My B.Tech Thesis - Was among the top three nominations for the best B.Tech project award in Department of Civil Engineering,IIT Kharagpur

1. Modeling of Dent Test in Mild Steel Barrels
Project II (CE47002) report submitted to
Indian Institute of Technology, Kharagpur
In partial fulfillment for the award of the degree
Of
Bachelor of Technology (Hons)
In Civil Engineering
by
Suneel Palukuri
(06CE1036)
Under the guidance of
Prof. Arghya Deb
DEPARTMENT OF CIVIL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY KHARAGPUR
May 2010

2. DECLARATION BY STUDENT
I certify that
a. the work contained in this report has been done by me under the guidance of my
supervisor(s).
b. the work has not been submitted to any other Institute for any degree or diploma.
c. I have conformed to the norms and guidelines given in the Ethical Code of
Conduct of the Institute.
d. whenever I have used materials (data, theoretical analysis, figures, and text) from
other sources, I have given due credit to them by citing them in the text of the
thesis 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

3. CERTIFICATE BY SUPERVISOR(S)
This is to certify that the project report entitled Modeling of Dent Test in Mild Steel
Barrels , submitted by Suneel Palukuri to Indian Institute of Technology, Kharagpur, is
a record of bona fide project (II) work carried out by him under my (our) supervision.
__________________________ ______________________
Superviser Superviser
Date:

4. ACKNOWLEDGEMENT
This report is a result of project performed under the guidance of Dr. Arghya Deb at the
department of Civil Engineering of Indian Institute of Technology, Kharagpur, India.
I am deeply grateful to Dr. Arghya Deb for having given me the opportunity of
working as part of his research group and for constantly encouraging and motivating me
towards achieving my project goals.
Date : Signature of the Student

5. LIST OF SYMBOLS
- Pressure
- Density
- Internal energy per unit mass
- Material Constant
- Viscosity
C0 & – Constants
FLD – Forming Limit Diagram
uf - Displacement at fracture
L - Characteristic element length
D - Damage Variable
ef - Plastic strain at fracture

6. LIST OF TABLES
Table1- Material Properties of Mild Steel
Table 2 - Forming Limit Diagram
Table 3 – Material Parameters for Water

7. LIST OF FIGURES
Figure 1 - Lagrangian Mesh
Figure 2 - Eulerian Mesh showing the material moving in the mesh
Figure 3 - Eulerian Mesh with material filled in it
Figure 4 - Initial Experimental Setup
Figure 5 - Stress vs Strain Curve for Mild Steel
Figure 6 - Bi-linear Damage Evolution
Figure 7 – Damage Initiation vs Thickness plot for non-corrugated barrels half filled
with water
Figure 8 - Depth of indent vs Thickness plot for a non-corrugated half filled barrel
Figure 9 - Damage Initiated vs Thickness for a corrugated barrel half filled with water
Figure 10 - Indent Depth vs Thickness for a corrugated barrel half filled with water
Figure 11 - Comparison of indent depth trends between corrugated and non-corrugated
barrels.
Figure 12 - Comparison of Damage Initiation trends between Corrugated and non-
Corrugated barrels
Figure 13 - comparison of damage Initiated for 10mm corrugated and non-corrugated
barrels
Figure 14 - Comparison of indent depth for a 10mm corrugated and non-corrugated
barrels
Figure 15 - Comparison of damage initiated between 4mm corrugated and non-
corrugated barrel
Figure 16 - Comparison of indent depth between 4mm corrugated and non-corrugated
barrel
Figure 17 - Variation of damage initiated in corrugated and non corrugated 10mm barrel
on variation of water level
Figure 18 - Variation of Indent depth in 10mm corrugated and non-corrugated barrel on
variation of water level.

