Advanced Material Models for Stamping of AW 5754 Aluminum Alloy
Predictions by numerical simulations are strongly influenced by availability and reliability of input data. In the most used computational models, the material behavior during deformation is described only by static tensile test in combination with Lankford coefficients of anisotropy. However, for s...
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Slota, J. Šiser, M. 2020-12-07T20:09:22Z 2020-12-07T20:09:22Z 2016 Advanced Material Models for Stamping of AW 5754 Aluminum Alloy / J. Slota, M. Šiser // Проблемы прочности. — 2016. — № 4. — С. 21-29. — Бібліогр.: 9 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/173503 539.4 Predictions by numerical simulations are strongly influenced by availability and reliability of input data. In the most used computational models, the material behavior during deformation is described only by static tensile test in combination with Lankford coefficients of anisotropy. However, for some specific materials like highly anisotropic aluminum alloys, such description of material behavior is insufficient and, in many cases, the calculated results are not in good agreement with the measured ones. In this paper, the implementation of advanced material model for deep-drawing process to explicit FE code and the procedure of measurement of the most important input material data for calculations on the aluminum alloy AW 5754 are discussed. Results of the numerical simulation are compared with the experimental ones and exhibit a close correlation. The authors gratefully acknowledge the financial support of the project VEGA 1/0872/14. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Advanced Material Models for Stamping of AW 5754 Aluminum Alloy Применение комплексной модели материала для описание процесса штамповки алюминиевого сплава AW5754 Article published earlier |
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Advanced Material Models for Stamping of AW 5754 Aluminum Alloy |
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Advanced Material Models for Stamping of AW 5754 Aluminum Alloy Slota, J. Šiser, M. Научно-технический раздел |
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Advanced Material Models for Stamping of AW 5754 Aluminum Alloy |
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Advanced Material Models for Stamping of AW 5754 Aluminum Alloy |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Применение комплексной модели материала для описание процесса штамповки алюминиевого сплава AW5754 |
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Predictions by numerical simulations are strongly influenced by availability and reliability of input data. In the most used computational models, the material behavior during deformation is described only by static tensile test in combination with Lankford coefficients of anisotropy. However, for some specific materials like highly anisotropic aluminum alloys, such description of material behavior is insufficient and, in many cases, the calculated results are not in good agreement with the measured ones. In this paper, the implementation of advanced material model for deep-drawing process to explicit FE code and the procedure of measurement of the most important input material data for calculations on the aluminum alloy AW 5754 are discussed. Results of the numerical simulation are compared with the experimental ones and exhibit a close correlation.
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Advanced Material Models for Stamping of AW 5754 Aluminum Alloy / J. Slota, M. Šiser // Проблемы прочности. — 2016. — № 4. — С. 21-29. — Бібліогр.: 9 назв. — англ. |
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| first_indexed |
2025-11-27T08:47:27Z |
| last_indexed |
2025-11-27T08:47:27Z |
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1850806715300184064 |
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UDC 539.4
Advanced Material Models for Stamping of AW 5754 Aluminum Alloy
J. Slota1 and M. Ðiser2
Technical University, Koðice, Slovakia
1 jan.slota@tuke.sk
2 marek.siser@tuke.sk
Predictions by numerical simulations are strongly influenced by availability and reliability of input
data. In the most used computational models, the material behavior during deformation is described
only by static tensile test in combination with Lankford coefficients of anisotropy. However, for some
specific materials like highly anisotropic aluminum alloys, such description of material behavior is
insufficient and, in many cases, the calculated results are not in good agreement with the measured
ones. In this paper, the implementation of advanced material model for deep-drawing process to
explicit FE code and the procedure of measurement of the most important input material data for
calculations on the aluminum alloy AW 5754 are discussed. Results of the numerical simulation are
compared with the experimental ones and exhibit a close correlation.
Keywords: aluminum alloy, anisotropic yield criterion, numerical simulation, stamping.
