-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
1/34
Finite element simulation of stretch forming
behaviour of four different processed
Mg alloy sheets
Thesis submitted in the fulfilment of the requirements for the award of the
degree of
BACHELOR OF TECHNOLOGY (HONS.)
IN
MECHANICAL ENGINEERING
BY
B.Venkata Sainath
Roll No: 10MF3IM05
Under the guidance of
Prof. S.K. Panda
DEPARTMENT OF MECHANICAL ENGINEEERING
INDIAN INSTITUTE OF TECHNOLOGY KHARAGPUR
JULY 2014
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
2/34
CERTICATE
This is to certify that the thesis entitled Finite element simulation of
stretch forming behaviour of four different processed Mg alloy sheets
submitted by Mr B. Venkata Sainath (10MF3IM05) to the Department ofMechanical Engineering, Indian Institute of Technology, Kharagpur, in partial
fulfilment for the award of degree of Bachelor of Technology (Hons.) is a bona
fide record work carried out by him under my supervision and guidance. This
thesis has fulfilled all the requirements as per the regulations of this Institute
and, in my opinion, has reached the standard needed for submission.
_______________________
Prof. S. K Panda
Department of Mechanical Engineering
IIT Kharagpur
.
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
3/34
DECLARATION BY STUDENT
I certify that
a) The work contained in this report has been done by me under theguidance of my supervisor.
b) The work has not been submitted to any other Institute for any degree ordiploma.
c) I have confirmed to the norms and guidelines given in the Ethical Code ofconduct the Institute.
d) Whenever I have used materials (data, theoretical analysis, figures andtext) from other sources, I have given due credit to them by citing them in
the text of report and giving their details in the references. Further, I have
taken permission from the copyright owners of the sources, whenever
necessary.
DATE: Signature of the Student
B.Venkata Sainath
10MF3IM05
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
4/34
ACKNOWLEDGEMENT
I would like to acknowledge and extend my heartfelt gratitude to my
guide, Prof. S. K Panda, Mechanical Engineering Department, Indian Institute
of Technology Kharagpur for guiding me through the entire course of the
project. Without his guidance, I would not have been able to complete my work.
I would like to extend my gratitude to research scholars Kaushik
Bandyopadhyay and Sudhy of the foundry lab, mechanical engineeringdepartment for their continuous support throughout my project.
Date:
B.Venkata Sainath
10MF3IM05
Department of Mechanical Engineering
IIT Kharagpur
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
5/34
Table of Contents
Chapter.1 ............................................................................................................... 8
1. Introduction:- ................................................................................................. 8
1.1 Stretch Forming: ....................................................................................... 9
1.2. Limiting Dome Height Test: .................................................................. 10
Chapter.2 ............................................................................................................. 12
2. Literature Review:- ...................................................................................... 12Chapter.3 ............................................................................................................. 14
3. Objectives:- .................................................................................................. 14
4. Methodology:- ............................................................................................. 15
4.1 STEP1 (Obtaining n, K and E values from the stress-strain graph):- .... 15
4.2 STEP2 (Finite element modelling and simulation of LDH test set up) 18
5. Results and Discussion:- .............................................................................. 22
5.1. Limiting Dome Height (LDH):- ............................................................ 22
5.2. Forming limit diagram (FLD):- ............................................................. 23
5.2.1. FLD obtained through Keeler-Brazier equation: ................................ 23
5.2.2. FLD obtained from simulation: .......................................................... 25
5.3. Thickness distribution:- ......................................................................... 28
5.3.1. Thickness distribution of TRC & rolled ZKQX alloy sheet: ............. 28
5.3.2 Comparison of Thickness distribution of ZKQX alloy sheets: ........... 29
Chapter.6 ............................................................................................................. 33
Conclusions:- ................................................................................................... 33
7. References :- ................................................................................................... 34
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
6/34
Table of Figures
Figure 1 Simple stretch forming process of a sample sheet ............................... 9
Figure 2 A schematic of the tool set-up for hemispherical limiting dome
height tests.[1] ..................................................................................................... 10
Figure 3 Engineering stress-strain diagrams of different ZKQX alloy sheets ... 15
Figure 4 Finite element modelling of limiting dome height set up
a) Front view b) Isometric view .......................................................................... 18
Figure 5 Simulation of the stretch forming of TRC & rolled alloy sheet .......... 20
Figure 6 Thickness distribution of the cup at the limiting dome height - top view
