THE TERM FORMABILITY refers to the ease with which a metal can be shaped through plas-tic deformation. Evaluation of the formability of a metal involves measurement of strength, duc-tility, and the amount of deformation required to cause fracture. The term “workability” is used interchangeably with formability; however, formability refers to the shaping of sheet metal, while workability refers to shaping materials by bulk forming processes such as forging and ex-trusion.
Sheet metal forming operations consist of a large family of processes, ranging from simple bending to stamping and deep drawing of com-plex shapes. Because sheet forming operations are so diverse in type, extent, and rate, no single test provides an accurate indication of the form-ability of a material in all situations. However, as will be discussed in this chapter, the uniaxial tensile test is one of the most widely used tests for determining sheet metal formability. It should also be noted that tensile testing at ele-vated temperatures is also widely used to deter-mine the workability of materials. See Chapter 13, “Hot Tensile Testing,” for details.
Effect of Material
Properties on Formability
The properties of sheet metals vary consid-erably, depending on the base metal (steel, alu-minum, copper, and so on), alloying elements present, processing, heat treatment, gage, and level of cold work. In selecting material for a particular application, a compromise usually must be made between the functional properties required in the part and the forming properties of the available materials. For optimal
forma-bility in a wide range of applications, the work material should:
● Distribute strain uniformly
● Reach high strain levels without necking or fracturing
● Withstand in-plane compressive stresses without wrinkling
● Withstand in-plane shear stresses without fracturing
● Retain part shape upon removal from the die
● Retain a smooth surface and resist surface damage
Some production processes can be success-fully operated only when the forming properties of the work material are within a narrow range.
More frequently, the process can be adjusted to accommodate shifts in work material properties from one range to another, although sometimes at the cost of lower production and higher ma-terial waste. Some processes can be successfully operated using work material that has a wide range of properties. In general, consistency in the forming properties of the work material is an important factor in producing a high output of dimensionally accurate parts.
Strain Distribution
Three material properties determine the strain distribution in a forming operation:
● The strain-hardening coefficient (also known as the work-hardening coefficient or expo-nent) or n value
● The strain rate sensitivity or m value
● The plastic strain ratio (anisotropy factor) or r value
The ability to distribute strain evenly depends on the n value and the m value. The ability to
reach high overall strain levels depends on many factors, such as the base material, alloying ele-ments, temper, n value, m value, r value, thick-ness, uniformity, and freedom from defects and inclusions.
The n value, or strain-hardening coefficient, is determined by the dependence of the flow (yield) stress on the level of strain. In materials with a high n value, the flow stress increases rapidly with strain. This tends to distribute fur-ther strain to regions of lower strain and flow stress. A high n value is also an indication of good formability in a stretching operation.
In the region of uniform elongation, the n value is defined as:
d lnrT
n⳱ (Eq 1)
d lne
whererT is the true stress (load/instantaneous area). This relationship implies that the true stress-strain curve of the material can be ap-proximated by a power law constitutive equation proposed in Ref 1:
r ⳱ keT n (Eq 2)
where k is a constant known as the strength co-efficient.
Equation 2 provides a good approximation for most steels, but is not very accurate for dual-phase steels and some aluminum alloys. For these materials, two or three n values may need to be calculated for the low, intermediate, and high strain regions.
When Eq 2 is an accurate representation of material behavior, n⳱ ln (1 Ⳮ eu), where euis the uniform elongation, or elongation at maxi-mum load in a tensile test. By definition, ln (1 Ⳮ eu) is identical toeu, which is the true strain at uniform elongation.
Most steels with yield strengths below 345 MPa (50 ksi) and many aluminum alloys have n values ranging from 0.2 to 0.3. For many higher yield strength steels, n is given by the relation-ship (Ref 2):
n⯝ 70 (Eq 3)
(yield strength in MPa)
A high n value leads to a large difference be-tween yield strength and ultimate tensile strength (engineering stress at maximum load in
a tensile test). The ratio of these properties there-fore provides another measure of formability.
The m value, or strain rate sensitivity, is de-fined by:
d lnrT
m⳱ (Eq 4)
d ln ˙e
wheree˙ is the strain rate, de/dt. This implies a relationship of the form:
r ⳱ f(e) • ˙eT m
or
n m
r ⳱ ke • ˙eT (Eq 5)
where Eq 5 incorporates Eq 2 between stress and strain.
