles composing a material to
be worked are the key to its behavior. Simple internal structures contain
only a single element, as pure copper, silver, or iron. Relatively more
difficult to work are the solid solutions in which one element tends to
distribute uniformly in the structural pattern of another. Thus silver and
gold form a continuous series of solid-solution alloys as their proportions
vary. Next are alloys in which strongly bonded molecular groups
dispersed through or along the grain boundaries of softer metals offer
increasing resistance to working, as does iron carbide (Fe3C) in solution
in iron.
Bonding forces are supplied by electric fields characteristic of individual
atoms. These forces in turn are subject to modification by temperature
as energy is added, increasing electron activity.
The particles which constitute an atom are so small that most of its
volume is empty space. For a similar energy state, there is some rough
uniformity in the outside size of atoms. In general, therefore, the more
complex elements have their larger number of particles more densely
packed and so are heavier. For each element, the energy pattern of its
electric charges in motion determines the field characteristics of that
atom and which of the orderly arrangements it will seek to assume with
relation to others like it in the orderly crystalline form.
Space lattice is the term used to describe the orderly arrangement of
rows and layers of atoms in the crystalline form. This orderly state is
also described as balanced, unstrained, or annealed. The working or
deforming of materials distorts the orderly arrangement, unbalancing
the forces between atoms. Cubic patterns or space lattices characterize
the more ductile or workable materials. Hexagonal and more complex
patterns tend to be more brittle or more rigid. Flaws, irregularities, or
distortions, with corresponding unbalanced strains among adjacent
atoms, may occur in the pattern or along grain boundaries. Slip-plane
movements in working to new shapes tend to slide the once orderly
layers of atoms within the grain-boundary limitations of individual
crystals. Such sliding movement tends to take place at 45° to the direction
of the applied load because much higher stresses are required to
pull atoms directly apart or to push them straight together.
Chemical combinations, in liquid or solid solutions, or molecular compounds
depend upon relative field patterns of elements or upon actual
displacement of one or more electrons from the outer orbit of a donor
element to the outer orbit of a receptor element. Thus the molecules of
hard iron carbide, Fe3C, may be held in solid solution in soft pure iron
(ferrite) in increasing proportions up to 0.83 percent of carbon in iron,
which is described as pearlite. Zinc may occupy solid-solution positions
in the copper space lattice up to about 45 percent, the range of the
ductile red and yellow brasses.
Thermal Changes Adding heat (energy) increases electron activity and therefore also the mobility of the atom. Probability of brittle failure
at low temperatures usually becomes less as temperature increases.
Transition temperatures from one state to another differ for different
elements. Thermal transitions therefore become more complex as such
differing elements are combined in alloys and compounds. As temperatures
rise, a stress-relieving range is reached at which the most severely
strained atoms are able to ease themselves around into less strained
positions. At somewhat higher temperatures, annealing or recrystallization
of worked or distorted structure takes place. Old grain boundaries
disappear and small new grains begin to grow, aligning nearby atoms
into their orderly lattice pattern. The more severely the material has
been worked, the lower is the temperature at which recrystallization
begins. Grain growth is more rapid at higher temperatures. In working
materials above their recrystallization range, as in forging, the relief of
interatomic strains becomes more nearly spontaneous as the temperature
is increased. Creep takes place when materials are under some
stress above the recrystallization range, and the thermal mobility permits
individual atoms to ease around to relieve that stress with an accompanying
gradual change of shape. Thus a wax candle droops due to
gravity on a hot day. Lead, which recrystallizes below room temperature,
will creep when used for roofing or spouting. Steels in rockets and
jet engines begin to creep around 1,300 to 1,500°F (704 to 815°C).
Creep is more rapid as the temperature rises farther above the recrystallization
range.
PLASTICITY
Plasticity is that property of materials which commends them to the
mass-production techniques of pressure-forming desired shapes. It is
understood more easily if several types of plasticity are considered.
Crystoplastic describes materials, notably metals, which can be
worked in the stable crystalling state, below the recrystallization range.
Metals which crystallize in the cubic patterns have a wider plastic range
than those of hexagonal pattern. Alloying narrows the range and increases
the resistance to working. Tensile or compressive testing of an
annealed specimen can be used to show the plastic range which lies
between the initial yield point and the point of ultimate tensile or compressive
failure.
The plastic range, as of an annealed metal, is illustrated in Fig. 13.2.1.
Changing values of true stress are determined by dividing the applied
load at any instant by the cross-section area at that instant. As material is
worked, a progressive increase in elastic limit and yield point registers
the slip-plane movement or work hardening which has taken place and
the consequent reduction in residual plasticity. This changing yield
point or resistance, shown in Fig. 13.2.1, is divided roughly into three
characteristic ranges. The contour of the lower range can be varied by
nonuniformity of grain sizes or by small displacements resulting from
prior direction of working. Random large, soft grains yield locally under
slight displacement, with resulting surface markings, described as orange
peel, alligator skin, or stretcher strain markings. These can be
Fig. 13.2.1 Three ranges of crystoplastic work hardening of a low-carbon steel.
(ASME, 1954, W. S. Wagner, E. W. Bliss Co.)
prevented by preparatory roller leveling, which gives protection in the
case of steel for perhaps a day, or by a 3 to 5 percent temper pass of
cold-rolling, which may stress relieve in perhaps 3 months, permitting
recurrent trouble. The middle range covers most drawing and forming
operations. Its upper limit is the point of normal tensile failure. The
upper range requires that metal be worked primarily in compression to
inhibit the start of tensile fracture. Severe extrusion, spring-temper rolling,
and music-wire drawing use this range.