............................................................................................................................. 21
Figure 7 Comparison of FLDs of ZKQX alloy sheets obtained through
Keeler-Brazier equation ...................................................................................... 24
Figure 8 FLDs of all ZKQX sheets obtained through simulation ..................... 27
Figure 9 Thickness distribution of TRC & rolled ZKQX alloy sheet ................ 28
Figure 10 Comparison of thickness distribution of ZKQX alloy sheets ............ 30
Figure 11 Thickness distribution of ZKQX alloy sheets ................................... 31
Figure 12 Variation of minimum thickness of the cup along the curvilinear.....32
distance from the centre
http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507233http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507234http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507234http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507237http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507240http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507243http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507243http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507243http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507240http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507237http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507234http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507234http://c/Users/sainath/Downloads/btp%20finally%20doing--incomplete.docx%23_Toc392507233 -
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
7/34
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
8/34
Chapter.1
1. Introduction:-
Magnesium alloys are subjects of intensive research interest as potential
structural materials for weight reduction in transportation vehicles[1]. Currently
magnesium alloys are mainly used as cast products because of their excellent
castability. However, due to their limited formability and their low strength
compared to aluminium alloys, very few magnesium alloys are used as wrought
products. High-strength sheet alloys should find use in many applications, not
only for automotive applications but also for lightweight casing of electronic
products. The ability of plastic deformation of the magnesium alloys is poor.
Therefore, the conventional production process of the magnesium alloy strips
takes many steps, including multi-hot rolling and multi-heat- treatment, which is
long and needs high energy cost. By the twin-roll casting, the magnesium alloy
cast strip with thickness ranging from 2mm-8mm can be produced and then be
rolled to the needed thickness, which is a highly effective, time-saving, and
energy saving process.
Many magnesium alloys were casted recently using this twin roll casting
technology. The TRC Mg2.4Zn3Al0.3Mn alloy sheet with a T6D heat
treatment (solution treatment and double ageing) showed a tensile yield strength
of about 319 MPa with an elongation to failure of 6.3%. This yield strength is
significantly higher than that reported for the conventionally rolled AZ31 (Mg
3Al0.5Zn (at.%)) (235 MPa). It was reported that reported that trace additions
of Ag and Ca enhanced the age hardening of MgZn alloys.
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
9/34
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
10/34
For the simple stretch forming process, the sheet sample which has to be
formed, is clamped between two gripping jaws located on opposite ends, see
Figure 1.The forming tool or block is fixed on to a tool table which can be
moved hydraulically in a vertical direction. The forces necessary for the
forming are transferred through the form block to the sheet sample. The part to
be formed receives its contours during the motion of the forming block, the
gripping jaws remaining stationary.
1.2. Limiting Dome Height Test:
It is a method to evaluate the formability of a sheet metal. In this test, the
sheet sample is firmly clamped between the two gripping jaws located on
opposite ends and is stretched by a hemispherical punch in transverse direction
as shown in figure 2. During the motion of the forming block, the blank sheet
receives its contours.
Figure 2 A schematic of the tool set-up for hemispherical limiting
dome height tests.[1]
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
11/34
Due to the large area of contact between the hemispherical punch and the
blank, the frictional forces prevent a deformation of the sheet in this region.
This is especially true for flat shapes where even a small motion of thehemispherical punch is sufficient to allow a large part of the blank to "hug" the
punch.
A further motion of the hemispherical causes the sheet blank to be
strained, but mainly in the region of the frame. Due to the frictional forces
acting between form block and blank, the middle regions hardly undergo any
deformation, i.e., the maximum possible straining capacity of the sheet is notattained. This means that the maximum attainable theoretical elongation,
calculated on the basis of the length of blank between the gripping jaws, cannot
be attained, since the middle regions of flat shapes are hardly deformed and,
therefore, do not contribute much to the total deformation strain. The sheet
material flows under the tensile stress only out of the sheet thickness, so that the
surface of the sheet expands. When the hemispherical punch reaches critical
depth, cracking of sheet metal occurs. The greatest depth that the blank can
withstand under the pure stretching of the hemispherical punch without crackingis called limiting dome height. This is a standard measurement of stretchability.
