A finite-element analysis of the deep

drawing process

NEVILLE LAWLESS

10212298

20/4/11

School of Mechanical and Manufacturing engineering

DUBLIN CITY UNIVERSITY

Glasnevin, Dublin 9,

Ireland

II

Abstract

The primary goal of this research has been to validate the use of numerical simulation

software to model the deep drawing process. This was conducted using ANSYS12.1, in

which, 3 models have been constructed and tested. Model 1 constructed solely out of

PLANE82 elements, model 2 solely from SHELL208 elements and model 3 which has

been formed from a combination of both. These axisymmetric models have been used

to simulate the drawing process of drawing quality mild steel EN10130 FeP01 of 1 mm

thickness using both punch and die radii of 2mm Unconverging solutions and negative

jacobian errors have led to the failure of models 1 & 2, however model 3 has provided

satisfactory results with which comparisons have been made against experimental and

numerical results found in literature.

It has been shown that the areas of maximum strain in the cup occur on the inside wall

of the blank holder radii, and on the outside wall of the punch radii. A maximum value

of strain has been shown to be 0.6179.

Values for thickness distribution have also been obtained and compared against those

mentioned; the max and min values were found to be 1.108mm & 0.717mm. For

sections along the flange and cup wall, the average difference when compared against

experimental values is less than 5%, discrepancies begin to arise however when

approaching the cup base radii and then along its base. It has been discussed that

possible local variations of the frictional coefficient is the foremost reason for the large

inconsistencies between the experimental and numerical results. Further work is

needed to provide higher level of accuracies here.

Key words: Deep drawing, Finite element analysis, FEA, ANSYS, mild steel, sheet

forming processes.

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III

Contents

1. Introduction ....................................................................................1

2. Literature Review ..........................................................................2

3. Details of Finite Element Model ...................................................4

3.1. Environment .............................................................................................. 4

3.2. Material Properties ................................................................................... 5

3.3. Modelling ................................................................................................... 6

Creating Geometry ................................................................................ 6 3.3.1.

3.4. Meshing ...................................................................................................... 7

3.5. Loading ...................................................................................................... 9

Coupling nodes: .................................................................................... 9 3.5.1.

Boundary conditions........................................................................... 10 3.5.2.

3.6. Solution and Post-processing: ............................................................... 10

3.7. Convergence Testing: ............................................................................. 10

4. Results ........................................................................................... 11

4.1. Finite element results ............................................................................. 11

4.2. Comparison of results with literature .................................................. 14

5. Discussion: A Critical evaluation of the results. ....................... 15

5.1. Discussion of finite element analysis results ...................................... 15

5.2. Comparison with results from literature............................................. 17

6. Conclusions .................................................................................. 18

7. References ..................................................................................... 19

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1. Introduction

This work intends to approach the deep drawing process of thin walled, mild steel,

cylindrical containers, by means of a finite element analysis.

The objective of the work is to successfully simulate the deep drawing process and

validate any results found, by making a comparison with previously published

literature. This literature contains both experimental and numerical results which

are in close agreement with each other and so and is being set as the benchmark to

which comparisons can be made.

The incentive for doing this research is that deep drawing has come to a stage in the

current industrialised world that requires the most efficient, low-cost, manufacturing

route to be taken at all times. This needs to be done whilst also maintaining the

highest level of recyclability during the material pre-processing stage (cold rolling

etc.), the drawing stage and subsequent finishing stage. This efficiency and

recyclability is demanded by both the environment and the manufacturers.

Currently, the demand for metal containers in the world is in the region of 410 billion

units per annum. Out of this then, drink cans account for 320 billion and processed

food cans account for 75 billion. It is also known, that for the majority of food and

drink containers, the cost of the processed metal accounts for 50-70% of the total cost

[1]. From the manufacturer’s point of view then, a reduction in material usage is of

huge importance to cost reductions.

Reduction of material can be done by decreasing the wall thickness of the containers,

whilst also retaining adequate strength to allow the container to serve its purpose,

without fear of failure occurring. The designer must meet these expectations, but

also, must determine the material requirements and properties which are suitable for

the food or drink being packaged.

This brings us back to the objective of this work mentioned previously, the ability for

the designer/engineer to successfully numerically model the deep drawing process.