A positive strain rate sensitivity indicates that the flow stress increases with the rate of defor-mation. This has two consequences. First, higher stresses are required to form parts at higher rates.
Second, at a given forming rate, the material re-sists further deformation in regions that are be-ing strained more rapidly than adjacent regions by increasing the flow stress in these regions.
This helps to distribute the strain more uni-formly.
The need for higher stresses in a forming operation is usually not a major consideration, but the ability to distribute strains can be crucial.
This becomes particularly important in the post-uniform elongation region, where necking and high strain concentrations occur. An approxi-mately linear relationship has been reported be-tween the m value and the post-uniform elon-gation for a variety of steels and nonferrous alloys (Ref 3). As m increases fromⳮ0.01 to Ⳮ0.06, the post-uniform elongation increases from 2 to 40%.
Metals in the superplastic range have high m values of 0.2 to 0.7, which are one to two orders of magnitude higher than typical values for steel.
At ambient temperatures, some metals, such as aluminum alloys and brass, have low or slightly negative m values, which explains their low post-uniform elongation.
High n and m values lead to good formability in stretching operations, but have little effect on drawability. In a drawing operation, metal in the flange must be drawn in without causing fracture in the wall. In this case, high n and m values strengthen the wall, which is beneficial, but they
Fig. 2 Typical forming limit diagram for steel
Fig. 1 Drawn cup with ears in the directions of high r value
also strengthen the flange and make it harder to draw in, which is detrimental.
The r value, or plastic strain ratio, relates to drawability and is known as the anisotropy fac-tor. This is defined as the ratio of the true width strain to the true thickness strain in the uniform elongation region of a tensile test:
ln冢 冣ww
ew o
r⳱ ⳱ (Eq 6)
et t
ln冢 冣to
The r value is a measure of the ability of a material to resist thinning. In drawing, material in the flange is stretched in one direction (radi-ally) and compressed in the perpendicular direc-tion (circumferentially). A high r value indicates a material with good drawing properties.
The r value frequently changes with direction in the sheet. In a cylindrical cup drawing opera-tion, this variation leads to a cup with a wall that varies in height, a phenomenon known as earing (Fig. 1). It is therefore common to measure the average r value, or average normal anisotropy, rm, and the planar anisotropy,Dr.
The property rmis defined as (r0 Ⳮ 2r45 Ⳮ r90)/4, where the subscripts refer to the angle between the tensile specimen axis and the rolling direction. The valueDr is defined as (r0ⳮ 2r45
Ⳮ r90)/2. It is a measure of the variation of r with direction in the plane of a sheet. The value rmdetermines the average depth (that is, the wall height) of the deepest draw possible. The value Dr determines the extent of earing. A combi-nation of a high rm value and a low Dr value provides optimal drawability.
Hot-rolled low-carbon steels have rm values ranging from 0.8 to 1.0, cold-rolled rimmed steels range from 1.0 to 1.4, and cold-rolled alu-minum-killed (deoxidized) steels range from 1.4 to 2.0. Interstitial-free steels have values ranging
from 1.8 to 2.5, and aluminum alloys range from 0.6 to 0.8. The theoretical maximum rmvalue for a ferritic steel is 3.0; a measured value of 2.8 has been reported (Ref 4).
Maximum Strain Levels:
The Forming Limit Diagram
Each type of steel, aluminum, brass, or other sheet metal can be deformed only to a certain level before local thinning (necking) and frac-ture occur. This level depends principally on the combination of strains imposed, that is, the ratio of major and minor strains. The lowest level oc-curs at or near plane strain, that is, when the minor strain is zero.
This information was first represented graph-ically as the forming limit diagram, which is a graph of the major strain at the onset of necking for all values of the minor strain that can be re-alized (Ref 5, 6). Figure 2 shows a typical form-ing limit diagram for steel. The diagram is used in combination with strain measurements, usu-ally obtained from circle grids, to determine how close to failure (necking) a forming operation is or whether a particular failure is due to inferior work material or to a poor die condition (Ref 7).