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
12/34
Chapter.2
2. Literature Review:-
Magnesium alloys are promising structural light materials due to their
high specific strength, high specific stiffness, and so on. The use of Mg alloys is
expanding, particularly in automobile industry and consumer electronics
industry and. For their greater applicability, forming technology for high-
performance Mg alloy sheets should be developed. Deformation modes of Mg
crystals are mainly the (0001) (1120) basal slip, the prismatic slip,
the pyramidal slip, the second-order pyramidalslip and the twinning. Because the critical resolved shear stresses
for non-basal slips are higher than that for a basal slip near room temperature,
formability of Mg alloys strongly depends on texture. Additionally, since rolled
Mg alloy sheets show strong basal texture and, rolled Mg alloy sheets often
exhibit low press formability at near room temperature.
Recently, twin roll casting (TRC) has been applied to magnesium alloys toreduce the strong basal texture and grain size. So far, only a few heat-treatable
TRC alloys, such as Mg2.4Zn0.3Mn (at.%) and Mg2.4Zn(13)Al0.3Mn
(at.%) alloys have been reported [6]. The TRC Mg2.4Zn3Al0.3Mn alloy
sheet with a T6D heat treatment (solution treatment and double ageing) showed
a tensile yield strength of about 319 MPa with an elongation to failure of 6.3%
[6]. This yield strength is significantly higher than that reported for the
conventionally rolled AZ31 (Mg3Al0.5Zn (at.%)) (235 MPa).
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
13/34
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
14/34
Chapter.3
3. Objectives:-
The objective is to study the stretch formability of four different
processed Mg alloy sheets by finite element simulation to get insight into the
influence of pre processed conditions on formability and hence automotive
industries will select the suitable manufacturing process for the production of
Mg alloy sheet metals.
These four different processed sheets are:
(i) Twin roll casted (TRC) and rolled ZKQXsheet
(ii) Twin roll casted (TRC) and heated ZKQXsheet
(iii) Ingot casted and extruded ZKQXsheet
(iv) Ingot casted, extruded and heat treated ZKQXsheet
Hence the following are the specific objectives of the present study:
1. To develop finite element (FE) model of limiting dome height (LDH) test to
evaluate formability of the four different processed Mg alloy sheets.
2. To predict failure during stretch forming by incorporating forming limit
diagram (FLD) of all the four different processed Mg alloy sheets.
3. To predict and compare thickness distribution in stretch formed cups for all
the four different processed Mg alloy sheets.
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
15/34
Chapter.4
4. Methodology:-
4.1 STEP1 (Obtaining n, K and E values from the stress-strain graph):-
Engineering stress-strain diagrams of the ZKQX alloys sheets having
undergone different forming processes plotted in the same graph are obtained
from the literature review as shown in figure2.
Figure 3 Engineering stress-strain diagrams of different ZKQX alloy sheets
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
16/34
Engineering stress-strain data has been collected for each of the curve
in the above figure using plot digitizer software. Engineering stress and
engineering strain are converted into true stress and true strain using the
following standard equations (1) and (2).
ln( ......(1)
= ( ......(2)
Where = true stress, = engineering Stress ,
= true Strain , engineering Strain
The relationship between stress and strain in the plastic region (between
yield point and UTS) of the true stress-true strain diagram is given by the
Hollomons equation(3) as follows:
= K......(3)
where = true stress
K = strength coefficient
= true Strain n = strain-hardening exponent
The value of n lies between 0 and 1. A value of 0 means that a material is a
perfectly plastic solid, while a value of 1 represents a 100% elastic solid. Most
metals have an n value between 0.10 and 0.50.
The equation (3) can be converted to linear form by taking logarithm on both
sides as follows
( + ......(4)
True Stress and true strain data is plotted on log-log graph and K and n
values are obtained for each of the curve. Youngs modulus(E) for each of the
curve is also calculated by collecting the data on the linear portion of the
engineering stress-strain diagram. The values of theses mechanical properties
(n, K and E values) are provided in table 1.