8. ABSTRACT
Cylindrical steel barrels, manufactured from a single steel sheet with a weld joint, are
often used for storage and transportation of oil and water. During transportation and
storage these barrels may collide or be subjected to large impacts with extraneous bodies.
This may cause denting in the barrels, and for large impact forces, damage to the barrel,
that would allow escape of the stored fluid. Hence it is important to design barrels to
withstand impacts that are likely to occur during their service lives. Standard dent tests
that specify the size of the indenter, the magnitude of the impact force, etc. exist. The
purpose of this project is to investigate whether such tests can be numerically simulated
to yield physically reasonable results. “Numerical” dent tests of barrels if carried out on a
routine basis during design, are likely to lead to better designs with smaller turn-around
times. In this work, the ABAQUS commercial finite element software was used for
modeling a dent test. The dent test of a barrel is complicated by the fact that any realistic
simulation must include the fluid inside the barrel. Thus a multi-physics simulation is
called for, along with the fluid-structure interaction between the fluid and the elasto-
plastic shell of the barrel. The Coupled-Eulerian-Lagrangian formulation available in
ABAQUS/Explicit is used for the purpose. Damage and degradation of the barrel
material was modeled using the FLD damage initiation criterion and a displacement
based damage evolution law. The effect of corrugations in the barrel shell on the denting
response was investigated. Barrels of different thicknesses with varying water levels were
tested and the depth of indent and maximum damage were evaluated and compared.

9. CONTENTS
Title Page i
Declaration by the Student ii
Certificate by the Supervisor iii
Acknowledgement
List of Symbols v
List of Tables
List of Figures
Abstract …
Contents
Chapter 1 Introduction 1
1.1 Problem Discussion
1.2 About Abaqus
Chapter 2 Literature Review
Chapter 3 Theory
3.1 Coupled Eulerian Lagrangian Analysis
3.2 Equation of State
Chapter 4 Experimental Study
4.1 Model Description and Finite Element Discretization
4.2 Material Modeling and Damage Model Parameters:
Chapter 5 Results, Discussion
Chapter 6 Conclusions
List of References

10. Chapter 1
Introduction
1.1 Problem Discussion:
Cylindrical mild steel barrels which are used for storage and transportation of oil and
water are liable to hazards during their transportation. Having identified the possible
hazards encountered by them during their transportation, the need for Drop and Dent test
has been identified (Dynamic analysis). Dent tests, which simulate an object impacting a
sphere, are often used to investigate the object’s response under harsh handling
conditions. The study can also be helpful in the optimum design of steel barrels
considering the hazards of denting. . Moreover introduction of stiffeners has its influence
on the damage and denting encountered by the barrel. Hence a parametric study has been
done varying the parameters like level of water in the barrel, thickness of barrel and
corrugations and the influence of each of these has been observed and analyzed.
1.2 About Abaqus:
Abaqus/Explicit is a special-purpose analysis product that uses an explicit dynamic finite
element formulation. It is suitable for modeling brief, transient dynamic events, such as
impact and blast problems, and is also very efficient for highly nonlinear problems
involving changing contact conditions, such as forming simulations. We have used
Abaqus Explicit for the Dynamic Analysis of mild steel Barrel.

11. Chapter 2
Literature review
Hogstro et al. (2009) recently studied the effect of length scale on necking and
fracture behavior in sheet metals. In order to validate existing failure models used in
finite element (FE) simulations in terms of dependence on length scale and strain state,
tests recorded with the optical strain measuring system ARAMIS were conducted. With
this system, the stress–strain behaviour of uniaxial tensile tests was examined locally, and
from this information true stress–strain relations were calculated on different length
scales across the necking region. Forming limit tests were conducted to study the multi
axial failure behaviour of the material in terms of necking and fracture. The influence of
the element size of the mesh, the length scale dependence on the failure limit and damage
evolution models were studied in the research paper. .All the input that has been used for
this analysis of barrel has been taken from this report. Uniaxial tensile tests conducted on
mild steel using Aramis in the research paper gave a stress-strain graph for mild steel.
Engineering fracture strain, yield stress etc were obtained from this test. From the
forming limit test conducted, a FLD curve is obtained which is taken as an input for FLD
based damage initiation criteria in our report. Moreover the author has concluded in the
report that Bi-Linear Damage evolution law showed closer resemblance to the
experimental results over linear damage evolution law. Hence on the basis of his
conclusion, Bilinear Damage evolution law has been considered for more accurate
results. The effect of length scale as discussed in the paper comes in the calculation of
displacement at failure (used in defining Damage Evolution Law) which is the product of
characteristic element length and plastic strain at fracture.
Abaqus Documentation was used in deciding the damage initiation criteria that
has to be used for the analysis, the inputs that have to be given for the criteria selected
and in deciding the damage evolution criteria. The material damage initiation capability
in ABAQUS for ductile metals includes ductile, shear, forming limit diagram (FLD),
forming limit stress diagram (FLSD) and Müschenborn-Sonne forming limit diagram
(MSFLD) criteria. But based on the availability of input data, FLD Damage initiation