For most low-carbon steels, the forming limit diagram has the same shape as the one shown in Fig. 2, but the vertical position of the curve de-pends on the sheet thickness and the n value.
The intercept of the curve with the vertical axis, which represents plane strain and is also the minimum point on the curve, has a value equal to n in the (extrapolated) zero thickness limit.
Fig. 3 Effect of thickness and n value on the plane-strain in-tercept of a forming limit diagram. Source: Ref 8
The intercept increases linearly with thickness to a thickness of about 3 mm (0.12 in.).
The rate of increase is proportional to the n value up to n⳱ 0.2, as shown in Fig. 3. Beyond these limits, further increases in thickness and n value have little effect on the position of the curve. The level of the forming limits also in-creases with the m value (Ref 3).
The shape of the curve for aluminum alloys, brass, and other materials differs from that in Fig. 2 and varies from alloy to alloy within a system. The position of the curve also varies and rises with an increase in the thickness, n value, or m value, but at rates that are generally not the same as those for low-carbon steel.
The forming limit diagram is also dependent on the strain path. The standard diagram is based on an approximately uniform strain path. Dia-grams generated by uniaxial straining followed by biaxial straining, or the reverse, differ con-siderably from the standard diagram. Therefore, the effect of the strain path must be taken into account when using the diagram to analyze a forming problem.
Material Properties and Wrinkling
The effect of material properties on the for-mation of buckles or wrinkles is the subject of extensive research. In drawing operations, there is general agreement, based primarily on exper-iments with conical and cylindrical cups, that a high rmvalue and a lowDr value reduce buck-ling in both flanges and walls (Ref 9–11). In addition to the above correlations, a low flow-stress-to-elastic-modulus ratio (rF/E) decreases wall wrinkling (Ref 12). The n value has an in-direct effect. When the binder force is kept con-stant, the n value has no effect. However, high n values enable higher binder forces to be used, which reduces buckling.
In stretching operations, the situation appears to be different. A close correlation between the formation of buckles at low strain levels and the yield-strength-to-tensile-strength ratio (YS/TS) has been reported, as well as an inverse corre-lation with the low strain n value and an absence of correlation with the rm value and uniform elongation (Ref 13). Some of the differences be-tween these results may be attributed to the fact that the experiments with cups involved high strains and high compressive stresses, while the stretching experiments were conducted at low strain and low compressive stress levels. In both situations, the problem becomes significantly more severe as the sheet thickness decreases.
Material Properties and Shear Fracture Shear fractures due to in-plane shear stresses are more prevalent in high-strength cold-worked materials, particularly when internal defects such as inclusions are present. Typical strain combinations that cause shear fracture are shown on the forming limit diagram in Fig. 4.
For this material, Fig. 4 shows that, at high strain levels in the regions close toe2⳱ Ⳳe1, failure occurs by shearing before the initiation of neck-ing.
The position and shape of the shear fracture curve depends on the material, its temper, and the type and degree of prestrain or cold work (Ref 14–16). Limited data are available on shear fracture.
Material Properties and Springback
Material properties that control the amount of springback that occurs after a forming operation are:
● Elastic modulus, E
● Yield stress,ry
● Slope of the true stress/strain curve, or tan-gent modulus, drT/de
Springback is best described by means of three examples involving a rectangular beam: elastic bending below the yield stress, simple bending with the yield stress exceeded in the outer layers of the beam, and combined stretching and bend-ing. In an actual part, springback is determined by the complex interaction of the residual inter-nal elastic stresses, subject to the constraints of the part geometry.
Fig. 5 Springback of a beam in simple bending. (a) Elastic bending. (b) Elastic and plastic bending. (c) Bending and stretching
Fig. 4 Forming limit diagram including shear fracture. Source: Ref 14
Elastic Bending Below the Yield Stress.
Tensile elastic stresses are generated on the out-side of the bend. These stresses decrease linearly from a maximum at the surface to zero at the center (neutral axis). They then become com-pressive and increase linearly to a maximum at the inner surface. Upon removal of the exter-nally applied bending forces, the internal elastic forces cause the beam to unbend as they de-crease to zero throughout the cross section (Fig. 5a).