Traditionally, this process, and all metal forming techniques have been tested

experimentally using trial-and-error or empirical methods, which is an expensive

and time consuming approach, as dies, blank holders and punches all need to be

manufactured.

By making use of finite element analysis packages and statistical methods, the

prediction of results such as the punch force, the blank holder force, the thickness

distribution through sections of the metal and the lubrication requirements can be

determined. This can significantly reduce the production costs, for higher quality

containers by reducing the lead time to production and provides engineers the ability

to respond to market changes with greater speeds.

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In doing this, the level of knowledge in how various materials interact and the banks

of data for specific materials are also increased which is another positive outcome.

2. Literature Review

Prior to the development of any simulation models, an evaluation of previous work

in this field was undertaken. This was required so a greater understanding of the

task at hand could be reached and also in the hopes that similar work could provide

as a means of comparison once results have been found.

The first of these works is published by Colgan and Monaghan [2] and has taken a

statistical approach, based on Experimental design using orthogonal arrays to

ascertain which factors most influence the deep drawing process. As will be seen in

sections to follow, the geometries for the deep drawing process have been

reproduced by the author of this work, and a critical comparison made against them.

400 tests were carried out on blanks cut from drawing quality mild steel EN10130

FeP01 of 1 mm thickness and it was established that that the punch/die radii have the

greatest effect on the thickness of the deformed mild steel cups. It was made

apparent that the smaller the die radii, the greater the force on the blank, resulting in

thinner wall thicknesses. It was also shown that the type of lubrication is significant

to the force on the punch.

The authors explain that for the experimental component of the research, hydraulic

cylinders are the means by which the blank holder force is delivered. They also go on

to mention that a pressure gauge is currently being used to measure the pressure in

the cylinders in conjunction with a needle valve. Although providing adequate

results, it would be desirable to employ the use of strain gauges in this instance, so as

to gain a higher level of accuracy and confidence in the values obtained. From

Colgan and Monahan’s work [2], the die radii were noted as a prominent factor, but

not enough substance has been included to account for other factors affecting the

deep drawing process.

This is addressed in another approach seen in a paper by Demirci et al, [3] which

analyses the deep drawing process of AL1050 by performing experiments and a finite

element analysis using ANSYS/LS-DYNA on the effects of the blank holder forces on

differences in the cup wall thickness. They have shown that under constant pressure

the base of drawn cups remains at a constant value until thickness drops

dramatically towards the cup corners and then begins to rise exponentially towards

the outer edge on the cup flange. By taking into account the anisotropic properties of

the material they concluded that for forces above 10 MPa tearing in the cup would

occur.

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A paper published in 2007 by Dr. Waleed Khalid Jawad [4] confirms the previously

stated point that increasing the punch radii can decrease the punch load and vice

versa, if even only slightly. His work investigates the effect which punch radii holds

over the interfacial contact between the punch and the blank, punch load, thickness

through a section of the drawn cup, and the resulting localized strain and stress

distribution. Jawad concludes that frictional forces act mainly through the edge of the

punch in a shearing manner and that its flat section has little effect. It should be

noted here that the distribution of strain for the geometries created has a very similar

shape in most cases. This can be used as a means of comparison later in this work as

material models for mild steel have been selected from this paper.

Vladimirov et al, [5] present in their work, the derivation of a finite strain material

model for plastic anisotropy and nonlinear kinematic and isotropic hardening.

Following this, the work is applied numerically to the drawing of cylindrical and

square shaped cups. They show that the numerical simulations, can be suitably

prepared from the complex mathematical material models and that the phenomena

of anisotropic properties can still be accounted for even with large deformations.

They further go on to show the applicability of the mathematical work to account for

the occurrence of earring during the drawing process.

Having arrived at a point where the material can be modelled to a very high degree

of accuracy leaves the necessity for the selection of a drawing machine that can be

operated at a suitable capacity. By predicting the forming load required to complete

the drawing, cost analyses can be carried out for the manufacture of the container. In

a paper by Fereshteh-Saniee and Montazeran [6] forming load predictions are made

for various element types in the finite element method, and the strain thickness

distributions are once again produced, as seen in [4]. The authors also show that the

use of shell 51 elements in the finite element package hold a much higher agreement

with the experimental results, than those of when modelled with visco solid 106

elements. In making these comparisons, Fereshteh-Saniee and Montazeran use a

formula derived by Siebel in [7] to produce an analytical solution to which the level

of agreement between the various methods is generally acceptable.