Dispersion hardening of metal alloys by heat treatment (see Fig.
13.2.2) reduces the plastic range and increases the resistance to work
hardening. Figure 13.2.2 also shows the common methods of plotting
change of true stress against percentage of reduction—e.g., reduction of
thickness in rolling or compressive working, of area in wire drawing,
ironing, or tensile testing, or of diameter in cup drawing or reducing
operations—and against true strain, which is the natural logarithm of
change of area, for convenience in higher mathematics.
Fig. 13.2.2 High-range plasticity (dotted) of an SAE 4140 steel, showing the
effect of dispersion hardening. Two plotting methods. (ASME, 1958, Crane and
Wagner, E. W. Bliss Co.)
For metals, thermoplastic working is usually described as hot working,
except for tin and lead, which recrystallize below room temperature.
Hot-worked samples may be etched to show flow lines, which are usually
made up of old-grain boundaries. Where these show, recrystallization
has not yet taken place, and some work hardening is retained to improve
physical properties. Zinc and magnesium, which are typical of the hexagonal-
structure metals, take only small amounts of cold working but
can be drawn or otherwise worked severely at rather moderate temperatures
[Zn, 200 to 400°F (90 to 200°C); Mg, 500 to 700°F (260 to
400°C)]. Note that, although hexagonal-pattern metals are less easily
worked than cubic-pattern metals, they are for that same reason structurally
more rigid for a similar relative weight. Advantageous forging
temperatures change with alloy composition: copper, 1,800 to 1,900°F
(980 to 1,040°C); red brass, Cu 70, Zn 30, 1,600 to 1,700°F (870 to
930°C); yellow brass, Cu 60, Zn 40, 1,200 to 1,500°F (650 to 815°C).
See Sec. 6 for general physical properties of metals.
Substantially pure iron shows an increasing elastic limit and decreasing
plasticity with increasing amounts of work hardening by cold-rolling.
The rate at which such work hardening takes place is greatly increased,
and the remaining plasticity reduced, as alloying becomes more
complex.
In steels, the mechanical working range is conventionally divided into
cold, warm, and hot working. Figure 13.2.3 is a plot of flow stress, limit
strain, scale factor, and dimensional error for different values of forging temperature and for two different strain rates. The flow stress is the
resistance to deformation. As the temperature rises from room temperature
to 2,072°F (1,100°C), the flow stress decreases first gradually and
then rapidly to about 25 percent of its value [cold working 114 ksi (786
MPa) and hot working 28 ksi (193 MPa) at a strain of 0.5 and strain rate
of 40 per second].
One measure of workability is the strain limit. As the temperature
rises, the strain limit for the 70-in (in ? s) strain rate (typical of mechanical
press forging) decreases slightly up to 500°C (932°F), rises until
750°C (1,382°F), drops rapidly at 800°C (1,472°F) (often called blue
brittleness), and beyond 850°C (1,562°F) increases rapidly to hot forging
temperature of 1,100°C (2,012°F). Therefore, substantial advantages
of low material resistance (low tool pressures and press loads) and
excellent workability (large flow without material failure) can be realized
in the hot-working range. Hot-working temperatures, however,
also mean poor dimensional tolerance (total dimensional error), poor
surface finish, and material loss due to scale buildup. Forging temperatures
above 1,300°C (2,372°F) can lead to hot shortness manifested by
melting at the grain boundaries.
PLASTIC-WORKING TECHNIQUES
In the metalworking operations, as distinguished from metal cutting,
material is forced to move into new shapes by plastic flow. Hot-working
is carried on above the recovery temperature, and spontaneous recovery,
or annealing, occurs about as fast as the properties of the material are
altered by the deformation. This process is limited by the chilling of the
material in the tools, scaling of the material, and the life of the tools at
the required temperatures. Cold-working is carried on at room temperature
and may be applied to most of the common metals. Since, in most
cases, no recovery occurs at this temperature, the properties of the metal
are altered in the direction of increasing strength and brittleness
throughout the working process, and there is consequently a limit to
which cold-working may be carried without danger of fracture.
A convenient way of representing the action of the common metals
when cold-worked consists of plotting the actual stress in the material
against the percentage reduction in thickness. Within the accuracy required
for shop use, the relationship is linear, as in Fig. 13.2.4. The
lower limit of stress shown is the yield point at the softest temper, or
anneal, commercially available, and the upper limit is the limit of tensile
action, or the stress at which fracture, rather than flow, occurs. This
latter value does not correspond to the commercially quoted ‘‘tensile
strength’’ of the metal, but rather to the ‘‘true tensile strength,’’ which is
the stress that exists at the reduced section of a tensile specimen at
fracture and which is higher than the nominal value in inverse proportion
to the reduction of area of the material.
Fig. 13.2.4 Plastic range chart of commonly worked metals.
As an example of the construction and use of the cold-working plots
shown in Fig. 13.2.4, the action of a very-low-carbon deep-drawing
steel has been shown in Fig. 13.2.5. Starting with the annealed material
with a yield point of 35,000 lb/in2 (240 MN/m2), the steel was drawn to
successive reductions of thickness up to about 58 percent, and the
corresponding stresses plotted as the heavy straight line. The entire
graph was then extrapolated to 100 percent reduction, giving the modu- lus of strain hardening as indicated, and to zero stress so that all materials
might be plotted on the same graph. Lines of equal reduction are slanting
lines through the point marking the modulus of strain hardening at
theoretical 100 percent reduction. Starting at any initial condition of
previous cold work on the heavy line, a percentage reduction from this
condition will be indicated by a horizontal traverse to the slanting reduction
line of corresponding magnitude and the resulting increase in
stress by the vertical traverse from this point to the heavy line.
