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Analysis of punch stretching formability test of DP1000 steel measured using

3D DIC and compared with results of FEA

Article · January 2015

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 International Journal of Applied Engineering Research ISSN 0973-4562 Volume 10, Number 19 (2015)
© Research India Publications ::: http://www.ripublication.com

Analysis of Punch Stretching Formability test of DP1000 Steel measured using 3D DIC
and compared with results of FEA

A.S.Noor Mohammed K.S. Sridhar Raja

Depratment of Mechanical & Production EngineeringDept. Dept.of Mechanical & Production EngineeringDept. name of
Sathyabama University Sathyabama University
Chennai, India Chennai, India

Abstract—A punch-stretching formability test has been carried

out on a newly developed automotive Advanced High Strength Steel B. DIC
(DP1000) often used for body-in-white structural and Digital Image Correlation is an optical method that provides
reinforcement components like pillar reinforcements and crash image registration and tracking techniques for perfect 2D and
structures as well as for lightweight seat structures in order to
3D measurements of changes occurring in images. This is
characterise the formability of the material and in particular the
extent of plastic deformation before failure. Displacement and often used to measure deformation (engineering),
strain profiles have been measured on the top surface of the displacement, strain, and many areas of science and
specimen using 3D Digital Image Correlation (DIC). The specimen engineering. DIC has proven to be very effective in mapping
is a 90 mm diameter circular blank with a thickness of 1.5 mm. The deformation in mechanical testing and thus will provide more
specimen is loaded through a vertical displacement upward of the accurate results than Ansys which may have mesh distortion.
machine cross-head at a speed of 2.5 mm/min, the blank holder
being fixed in space during the test. A finite element model of this
test is produced in ANSYS Mechanical 14; the displacement and
strain distribution results are compared with the experimental
results.

Keywords— Formability, FEA , DIC, DP Steel

I. INTRODUCTION
A non-linear Finite Element simulation was conducted on Fig: 2. Mapping of DIC
ANSYS Workbench Version 14.0 to simulate a punch-
stretching formability test of DP 1000 Steel. Strain and C. DUAL PHASE 1000 STEEL
deformation plots of the simulation were compared with DP steels consist of a ferritic matrix containing a hard
corresponding plots of the actual test, measured by 3D Digital martensitic second phase that increases the volume fraction of
Image Correlation (DIC). The test was simulated in the Static the hard second phases which generally increases the strength.
Structural module of ANSYS and three Non-linearities were figure 3 shows a microstructure image of DP steel. The soft
modelled namely; Plasticity, Large Deformation and contact. ferrite phase being continuous gives the steel a good ductility.
The simulation results were compared with the experimental As deformation occurs in the steel, strain is can be seen in the
measurements of the out-of-plane displacement, Ɛ xy, Ɛ xx ferrite phase surrounding of martensite, showing the high
and Ɛ yy maps provided. work-hardening rate exhibited by these steels.

A. FORMABILITY TEST
The ability of a metal work piece to undergo plastic
deformation without being damaged is called as formability.
The plastic deformation of metallic materials is limited to a
certain point after which the material could verily experience
breakage.
Fig: 3. Schematic microstructure of DP steel

D. STRUCTURAL NON LINEARITY

Nonlinear structural behaviour arise from many causes, which
can be grouped into three principal categories:

Fig: 1. Stress-Strain Graph showing fracture

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1. Changing Status (Including Contact)

Nonlinear behaviour can be shown by many common

structural features that are status-dependent. Situations in
which contact occurs are common to many different
applications of non-linearity.

2. Geometric Nonlinearities
When large deformations are experienced by a structure, its
changing geometric configuration can cause the structure to
respond nonlinearly. Geometric nonlinearity can be
characterized by large displacements, large rotations or both.

3. Material Nonlinearities

When large deformations are experienced by a structure, its

changing geometric configuration can cause the structure to
respond nonlinearly. Geometric nonlinearity can be
characterized by large displacements, large rotations or both.