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
17/34
Table 1: strain hardening exponent (n), strength coefficient (K) and Youngs
modulus (E) of four different processed ZKQX alloy sheets
Sl.No ZKQX alloy n
value
K (MPa)
value
E(Youngs
modulus in
GPa)
1 TRC & rolled 0.22 490.9 42.3
2 TRC & Heat Treated 0.07 444.6 34.8
3 Extruded 0.11 503.5 34.8
4 Extruded & Heat Treated 0.09 480.3 34.8
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
18/34
4.2 STEP2 (Finite element modelling and simulation of LDH test set up)
Different tools used in limiting dome height test such as die, binder,
tool and draw bead are modelled in the eta/DYNAFORM version 5.7.1 softwarealong with the blank as shown in figure 4. Quarter model has been employed for
modelling and simulation because of less computational time. Two different
views of the model (X-Z view) front view and isometric view of the model are
shown in figure 3.The detailed geometrical properties used for the modelling are
mentioned in the table 2.
a) Front view of FE modelling b) Isometric view of FE modelling
Figure 4 Finite element modelling of limiting dome height set up
a) Front view b) Isometric view
Table 2: Geometrical properties considered for FE modelling
Sl.No Parameter Size(mm)
1 Thickness of the blank 1.2
2 Radius of the blank 47.4
3 Inner radius of the die, binder 27
4 Outer radius of the die, binder 90
5 Radius of the hemispherical punch 25
6 Radius of the draw bead 36
7 Corner radius of the die 10
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
19/34
The designed model as shown in the above figures has been analysed
using LS-DYNA Program manager and simulated in ETA/post-processor 1.8.0
using material properties of the blank such as (n) strain-hardening exponent, (K)
strength coefficient and E (Youngs modulus). Simulation has been carried out
for all the four different types of alloy blank sheets. Many parameters were
assumed during the simulation.
Parameters assumed in the simulation:
1. Tooling such as die, binder, punch, draw bead are rigid bodies and blankis deformable.
2. Static friction between the die and the blank is equal to 0.1.3. Static friction between the punch and the blank is equal to 0.1.4. Poissons ratio of all the alloys is 0.29.5. Binder force applied on the blank is 5000N.6. Von-Mises criterion is used as failure criteria for the blank.7. Stroke distance is 30mm.8. Stretching is considered to be symmetric along x-z and y-z planes.
Simulation for all the blanks has been carried in 150 steps and some of
these intermediate steps are shown in the figure 5. Limiting Dome Height is
obtained by measuring the height of the cup at one step before onset of
cracking. Forming limit diagrams are also obtained for each of the sheets and
the results have been discussed in section 5.2.
Thickness of the cup at various nodes at the limiting dome height has been
calculated as shown in the figure 6 and curvilinear distance of these points from
the centre of the cup is measured. Using this data, variation of the thickness of
the cup at the limiting dome height has been plotted against the curvilinear
distance from the centre of the cup.
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
20/34
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
21/34
Figure 6 Thickness distribution of the cup at the limiting dome height - top view
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
22/34
Chapter.5
5. Results and Discussion:-
5.1. Limiting Dome Height (LDH):-
It is the greatest depth that a material can withstand under the pure
stretching of a hemispherical punch .This is a standard measurement of
stretchability. LDH values of all the four sheets obtained from the simulation
are mentioned in Table 3.
Table 3: LDH values of different ZKQX alloy sheets
Sl.No ZKQX alloy n value UTS(M Pa) Yield
strength(M Pa)
LDH(mm)
1 TRC & rolled 0.22 285 177 25.17
2 TRC & HeatTreated
0.07 342 320 15.53
3 Extruded 0.11 352 305 19.30
4 Extruded &
Heat Treated
0.09 360 325 16.98
It is observed that TRC & rolled ZKQX sheet shows higher value of
limiting dome height of 25.17 mm compared to other sheets. Generally LDH
increases with decrease in yield strength. If yield strength is low, material starts
undergoing plastic deformation at an earlier stage. Since TRC & rolled ZKQX
sheet has very low yield strength value (177 M Pa) compared to other sheets, it
has shown exceptionally higher value of LDH or formability.