Finally, research has led to the development of an analytical method to model the

frictional contact in elastoplastic models which undergo large deformations. This

paper by Meguid and Refaat [8] uses a method of variational inequalities to

implement this. The effect of nonlinearities arising due to the geometry or the

materials used in the model is met by using the updated Lagrangian formulation. As

with all of the previous literature these methods were applied to simulations of the

drawing process and have achieved satisfactory solutions.

Having carried out this review of work, it has become clear what factors have the

biggest influence during the sheet forming process and a number of methods of

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measurement and comparison have been identified. These shall be put into practice

in the research component of this work to follow.

3. Details of Finite Element Model

3.1. Environment

Element Types

PLANE82 is a 2-D, 8-Node Structural Solid. The eight node element is defined

by 4 nodes at each corner of the element and 4 along the length of each

connecting line. Each node has two degrees of freedom, correlating to

translations in the x and y directions.

This element type is a higher order form of PLANE42 and thus lends itself to

more accurate solutions. This element type is well suited for modelling plane

stress or axisymmetric problems and so it has been used to mesh the punch

and die components in the model. PLANE82 was chosen over PLANE42 as

there was a need for a circular fillet on the die and punch, the quadratic

nature of this element type leads to a better resulting mesh than the 4 node

element. [9]

Figure 1: Quadrilateral and triangular 8 node elements used in ansys [9]

SHELL208: is a 2 node element which has 3 degrees of freedom at each node. These

are translations in the x and y axes and also rotation about the z-axis. It is designed to

model thin to moderately thick axisymmetric shell based structures. It was chosen as

it models well finite strain while transverse shear strains are assumed small. [10]

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Figure 2: Shell 208 element shapes in ansys [10]

3.2. Material Properties

Three material models were utilised in this analysis:

Material model 1: used for punch/die/blank holder

This was set as tool steel which was selected as structural-> linear elastic

material with a young’s modulus of 210 GPa and poisons ratio of 0.3

Material model 2: used for the blank material.

It was selected as a structural -> Non-linear -> Inelastic-> Rate independent ->

Isotropic Hardening-> Bilinear material model.

The material which has been modelled as the blank in this research was as stated in

section 2.1, a mild steel. A paper by Jawa (2007) [4], investigates the effects of contact

in the deep drawing process and models the blanks from a very similar mild steel as

required in this instance. The properties which were specified in that paper were

taken directly. They are listed below in table 1

Table 1: Property table for Blank being formed.

Annealed mild steel

Property Value

Carbon content 0.15 %

Yield stress 200 MPa

Tangent modulus 0.5 GPa

Modulus of elasticity 200 Gpa

Poisson’s Ratio 0.3

Friction Coefficient 0.1

Material model 3: Coefficient of friction for all contact set as 0.1

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3.3. Modelling

Creating Geometry 3.3.1.

For this research, 3 separate models were built and tested. The reason for this was the

occurrence of errors and un-converging solutions in the two initials models (1 & 2),

the model types were:

1. 2-D Axisymmetric solid model built using all PLANE82 elements

2. 2-D Axisymmetric shell model built using all SHELL208 elements

3. 2-D Axisymmetric model built using a combination of PLANE82 for the die

and punch elements and SHELL208 for the blank elements.

The model dimensions were taken from a paper by Colgan and Monaghan [2].

Figure 3: Schematic illustration of the deep drawing process with table of inputs [6]

Models 1, 2 and 3 were modelled by inputting a log file containing commands to generate

key points and lines; this was done so if any changes needed to be made they could be

done with haste.

Areas which were desired to be map meshed needed to be either three or four sided. This

was done by concatenating any adjacent lines.

Figure 4 below indicates the line geometries constructed. An area was modelled to

represent the radius of 0.002m for both die and punch so that it could be altered if

required. The image on the left displays the blank as an area; this was altered to a shell

with thickness 0.001m in model 3, (The model for which a solution was found).