Fig. 13.2.5 Graphical solution of a metalworking problem.
The traverse shown involved three draws from the annealed condition
of 30, 25, and 15 percent each, and resulting stresses of 53,000, 63,000,
and 68,000 lb/in2 (365, 434, and 469 MN/m2). After the initial 30 percent
reduction, the next 25 percent uses (1.00 2 0.30) 3 0.25, or 17.5
percent more of the cold-working range; the next 15 percent reduction
uses (1.00 2 0.30 2 0.175) 3 0.15, or about 8 percent of the original
range, totaling 30 1 17.5 1 8 5 55.5 percent. This may be compared
with the test value percent reduction in area for the particular material.
The same result might have been obtained, die operation permitting, by
a single reduction of 55 percent, as shown. Any appreciable reduction
beyond this point would come dangerously close to the limit of plastic
flow, and consequently an anneal is called for before any further work is
done on the piece.
Figure 13.2.6 shows the approximate true stress vs. true strain plot of
common plastic range values, for comparison with Fig. 13.2.4. In metal
forming, a convenient way of representing the resistance of metal to
deformation and flow is the flow stress s, also known as the logarithmic
stress or true stress. For most metals, flow stress is a function of the
amount of deformation at cold-working temperatures (strain «) and the
deformation rate at hot-working temperatures (strain rate ~«). This relationship
is often given as a power-law curve; s 5 K«n for cold forming
and s 5 C~«m for hot forming. For commonly used materials, the values
of the strength coefficients K and C and hardening coefficients n and m
are given in Tables 13.2.1a and b.
A practical manufacturing method of judging relative plasticity is to
compute the ratio of initial yield point to the ultimate tensile strength as
developed in the tensile test. Thus a General Motors research memo
listed steel with a 0.51 yield/tensile ratio [22,000 lb/in2 (152 MN/m2)
yp/43,000 lb/in2 (296 MN/m2) ultimate tensile strength] as being suitable
for really severe draws of exposed parts. When the ratio reaches
about 0.75, the steel should be used only for flat parts or possibly those
with a bend of not more than 90°. The higher ratios obviously represent
a narrowing range of workability or residual plasticity.
ROLLING OPERATIONS
Rolling of sheets, coils, bars, and shapes is a primary process using
plastic ranges both above and below recrystallization to prepare metals
for further working or for fabrication. Metal squeezed in the bit area of the rolls moves out lengthwise with very little spreading in width. This
compressive working above the yield point of the metal may be aided in
some cases by maintaining a substantial tensile strain in the direction of
rolling.
A cast or forged billet or slab is preheated for the preliminary breakdown
stage of rolling, although considerable progress has been made in
continuous casting, in which the molten metal is poured continuously
into a mold in which the metal is cooled progressively until it solidifies
(albeit still at high temperature), whence it is drawn off as a quasi-continuous
billet and fed directly into the first roll pass of the rolling mill.
The increased speed of operation and production and the increased efficiency
of energy consumption are obvious. Most new mills, especially
minimills, have incorporated continuous casting as the normal method
of operation. A reversing hot mill may achieve 5,000 percent elongation
of an original billet in a series of manual or automatic passes. Alternatively,
the billet may pass progressively through, say, 10 hot mills in
rapid succession. Such a production setup requires precise control so
that each mill stand will run enough faster than the previous one to make
up for the elongation of the metal that has taken place. Hot-rolled steel
may be sold for many purposes with the black mill scale on it. Alternatively,
it may be acid-pickled to remove the scale and treated with oil or
lime for corrosion protection. To prevent scale from forming in hot-rolling,
a nonoxidizing atmosphere may be maintained in the mill area, a
highly special plant design.
Pack rolling of a number of sheets stacked together provides means of
retaining enough heat to hot-roll thin sheets, as for high-silicon electric
steels.
Cold-rolling is practical in production of thin coil stock with the more
ductile metals. The number of passes or amount of reduction between
anneals is determined by the rate of work hardening of the metal. Successive
stands of cold-rolling help to retain heat generated in working.
Tension provided by mill reels and between stands helps to increase the
practical reduction per step. Bright annealing in a controlled atmosphere
avoids surface pockmarks, which are difficult to get out. For high-finish
stock, the rolls must be maintained with equal finish.
Protective coating is best exemplified by high-speed tinplate mills in
which coil stock passes continuously through the necessary series of
cleaning, plating, and heating steps. Zinc and other metals are also
applied by plating but not on the same scale. Clad sheets (high-strength
aluminum alloys with pure aluminum surface for protection against
electrolytic oxidation) are produced by rolling together; e.g., an alloyaluminum
billet is hot-rolled together with plates of pure aluminum
above and below it through a series of reducing passes, with precautions
to ensure clean adhesion.
On the other hand, prevention of adhesion, as by a separating film, is
essential in the final stages of foil rolling, where two coils may have to be
rolled together. Such foil may then be laminated with suitable adhesive
to paper backing materials for wrapping purposes. (See also Sec. 6.)