Introduction. Nowadays, there is a great demand for high-quality FE models within
the numerical simulations, because significant part of the production problems can be
eliminated in the preproduction phase using the finite element analysis (FEA). For precise
prediction of the true forming process, the selection and accuracy of material input data are
very important. Most of phenomena observed in sheet metal forming like hardening,
anisotropy, failure and fracture occur simultaneously and may deeply affect the behavior of
the material due to the important changes they cause in its physical and mechanical
properties, such as formability, hardness, strength, springback and others [1]. Numerical
simulation of the sheet metal forming processes requires the implementation of several
types of models. The first type comprises the flow behavior, i.e., hardening models and
yield criteria of the sheet metal, while others predict the forming limits under specific
processing conditions. Recently, a lot of computational models within the metal forming
regard yield criteria were developed [2–4], one of these being the anisotropic yield criterion
proposed by Vegter [5], where the yield function is based on the yield locus description.
The prediction of forming limits in [5, 6] has shown a strong influence of the shape of the
yield function relating the plane strain and equi-biaxial stress states.
The aim of this paper is to describe the Vegter model implementation for the explicit
FE code and the procedure of measurement of the most critical input material data required
for numerical simulations of the AW 5754 aluminum alloy. Such measurements comprise
the experimental results of not only static tensile tests, but also of hydraulic bulge tests, in
order to determine the so-called biaxial point and biaxial anisotropy in the Vegter model,
respectively. The results of numerical simulation are compared with those obtained using the
conventional Hill 48 yield criterion [7], which is still frequently used in case of the material
input data lack.
Experimental Procedure. In this work, an AW 5754 H11 aluminum alloy, which is
widely applied in the automotive industry for production of inner body parts, was used (as a
sheet material of 0.8 mm thickness). Its chemical composition being shown in Table 1, this
alloy has a medium strength, is age-hardened and can not be heat-treated.
Since aluminum alloys are characterized by a high anisotropy, their behavior has to be
described in the FEM code within framework of the advanced material model. Elaboration
© J. SLOTA, M. ÐISER, 2016
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4 21
of advanced material models like the Vegter or Barlat ones requires the conduction of
numerous basic mechanical tests. The Vegter model was developed, in order to obtain a
high accuracy combined with a simple mathematical description and a large flexibility. The
original Vegter model uses the experimental results from from nine types of tests. In order
to reduce the number of parameters in the model, a new variant, the so-called Vegter lite
model has been developed [6]. Actually, only two test types are required for construction of
the Vegter yield function, the first one being the static tensile test and the second one –
the hydraulic bulge test, which is required for finding position of the biaxial stress � biaxial
point.
Static tensile tests were carried out using an universal testing machine TiraTEST
2300, which is a microprocessor-controlled machine for strength tests with the maximum
test load of 100 kN and measuring ranges of 1, 10, and 100 kN. Specimens used in this test
were cut in three directions (0, 45, and 90�) related to rolling direction. The basic
mechanical properties with planar anisotropy are shown in Table 2.
The hydraulic bulge test is a method to test a sheet metal under the equibiaxial stress
state. A sheet metal specimen is clamped between blankholder and die while it is subjected
to increasing fluid pressure as it is shown in Fig. 1. As the sheet specimen bulges, the
region near the pole of bulge becomes almost spherical. This test is used to identify a very
important point on the yield curve, which determines the yield stress at the equibiaxial
stress state.
Due to the stress state observed in this case being different from that in the static
tensile test, for construction of its stress–strain curve it is necessary to calculate the
J. Slota and M. Ðiser
22 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4
T a b l e 1
Chemical Composition of Aluminum Alloy AW 5754 H11 (wt.%)
Mg Mn+Cr Mn Si Fe Cr Zn Ti Cu Other
3.60 0.60 0.50 0.40 0.40 0.30 0.20 0.15 0.10 0.15
T a b l e 2
Basic Mechanical Properties of AW 5754 H11
Direction
(deg)
Re ,
MPa
Rm ,
MPa
A80 ,
%
r rm �r n nm �n
0 115 231 19.6 0.655
0.797 �0.214
0.282
0.283 �0.000245 112 220 26.1 0.904 0.283
90 116 221 25.4 0.723 0.283
Fig. 1. Schematic of the hydraulic bulge test.