Blank holder force: 18KN

Dp 0.0394m

Do 0.076m

C 0.00015

Rp 0.002

RD 0.002

t 0.001m

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Figure 4: line diagram displaying the lines and area geometries created. Model 1&3 left, model 2, right.

3.4. Meshing

Model 1: For the initial model construction, a free mesh was employed on the punch

and die, with the corner radii being refined to accurately reflect any stress

concentrations occurring. A mapped mesh was generated on the blank holder and

blank as they were both 4 sided and meshed easily. The blank holder set to a size of

0.001m and the blank at a size of 0.00025m.

Figure 5: Model 1: Original Free mesh on die/punch and mapped mesh on blank @ 0.00025m

Again using model 1, A quadrilateral mapped mesh was generated on all areas apart

from the punch/die corner radii, which were triangular. This was done to achieve a

higher number of elements along this line so a solution using contact conditions

could be found easier.

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Figure 6: Model 1: Triangular mapped mesh on radii of blank/die and @0.0001m on blank

Model 2: Created from 4 lines (figure 5); this model was attempting to model the

deep drawing process using only shell elements. The shells were meshed with a

global element size of 0.0025m (figure 8).

Figure 7: Model 2: Mesh generated at 0.0005m

Model 3: The final model constructed was built using the PLANE82 material model

to represent the solid components; punch, die, blank holder. These were all mapped

meshed to size 0.0005m. The blank was modelled using the SHELL208 material

model and element size set to 0.00025m.

Figure 8: Model 3 (solved): complete mapped mesh. Die/punch @ 0.0005, Blank shell at 0.00025m

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3.5. Loading

Coupling nodes: 3.5.1.

Model 1 & 3: Nodes were coupled at various locations in all models so that loads

and displacements could be modelled successfully. Figure 9 below clarifies the

following description. On the blank holder (B) all nodes along the top surface were

coupled using the coupled node option (CP). A force applied to one node causes the

load to be applied evenly over the top surface of the area and not cause a stress

concentration to arise at the point of load application.

The area of the punch (A) has all nodes coupled in the Y-direction. This prevented

the deformation of elements up through the punch which could cause errors to arise.

Figure 9: Model which indicates areas which have had nodes coupled.

Model 2: Again the blank holder, modelled using shells, has all nodes coupled in the

y-direction, to evenly distribute the load. The punch and die has all nodes coupled in

all directions preventing bending unless a prescribed displacement is set.

Figure 10: Model 2 with nodes being coupled in their respective degrees of freedom.

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Boundary conditions 3.5.2.

Model 1 & 3: For the required deformation to be applied, a displacement was set on

the punch area A to a distance of 0.02m. Also this area was constrained in the x-

direction so no rigid body rotation could take place. The blank holder, area B, was

constrained in the X direction and the die, area C, was constrained to no movement

in all degrees of freedom.

Finally the blank, area D is constrained at its last node at the centre point (Far left)

from moving in the X- direction.

Model 2: As above, the shell model has a displacement applied to the punch shell of

0.02m and the blank shell constrained at its last node at the centre point (Far left)

from moving in the X- direction.

3.6. Solution and Post-processing:

Following the successful modelling of geometry, then meshing and correctly

applying boundary conditions and loads, a solution was run.

The solution was a large static displacement analysis. It was carried out with time

increments, having the max number of substeps set as 1000, minimum as 10, and a

desired number of 100 specified.

One of the primary objectives for carrying out this research, as stated previously, was

to make a comparison of values obtained, against a paper by Colgan and Monaghan

[2]. Values for plastic strain and cross sectional thickness were thus required.

The Von mises plastic strain was plotted on a contour plot to give a visual indication

of strain through the now deformed blank, and an elemental table was defined so a

list of values could be exported to excel to be graphed.

The same method was applied to ascertain values for thickness along a section of the

drawn cup.

3.7. Convergence Testing:

It has been seen that various models have been constructed. This has been due to the

unconverging solutions in each, or the simulations causing a negative jacobian error.

For the final model, (model 3) a solution was obtained. However, further refining the

mesh led to errors once again. So no proper convergence test has been carried out.