Shape-rolling of structural shapes and rails is usually a hot operation
with roll-pass contours designed to distribute the displacement of metal
in a series of steps dictated largely by experience. Contour rolling of
relatively thin stock into tubular, channel, interlocking, or varied special
cross sections is usually done cold in a series of roll stands for lengthwise
bending and setting operations. There is also a wide range of
simple bead-rolling, flange-rolling, and seam-rolling operations in relatively
thin materials, especially in connection with the production of
barrels, drums, and other containers.
Oscillating or segmental rolling probably developed first in the manually
fed contour rolling of agricultural implements. In some cases, the
suitably contoured pair of roll inserts or roll dies oscillates before the
operator, to form hot or cold metal. In other cases, the rolls rotate
constantly, toward the operator. The working contour takes only a portion
of the circumference, so that a substantial clearance angle leaves a
space between the rolls. This permits the operator to insert the blank to
the tong grip between the rolls and against a fixed gage at the back.
Then, as rotation continues, the roll dies grip and form the blank, moving
it back to the operator. This process is sometimes automated; such
units as tube-reducing mills oscillate an entire rolling-mill assembly and
feed the work over a mandrel and into the contoured rolls, advancing it
and possibly turning it between reciprocating strokes of the roll stands
for cold reduction, improved concentricity, and, if desired, the tapering
or forming of special sections.
Spinning operations (Fig. 13.2.7) apply a rolling-point pressure to
relatively limited-lot production of cup, cone, and disk shapes, from
floor lamps and TV tube housings to car wheels and large tank ends.
Where substantial metal thickness is required, powerful machines and
hydraulic servo controls may be used. Some of the large, heavy sections
and difficult metals are spun hot.
Fig. 13.2.7 Spinning operations.
Rolling operations are distinguished by the relatively rapid and continuous
application of working pressure along a limited line of contact.
In determining the working area, consider the lineal dimension (width
of coil), the bit or reduction in thickness, and the roll-face deflection,
which tends to increase the contact area. Approximations of rolling-mill
load and power requirements have been worked out in literature of the
AISE and ASME.
SHEARING
The shearing group of operations includes such power press operations as
blanking, piercing, perforating, shaving, broaching, trimming, slitting,
and parting. Shearing operations traverse the entire plastic range of
metals to the point of failure.
The maximum pressure P, in pounds, required in shearing operations
is given by the equation P5pDtS5Lts, where s is the resistance of the
material to shearing, lb/in2; t is the thickness of the material, in; L is
the length of cut, in, which is the circumference of a round blank pD or
the periphery of a rectangular or irregular blank. Approximate values of
s are given in Table 13.2.2.
Shear (Fig. 13.2.8) is the advance of that portion of the shearing edge
which first comes in contact with the material to be sheared over the last
portion to establish contact, measured in the direction of motion. It
should be a function of the thickness t. Shear reduces the maximum
pressure because, instead of shearing the whole length of cut at once, the
shearing action takes place progressively, shearing on only a portion of
the length at any instant. The maximum pressure for any case where the
shear is equal to or greater than t is given by Pmax 5 Pav t /shear, where
Pav is the average value of the pressure on a punch, with shear 5 t, from
the time it strikes the metal to the time it leaves.
Distortion results from shearing at an angle (Fig. 13.2.8) and accordingly,
in blanking, where the blank should be flat, the punch should be
flat, and the shear should be on the die. Conversely, in hole punching,
where the scrap is punched out, the die should be flat and the shear should be on the punch. Where there are a number of punches, the effect
of shear may be obtained by stepping the punches.
Crowding results during the plastic deformation period, before the
fracture occurs, in any shearing operation. Accordingly, when small
delicate punches are close to a large punch, they should be stepped
shorter than the large punch by at least a third of the metal thickness.
􀀀􀀀􀀀
L
(a)
5 shearing angle
t 5 h 5 thickness of sheet
L 5 shearing length
(b)
h
a
a
􀀀􀀀􀀀
(c)
Fig. 13.2.8 Shearing forces can be reduced by providing a rake or shear on
(a) the blades in a guillotine, (b) the die in blanking, (c) the punch in piercing.
(J. Schey, ‘‘Introduction to Manufacturing Processes,’’ McGraw-Hill, 1987.)
Clearance between the punch and die is required for a clean cut and
durability. An old rule of thumb places the clearance all around the
punch at 8 to 10 percent of the metal thickness for soft metal and up to
12 percent for hard metal. Actually, hard metal requires less clearance
for a clean fracture than soft, but it will stand more. In some cases, with
delicate punches, clearance is as high as 25 percent. Where the hole
diameter is important, the punch should be the desired diameter and the
clearance should be added to the die diameter. Conversely, where the
blank size is important, the die and blank dimensions are the same and
clearance is deducted from the punch dimensions.
The work per stroke may be approximated as the product of the maximum
pressure and the metal thickness, although it is only about 20 to 80
percent of that product, depending upon the clearance and ductility of
the metal. Reducing the clearance causes secondary fractures and increases
the work done. With sufficient clearance for a clean fracture, the
work is a little less than the product of the maximum pressure, the metal
thickness, and the percentage reduction in thickness at which the fracture
occurs. Approximate values for this are given in Table 13.2.2. The
power required may be obtained from the work per stroke plus a 10 to 20
percent friction allowance.