so-called effective stress � i and effective strain �i . The respective values are derived
from Eqs. (1)–(3), as follows
� i
pR
t
�
2
, (1)
t t�
�
�
�
0
2sin
,
�
�
(2)
� �i t t�� ��3 0ln( ), (3)
where � i is effective stress (MPa), p is pressure (MPa), �i is effective strain, R is the
radius of curvature (mm), and t and t0 are the actual and initial thickness values (mm),
respectively.
During the test, the pressure and the actual height of dome are measured. Using
Eqs. (1)–(3) the stress–strain curve can be constructed. Comparison of stress–strain curves
based on the uniaxial tensile and hydraulic bulge tests is shown in Fig. 2. The test sequence
was recorded using ARAMIS system to measure strain distribution and determine the
biaxial coefficient rbiaxial .
Based on these calculated results, it was necessary to create a material model in the
simulation software (Fig. 3) that accurately describes the behavior of the sheet material.
Numerical simulations of Swift drawing test were carried out with the PAM-STAMP 2G
software for prediction of metal forming processes. This FEM code offers numerous
combinations of different hardening laws and yield functions. In this work, two different
yield functions were evaluated in combination with the Krupkowski hardening law, which
implies two regions of deformation. In the first region, the hardening effect exceeds the
thickness reduction egffect. The second area is characterized by the condition that
hardening can not be compensated by the reduction of tractive force due to reduction of
thickness. The Krupkowski formula can be expressed by the following equation:
� � �� �K p
n( ) ,0 (4)
where � p is plastic strain, �0 is offset strain, n is strain-hardening exponent, and K is
the material constant. Parameters for the Krupkowski law in the direction parallel to the
rolling direction were fitted and set to K � 0.3481 GPa, n� 0.137, �0 � 0.00032. The
value of rbiaxial was determined from the hydraulic bulge test. Parameters of the
Krupkowski law were obtained from the uniaxial tensile test and processed in Excel.
Advanced Material Models for Stamping ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4 23
Fig. 2. Comparison of stress–strain curves from uniaxial tensile and hydraulic bulge tests.
The yield function can describe plastic behavior of a sheet material in the multiaxial
stress state. As it was mentioned above, two yield functions were applied to compare the
accuracy of the material model. For aluminum alloys, the Vegter model should be more
suitable due to more convenient results. Simulation results were compared with those
obtained via the Hill 48 model [7], because this yield function is still one of most
commonly used material models in numerical simulations. The material data required for
defining the yield function are shown in Fig. 3.
In 1948, Hill introduced the concept of material anisotropy into the yield function
equations for the first time [7]. According to the Hill yield function, in case of uniaxial
stress state, the local thickness reduction occurs along the most vulnerable direction, which
is the loading direction. Hill assumed that the direction of thickness reduction is compliant
with the direction of zero extension, and therefore the deformation of narrowed areas
appears only as reduction in thickness. Hill 48 is one of the most commonly used material
model for conventional steel sheets. This yield function is set to be used with isotropic
hardening law. The yield function was proposed for orthotropic materials. Based on the von
Mises yield function, Hill has created a reasonable mathematical model to describe the
anisotropic plastic flow. The latter led to establishment of the theory of anisotropic plastic
deformation,
F G H L Myy zz zz xx xx yy yz zx( ) ( ) ( )� � � � � � � �� � � � � � � �2 2 2 2 22 2 2 12N xy� � . (5)
In the above formula, x y z, , are the orthotropic axes. Parameters F G H L M, , , , ,
and N are the independent anisotropic characteristic parameters determined by experiments
for different materials. In the numerical simulation, a simplified quadratic yield function
corresponding to the planar anisotropic and normal anisotropies is used:
Fig. 3. The material data required for both applied yield functions.