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4. Results

4.1. Finite element results

Having solved the model (model 3) with no errors being generated, the now

deformed cup can be plotted. A displacement of 20 mm or 0.02m can be seen as the

deformation applied below. Figures 11-17 represent the various results achieved

from the finite element analysis.

Figure 11: 2-D plot showing the deformed and undeformed edge of the cup in purple with the punch,

die and blank holder in cyan.

Figure 12: Contour plot of deformed cup with the von mises plastic strain plotted along the length of

the cup.

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Figure 13: As figure 13, enlarged, without punch/die/blank holder. Contour plot of von mises plastic

strain along length of deformed blank/cup

Figure 14: A 90o 2-D axisymmetric symmetry expansion of the deformed cup.

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Figure 15: A 360o 2-D axisymmetric symmetry expansion of the deformed cup.

Figure 16 below represents the distribution of von mises strain across the length of

the drawn cups cross section.

Figure 16: Percentage strain (von mises) along length of cup section.

4940 4960 4980 5000 5020 5040 5060

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Nodal numbers

Stra

in %

Strain

Von mises plastic …

14

Figure 17: Contour plot of the shell thickness along the length of the cup.

4.2. Comparison of results with literature

To validate results which were obtained from this finite element analysis, It was

required that a comparison be made against similar work in this field. This

comparison was made against the paper by Colgan and Monahan referred to in

section 4.6 [2]. Table 2 below, contains the thickness values of a cup section for the

experimental results found from deep drawing a sample of cups in [2], then the

Finite element analysis predication for the processes and below them, from this

authors work, the finite element results which were obtained. These have been

appropriately selected to correspond to the same distance across the section of the

drawn cup. A Percentage difference was also calculated between the experimental

results and the predicted values in this paper.

Table 2: Experimental and numerical results obtained from literature alongside results obtained in

this work.

1 2 3 4 5 6 7 8 Average StD.

Experimental 1.13 1.03 0.89 0.83 0.82 0.87 0.97 0.98 0.94013 0.10742

FEA Predicted 1.11 1.08 1.01 0.96 0.8 0.84 0.94 0.96 0.96225 0.10629

FEA carried out 1.11 1.11 0.84 0.83 0.72 0.72 0.72 0.72 0.84675 0.16831

% Difference

between Exp & FEA

carried out

2.12 -7.3 5.74 -0.4 12.9 16.9 25.1 26 10.1363 12.1022

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Figure 18 below gives a visual indication of how the three sets of data compare.

Figure 18: Shell thickness after deformation plotted against data from literature.

5. Discussion: A Critical evaluation of

the results.

5.1. Discussion of finite element analysis results

Model 1: A 2-D Axisymmetric solid model built using all PLANE82 elements. This

first attempt at modelling the deep drawing process was unable to be solved

successfully. The model failed to converge after being modelled with a course mesh

and once again with a much more refined mesh. All care was taken to ensure that

correct boundary conditions, loads and displacement were put in place and that the

material models matched the requirements of the research.

The major error which has been constantly seen when running the solution is the

occurrence of negative jacobian errors. This is possibly due to the deformation of the

elements in the blank as they deform around the corners of the die and punch. It is

possible that the elements twist in on themselves after becoming severely plastically

deformed, thus leading to this error.

0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

4940 4960 4980 5000 5020 5040 5060

Cu

p t

hic

nke

ss (

m)

Nodal numbers left= cup centre

Cup thickness along section

FEA Carried out

Experimental

FEA Predicted

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Model 2: A 2-DAxisymmetric shell model built using all SHELL208 elements.

Having not been able to ascertain results for the previous model it was felt that

taking a new approach to the problem might lead to a more elegant solution which

was initially overlooked. It was anticipated that by simplifying the model to only

four lines (figure 4) to represent the deep drawing process, that a solution may

converge easier.

As described in section 3, all the shells were specified to a thickness of 1mm or

0.001m and give an element length of 0.00025m. At this point numerous

consultations were made with more experienced users of Ansys/FEA as to how the

model could be correctly constrained. This was not successful however, as with

every attempt at solving, the same error: “Specified constraint not allowed on slave

degree of freedom in coupled set” was given. The constraints have been manipulated

numerous times to determine if a workaround could be found, but attempts have not

been successful.