Shaving A sheared edge may be squared up roughly by shaving
once, allowing for the shaving of mild sheet steel about 10 percent of the
metal thickness. This allowance may be increased somewhat for thinner
material and should be decreased for thicker and softer material. In
making several cuts, the amount removed is reduced each time. For
extremely fine finish a round-edged burnishing die or punch, say 0.001
or 0.0015 in tight, may be used. Aluminum parts may be blanked (as for
impact extrusion) with a fine finish by putting a 30° bevel, approx
one-third the metal thickness on the die opening, with a near metal-tometal
fit on the punch and die, and pushing the blank through the highly
polished die.
Squaring shears for sheet or plate may have their blades arranged in
either of the ways shown in Fig. 13.2.9. The square-edged blades in Fig.
13.2.9a may be reversed to give four cutting edges before they are
reground. Single-edged blades, as shown in Fig. 13.2.9b, may have a
clearance angle on the side where the blades pass, to reduce the working
friction. They may also be ground at an angle or rake, on the face which
comes in contact with the metal. This reduces the bending and conse- quent distortion at the edge. Either type of blade distorts also in the other
direction owing to the angle of shear on the length of the blades (see Fig.
13.2.8). Cutting speed is 3 to 30 ft /min (1 to 10 m/min), depending in
part upon the thickness of the material.
Circular cutters for slitters and circle shears may also be square-edged
(on most slitters) or knife-edged (on circle shears). According to one
rule, their diameter should be not less than 70 times the metal thickness.
Cutting speeds vary from 50 to 200 ft/min (17 to 65 m/min), depending
largely upon metal thickness (inverse proportion).
Knife-edge hollow cutters working against end-grain maple blocks represent
an old practice in cutting leather, rubber, and cloth in multiple
thicknesses. Steel-rule dies, made up of knife-edge hard-steel strip economically
mounted against a steel plate in a wood matrix with rubber
strippers and cutting against hard saw-steel plates, extend the practice to
corrugated-carton production and even some limited-lot metal cutting.
Higher precision is often required in finish shearing operations on
sheet material. For ease of subsequent operations and assembly, the cut
edges should be clean (acceptable burr heights and good surface finish)
and perpendicular to the sheet surface. The processes include precision
or fine blanking, negative clearance blanking, counterblanking, and
shaving, as shown in Fig. 13.2.10. By these methods either the plastic
behavior of material is suppressed, or the plastically deformed material
is removed.
Ps Ps Ps
Pcounter
(a)
Pcounter Pcounter
35° 45°
Before During
(b) (c)
Step 2
Step 1
(d)
Fig. 13.2.10 Parts with finished edges can be produced by (a) precision blanking,
(b) negative-clearance blanking, (c) counterblanking, (d ) shaving a previously
sheared part. (J. Schey, ‘‘Introduction to Manufacturing Processes,’’
McGraw-Hill, 1987.)
BENDING
The bending group of operations is performed in presses (variety),
brakes (metal furniture, cornices, roofing), bulldozers (heavy rolled sections),
multiple-roll forming machines (molding, etc.), draw benches (door
trim, molding, etc.), forming rolls (cylinders), and roll straighteners
(strips, sheets, plates).
Spring back, due to the elasticity of the metal and amount of the bend,
may be compensated for by overbending or largely prevented by striking
the metal at the radius with a coining (i.e., squeezing, as in production
of coins) pressure sufficient to set up compressive stresses to counterbalance
surface tensile stresses. A very narrow bead may be used to
localize the pinch where needed and minimize danger to the press in
squeezing on a large area. Under such conditions, good sharp bends in V
dies have been obtained with two to four times the pressure required to
shear the metal across the same section.
These are illustrated in Fig. 13.2.11, where Pb is the bending load on
the press brake, Wb is the width of the die support, and Pcounter is the
counterload. The bending load can be obtained from
Pb 5 wt2(UTS)/Wb
where t and w are the sheet thickness and width, respectively, and UTS
is the ultimate tensile strength of the sheet material.
Bending Allowance The thickness of the metal over a small radius
or a sharp corner is 10 or 15 percent less than before bending because
the metal moves more easily in tension than in compression. For the
same reason the neutral axis of the metal moves in toward the center of
the corner radius. Therefore, in figuring the length of blank L to be
allowed for the bend up to an inside radius r of two or three times the
Pb
Wb
Pb
Pcounter
Pb Pb
, 90° , 90° 90° 90°
(a) (b) (c) (d)
Fig. 13.2.11 Springback may be neutralized or eliminated by (a), (b) overbending;
(c) plastic deformation at the end of the stroke; (d ) subjecting the bend
zone to compression during bending. [Part (d ) after V. Kupka, T. Nakagawa, and
H. Tyamoto, CIRP 22:73–74 (1973).] (Source: J. Schey, ‘‘Introduction to Manufacturing
Processes,’’ McGraw-Hill, 1987.)
metal thickness t, the length may be figured closely as along a neutral
line at 0.4t out from the inside radius. Thus, with reference to Fig.
13.2.12, for any angle a in deg and other dimensions in inches, L 5
(r 1 0.4t)2pa/360 5 (r 1 0.4t)a/57.3.
The factor 0.4t, which locates the neutral axis, is subject to some
variation (say 0.35 to 0.45t) according to radius, condition of metal, and
angle. In figuring allowances for sharp bends, note that the metal builds
up on the compression side of the corner. Therefore, in locating the
neutral axis, consider an inside radius r of about 0.05t as a minimum.
