Page 44 - MetalForming Magazine August 2022

Metal Properties: Elastic Modulus
Interatomic bonds hold atoms
together, and metal flow
requires breaking these atom-
ic bonds. During the metal
stamping process, when a punch
first contacts a sheet metal blank
and prior to these bonds break-
ing, the forces produced move
the metal atoms away from their
neutral state and the blank
begins to deform. At the atomic
level, the applied force leads to
elastic stresses that result in
deformation known as elastic
strain. Forces within the atomic
cell are extremely strong; high
values of elastic stress result in
only a small amount of elastic
strain. Removing the force while
causing only elastic strain allows
atoms to return to their original
lattice positions, with no per-
manent or plastic deformation. The stresses and strains return to zero.
Hooke’s Law characterizes the linear relationship between stress and strain at these low strain values where atoms experience only a small deviation from their neutral positions. The initial linear section of a stress-strain curve highlights this proportional relationship. The slope in this area is called the elastic modulus, Young’s modulus or the modulus of elasticity (typically abbreviated as E). Beyond this linear region, strain becomes nonproportional with the onset of plastic or permanent deformation (Fig. 1).
The atomic structure of the metal influences the slope of the modulus line. Most steels have a body-centered cubic structure—an atomic unit cell with one atom located at
Dr. Danny Schaeffler, with 30 years of materials and applications experience, is president of Engineering Quality Solutions (EQS) and chief content officer of 4M Partners. EQS provides product-applications assistance to materials and manufacturing compa- nies; 4M teaches fundamentals and practical details of material properties, forming technologies, process- es and troubleshooting needed to form high-quality components. Schaeffler is the metallurgy and forming technical editor of the AHSS Application Guidelines available from WorldAutoSteel at AHSSinsights.org.
Danny Schaeffler
248/66-STEEL • www.EQSgroup.com
E-mail ds@eqsgroup.com or Danny@learning4m.com
each corner of a cube and one atom in the center of the cube. The elastic modulus for steel typical- ly is 210 GPa (30 million psi). In contrast, alu- minum and many other nonferrous metals have one atom at each corner of the cube and one on each face of the cube, cre- ating what is known as a Face Centered Cubic (FCC) atomic structure. Many aluminum alloys have an elastic modulus of approximately 70 GPa (10 million psi).
Springback
The deformed panel shape under full press load at bottom dead center combines elastic and plastic stresses and strains. The formed part out of the press incor- porates the permanent deformation of the blank, with the release of the elastic stress and strain being the root cause of springback. The difference in atomic structure of steel and aluminum alloys, and the associated difference in elastic modulus, form the basis for the different springback response
between these sheet metals.
Panel and process design may prevent the elimination
of all elastic stresses when removing the drawn panel from the press. The elastic stress remaining in the stamped part is called residual or trapped stress. Any additional change to the panel condition, such as from trimming, hole punch- ing, bracket welding, reshaping or other plastic deformation, can change the amount and distribution of residual stresses and, therefore, potentially change the part shape and dimensions.
The amount of springback is inversely proportional to the material’s modulus of elasticity. Therefore, for the same yield stress, steel (with three times the modulus of aluminum) will have one-third the amount of springback.
Forming Alters the Elastic Modulus
Forming-simulation analysts incorrectly treat the elastic modulus as a constant. While the standard 210-GPa and 70- GPa values serve as reasonable approximations for generic
Fig. 1—The slope of the stress-strain curve before the onset of plastic deformation measures the elastic modulus.
Metal Matters
By Daniel J. Schaeffler, Ph.D.
Tensile Strength (TSor Rm)
Yield Strength (YS or Rp0.2)
0.2%
Engineering Strain (%)
Slope
= Elastic Modulus
= Young’s Modulus
= Modulus ofElasticity
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Engineering Stress (ksi or MPa)