The maximum amount of elastic deflection that can be produced without entering the plastic
range is proportional to the yield stress divided by the elastic modulus. The strain at the yield point is equal tory/E (E⳱ r/e). The springback moment for a given deflection is therefore pro-portional to the elastic modulus (r ⳱ Ee).
Simple Bending. In this example, the yield stress is exceeded in the outer layers of the beam. The outer layers deform plastically, and their stored elastic stresses continue to increase, but at a much lower rate that is proportional to the slope of the true stress-strain curve, or tan-gent modulus, drT/de, instead of the elastic modulus. Figure 5(b) illustrates this condition
for a beam bent so that 50% of its volume is in the plastic range.
Upon removal of the externally applied bend-ing forces, the stored elastic stresses cause the beam to unbend until their combined bending moment is zero. This produces compressive stresses at the outer surface and tensile stresses at the inner surface.
The springback in this case is less than for a material whose yield strength is not exceeded at the same strain level. This can result from either a higher yield stress or a lower elastic modulus.
It is also apparent that higher values of the tan-gent modulus cause greater springback when the yield strength is exceeded.
In actual conditions, the neutral axis moves inward upon bending because the outer part of the beam is stretched and becomes thinner and because the inner part is compressed and be-comes thicker. This effect is analyzed in detail in Ref 17.
Combined Stretching and Bending. In this case, the entire beam can be plastically deformed in tension by as little as 0.5% stretching. How-ever, a stress gradient still exists from the outer to the inner surface (Fig. 5c). Upon removing the external forces, the internal elastic stresses recover.
This causes unbending, but to a lesser extent than in the previous cases. As the level of stretching is increased, the amount of springback decreases because the tangent modulus and therefore the stress gradient through the beam decrease at higher strains. The yield strength ceases to be a factor in springback once all re-gions are plastically deformed in tension.
In the bending of wide sheets, the metal is deformed in plane strain, and the plane-strain properties (elastic modulus, yield stress, and tan-gent modulus) should be used. The effects of a low elastic modulus and a high yield stress and tangent modulus in increasing springback have been experienced in forming operations. Spring-back is more severe with aluminum alloys than with low-carbon steel (1 to 3 modulus ratio).
High-strength steels exhibit more springback than low-carbon steels (2 to 1 yield strength ratio), and dual-phase steels spring back more than high-strength steels of the same yield strength (higher tangent modulus).
The effect of stretching in reducing spring-back to very low levels has also been reported (Ref 18). Springback is also greatly influenced by geometrical factors, and it increases as the bend angle and ratio of bend radius to sheet thickness increase.
Surface Quality
The previously mentioned conditions that lead to undesirable surface textures can be min-imized or prevented. The formation of orange peel in heavily deformed regions can be mini-mized by using a fine-grain material. The de-velopment of Lu¨ders lines in rimmed steels can be prevented by temper rolling to 0.25 to 1.25%
extension or by flex rolling, which produces mo-bile dislocations for a limited period of time, un-til they are trapped by nitrogen atoms. This also reduces elongation slightly. This problem is be-coming less common with the increased use of continuous casting, which requires killed steels.
These steels have less free nitrogen to interact with the dislocations and do not develop Lu¨ders lines. Similar treatments can be applied to alu-minum-magnesium alloys to prevent this defect.
Effect of Temperature on Formability A change in the overall temperature alters the properties of the material, which thus affects formability. In addition, local temperature dif-ferences within a deforming blank lead to local differences in properties that affect formability.
At high temperatures, above one-half of the melting point on the absolute temperature scale, extremely fine-grain aluminum, copper, mag-nesium, nickel, stainless steel, steel, titanium, zinc, and other alloys become superplastic. Su-perplasticity is characterized by extremely high elongation, ranging from several hundred to more than 1000%, but only at low strain rates (usually below about 10ⳮ2/sⳮ1) at high tem-peratures.
The requirements of high temperatures and low forming rates have limited superplastic forming to low-volume production. In the aero-space industry, titanium is formed in this man-ner. The process is particularly attractive for zinc alloys because they require comparatively low temperatures (270 C, or 520 F).
At intermediate elevated temperatures, steels
At intermediate elevated temperatures, steels