Roll straighteners work on the principle of bending the metal beyond
its elastic limit in one direction over rolls small enough in diameter, in
proportion to the metal thickness, to give a permanent set, and then
taking that bend out by repeatedly reversing
it in direction and reducing it in
amount. Metal is also straightened by gripping
and stretching it beyond its elastic
limit and by hammering; the results of the
latter operation depend entirely upon the
skill of the operator.
For approximating bending loads, the
beam formula may be used but must be
very materially increased because of the
Fig. 13.2.12 Bending allowance.
short spans. Thus, for a span of about 4 times the depth of section, the
bending load is about 50 percent more than that indicated by the beam
formula. It increases from this to nearly the shearing resistance of the
section where some ironing (i.e., the thinning of the metal when clearance
between punch and die is less than the metal thickness) occurs.
Where hit-home dies do a little coining to ‘‘set’’ the bend, the pressure
may range from two or three times the shearing resistance, with striking
beads and proper care, up to very much higher figures.
The work to roll-bend a sheet or plate t in thick with a volume of V
in3, into curved shape of radius r in, is given as W 5 CS(t /r)V/48 ft ? lb,
in which S is the tensile strength and C is an experience factor between
1.4 and 2.
The equipment for bending consists of mechanical presses for short
bends, press brakes (mechanical and hydraulic) for long bends, and roll
formers for continuous production of profiles. The bends are achieved
by bending between tools, wiping motion around a die corner, or bending
between a set of rolls. These bending actions are illustrated in Fig.
13.2.13. Complex shapes are formed by repeated bending in simple
tooling or by passing the sheet through a series of rolls which progressively
bend it into the desired profile. Roll forming is economical for
continuous forming for large production volume. Press brakes can be
computer-controlled with synchronized feeding and bending as well as
spring-back compression.
DRAWING
Drawing includes operations in which metal is pulled or drawn, in suitable
containing tools, from flat sheets or blanks into cylindrical cups or
rectangular or irregular shapes, deep or shallow. It also includes reduc- ing operations on shells, tube, wire, etc., in which the metal being drawn
is pulled through dies to reduce the diameter or size of the shape. All
drawing and reducing operations, by an applied tensile stress in the
material, set up circumferential compressive stresses which crowd the
metal into the desired shape. The relation of the shape or diameter
before drawing to the shape or diameter after drawing determines the
magnitude of the stresses. Excessive draws or reductions cause thinning
or tearing out near the bottom of a shell. Severe cold-drawing operations
require very ductile material and, in consequence of the amount of
plastic deformation, harden the metal rapidly and necessitate annealing
to restore the ductility for further working.
The pressure used in drawing is limited to the load to shear the bottom
of the shell out, except in cases where the side wall is ironed thinner,
when wall friction makes somewhat higher loads possible. It is less than
this limit for round shells which are shorter than the limiting height and
also for rectangular shells. Drawing occurs only around the corner radii
of rectangular shells, the straight sides being merely free bending.
A holding pressure is required in most initial drawing and some redrawing,
to prevent the formation of wrinkles due to the circumferential
compressive stresses. Where the blank is relatively thin compared with
its diameter, the blank-holding pressure for round work is likely to vary
up to about one-third of the drawing pressure. For material heavy
enough to provide sufficient internal resistance to wrinkling, no pressure
is required. Where a drawn shape is very shallow, the metal must
be stretched beyond its elastic limit in order to hold its shape, making it
necessary to use higher blank-holding loads, often in excess of the
drawing pressure. To grip the edges sufficiently to do this, it is often
advisable to use draw beads on the blank-holding surfaces if sufficient
pressure is available to form these beads.
In sheet/deep-drawing practice, the punch force P can be approximated
by
P 5 pDp t0(UTS)(D0 /Dp 2 0.7)
where t0 is the blank thickness and D0 and Dp are the diameters of the
blank and the punch.
The blank holder pressure for avoiding defects such as wrinkling of
bottom/wall tear-out is kept at 0.7 to 1.0 percent of the sum of the yield
and the UTS of the material. Punch/die clearances are chosen to be 7 to
14 percent greater than the sheet blank thickness t0 . The die corner radii
are chosen to avoid fracture at the die corner from puckering or wrinkling.
Recommended values of D0 /t0 for deep-drawn cups are 6 to 15
for cups without flange and 12 to 30 for cups with flange. These values
will be smaller for relatively thick sheets and larger for very thin blank
thickness. For deeper-drawn cups, they may be redrawn or reversedrawn,
the latter process taking advantage of strain softening on reverse
drawing. When the material has marked strain-hardening propensities,
it may be necessary to subject it to an intermediate annealing process to
restore some of its ductility and to allow progression of the draws to
proceed.
Some shells, which are very thick or very shallow compared with
their diameter, do not require a blank holder. Blank-holding pressure
may be obtained through toggle, crank, or cam mechanisms built into
the machine or by means of air cylinders, spring-pressure attachments,
or rubber bumpers under the bolster plate. The length of car springs
should be about 18 in /in (18 cm/cm) of draw to give a fairly uniform
drawing pressure and long life. The use of car springs has been largely
superseded by hydraulic and pneumatic cushions. Rubber bumpers may
be figured on a basis of about 7.5 lb/in2 (50 kN/m2) of cross-sectional area per 1 percent of compression. In practice they should never be
loaded beyond 20 percent compression, and as with springs, the greater
the length relative to the working stroke, the more uniform is the pressure.