Extruded ZKQX sheet has shown LDH of 19.31 mm, higher than that of
TRC & heat Treated and extruded & heat treated ZKQX sheets because its yield
strength of 305MPa, slightly lower than that of them. LDH values of TRC &
heat treated sheet and extruded and heat treated sheet are close because their
yield strength values are close.
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
23/34
Though extruded and heat treated ZKQX sheet has slightly higher yield
strength than TRC & heat treated alloy, it has higher LDH. The reason for this
can be extruded & heat treated alloy has a wider plastic zone (between yield
strength and UTS) than the TRC & heat treated alloy.
The order of formability of sheets based on LDH values is as follows:
TRC & rolled > Extruded > Extruded and Heat treated > TRC & Heat treated
5.2. Forming limit diagram (FLD):-
5.2.1. FLD obtained through Keeler-Brazier equation:
FLDs for all the ZKQX alloy sheets were drawn by calculating
(Plain-strain intercept) using KeelerBrazier equation:
(%) = (23.3+ 14.3*t)(n/0.21) ......(5)
Where t= initial thickness of the strip in mm
n= strain-hardening exponent
and sliding the Goodwin and Keeler Forming limit diagram downwards along
the major engineering strain axis by distance equal to the difference between
of the Goodwin and Keeler Forming limit diagram (43.3%) and of
the respective sheet calculated from the above equation. These values are given
in table 4.
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
24/34
Table 4: values of ZKQX alloy sheets
Sl.No ZKQX alloy Thickness (mm)
1 TRC & rolled 1.2 42.4
2 TRC & Heat treated 1.2 13.4
3 Extruded 1.2 21.5
4 Extruded and Heat
treated
1.2 16.3
FLDs of all the ZKQX alloy sheets obtained using Keeler-Brazier
equation are shown in the figure8.
Figure 7 Comparison of FLDs of ZKQX alloy sheets obtained throughKeeler-Brazier equation
0
20
40
60
80
100
120
140
160
180
200
-80 -60 -40 -20 0 20 40 60 80
MajorE
ngineeringStrain,%
Minor Engineering Strain,%
FLD of ZKQX alloy sheets
extruded and heat treated
Extruded
TRC
TRC and heat treated
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
25/34
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
26/34
Forming limit diagrams obtained from the simulation are shown in the
figure .Their values are estimated using Plot Digitizer and are compared
with that of the values obtained theoretically using Keeler-Brazier equation in
the table5.
Table5: Comparison of values obtained theoretically and from simulation
Sl.No ZKQX alloy %(eng.strain)
%(True strain)
theoretical
%(True strain)
-simulation
Error
(%)
1 TRC &
rolled
42.4 35.3 35.2 0.43
2 TRC and
heat treated
13.4 12.6 12.7 -0.64
3 Extruded 21.5 19.5 19.3 1.03
4 Extruded
and heat
treated
16.3 15.1 14.9 1.66
The values obtained from the simulation and form the Keeler-
Brazier equation are very close to each other. The reason for the minute
difference might be in collecting data using plot digitizer.
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
27/34
FLD of TRC ZKQX sheet FLD of TRC and Heat treated
ZKQX sheet
FLD of extruded ZKQX sheet FLD of extruded and heat
treated ZKQX sheet
Figure 8 FLDs of all ZKQX sheets obtained through simulation
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
28/34
5.3. Thickness distribution:-
5.3.1. Thickness distribution of TRC & rolled ZKQX alloy sheet:
Thickness at various points along the cup has been obtained at the
limiting dome height for all the ZKQX alloy sheets form the simulation. The
displacement between the successive points has been measured and it is
assumed to be equal to the curvilinear distance between them. Using this data,
distribution of thickness along the curvilinear distance from the centre of the
cup is plotted as shown in figure 9.
Figure 9 Thickness distribution of TRC & rolled ZKQX alloy sheet
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 10 20 30 40 50 60
Thicknessofthe
cup(mm)
Curvilinear distance from the centre of the cup(mm)
Series1
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
29/34
It can be observed that thickness first decreases till 15.1mm from the
centre of the cup and then increases till the flange region and attains a constant
value. It can also be observed that maximum thinning occurred at the punch
corner with a thickness value of 0.6 mm and maximum thickness occurs at the
flange region.