12. criteria were selected. The maximum strains that a sheet material can sustain prior to the
onset of damage are referred to as the forming limit strains. A FLD is a plot of the
forming limit strains in the space of principal (in-plane) logarithmic strains. The major
limit strain is usually represented on the vertical axis and the minor strain on the
horizontal axis. The line connecting the states at which deformation becomes unstable is
referred to as the forming limit curve (FLC).Principal strains computed numerically by
Abaqus can be compared to a user prescribed FLC to determine the feasibility of onset of
damage in the model being analyzed. The damage initiation criterion for the FLD is given
by the condition ωfld = 1, where the variable ωfld is a function of the current deformation
state and is defined as the ratio of the current major principal strain, to the major limit
strain on the FLC evaluated at the current values of the minor principal strain. If the value
of the minor strain lies outside the range of the specified tabular values, Abaqus will
extrapolate the value of the major limit strain on the FLC by assuming that the slope at
the endpoint of the curve remains constant.
Figure : Forming limit diagram
Following the onset of damage, ABAQUS allows modeling of the evolution of damage.
For Damage evolution, a bi-linear(Tabular) damage evolution law based on effective
plastic displacement has been used. The fracture is said to have occurred if the damage
variable, d which is the ratio of effective plastic displacement to plastic displacement at
fracture reaches a value of 1. If d reaches a value of 1, the material stiffness will be fully
degraded.

13. Chapter 3
Theory
3.1 Coupled Eulerian Lagrangian Analysis:
Coupled Eulerian Lagrangian (CEL) analysis is used for problems involving fluid-
structure interactions where extreme deformations are encountered. Eulerian-Lagrangian
contact formulation is used to simulate a highly dynamic event involving a fluid material
(modeled using Eulerian elements) interacting with structural boundaries (modeled using
Lagrangian elements). In a traditional Lagrangian analysis nodes are fixed within the
material, and elements deform as the material deforms. Lagrangian elements are always
100% full of a single material, so the material boundary coincides with an element
boundary as shown in Figure 1. But in an Eulerian analysis, nodes are fixed in space, and
material flows through elements that do not deform. The Eulerian mesh is typically a
simple rectangular grid of elements constructed to extend well beyond the Eulerian
material boundaries, giving the material space in which to move and deform as shown in
Figure 2.
Figure 3: Lagrangian Mesh

14. Figure 4: Eulerian Mesh showing the material moving in the mesh.
Figure 3: Eulerian Mesh with material filled in it

15. Eulerian elements may not always be 100% full of material. In fact many may be
partially or completely void as shown in Figure 3. If any Eulerian material moves outside
the Eulerian mesh, it is lost from the simulation. Hence the Mesh has to be sufficiently
large to account for the movement of material. Eulerian material can interact with
Lagrangian elements through Eulerian-Lagrangian contact. Thus Eulerian element
formulation allows the analysis of bodies undergoing severe deformation without the
difficulties traditionally associated with mesh distortion. In an Eulerian mesh material
flows through fixed elements, so a well-defined mesh at the start of an analysis remains
well-defined throughout the analysis. Eulerian analyses are effective for applications
involving extreme deformation like fluid flow etc. In these applications, traditional
Lagrangian elements become highly distorted and lose accuracy. Eulerian-Lagrangian
contact allows the Eulerian materials to be combined with traditional nonlinear
Lagrangian analysis. The material definition in Eulerian Analysis is given using the
Eulerian Volume fraction. Even later on, material is tracked as it flows through the mesh
by computing its Eulerian volume fraction (EVF) within each element at the particular
instant. By definition, if a material completely fills an element, its volume fraction is one
and if no material is present in an element, its volume fraction is zero.
3.2 Equation of State:
An equation of state is a thermodynamic equation describing the state of matter under a
given set of physical conditions. It is a constitutive equation which provides a
mathematical relationship between two or more state functions associated with the
matter, such as its temperature, pressure, volume, or internal energy. Equations of state
are useful in describing the properties of fluids, mixtures of fluids, solids etc. The most
prominent use of an equation of state is to predict the state of gases and liquids. The
linear Us – Up Hugoniot form of the Mie-Grüneisen equation of state best represents the
water and hence it can be used to model water.