Dimensions of Drawn Shells The smallest and deepest round shell
that can be drawn from any given blank has a diameter d of 65 to 50
percent of the blank diameter D. The height of these shells is h 5 0.35d
to 0.75d, approximately. Higher shells have occasionally been drawn
with ductile material and large punch and die radii. Greater thickness of
material relative to the diameter also favors deeper drawing.
The area of the bottom and of the side walls added together may be
considered as equal to the area of the blank for approximations. If the
punch radius is appreciable, the area of a neutral surface about 0.4t out
from the inside of the shell may be taken for approximations. Accurate
blank sizes may be obtained only by trial, as the metal tends to thicken
toward the top edge and to get thinner toward the bottom of the shell
wall in drawing.
Approximate diameters of blanks for shells are given by the expression
Öd2 1 4dh, where d is the diameter and h the height of the shell.
In redrawing to smaller diameters and greater depths the amount of
reduction is usually decreased in each step. Thus in double-action redrawing
with a blank holder, the successive reductions may be 25, 20,
16, 13, 10 percent, etc. This progression is modified by the relative
thickness and ductility of the metal. Single-action redrawing without a
blank holder necessitates smaller steps and depends upon the shape of
the dies and punches. The steps may be 19, 15, 12, 10 percent, etc.
Smaller reductions per operation seem to make possible greater total
reductions between annealings.
Rectangular shells may be drawn to a depth of 4 to 6 times their corner
radius. It is sometimes desirable, where the sheet is relatively thin, to
use draw beads at the corners of the shell or near reverse bends in
irregular shapes to hold back the metal and assist in the prevention of
wrinkles.
Work in drawing is approximately the product of the length of the
draw, and the maximum punch pressure, as the load rises quickly to
the peak, remains fairly constant, and drops off sharply at the end of the
draw unless there is stamping or wall friction. To this, add the work of
blank holding which, in the case of cam and toggle pressure, is the
product of the blank-holding pressure and the spring of the press at the
pressure (which is small). For single-action presses with spring, rubber,
or air-drawing attachments it is the product of the average blank-holding
pressure and the length of draw.
Rubber-die forming, especially of the softer metals and for limited-lot
production, uses one relatively hard member of metal, plaster, or plastic
with a hard powder filler to control contour. The mating member may
be a rubber or neoprene mattress or a hydraulically inflatable bag, confined
and at 3,000 to 7,000 lb/in2 (20 to 48 MN/m2). Babbitt, oil, and
water have also been used directly as the mobile member. A large
hydraulic press is used, often with a sliding table or tables, and even
static containers with adequate pumping systems.
Hot drawing above the recrystallization range applies single- and
double-action drawing principles. For light gages of plastics, paper, and
hexagonal-lattice metals such as magnesium, dies and punches may be
heated by gas or electricity. For thick steel plate and heat-treatable
alloys, the mass of the blank may be sufficient to hold the heat required.
Lubricants for Presswork Many jobs may be done dry, but better
results and longer life of dies are obtained by the use of a lubricant. Lard
or sperm oil is used when punching iron, steel, or copper. Petroleum
jelly is used for drawing aluminum. A soap solution is commonly used
for drawing brass, copper, or steel. One manufacturer uses 90 percent
mineral oil, 5 percent rosin, and 5 percent oleic acid for light work and
an emulsion of a mineral oil, degras, and a pigment consisting of chalk,
sulfur, or lithopone for heavy work. (See also Sec. 6.)
For heavy drawing operations and extrusion, steels may have a zinc
phosphate coating bonded on, and a zinc or sodium stearate bonded to
that, to withstand pressures over 300,000 lb/in2 (2,070 MN/m2). An anodized coating for aluminum may be used as a host for the lubricant.
It is reported that such a chemical treatment plus a lacquer or plastic
coating and a lubricant is effective for severe ironing operations.
The problem is to prevent local pressure welding from starting as
galling or pickup, with resulting scratching, by maintaining a fluid film
separation between metal surfaces. At moderate pressures, almost any
viscous liquid lubricant will do the job. Rust protection and easy removal
of the lubricant are often major factors in the choice.
Lubricants for metalworking are often classified based on their interface
friction coefficient, which depends on the workpiece material and
the lubricant being used. The interface friction coefficient m is often defined
as the ratio of the friction force to the normal force at the interface.
Typical values of m for different workpiece-lubricant pairs are included
in Table 13.2.3.
Shock-wave forming for limited lots is developing in several ways.
Explosive forming, especially for large-area drawn or formed shapes,
usually requires one metal contour-control die immersed in a large container
of fluid, or even in a lake or pond. Explosives manufacturers have
developed means of computing the charge and the distance that it
should be suspended above the blank to be formed. The space back of
the blank in the die has to be evacuated. A blank-holding ring to minimize
wrinkle formation in the flange area is bolted very tightly to the
die, with an O-ring seal to prevent leakage.
Electrohydraulic forming is similar to explosive forming except that
the shock wave is imparted electrically from a large battery of capacitors.
Magnetic forming uses the same source of power but does not require
a fluid medium. A flexible pancake coil delivers the magnetic
shock pulse.
BULK FORMING
The squeezing group of operations are those in which the metal is
worked in compression. Resultant tensile strains occur, however; in
cases where the metal is thin compared with its area and there is an
appreciable movement of the metal, there results a pyramiding of pressure
toward the center of the die which may prove serious. The metal is
incompressible (beyond about 1 percent), and consequently, to reduce
the thickness of any volume of metal in the center of the blank, its area
must be increased, which involves spreading or stretching all the metal
around it. The surrounding metal acts like shrunk bands and offers a
resistance increasing toward the center and often many times the compressive
resistance of the material.