24 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4
J. Slota and M. Ðiser
� � � � �Y Y
r
r
2
1 2 2
2 22
1
�
�
� � , (6)
where �Y is the yield stress and r is the Lankford coefficient of normal anisotropy.
The Vegter criterion provides a possibility of a more accurate description of the yield
locus by a series of experimental points. Vegter was able to establish a first quadrant of the
yield function using the points obtained from the basic experimental measurements. The
Bezier interpolation is performed between points to construct the ellipses. Each point must
have 3 parameters (two main stresses �1, � 2 and strain vector � � �� d d2 1). In order to
describe a planar anisotropy by this model, it is necessary to have 17 parameters from 9
mechanical tests. Figure 4 illustrates the requirements for the conventional and lite Vegter
material models. Mathematical expression of this yield function is as follows:
�
�
�
�
�
� �
�
�
1
2
2 1
2
1
2
1 2 1
�
�
�
� �
�
�
�
� �
�
�
�
�( ) ( )
i
r
i
h
�
�
�
2 1
2 1
�
�
�
�i
r
, (7)
where � is the parameter for the Bezier interpolation.
There is a possibility to use a simplified (the so-called Vegter lite formula). It is an
optional model that uses only 7 parameters instead of 17 by skipping plane strain and pure
shear information. To define this 7 parameters, only 3 mechanical tests are needed,
including the static tensile test, hydraulic bulge test and measurements of the anisotropy
( ,� uniaxial
45� � uniaxial
90� , � biaxial , runiaxial
0� , runiaxial
45� , runiaxial
90� , and rbiaxial ). From the static tensile
and hydraulic bulge tests, the reference points � uniaxial , � biaxial are determined, which is
shown in Fig. 5a. Then, using the planar anisotropy data, points normal to reference points
are constructed (Fig. 5b). After this, these points are used to derive tangents to the Vegter
lite model. Using the Bezier interpolation between reference points (Fig. 5c), the hinge
points (as intersections points from the known slope in these reference points) are also
identified.
For the purpose of verifying the accuracy of used yield functions, the deep drawing
cupping test was carried out in explicit dynamic finite element code. In the numerical
simulation, the tools were assumed to be rigid and the blank was elastic-plastic. We used
the die with inner diameter of 52.5 mm and radius of 2.5 mm. The punch diameter of 50 mm
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4 25
a b
Fig. 4. The Vegter lite model (a) with NURBS interpolation and the Vegter yield locus (b) with the
Bezier interpolation between points.
Advanced Material Models for Stamping ...
and radius of 5 mm was assumed. The blankholder force is approximated to be 8 kN. The
friction coefficient was 0.12 mm, which simulated the conditions similar to drawing with
lubrication. In the numerical simulation, the shell mesh type was used with mesh size of
5 mm. Mesh size after final refinement was 1.25 mm. During the deep drawing simulation,
the circular blank was clamped between blankholder and die, and then the punch was
shifted down until the assigned stroke was reached. Positioning of the forming tool and
blank before drawing process is shown in Fig. 6. Comparison of several yield criteria for
AW 5754 H11 alloy, which can be set in simulation FEM code as shown in Fig. 7.
26 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4
Fig. 6. Rapid drawing cup test.
Fig. 7. Comparison of yield functions for AW 5754 aluminum alloy.
a b c
Fig. 5. The Bezier interpolation between the reference points for the Vegter lite material model.
J. Slota and M. Ðiser
Results and Discussion. For numerical simulation simple drawing of axisymmetric
cup with the diameter of 50 mm was chosen. In order to achieve the formability limits, the
initial blank diameter was 90 mm, which indicates the computational model influence on
the forming limit strains. For a contact between the tool and the formed sheet, the friction
coefficient of 0.12 was selected, while the blank holding force was set to 8 kN.
