Page 33 - MetalForming September 2009

Failure ABC
B A,C
n>0
Strain A B C Location
ab
Fig. 2—Schematic a shows work hardening forces zones A and C to follow zone B up the stress-strain curve as the tensile force is increased. The strain distribu- tions in schematic b remain almost flat at different amounts of deformation.
formly loaded in tension throughout its entire length. Most sheetmetal stamp- ings are more complex and generally involve a punch being pushed into the sheetmetal blank (Fig. 3b). This local application of the punch force plus the bending deformation often concen- trates the deformation in one area. The amount of stress in the forming area can be much higher than the stress in the surrounding areas. A strain gradient wants to develop.
A material with a low amount of work hardening must undergo a large amount of strain before the rest of stamping can begin contributing to the deformation. In Fig. 3a, assume a stress level of x is required to yield the entire blank. The lower n-value sheetmetal must deform to a high strain level (L) to achieve a stress of x necessary to yield the rest of the blank. The high strain under the punch and the low strain in the rest of the blank create a severe strain gradient (Fig. 3b). However, a higher n- value sheetmetal (Fig. 3a) reaches the same stress level of x with a much small- er level of strain (H) that results in a lesser strain gradient (Fig. 3b).
A good understanding of work hard- ening is invaluable for design, tryout and production in press shops in most industries. Therefore, the discussion of work hardening and the associated n- value continues next month. Included topics are how n-value changes with different materials, strengths, processing and applications. MF
x
Higher n Lower n
Low n
High n
Location
HL Strain
ab
Fig. 3—The higher rate of work hardening (higher n-value) in schematic a allows the same stress increase to be attained with less strain. This reduces the severity of the strain gradient (schematic b).
the true stress, K is a material constant, 􏰀 is the true strain and n is the work hardening exponent. A nigh n-value means a higher rate of strain hardening. In contrast to the zero work hardening capability described above, sheetmetal with work hardening has a drastically different deformation sequence.
Using the same deformation mode in the above example (Fig. 2b), the higher stress in zone B again causes this zone to reach the yield strength first and deform. However, because of work hardening, the strength in zone B increases and the deformation stops. To continue deformation, the tensile force on the sample must be increased. Now all zones plastically deform, work
harden and climb up the stress-strain curve (Fig. 2a). The strain gradient is zero except for the small bump at zone B (Fig. 2b). The tensile load must be increased to continue further deforma- tion. Each increase in load creates the same deformation pattern but at high- er levels of strain. Under these condi- tions, a very high average strain (useful deformation) can be attained in the sample before the failure limit is reached.
If a small amount of work hardening does such an excellent job of preventing a sharp strain gradient, why would one need a large amount of work hardening? Remember that the two previous exam- ples used a flat sample that was uni-
The Science of Forming, Vol. 1 & 2
By Stuart Keeler, ScD, President, Keeler Technologies, LLC
Volume 1 articles help stamping- plant engineers and managers overcome problems related to springback, tool design and other formability issues. Also included are articles on advanced high-strength steels.
Volume 2 includes dozens of MetalForming magazine columns on springback, tool design and material formability. Multimedia presentations
bring forming issues to life; and presentations cover forming of higher-strength steels, statistical deformation control and virtual sheetmetal forming. To order visit www.metalformingmagazine.com or contact Marlene O’Brien, 216/901-8800; mobrien@pma.org
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METALFORMING / SEPTEMBER 2009 31
Stress
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Strain
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