IML 401 – MANUFATCURING LAB I
FORMING LIMIT DIAGRAM IN SHEET METAL
1.
Purpose of the Experiment
In order to define formability limits under multiaxial loading in sheet metal forming Forming
Limit Diagrams (FLD’s) have been used as defining materials properties. The purpose of this
experiment is to obtain sheet metals forming limit diagrams.
2.
Required Conditions for the Experiment
Materials as in sheet metal form are usually defined as plane stress condition (σthickness=0) in
metal forming, this approach provides convenience in calculations. Therefore, one of the three
principal stress is equal to zero and the other ones are named as major stress (σmaj) and minor
stress (σmin). Figure 1 displays strain values in the same direction are named as major strain (ε1)
and minor strain (ε2). The Forming Limit Diagram (FLD) is constructed based on the strain
paths obtained from biaxial stretching experiments on different sample geometries. The region
under the curve is considered to be safe for any particular deformation mode, while everything
above the FLD curve is considered to be potential for fracture. Sometimes, another curve, which
is called a safe FLD curve, is plotted 10% below the FLD. The main reason for this is an
observation of necking is a subjective process, which depends on the accuracy of equipment
and capability of the experimenter. A higher FLD curve indicates that the material has greater
formability.
Figure 1: Major and Minor Strain Values After Deformation
From point of view, the formability of sheet metal is critical to a successful sheet forming
operation, for which the forming limit diagram (FLD) is well-known and is widely applied. The
FLD defines, in a way, the onset of localized necking, which may be used as a measure of the
maximum formability of sheet metal by means of deep drawing experimental setups as shown
in Figure 2.
Figure 2: Schematic View of Deep Drawing Experimental Setup
Major and minor strains are obtained by measuring grids (Figure 3) which are electrochemically
etched on sheet metal specimen. Moreover, in Figure 4, grid forms after deformation of the
specimen is shown.
Figure 3: Electrochemically Etched Grids on the Specimen
Figure 4: Grid Forms on the Sheet Metal Specimen after Deformation
3. Theoretical Approach
Measurement of plastic strain on sheet metals are obtained by grids. The grids which have 2 –
5 mm diameter are applied by electrochemical etching, photochemical and laser method on
sheet metal specimen. After deformation, the grid forms have elliptical or circular shapes. The
dimension of grids in the marginal region (Between teared and safe region) are measured by
magnifier. Major and minor strains are calculated by the formulas below.
Strain values are gathered on an analytical plane in Figure 5, provided by measuring grid
dimension values and calculation of major and minor strains (εmaj and εmin). Forming Limit
Curves (FLCs) are capable of predicting the strain levels that can lead to material failure under
different strain paths.
Figure 5: Schematic View of Forming Limit Diagram
Calculations are made due to conditions below;
a) Uniaxial Tension Condition:
σ1>0, σ2=0 ve σ3=0
ε1>0, 𝜀2 =
𝜀1
2
ve 𝜀3 = −
𝜀1
2
(Constant volume principal)
b) Plane Strain Condition:
ε1>0, ε2=0 ve ε3=-ε1 (Constant volume principal)
σ1>0, 𝜎3 = −
𝜎1
2
ve 𝜎3 = 0 (σ3 stress on the direction of thickness)
c) Biaxial Tension Condition:
ε1>0, ε2=ε1 ve ε3=-2ε1=-2ε2
σ1>0, σ2=σ1 ve σ3=0 (σ3 stress on the direction of thickness)
4. Required Devices and Materials for Experiment
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600 kN servo – hydraulic universal tension – compression device
Semi – spherical punch and dies made of hardened tool – steel
Micrometer and caliper for precise thickness measurements
Scaled magnifier for optical dimension measurement
Specimen: Sheet metal
Electrochemical grid etching device, apparatus, stencil and asidic solution
Grease oil for lubrication
Alcohol and acetone for surface cleaning
5. Application of the Experiment
a) Specimens are prepared in order to obtain conditions; uniaxial tension, plane compression
and biaxial tension. The specimens should be in different dimensions and have enough
number.
b) Thickness of the sheet metal specimen (t0) is measured.
c) Circular grids are electrochemically etched on the specimen.
d) Contact surfaces of specimen and punch are lubricated with grease oil.
e) Specimen is mounted between dies and semi – spherical punch compress on the specimen.
f) Compression is proceded until local necking and tearing.
g) Compression is stopped and specimen is gathered.
h) Dimension of the grids in the marginal zone is measured after cleaning of the specimen.
i) Strain values are calculated and forming limit curves are obtained.
6. Preparation of the Report
After the experiment, the report will be prepared by the group members and delivered to
responsible laboratory personnel within two weeks. Experimental report will contain not only
experimental procedure and theoretical explanation of the work but also;
a) All the experimental values in the table
b) Forming Limit Diagram by using values gathered in the experiment.
References
1. Duncan, J., Marciniak, Z. Ve Hu, S.J., Mechanics of Sheet Metal Forming, 2nd Ed.,
Butterworth Heinemann, 2002.
2. Hosford, W.F. ve Caddell, R.M., Metal Forming: Mechanics and Metallurgy, Prentice Hall,
1993.
3. Ozturk,Fve Lee, D., Experimental and numerical analysis ofout-of-plane formability test, J.
of Materials Processing Technology 170 (2005) 247–253.
4. Arcelor, Forming Limit Curves, 2005.