Elastic Modulus

Elastic Modulus

Elastic Modulus (Young’s Modulus)

When a punch initially contacts a sheet metal blank, the forces produced move the sheet metal atoms away from their neutral state and the blank begins to deform. At the atomic level, these forces are called elastic stresses and the deformation is called elastic strain. Forces within the atomic cell are extremely strong: high values of elastic stress results in only small magnitudes of elastic strain. If the force is removed while causing only elastic strain, atoms return to their original lattice position, with no permanent or plastic deformation. The stresses and strains are now at zero.

A stress-strain curve plots stress on the vertical axis, while strain is shown on the horizontal axis (see Figure 2 in Mechanical Properties). At the beginning of this curve, all metals have a characteristic linear relationship between stress and strain. In this linear region, the slope of elastic stress plotted against elastic strain is called the Elastic Modulus or Young’s Modulus or the Modulus of Elasticity, and is typically abbreviated as E. There is a proportional relationship between stress and strain in this section of the stress-strain curve; the strain becomes non-proportional with the onset of plastic (permanent) deformation (see Figure 1).

Figure 1: The Elastic Modulus is the Slope of the Stress-Strain Curve before plastic deformation begins.

Figure 1: The Elastic Modulus is the Slope of the Stress-Strain Curve before plastic deformation begins.

 

The slope of the modulus line depends on the atomic structure of the metal. Most steels have an atomic unit cell of nine iron atoms – one on each corner of the cube and one in the center of the cube. This is described as a Body Centered Cubic (BCC) structure. The common value for the slope of steel is 210 GPa (30 million psi). In contrast, aluminum and many other non-ferrous metals have 14 atoms as part of the atomic unit cell – one on each corner of the cube and one on each face of the cube. This is referred to as a Face Centered Cubic (FCC) atomic structure. Many aluminum alloys have an elastic modulus of approximately 70 GPa (10 million psi).

Under full press load at bottom dead center, the deformed panel shape is the result of the combination of elastic stress and strain and plastic stress and strain. Removing the forming forces allows the elastic stress and strain to return to zero. The permanent deformation of the sheet metal blank is the formed part coming out of the press, with the release of the elastic stress and strain being the root cause of the detrimental shape phenomenon known as springback. Minimizing or eliminating springback is critical to achieve consistent stamping shape and dimensions.

Depending on panel and process design, some elastic stresses may not be eliminated when the draw panel is removed from the draw press. The elastic stress remaining in the stamping is called residual stress or trapped stress. Any additional change to the stamped panel condition (like trimming, hole punching, bracket welding, reshaping, or other plastic deformation) may change the amount and distribution of residual stresses and therefore potentially change the stamping shape and dimensions.

The amount of springback is inversely proportional to the 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.

 

Elastic Modulus Variation and Degradation

Analysts often treat the Elastic Modulus as a constant. However, Elastic Modulus varies as a function of orientation relative to the rolling direction (Figure 2). Complicating matters is that this effect changes based on the selected metal grade.

Figure 4:  Modulus of Elasticity as a Function of Orientation for Several Grades (Drawing Steel, DP 590, DP 780, DP 1180, and MS 1700) D-11

Figure 2:  Modulus of Elasticity as a Function of Orientation for Several Grades (Drawing Steel, DP 590, DP 980, DP 1180, and MS 1700) D-11

 

It is well known that the Bauschinger Effect leads to changes in the Elastic Modulus, and therefore impacts springback. Elastic Modulus determined in the loading portion of the stress-strain curve differs from that determined in the unloading portion. In addition, increasing prestrain lowers the Elastic Modulus, with significant implications for forming and springback simulation accuracy. In DP780, 11% strain resulted in a 28% decrease in the Elastic Modulus, as shown in Figure 3.K-7

Figure 3: Variation of the loading and unloading apparent modulus with strain for DP780K-7

Figure 3: Variation of the loading and unloading apparent modulus with strain for DP780K-7

 

Microstructural Components

Steel grades are engineered to achieve specific properties and characteristics by the manipulation of mill processing parameters to achieve a targeted balance of microstructural components. Among the tools available to the steelmaker are alloy composition, rolling and processing temperatures, and cooling profile.

If steel is slowly cooled, only two components exist at room temperature: ferrite (abbreviated by the Greek letter α) and cementite (iron carbide, Fe3C). Alternating layers of ferrite and cementite appear under a microscope in a pattern similar to Mother-of-Pearl, leading to the term pearlite.

A steel alloy having approximately 0.80% carbon will contain only pearlite in the microstructure. Lower carbon levels create an alloy that combines ferrite and pearlite. Ferrite-pearlite microstructures form the basis of many C-Mn steels and some of the initial HSLA steels. At a given strength level, pearlite limits sheet formability.

At carbon levels below 0.008% or 80 ppm, only ferrite exists. Ferrite is low strength but very ductile, and is the microstructural phase in ultra-low carbon steels.

Additional phases are formed when the cooling profile can be changed. Some modern annealing furnaces are capable of controlling the cooling rate as well as holding at specific temperatures. This ability is a key facilitator in the production of most Advanced High Strength Steels. In addition to ferrite and pearlite, microstructural phases of bainite, austenite, and martensite can be produced, depending on the chemistry and the thermal cycle profile including quench rate and hold temperature.

Bainite is a phase that is associated with enhanced sheared edge ductility. Accelerated cooling in the hot mill run out table allows for the production of Ferrite-Bainite steels.

Austenite is not stable at room temperature under equilibrium conditions. An austenitic microstructure is retained at room temperature with the use of a combined chemistry and controlled thermal cycle. Deforming retained austenite is responsible for the TRIP effect.

Martensite is a very high strength phase, but has limited toughness.  Steels with both ferrite and martensite in the microstructure are known as dual phase steels.  A structure of 100% martensite can be produced directly at those sheet mills having equipment capable of achieving a minimum critical cooling rate. The ductility of this product is not sufficiently high for most stamping operations. However, sheet martensite is well suited for properly designed roll forming applications.

Martensite is the microstructural component of processed Press Hardening Steels. An elevated temperature and a more formable microstructure exist at the time of complex forming of these grades. Rapid cooling while the part is under full press load converts the microstructure to the high strength martensite.