16. The equation of state for pressure is a function of the current density, viscosity and
internal energy per unit mass (Em) where,
- Pressure
- Density
- Internal energy per unit mass
- Material Constant
- Viscosity
C0 & - Constants

17. Chapter 4
Numerical study
4.1 Model Description and Finite Element Discretization:
For FE simulation a mild steel cylinder of 880 mm length was taken. The diameter of the
cylinder was taken as 586mm.For modeling the dent test, two different types of models
were considered. One model is a barrel which does not have any corrugations and the
other is a barrel having corrugations. For each type of model, four cases having
thicknesses of 1mm, 4mm, 8mm and 10mm were considered and analyzed. Moreover
two different levels of water were taken as well. Tests were conducted on barrels half
filled with water and fully filled with water. The cylinder is modeled using S4R shell
elements in FEM software ABAQUS. The cylindrical barrel is subjected to dent test
using a spherical denting tool mounted on a pendulum dropped from a height H (height
of cylinder = 880mm) from the point of impact (center of the barrel). The spherical
denting tool had been modeled as a rigid body with a mass of 5kg that does not undergo
any deformation. ABAQUS/Explicit, which is an explicit dynamic code, was used for the
simulations. The cylinder was modeled as an elasto-plastic mild steel barrel. Water was
modeled using Us – Up Hugoniot form of the Mie-Grüneisen equation of state which can
be used to model water, assuming that some amount of compressibility is allowed. This
model also allows inclusion of small amounts of fluid viscosity as well. The Eulerian
Mesh was defined to be sufficiently large (1500mm x 1200mm x 1000mm) in order to
account for the movement of liquid during the analysis. Damage initiation has been
defined for the barrel to evaluate the damage. The forming limit diagram (FLD) damage
initiation criterion has been used here. The damage initiation criterion for the FLD is met
when the condition ω(FLD)=1 is satisfied. A bi-linear displacement based damage
evolution law was used to model damage evolution. The material is considered to be fully
degraded or failed when the damage variable, d which is the ratio of the current plastic
displacement to the plastic displacement at failure becomes 1.0 (d=1.0). The initial model
configuration is shown in Fig. 4.

18. Figure 4: Initial Experimental Setup
4.2 Material Modeling and Damage Model Parameters:
Finite element models of steel barrels are setup with the dimensions mentioned above. In
order to obtain material properties, damage initiation parameters and damage evolution
parameters, experimental results reported by Hogstrom et al. (2009) were consulted.
Table 1 lists the material properties used in the simulations. They are based on those used
by Hogstorm et al (2009). The stress strain curve used by Hogstorm et al.(2009) is shown
below. The Hardening modulus was obtained by approximating the stress vs strain curve
to be a straight line for plastic strains.
Material Properties of mild steel
Density = 7800 Kg/m3
Young’s Modulus = 210 GPa
Poisson’s Ratio = .3
Yield Stress = 310Mpa
Hardening Modulus = (400-310)/0.22 =
409Mpa
Table1: Material Properties of Mild Steel

19. Figure 5: Stress vs Strain Curve for Mild Steel
The plastic material behavior is governed by the Von-Mises yield criterion combined
with an isotropic hardening rule. The yield criterion relates the onset of yielding to the
states of stress and the hardening rule relates the yield surface with the development of
plastic strain. The FLD curve that was taken as input for FLD damage initiation criteria is
Major Principal Minor Principal
Strain Strain
0.4 -0.12
0.3 -0.033
0.25 0.05
0.31 0.2
0.39 0.37
Table 2: Forming Limit Diagram