This is because the blank receives its contours during the motion of the
punch, the gripping jaws remaining stationary. At the beginning of the stroke,
the sheet blank first drapes itself around the form block, following its contours.
Due to the large area of contact between form block and the blank, the frictional
forces prevent maximum deformation of the sheet in centre region and a further
motion of the punch causes the sheet to be strained mainly in the region near the
punch corner. Draw bead which is used to control the flow of the sheet into die
cavity is responsible for the constant thickness of the cup around 41mm distance
from the centre.
5.3.2 Comparison of Thickness distribution of ZKQX alloy sheets:
Thickness variation of the cup for all the alloy sheets is observed to
follow the same pattern as that of TRC and rolled alloy. However, there are
significant differences in the minimum thickness values obtained and the
elongation of the sheet (measured as curvilinear distance from the centre of the
cup to corner of the flange portion).Thickness distribution of all ZKQX alloy
sheets has been plotted in the figure 10 and simulation results of thickness
distribution of the sheets at limiting dome height are shown in figure 11.
Minimum thickness value and elongation of the sheets has been calculated andcompared in the table6. It can be observed from figure 10 that minimum
thickness of the cup occurs at different distances from the centre of the cup.
This variation of the minimum thickness of the cup with the curvilinear distance
from the centre of the cup has been plotted in figure 12.
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
30/34
Figure 10 Comparison of thickness distribution of ZKQX alloy sheets
Table 6: Minimum thickness of the cup and elongation of ZKQX alloy sheets
Sl.No ZKQX alloy Minimum
thickness
(mm)
Elongation(mm) n value
1 TRC & rolled 0.60 9.68 0.22
2 TRC & heat treated 0.83 3.62 0.07
3 Extruded 0.73 5.66 0.11
4 Extruded and heat
treated
0.79 4.44 0.09
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 10 20 30 40 50 60
Thic
knessofthecup(mm)
Curvilinear distance from the centre of the
cup(mm)
TRC and rolled
TRC and heat treated
Extruded
Extruded and heat treated
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
31/34
TRC & rolled TRC & Heat treated
Extruded Extruded and Heat treated
Figure 11 Thickness distribution of ZKQX alloy sheets
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
32/34
Figure 12 Variation of minimum thickness of the cup along the curvilinear
distance from the centre
Fig 11 shows the thickness distribution of all ZKQX alloy sheets. It can
observed that blank become thicker at outer portions and thinner ant the punch
corner .As the punch forces blank into die cavity, the blank diameter decreases
and causes the blank to become to thicker at its outer portion due to
circumferential compressive stresses to which the material material elements inthe outer portion is subjected to.
Thickness distribution of all ZKQX alloy sheets has been plotted in
figure 11. It can be observed that TRC & rolled sheet has the lowest value of
minimum thickness (0.60mm) and highest elongation (9.68mm) compared to
other alloy sheets where as TRC & heat treated alloy has the highest value of
minimum thickness (0.83mm) and lowest elongation (3.616mm).The reasonsfor these variations among the sheets are due to differences in yield strength
value and same as that of limiting dome height (LDH).
The order of formability of sheets based on elongation and minimum thickness
value of the cup is as follows:
TRC > Extruded > Extruded and Heat treated > TRC & Heat treated
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 2 4 6 8 10 12 14 16
Minimumthickn
essofthe
cup(mm
)
Curvilinear distance from the centre of the axis (mm)
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
33/34
Chapter.6
Conclusions:-
Finite element modelling and simulation of the four different processed
magnesium alloys has been successfully done.
1. The TRC & rolled ZKQX alloy sheet is found to have much higher limiting
dome height than ingot cast ZKQX alloy sheets because its n value is much
higher than the others.
2. value of the TRC & rolled ZKQX alloy sheet is found to much higher
than ingot cast ZKQX alloy sheets which means that it can undergo more
thinning and stretching than the other alloy sheets.
3. Failure location (minimum thickness) and thickness distribution of all the
four different processed ZKQX alloy sheets has been obtained.
Hence, automobile industries should use TRC and rolled ZKQX alloy
than ingot cast ZKQX alloy sheets for better formability and for better
automotive applications.
-
8/12/2019 Finite Element Simulation of Sheet Metal Forming - Project Report
34/34