II. EXPERIMENTAL APPROACH

A punch-stretching formability test has been carried out on a
newly developed automotive Advanced High Strength Steel Fig: 5. Experimental Setup
(DP1000) often used for body-in-white structural and
reinforcement components like pillar reinforcements and crash
structures as well as for lightweight seat structures in order to
III. ANALYSIS APPROACH
characterise the formability of the material and in particular
the extent of plastic deformation before failure. Displacement A. GEOMETRY
and strain profiles have been measured on the top surface of
the specimen using 3D Digital Image Correlation (DIC). A complete assembly of the test formability rig shown in the
figure is done in solid works to closely analyse the 3D model.
Figure 5 below shows the test set up with the DIC cameras
However, only the assembly of the die, punch and the
and figure 4 shows a schematic drawing of the test rig.
specimen were imported to Ansys for analysis purpose
considering that the die was given a fixed support and hence
the involvement of the supporting and connecting bars can be
eliminated. To save memory and computing time, only quarter
of the 3D model shown in figure 7 was used for running the
analysis as its clear that the result maps are symmetric from
the given experimental measurements.

Fig: 4. Schematic diagram of Test Rig

Fig: 6. Complete Assembly

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1. Large Deformation Effects – ON

This option is used in the analysis as there is a large
deformation and large strain occurring on the specimen. Large
deflections and large strains are geometric nonlinearities.
2. Newton Raphson
In the given test nonlinearity is caused by both the geometry
and the material. ANSYS employs the "Newton-Raphson"
approach to solve nonlinear problems. The load is subdivided
into a series of load increments in this method. The load
increments can be applied over several load steps. Figure 9
Fig: 7. Assembly of Punch, Die & Plate Illustrates the use of Newton-Raphson equilibrium iterations
in a single DOF nonlinear analysis.
B. MATERIAL
The material specified for the plate specimen is advanced
High Strength Steel DP 1000.The following properties of the
material are necessary in order to update in the engineering
data panel of the software so that it may produce results
according to the specific material given.

Density 7.8e-006 kg mm^-3

Young's Modulus MPa 1.4e+005 Fig: 9. Newton Raphson Iterative Solution

Poisson's Ratio 0.3 3. Displacement

There is no displacement in the X and Z direction but the Y
Bulk Modulus MPa 1.1667e+005 direction is given a displacement of 11.55 mm as the punch
moves upto that distance in the given experimental
Shear Modulus MPa 53846
measurement.

Table: 1. Material Properties

Multi linear isotropic hardening is added to the material apart

from the above mentioned properties as the values of Stress
and Plastic Strain of the material should be input in the
analysis.

Fig: 10. Displacement

4. Ramped Loads
Fig: 8. Comparison of Stress-Strain Curves
As more than one substep was specified in the load step, the
question of whether the loads should be stepped or ramped
C. STATIC ANALYSIS
arised. If a load is stepped, then its full value is applied at the
Static Analysis is used to determine displacements, stresses,
first substep and until the rest of the load step it will stay
etc. under static loading conditions. Nonlinearities like
constant. If it’s a ramped load there will be gradual increase at
plasticity, large deflection, large strain, contact surfaces, and
each substep. The full value will occur only at the end of the
creep can be include.Inertia and damping effects, such as
load step. This explanation and the figure 11 justifies the
those caused by time-varying loads are ignored here as its not
usage of the the ramped load option for the analysis.
dependant on time.

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Fig: 11. Graph of Ramped Load Steps

5. Fixed Support
The whole assembly of the stretch forming formability rig is
not used for the purpose of analysing. The simplified assembly
of the die, punch and plate specimen is used. The faces of the Fig: 11. Frictional Contact
die are given a fixed support so as to arrest the sliding
movement of the plate.