Squeezing operations and particularly the squeezing of steel are practically
the severest of all press operations. They may be divided into
four general classifications according to severity, although in every
group there will be found examples of working to the limit of what the
die steels will stand, which may be taken at about 100 tons/in2. The
severer operations, such as cold bottom extrusion and wall extrusion,
are limited to the softer metals. Squeezing operations ordinarily require
pressure through a very short distance, the pressure starting at the compressive
yield strength of the material over the surface being squeezed
and rising to a maximum at bottom stroke. This maximum is greatest
when the metal is thin compared with its area or when the die is entirely
closed as for coining. Care must be taken, on all squeezing operations,
in the setting of presses and avoidance of double blanks or extra-heavy
blanks as the presses must be stiff. In squeezing solidly across bottom
center the mechanical advantage is such that a small difference in thickness
or setup can make a very large difference in pressure exerted. For
this reason high-speed self-contained hydraulic presses, with automatic
pressure-control and size blocks, are now finding favor for some of this
work.
Sizing, or the flattening or surfacing of parts of forgings or castings, is
usually the least severe of the squeezing group. Tolerances are ordinarily
closer than for the milling operations which are supplanted. When
extremely close tolerances are required, say plus or minus one-thousandth
of an inch (0.025 mm), arrange substantial size blocks to take
half or two-thirds of the total load. These take up uniformly the bearingoil
films and any slight deflection of the bed and bolster and minimize
the error in springback due to variation in thickness, hardness, and area
of the rough forging or casting. The usual amount left for squeezing is
1⁄32 to 1⁄16 in (0.8 to 1.6 mm). Presses may be selected for this service on
a basis of 60 to 80 tons/in2 (830 to 1,100 MN/m2), although 100 tons/in2
(1,380 MN/m2) is more often used in the automobile trade for reserve
capacities. When figuring from experimental results obtained in testing
machines, the recorded loads are usually doubled in selecting a press, in
order to allow for the difference among the speed of the machines, the
positive action, and a safety margin.
Swaging or cold forging involves squeezing of the blank to an appreciably
different shape. Success in performing such operations on steel
usually depends upon squeezing a relatively small area with freedom to
flow without restraint. Dies for this work must usually be substantially
backed up with hardened steel plates. The edge of the blank after coining
is usually ragged and must be trimmed for appearance.
Hot forging is similar in certain respects to the above but permits
much greater movement of metal. Hot forging may be done in drop
hammers, percussion presses, power presses, or forging machines,
when dies are used, or in steam hammers, helve hammers, or hydraulic
presses, on plain anvils.
The pressure exerted by hydraulic presses and steam hammer for
jobbing work should be about as follows:
Ingot diam, in* 5 8 12 16 24 36 48 60 72
Press, tons† 100 200 400 600 1,000 1,500 2,000 3,000 4,000
Hammer, tons† 1⁄2 1 3 5 10 20 40 80 120
* 1 in 5 2.54 cm.
† 1 ton 5 8.9 kN.
Drop hammers are rated according to weight of ram. For carbon steel
they may be selected on a basis of 50 to 55 lb of ram weight per square
inch of projected area (3.5 to 3.9 kg/cm2) of the forging, including as
much of the flash as is squeezed. This allowance should be increased to
60 lb/in2 (4.2 kg/cm2) for 0.20 carbon steel, 70 lb/in2 (4.9 kg/cm2) for
0.30 carbon steel, and up to about 130 lb/in2 (9.2 kg/cm2) for tungsten
steel.
In figuring the forging pressure, multiply the projected area of the
forging, including the portion of the flash that is squeezed, by approximately
one-third of the cold compressive strength of the material. Another
method gives the forging pressure at three to four times the compressive
strength of the material at forging temperatures times the
projected area, for presses; or at ten times the compressive strength at
forging temperatures times the projected area, for hammers. The pressure
builds up to a rather high figure at bottom stroke owing to the
cooling of the metal particularly in the flash and to the small amount of
relief for excess metal which the flash allows.
For brass press forgings a good mixture is about Cu, 59; Zn, 39; Pb, 2
percent forged at 1,300 to 1,400°F (700 to 760°C). The power curve in
press forging rises sharply, from the compressive strength at forging
heat times the projected area of the slug to three or more times that
quantity at bottom stroke. A large flash area assists in driving the metal
into deep die recess.
In heading operations, hot or cold, the length of wire or rod that can be
gathered into a head, without side restraint, in a single operation, is
limited to three times the diameter. In coining and then heading large
heads, cold, wire of about 0.08 carbon must be used to avoid excessive
strain-hardening.
Forging Dies Drop-forge dies are usually of steel or steel castings.
A good all-around grade of steel is a 0.60 percent carbon open-hearth.
Dies of this steel will forge mild steel, copper, and tool steel satisfactorily
if the number of forgings required is not too large. For a large number of tool-steel forgings, tool-steel dies of 0.80 to 0.90 percent
carbon may be used and for extreme conditions, 31⁄2 percent nickel steel.
Die blocks of alloy steels have special value for the production of
drop forgings in large quantities. Widely used die materials and their
recommended hardness are listed in Table 13.2.4. For a typical hotworking
steel, the relationship between the hardness and the UTS is

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