Model 3: 2-DAxisymmetric model built using a combination of PLANE82 for the die

and punch elements and SHELL208 for the blank elements.

This final method has proved fruitful in providing a more respectable representation

of the deep drawing process via the finite element method. Figures 11-17 show the

final results which were reached using this model.

It is not yet fully understood why this model solved when comparing it against

model two, as the same constraints were applied to both. Nevertheless, the results

produced appear to be as required, so further investigation perhaps can be given at a

later time.

Examining figure 11 for any major points of interest does not lead to any particularly

insightful results. All deformations which have occurred appear to be as expected

and all materials boundaries remain intact which confirms that the model contact

conditions have held and a proper solution is presented.

A plot of the von mises plastic strain is given in Figures 12-15, it has been seen that

the areas of maximum strain through the thickness of the shell elements occur near to

where the maximum deformation is caused. This area is on the inside wall of the

blank holder radii, and on the outside wall of the punch radii. The value for the

maximum strain is 0.6179.

It should be noted at this point that along the base of the drawn cup, the distribution

of von mises strain is perfectly even once it has moved away from the corner area.

This, it is felt, is perhaps an erroneous value as it could be imagined that there would

be at least a small contouring present as the stain distribution fell off towards the

centre. No evidence could be found in other literature to confirm otherwise, however

a paper by Jawa [4], referred to in section 2, in which material properties which were

used for this analyses were found, hold strain graphs very similar to that in figure 17.

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A constant strain value of ~ 0.3 can be seen towards the centre of the cup which

travels horizontally before dropping and suddenly rising to a value of max strain

around 0.6/0.8. This suggests to the author that in fact the lack of a noticeable

contouring in this area is in fact correct, assuming similar material properties. This

shall be discussed further

5.2. Comparison with results from literature

The primary goal of this research has been to validate the use of a numerical

simulation of the deep drawing process. This was conducted using ANSYS12.1

which is based on the finite-element formulation. A paper selected by the research

supervisor “Deep drawing process: analysis and experiment, by Colgan and Monaghan

[2], performed an experimental and numerical analysis of the process and so a

comparison is to be made in this work against the values which have been recorded

for the cross sectional thickness of the deep drawn cup.

Table 2 has the values drawn from the literature in it, and also, the results which

have been found from the FEA analysis in ANSYS by the author of this work.

These values which have been found in this research correspond to the thickness at

every node along the cup cross section. Obviously these cannot be directly compared

to the 8 values provided in the reference literature. Therefore, 8 values were taken

from the generated data, at distances corresponding to these lengths in Figure 19

below.

Figure 19: Thickness measurement locations on the drawn cup.

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The maximum and minimum experimental values shown are: 1.132mm 0.823mm

and from this work are found to be 1.108mm & 0.717mm, which seems to hold in

reasonable agreement.

The average percentage difference between the experimental and FEA values can be

taken from table 2, and is 9.93%. Although this value seems to be quite large for the

1mm thick plate it, must be noted that the greatest error occurs at the base of the cup.

Here the cross section of the plate remains constant at a value of 0.724mm and so it is

felt that this area accounts for most of the discrepancies between values.

Examining the plot of the 3 different sets of values for thickness (figure 20) shows

that at locations 1-4, the results achieved in this work hold closer to the experimental

values. At location 5, where the maximum experimental thinning is found there

becomes a ~ 12% difference and parts 6-8 then show the biggest differences of 16-

26%. As of yet no substantial cause has been found to cause these large variations,

but it may be down to the frictional coefficient of 0.1 which has been set in the FEA

model in this report. There appears to be no set frictional value for the 8 values

reported in the paper by Colgan and Monaghan as they make use of a factorial

approach to the experiments and use either zero lubricant or use PE, which when

used in the deep drawing process can give values between 0.9 and 1.95.

It is felt by the author that the frictional modelling used in this work is not quite

adequate to deal with the real life contact conditions between punch-blank and die-

blank interfaces.