Fig: 12. Contact

7. Coefficient of Friction
Fig: 10. Fixed Supports The coefficient of friction can be any non-negative value.
ANSYS by default gives a frictionless contact between
6. Contacts surfaces. However, for this case different values like 0.1, 0.2
Contact problems involving friction produce non-symmetric etc. have been tried and the change did not affect the final
stiffness. Using an un symmetric solver is more result of the problem.
computationally expensive than a symmetric solver for each
iteration. For this reason, ANSYS uses a symmetry algorithm IV. RESULTS AND DISCUSSION
by which most frictional contact problems can be solved using A. MESH COMPARISON
solvers for symmetric systems. If frictional stresses have an
influence on the overall displacement field and the magnitude
of the frictional stresses is highly dependent on the solution, a
low rate of convergence may be seen if there is any symmetric
approximation to the stiffness matrix.
Three contact pairs have been identified for the analysis. One
between the top face of the lower die and the bottom face of
the specimen, next between the top surface of the specimen
and the lower surface of the upper die. The third contact was
created between the punch and the specimen which was
assigned as a frictional contact as there is a friction between
Fig: 13. Mesh Size Vs Max Strain
the punch and the plate when in motion. Here, the specimen
becomes the target surface and the punch tip is the contact
surface. Various mesh patterns had been tried for this model but the
one that best suited was creating a sphere of influence so that a
much refined mesh is obtained in the centre of the plate and

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the tip of the punch. Mesh sizes of 0.5 mm, 0.3 mm and 0.2 Experimental Result
mm were tried on the quarter model while a mesh of 0.8mm
was tried on the full model. The results obtained and depicted
in figure 14 and figure 15 clearly show that the mesh
influences the pattern and the numbers. The figure indicates
that as the mesh becomes finer the appearance of another
pattern begins to be visible as given in the experimental result.
If the mesh is refined more with increased radius of the sphere
of influence, then it may create the exact structure as given in
the experimental result for the XY Map which is XZ for my Fig: 16 –Experimental results of out-of plane displacement
model.
Analysis Result
0.2mm Mesh

Fig: 14 -0.2mm Mesh Fig: 17–Analysis results of out-of plane displacement

C. COMPARISON OF XZ
0.8mm Mesh
Experimental Result

Fig: 15.0.8mm Mesh

Fig: 18 – Experimental results of xz
Mesh 0.8mm(full plate) 0.2mm

Nodes 1,38,367 1,46,429 Analysis Result

Elements 89,815 86,596
Table: 2- Nodes and Elements
B. COMPARISON OF OUT OF PLANE
DISPLACEMENT
The figure 16 and figure 17 shows that the obtained results
from the model has been in a good agreement with the
Fig: 19 – Analysis results of xz
Experimental Result. The maximum displacement in the
experimental result is 11.55mm which exactly suits the data
The maximum shear strain is about 0.1008 (0.2mm mesh).
obtained from the model result. But, the minimum
However, DIC results show the strain to be about 0.126,
displacement value captured by DIC is 2.65, whereas the
which is almost the same. The minimum shear strain is -
output from ansys shows 1.282.This change in the minimum
0.43504(0.2mm mesh) but DIC gives a value of -0.12. This is
displacement value may be the result of using the simplified
an effect of using the quarter plate as the results obtained from
model. However, the colour varies in the outer rim of the plate
the full plate is -0.84453 minimum to 0.82353 maximum
which is again a result of mesh size.
(0.8mm mesh). This proves that if the full plate is refined to a
mesh of 0.2mm or lower the results obtained will
approximately be -0.1008 minimum to 0.1008 maximum
which is almost the same as obtained from DIC. But, the
overall pattern of Strain distribution near the centre of plate
seems to match with DIC images. The yellow region of 0.07

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to 0.018 strain magnitude also seems to match the DIC are different from DIC images. It’s clear that the FEA solution
images. Matching the scale of strain distribution for FEM with is dependent on the mesh and hence the mesh should be
DIC, may give us a better comparison. Also, since mesh was refined. Similarly, it can be seen that the overall strain
designed such that it coarsens radially outwards, it has failed contours do not match DIC images and seem coarse
to capture secondary zones of high strains that are visible in
DIC images. As can be seen in FEA solution, there is faint F. OVERALL STRAIN COMPARISON
hint of strain away from the centre. It can be said that due to
coarse mesh, the FEA solution has failed to resolve strain
distribution properly, in the radially outer regions of the plate. Comparison of Strain Values
1 0.835 0.845

