Page 43 - MetalForming March 2023 - PMA Chairman Jeff Aznavorian

Metal Matters By Daniel J. Schaeffler, Ph.D.
Metal Properties: Plastic Strain Ratio (r-Value)
The r-value, also called the Lank- ford coefficient or plastic strain ratio, provides a measure of a metal alloy’s resistance to thinning. Mathematically, it represents the ratio of the true width strain to the true thickness strain at a particular value of longitudinal strain up to that of uni- form elongation, using the formula:
r = w/t = {(ln w/w0 )/(ln t/t0 )}
Strains of 15 to 20 percent common- ly are used for determining the r-value of low-carbon sheet steel, while testing of aluminum sheets typically employs strains of 10 to 15 percent. Like n-value, the ratio will change depending on the chosen reference strain value. An r- value of 1 means that the sheet has similar response to deformation in the width and thickness directions.
Higher r-value material grades are more likely to draw deeper cup shapes successfully as these grades deform more in the plane of the sheet and less through the thickness. In some lower- strength steels, r-value exceeds 2.5 when tested perpendicular to the rolling direction, but for most high- strength steels, r-value is close to 1 in all directions.
Dr. Danny Schaeffler, with 30 years of materi- als 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 com-
panies; 4M teaches fundamentals and practical details of material properties, forming technolo- gies, processes and troubleshooting needed to form high-quality components. Schaeffler is the metallurgy and forming technical editor of the AHSS Application Guidelines available from World- AutoSteel at AHSSinsights.org.
Danny Schaeffler
248/66-STEEL • www.EQSgroup.com
E-mail ds@eqsgroup.com or Danny@learning4m.com
Thinning
becomes the pref-
erential metal-
flow direction
when forming
alloys with lower
r-value, increas-
ing the risk of fail-
1 ure in drawing
operations.
The ASTM
E517 specifica-
Major True Strain (ε ) 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 tion, Standard
Test Method for
Plastic Strain
Ratio r for Sheet
Metal, is the most
pertinent in the
United States,
with correspon-
ding ISO, EN and
JIS specifications
used around the
globe.
-0.20 0.00 0.20 -0.60 -0.40
Minor True Strain ( ε )
Effect of
2
Orientation Fig. 1—R-value limits the maximum achievable major strain in the
R-value uniaxial tension strain path prior to necking. changes with ori-
FLC
r =1
r = 1.25 r = 1.5
r = 1.75 r =2
Increasing r-value
entation relative to rolling direction. The normal anisotropy ratio (rm)—also called r̄, r-bar or r-average—defines the ability of a material to deform in the thickness direction relative to defor- mation in the plane of the sheet. The formula for rm:
rm= r̄=r–bar=(r0+r90+ 2r45)/4
where r0, r90 and r45 represent r- value at 0, 90 and 45 deg. relative to the rolling direction.
Delta r (Δr), the planar anisotropy parameter, indicates the ability of a material to demonstrate a non-earing behavior:
Δr = (r0 + r90 - 2r45)/2
A value of 0 is ideal for can making
or for deep drawing of cylinders, as this indicates equal sheet metal flow in all directions, eliminating the need to trim ears prior to subsequent processing.
High-strength steels with tensile strength greater than 450 MPa and hot- rolled steels have rm values close to 1. Therefore, conventional high-strength, low-alloy (HSLA) and advanced high- strength steels (AHSS) at similar yield strengths perform equally in forming modes influenced by the rm value. How- ever, r-value for higher-strength grades of AHSS (800 MPa or higher) can be lower than 1, and any performance influenced by r-value would be less than that for an HSLA steel of similar strength. For example, AHSS grades may struggle to form part geometries
40 MetalForming/March 2023
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