Finite Element Modeling of Dent Test In Mild Steel Barrels - A Parametric Study

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

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

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:

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

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

LIST OF TABLES

Table1- Material Properties of Mild Steel

Table 2 - Forming Limit Diagram

Table 3 – Material Parameters for Water

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.

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.

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

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.

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

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.

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

Figure 4: Eulerian Mesh showing the material moving in the mesh.

Figure 3: Eulerian Mesh with material filled in it

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.

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

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.

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

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

Strain

Minor Principal

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

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 uf,

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.

Table 3: Material Parameters for Water

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

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.

.

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

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

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

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.

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

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

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

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.

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.

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