Strain Value
D. COMPARISON OF XX A graph within a graph is an “inset”, not an “insert”.
The0.5word alternatively is preferred to the word
Experimental Result Analysis Result 0.621something that
“alternately” (unless
0.12 you really mean 0.50672
alternates).
0 0.1008
Do not useExythe word Exx “essentially” toEyy mean
“approximately” or “effectively”.
Strain Map
In your paper title, if the words “that uses” can
accurately replace
MaxtheStrain “using”,
word in DIC capitalize the “u”;
if not, keep using lower-cased.
Max Strain in Model Result

Fig: 22. Overall Comparison of Strain Values

Fig: 20 – Comparison of results of xx V. CONCLUSIONS

Although the model results do not exactly match the
experimental results considering the fact that mesh refinement
The Max strain is 0.621 which is significantly lower from DIC will produce better results shows that ANSYS will be able to
result of 0.835. However, it can be seen that the strain provide nearer values. On the other hand, DIC provides much
contours are not uniform, have sudden/abrupt changes. Hence, accurate results than ansys as it has been proved earlier.
it can be said the solution depends on mesh and the mesh is However the difference between these two results can be
needed to be refined. However, there are spikes of high strain minimized verily if an Arbitrary Lagrangian Eulerian method
at the centre, which are different from DIC images. It’s clear (ALE) is used for the mesh. In the normal Augmented
that the FEA solution is dependent on the mesh and hence the Lagrange that has been used for the model will have a
mesh should be refined. Similar, it can be seen that the overall movement of the nodes along with the material in the
strain contours do not match DIC images and seem coarse Lagrangian co ordinates. Hence, severe mesh distortion can
occur because the mesh will be deformed along with the
E. COMPARISON OF ZZ material. If ALE had been used the results of the model could
have verily improved.

VI. BIBLIOGRAPHY
1. ANSYS modeling and meshing guide : ANSYS
release 6.0. Canonsburg, PA: Canonsburg, PA :
ANSYS Inc, 2001, 2001.
2. C. Andrew and A. D. Crocombe, How to tackle
non-linear finite element analysis. Glasgow:
Glasgow : NAFEMS, 2001, 2001.
3. Ansys, Advanced structural nonlinearities :
Fig: 21 – Comparison of Model and Experimental results
release 6.0 : training manual. Canonsburg, PA:
of zz
Canonsburg, PA : Ansys Inc, 2001, 2001.
4. Ansys, Advanced structural nonlinearities :
release 6.0 : training manual. Canonsburg, PA:
The Max strain is 0.506 which is significantly lower from DIC
Canonsburg, PA : Ansys Inc, 2001, 2001.
result of 0.845. However, it can be seen that the strain
5. Ansys, ANSYS advanced analysis techniques
contours are not uniform, have sudden/abrupt changes.Hence,
guide : ANSYS release 6.1. Canonsburg, PA:
it can be said the solution depends on mesh and the mesh is
Canonsburg, PA : ANSYS, 2002, 2002.
needed to be refined. The strain at the center of the plate is in
6. Baguley and D. Baguley, How to - model with
the range of 0.39 to 0.5, which is about similar to 0.46 to 0.51.
finite elements. East Kilbride, Glasgow: East
However, there are spikes of high strain at the centre, which
Kilbride, Glasgow : NAFEMS, 1997, 1997.

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7. R. J. Owen and D. R. J. Owen, Finite elements in

plasticity : theory and practice. Swansea: Swansea
: Pineridge Press, 1980, 1980.
8. D. D. W. A. Rees, "The Mechanics of Solids and
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Nonlinear Solid and Structural, International
conference on finite elements in nonlinear solid
and structural mechanics : preprints. Vol. 1.
Trondheim : Gothenburg: Trondheim : Norwegian
Institute of Technology ; Gothenburg : Chalmers
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13. N. E. Dowling, Mechanical behaviour of material:
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