20. the bilinear damage evolution law used was as described below.
Figure 6: Bi-linear Damage Evolution
The results reported by Hogstrom et al. suggested that considering bilinear damage
evolution gives better results. Hence bilinear damage evolution was used with u f,
displacement at fracture is given by uf = L x ef where L is a characteristic element length,
and ef is the plastic strain at fracture. The size of the mesh was taken as 30mm so L is
taken as 30mm.
A linear Us – Up equation of state model can be used to model nearly
incompressible viscous fluids and inviscid laminar flow governed by the Navier-Stokes
equation of motion. Hence this has been used to model water. The properties of water
have been taken from Example 2.3.2 of Abaqus Documentation Version 6.9.
Parameter Value
Density 9.96 x 10-7 Kg/mm3
Viscosity 1 x 10-5 Ns/mm2
co 1.45 x 106 mm/s
s 0
To 0
Table 3: Material Parameters for Water

21. A 5 Kg rigid sphere impacts the barrel shell at its mid height. The rigid sphere was
mounted on a pendulum which drops from a height H=880mm. Hence the initial velocity
of the sphere at the point of collision is:
V = (2 x g x h)1/2 = (2 x 9800 x 880)1/2 = 4153 mm/sec.
The entire model was subject to a gravitational force of 9800mm/s2 and the vertical
motion of drum was constrained. The depth of indent and the damage of the barrel were
evaluated for various levels of water, barrel thicknesses and corrugations.
.

22. Chapter 5
Results and discussions
Tests are conducted on the barrels described in Chapter 4. The loading, material
properties and boundary conditions are also as described therein. The results reported
include the damage initiation variable (once this variable has attained a value of one
progressive failure of the barrel follows) as well as the maximum depth of the indent in
the barrel prior to the rebound of the impactor. Corrugated and uncorrugated barrels filled
to various water depths are tested.
Barrel without corrugations:
Initially dent test was conducted on a barrel which was half filled with water. The test
was conducted on 4 different barrels having thicknesses of 1mm, 4mm, 8mm and 10mm.
Fig. 7 shows a plot of damage initiation in the barrel as a function of shell thickness. The
following results were obtained when the barrels were analyzed.
Figure 7: Damage Initiation vs Thickness plot for non-corrugated barrels half filled with water

23. It is observed damage initiates for thin barrels only, i.e. for barrels of thicknesses of 4
mm or less. No damage was initiated for 8 mm and 10 mm barrels. As the thickness of
the barrel increases, the barrel becomes stiffer, both bending and membrane strains are
smaller, and hence the strain based FLD damage initiation criterion is not exceeded. The
level of water was kept constant in all of the above tests.
Figure 8: Depth of indent vs Thickness plot for a non-corrugated half filled barrel
For the same impact, the depth of indent was also found to vary with barrel thickness. A
similar trend was observed in the depth of indent. For a 1mm thick barrel, the sphere
actually penetrated the barrel. For thicknesses of 4mm, 8mm and 10mm decreasing
depths of indent were seen for increasing barrel thickness. Thus as the barrel becomes
stiffer, lesser indent depth was seen. Even though damage initiated in the 4mm thick
barrel, ultimate failure following damage evolution had not yet occurred. Hence the
barrel shell still had some residual stiffness which prevented the penetration of the indent

24. tool and hence an indent value could be reported for this case. The level of water was
kept constant for all of the four tests reported above.
Barrel with Corrugations:
Figure 9: Damage Initiated vs Thickness for a corrugated barrel half filled with water
Figure 10: Indent Depth vs Thickness for a corrugated barrel half filled with water

25. Similar trends were exhibited by corrugated barrel as those exhibited by non-
corrugated barrels which were half-filled with water. The notable difference being
that no damage initiation was seen for the 4mm corrugated barrel as opposed to the
non-corrugated barrel of the same thickness which showed damage initiation. The
indent depth and damage the initiated decreased with increase in thickness. Again the
1mm corrugated barrel was observed to have fully failed with the sphere penetrating
through the barrel. Thus no indent depth could be reported for the 1 mm thick barrel.
Figure 11 : Comparison of indent depth trends between corrugated and non-corrugated barrels.
On comparison of the depths of indent for corrugated and non-corrugated barrels, half
filled with water, it was seen that the corrugated barrels have smaller indentations as
compared to non-corrugated barrels. The corrugations act as stiffeners increasing the
stiffness of the shell between the corrugations. When the sphere collides with the barrel
in this stiff region, lesser indent depth is observed. Thus the provision of corrugations
resulted in smaller depths of indent for all thicknesses of the barrel.