A significant difference between the results using the Vegter lite and the Hill 48 yield
models was observed. As seen from Fig. 8, large differences in the limit strains were
observed. During the simulation, crack initialization with the Hill 48 yield function for the
transition between the bottom and wall of the cup occurs (see Figs. 8a and 9a), while within
the Vegter lite model the crack did not appear, as shown in Figs. 8b and 9b. The true
experiments of stamping under the same technological conditions as used in simulation
were performed. The Vegter lite results show a good agreement with the true drawn cup
(Figs. 10 and 11), but the results obtained by the Hill 48 function are different. On the basis
of the performed measurements and experiments, it is possible to conclude that the
computational Vegter lite model is much more suitable for special alloys and zones with
high deformation than model Hill 48. A similar conclusion has been reached by other
researchers [8, 9].
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4 27
Fig. 8. Comparison of the FLDs from numerical simulation for the Hill 48 (a) and the Vegter lite (b)
anisotropic yield criteria.
b
a
Advanced Material Models for Stamping ...
Conclusions. The influence of advanced material model on numerical simulation
results was evaluated. Predictive numerical simulations of deep drawing of a simple
axisymmetric cup of the anisotropic aluminum alloy AW 5754 were carried out. the
material model with the Hill 48 yield function was compared with the Vegter lite criterion.
The true cups under the same technological conditions as used in predictions were deep
drawn. Accurate forming simulations require accurate material models. The Vegter lite
yield function, due to its more complex description of material, offers more accurate
results. In FEM implementation, the CPU time was comparable to those of the Hill 48
model.
28 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4
a
b
Fig. 9. Comparison of predicted thicknesses for the Hill 48 (a) and the Vegter lite (b) anisotropic
yield functions.
Fig. 10. A final drawn cup with no crack.
J. Slota and M. Ðiser
Acknowledgments. The authors gratefully acknowledge the financial support of the
project VEGA 1/0872/14.
1. S. Bruschi, T. Altan, D. Banabic, et al., “Testing and modelling of material behavior
and formability in sheet metal forming,” CIRP Ann.-Manuf. Techn., 63, Issue 2,
727–749 (2014).
2. F. Barlat, H. Aretz, J. W. Yoon, et al., “Linear transformation-based anisotropic yield
functions,” Int. J. Plasticity, 21, 1009–1039 (2005).
3. D. Banabic, T. Kuwabara, T. Balan, and D. S. Comsa, “An anisotropic yield criterion
for sheet metals,” J. Mater. Process. Technol., 157-158, 462–465 (2004).
4. D. Banabic, D. S. Comsa, M. Sester, et al., “Influence of constitutive equations on the
accuracy of prediction in sheet metal forming simulation,” in: P. Hora (Ed.), Proc. of
7th Int. Conf. (NUMISHEET 2008, Sept. 1–5, 2008, Interlaken, Switzerland) (2008),
pp. 37–42.
5. H. Vegter and A. H. Boogaard, “A plane stress yield function for anisotropic sheet
material by interpolation of biaxial stress states,” Int. J. Plasticity, 22, 557–580
(2006).
6. H. Vegter, C. ten Horn, and M. Abspoel, “The Corus–Vegter lite material model:
simplifying advanced material modelling,” Int. J. Mater. Forming, 2, No. 1, 511–514
(2009).
7. R. Hill, “A theory of the yielding and plastic flow of anisotropic metals,” Proc. Roy.
Soc. Lond. A Math. Phys. Sci., 193, Issue 1033, 281–297 (1948).
8. P. Solfronk, J. Sobotka, M. Kolnerova, and L. Zuzanek, “Utilization of advanced
computational models for drawing process numerical simulation of titanium alloy,” in:
Proc. of 24th Int. Conf. on Metallurgy and Materials: Metal 2015 (June 3–5, 2015,
Brno, Czech Republic), pp. 1–6.
9. J. Novy, V. Vache, and J. Sobotka, “Influence of used yield function in deep drawing
simulation of highly anisotropic aluminum alloy,” in: Proc. of Int. Conf. IDDRG 2013
(June 2–5, 2013, Zurich, Switzerland), pp. 273–277.
Received 10. 08. 2016
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4 29
Fig. 11. Thinning at the punch stroke edge.
Advanced Material Models for Stamping ...
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