Page 42 - MetalForming November 2022

Cutting Edge
Fig. 1—The hardening curve can be calculated from force-extension curves in three conversions. Plots in this figure: (a) raw data from a tensile test yielding a force-extension curve, (b) engineering stress-strain curve, (c) true stress-strain curve (dashed portion should be omitted, shown only for information), (d) and the hardening curve, or true plastic strain-true stress curve. Shown here are data for a 2-mm-thick CR330Y590T-DP steel.
1000 900 800 700 600 500 400 300
Unbounded Model: Hollomon or Ludwik
Experimental Data
Saturation Model: Hockett-Sherby
0 0.1 0.2 0.3 0.4 0.5 0.5 0.7 0.8 0.9 1
True Plastic Strain (ɛp) [-]
information, a user may not be sure of springback results nor press-force estimations.
How to Create
the Hardening Curve?
First, try to reduce the need for extrapolation as much as possible. If the material to be tested starts necking at around 0.20 true plastic strain, how can we gain more true-strain data? Two methods: Use either a biaxial test— such as the hydraulic bulge test—or a digital image correlation (DIC) system.
A hydraulic bulge test involves clamping a square sheet of 200 by 200- mm square sheet of material with a lock bead, and hydraulic pressure intro- duced to freely bulge the material. Dur- ing the test, digital images provide for strain measurements/calculations with pressure recorded for stress calcula- tions. The minimum necking strain in a bulge test measures 0.36, and with increased strain hardening (n-value),
the necking strain
increases. This can
reduce the need
for extrapolation,
as reported by
many researchers.
Use caution when
using the hydraulic
bulge test on
tough materials
such as new-gen-
eration AHSS.
These material
sheets, with high elongation together with high strength, may burst at high- enough internal pressure and release great amounts of energy.
Using a 2D DIC system can help determine the true stress-true strain curve after diffuse necking in a tensile test. Once the local necking starts, the thickness of the sheet also significantly reduces (see Cutting Edge column in MetalForming’s February 2020 issue). Users also can determine the true
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MetalForming/November 2022 39
Fig. 2—Extrapolating tensile-test data may yield uncertainty at high strains.
stress-true strain curve all the way to fracture by using a 3D DIC system.
Best-Practice Idea
Even using a 3D DIC system may not deliver a hardening curve to 1.0 true plastic strain. We have recently developed a computer code that fits all of the hardening-curve models listed in Tables 1 and 2. The extrapolation ends at 1.0 true plastic strain and checks for the median value. Then, the
Force-Extension Curve (raw output of tensile test)
Engineering Stress-Strain Curve
27
24
21
18 500 15 400 12
800 700 600 500 400 300 200 100
0
0
800 700 600 500 400 300
ab
True Stress-Strain Curve
Hardening Curve (True Stress vs. True Plastic Strain)
700 600
9
6
3 00
0 2 4 6 8 10 12 14 16 18 20 22
Extension (∆L) [mm]
0 3 6 9 12 15 18 21 24 27
Engineering Strain (e) [%]
300 200 100
0.03
0.06
0.09
0.12
0.15
0.18
0.21
0.24
0
0.02 0.04
0.06 0.08 0.10 0.12
0.14 0.16
True Strain (ɛ) [-]
True Plastic Strain (ɛp) [-]
cd
True Stress (ơ) [MPa]
True Stress (σ) [MPa]
Force (F) [kN]
True Stress (σ) [MPa]
Eng. Stress (σe) [MPa]