26. Figure 12 : Comparison of Damage Initiation trends between Corrugated and non-Corrugated
barrels
It was observed that for lower thickness of barrels, there was comparatively less damage
initiated in the corrugated barrels as compared of non-corrugated barrels. However for
larger thicknesses (t > 4 mm) it was found that there was actually more damage initiation
for the corrugated barrels. This result is somewhat unexpected and an attempt has been
made to explain it in the discussion below.
Figure 13: comparison of indent depth for 8mm corrugated and non-corrugated barrels

27. Figure 14: Comparison of damage initiated for a 8mm corrugated and non-corrugated barrels
As seen in Figure 13, in the case of corrugations, the indentation is mostly confined to the
region between the corrugations due to the effect of the stiffeners which act as supports.
The stiffer response of the corrugated barrel results in smaller indentations. However the
presence of the stiffeners also results in the more localized damage distribution seen for
the corrugated barrel in Figure 14. Localized damage also results in higher damage values
for the corrugated barrel as compared to the barrel without corrugations. But in the case
of the 4mm thick barrel it is seen that there is comparatively less localization of damage
for the corrugated barrel (Figure 15). This is because in this case at least one of the
stiffeners has “failed” by local buckling, as shown in the figure. Thus this stiffener is not
as effective. This results in higher indentations and greater spread of damage.
Figure 15: Comparison of damage Initiated between 4mm corrugated and non-corrugated barrel

28. Figure 16: Comparison of indent depth between 4mm corrugated and non-corrugated barrel
Evaluation of effect of water depth:
The effect of water depth on indentation and damage has been studied by conducting
the tests on 1mm, 10mm barrels with two different water levels (half filled and fully
filled). The test has been done for both corrugated and non-corrugated barrels. Failure
was observed at both water levels for the corrugated as well as the non-corrugated
barrel. The sphere was seen to have penetrated through the barrel without leaving any
indent for a thickness of 1mm irrespective of the water level and corrugations. For the
10 mm barrel it was observed that indent depth and damage initiation decreased with
increase in water level. For two barrels filled with water to different depths,
hydrostatic pressure at a particular depth of barrel is higher for the barrel with more
water. Greater hydrostatic pressures results in greater resistance to indentation and
hence results in lesser damage. Hence the damage initiated and depth of indent
decrease with increase in level of water.
The effect of corrugation on indent depth and damage initiation was the same as
observed before

29. Figure 17: Variation of damage initiated in corrugated and non corrugated 10mm barrel on
variation of water level
Figure 18: Variation of Indent depth in 10mm corrugated and non-corrugated barrel on variation of
water level.

30. Chapter 6
Conclusions
1. The damage initiated and the depth of indent vary with variation of thickness of
barrel, level of water, and the presence of corrugations which proves that the damage
is sensitive to these variables.
2. Thicker barrels are found to perform better: resisting initiation of damage and
indentation following damage better than thinner barrels. However the thickness of
the barrel is limited by other factors like maximum allowable weight of the barrels,
the cost of material etc.
3. Corrugations have proved to be effective in resisting indentation and initiation of
damage. Hence it is desirable to design barrels with corrugations for better
performance. However the optimum location, shape and size of the corrugations need
to be determined from further tests.
4. Barrels with greater volume of water show greater resistance to indentation and
initiation of damage than those filled with smaller volumes of water. Thus filled
barrels are less susceptible to damage due to impacts that may occur during
transportation.
5. The above results emphasize the importance of properly conducted dent tests for the
design of barrels. Numerical solutions, similar to those obtained in this project, if
properly verified against benchmark experimental results, can prove invaluable to the
design process.

31. References :
1. P. Hogstro , J.W. Ringsberg and E. Johnson. "An experimental and numerical study
of the effects of length scale and strain state on the necking and fracture behaviours in
sheet metals”. International Journal of Impact Engineering 36 (2009) 1194–1203.)
2. ABAQUS Analysis User’s Manual (2008), Providence, Rhode Island, Simulia Corp
3. K.H.Brown, S.P. Burns and M.A.Christon. “Coupled Eulerian-Lagrangian methods
for earth penetrating weapon applications”. Issued by Sandia National Laboratories
(2002) SAND2002-1014.)
4. www.Wikiversity.org