It is suggested that the frictional coefficient of 0.1 is too high for the punch/blank

contact region over the base of the drawn cup. If this value was lessened then it is

possible that less stretching would occur and the large variation of thickness would

be less apparent. Holding with this idea, it would then appear that a better

understanding is needed of the local variation of friction as the material is deformed

around the radius of the die as the wall of the cup would experience mainly a

longitudinal tensile stress, whereas it encounters more of a hoop stress as it is held by

the blank holder.

In their paper Colgan and Monaghan [2] don’t go into detail on the FEA software

and approach which they used for their work, but a reference to being able to set

different friction values for the punch side and die side of the blank in auto form was

made.

Having noted this, it would be hope that all points be addressed in greater detail in

future work to arrive at a better numerical simulation of the deep drawing process.

6. Conclusions

Over the course of this work 3 models were built and tested, these were:

Model 1: 2-D Axisymmetric solid model built using all PLANE82 elements

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Model 2: 2-D Axisymmetric shell model built using all SHELL208 elements

Model 3: 2-D Axisymmetric model built using a combination of PLANE82 for

the die and punch elements and SHELL208 for the blank elements.

Unconverging solutions and negative jacobian errors accounted for the failure

to achieve results with models 1 and 2.

Model 3 has been successfully solved and has provided adequate results.

The von mises plastic strain has been found for the deformed blank, the areas

of maximum strain through the thickness of the shell elements occur near to

where the maximum deformation is caused. This area is on the inside wall of

the blank holder radii, and on the outside wall of the punch radii. The value

for the maximum strain is 0.6179. Questions still remain as to whether the

strain distribution along the base of the cup should be so even

A comparison has then been made to establish the validity of the finite

element model created in ANSYS 12.1. This is compared to a paper which has

both experimental work and numerical simulations carried out. Along a

section through the flange and cup wall, it was found that the results

obtained hold in great agreement (average less than 5%) with the values

obtained from the literature. However larger variations begin to arise just

approaching the radius of the cup base and also along the cup base

No work has been done as of yet to confirm this notion, but it is felt by the

author that the local variations for friction values are the predominant cause

for the deviations away from the experimental results, this idea is supported

by previously reviewed literature.

Lower frictional values along the cup base/punch interface could easily give

rise to a larger thickness throughout the base due to less stretching occurring.

7. References

[1] Richard Coles, Mark J. Kirwan, 2011, "Food and Beverage Packaging Technology,"

Wiley-Blackwell, pp. 344.

20

[2] Colgan, M., and Monaghan, J., 2003, "Deep Drawing Process: Analysis and

Experiment," Journal of Materials Processing Technology, 132(1-3) pp. 35-41.

[3] Ibrahim Demirci, H., Yaşar, M., Demiray, K., 2008, "The Theoretical and

Experimental Investigation of Blank Holder Forces Plate Effect in Deep Drawing

Process of AL 1050 Material," Materials & Design, 29(2) pp. 526-532.

[4] Dr. Waleed Khalid Jawa, 2007, "Investigation of Contact Interface between the

Punch andBlank in Deep Drawing Process," Engineering and Technology Journal,

25(3) pp. 370-382.

[5] Vladimirov, I. N., Pietryga, M. P., and Reese, S., 2010, "Anisotropic Finite

Elastoplasticity with Nonlinear Kinematic and Isotropic Hardening and Application

to Sheet Metal Forming," International Journal of Plasticity, 26(5) pp. 659-687.

[6] Fereshteh-Saniee, F., and Montazeran, M. H., 2003, "A Comparative Estimation of

the Forming Load in the Deep Drawing Process," Journal of Materials Processing

Technology, 140(1-3) pp. 555-561.

[7] K, L., 1985, "Handbook of Metal Forming." Society of Manufacturing Engineers, .

[8] Meguid, S. A., and Refaat, M. H., 1997, "Finite Element Analysis of the Deep

Drawing Process using Variational Inequalities," Finite Elements in Analysis and

Design, 28(1) pp. 51-67.

[9] Plane 82 element type documentation, "Ansys Release Documentation,"

Http://www.Kxcad.net/ansys/ANSYS/ansyshelp/Hlp_E_PLANE82.Html, .

[10] SHELL208 element type documentation, "Ansys Release Documentation,"

Http://www.Kxcad.net/ansys/ANSYS/ansyshelp/thy_el1208.Html, .