Stress Finite Element Analysis of a Simple HY-80 Steel Tension
Specimen Using Progressive Failure Feature in ABAQUS
by
Amy N. Sissala
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Engineering Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
August, 2012
(For Graduation December 2012)
i
© Copyright 2012
by
Amy N. Sissala
All Rights Reserved
ii
CONTENTS
Finite Element Analysis of a Simple Tension Specimen Using Progressive Failure
Feature in ABAQUS ..................................................................................................... i
LIST OF SYMBOLS ........................................................................................................ iv
LIST OF TABLES ............................................................................................................. v
LIST OF FIGURES .......................................................................................................... vi
LIST OF KEYWORDS ................................................................................................... vii
ACKNOWLEDGMENT ................................................................................................ viii
ABSTRACT ..................................................................................................................... ix
1. Introduction and Literature Review ............................................................................. 1
2. Problem Statement ....................................................................................................... 3
3. Theory .......................................................................................................................... 4
4. Methodology ................................................................................................................ 5
4.1
Model Geometry and Material Properties .......................................................... 5
4.2
Analysis .............................................................................................................. 9
5. Results........................................................................................................................ 12
5.1
Model without Element Deletion (ABAQUS/Standard).................................. 12
5.2
Model with Element Deletion (ABAQUS/Explicit) ........................................ 13
6. Conclusion ................................................................................................................. 16
7. References.................................................................................................................. 17
8. Appendices ................................................................................................................ 18
8.1
ABAQUS Keyword File .................................................................................. 18
iii
LIST OF SYMBOLS
σ = Stress [ksi]
E = Elastic Modulus [ksi]
ε = Strain [in/in]
γ = Poisson’s Ratio
τ = Shear Stress [ksi]
iv
LIST OF TABLES
Table 1: Type 1 Standard Tension Specimen Dimensions ................................................ 6
Table 2: HY-80 Material Properties .................................................................................. 7
Table 3: Stress-Strain Values for HY-80 Steel .................................................................. 8
Table 4: Finite Element Model Load Ramping ............................................................... 10
v
LIST OF FIGURES
Figure 1: Type 1 Standard Tension Specimen ................................................................... 5
Figure 2: Tension Specimen Finite Element Model .......................................................... 6
Figure 3: Stress-Strain Curve for HY-80 Steel at Various Temperatures (7).................... 7
Figure 4: Finite Element Model Boundary Conditions ..................................................... 9
Figure 5: Finite Element Loads ....................................................................................... 10
Figure 6: Finite Element Model without Element Deletion Option ................................ 12
Figure 7: Finite Element Model with Element Deletion Option Before Failure ............. 13
Figure 8: Finite Element Model with Element Deletion Immediately After Failure ...... 14
Figure 9: Final Finite Element Model with Element Deletion ........................................ 15
vi
LIST OF KEYWORDS
Finite Element Analysis
ABAQUS
Progressive Failure
HY-80
vii
ACKNOWLEDGMENT
I would like to thank my advisor, Ernesto Gutierrez-Miravete, for his advice and
guidance of this project. Also I thank Kevin Black for helping edit the grammar and
readability of the paper.
viii
ABSTRACT
The focus of this project is finite element modeling using progressive failure of HY-80
steel in tension. A piece of steel will fail through plasticity and cracking under tension.
The finite element code ABAQUS calculates the stress for each integration point in each
element. It also includes an addition feature to zero out the stresses at integration points
that pass a predefined limit. The ASTM A770/A770M-8 “Standard Specification for
Through-Thickness Tension Testing of Steel Plates for Special Applications” offers a
simple specimen and scenario to perform a study of how accurate the progressive failure
feature in ABAQUS is. Stress was tracked throughout each analysis. Failure stress is a
common variable reported for materials and can aid in designing structures. The areas of
highest stress occur near the failure point in the middle of the specimen. In the end the
ABAQUS progressive failure feature provides a more accurate view of the realistic
results of loading steel to failure by account for those elements that have failed and can
no longer carry any stress.
ix
1. Introduction and Literature Review
Material strength and failure govern engineering design of structures. The goal of design
is to optimize the strength while reducing weight and cost. This pushes materials to their
limits and makes it important to know their failure behavior. This helps the engineer
schedule adequate inspections and assists the inspector recognizing the manifestations of
material failure.
Ductile materials, such as high strength steel, fail through two processes:
plasticity and damage mechanics. Plasticity is a non-reversible change in shape in
response to applied forces due to dislocations along the slip planes inside the material’s
microscopic structure. Damage mechanics, on the other hand, is the nucleation, growth,
and coalescence of microdamages in regions of high stress (1).
Physical testing of every material in a load situation can be expensive and time
consuming. Therefore, many finite element software codes, such as ABAQUS/Explicit
6.11, offer a progressive failure element option. Chang-Sik Oh had success using
ABAQUS to create a stress-strain curve of a material loaded into deformation. The team
also performed various sensitivity tests on the element density of their model (2).
When loads are applied, deformation occurs in the component. As the component
deforms, it loses its ability to carry the applied stress. The load propagating through that
section is then applied elsewhere, possibly loading another microscopic section to
failure. As loading continues, the stress distribution and elastic modulus are decreased
(3). This process can continue until the specimen fractures and macro cracks appear.
In a standard finite element analysis, elements never lose their ability to carry
loads. However, the stress continues to climb until the loading reaches equilibrium, even
after reaching the material’s limit. It is the engineer’s responsibility during post
processing job to identify the areas where the material would fail. This does not
accurately represent what occurs in realistic application.
In an explicit finite element analysis, when the stress at an element’s integration
point reaches its defined maximum, the point is set equal to zero. In order to do this the
finite element code forces the particular value in the stress matrix to equal zero. This is
how progressive failure is modeled, which identifies more realistically the areas of the
1
model that fail and become ineffective at carrying stresses. The progressive failure
option also identifies the time the integration point fails for an increasing load (4).
In order to study the progressive failure element option, a test with known and
verified results was chosen for analysis. ASTM A770/A770M-8, “Standard Specification
for Through-Thickness Tension Testing of Steel Plates for Special Applications”, is a
common test that has been performed on various types of materials. By using a known
test, the area and values of maximum stress and failure are known.
2
2. Problem Statement
Engineers study failure in order to understand when and how it occurs in a structure. If
the engineer knows when failure occurs for various materials, the appropriate material
can be chosen from the beginning and a schedule of inspections can be established. By
studying how failure occurs, engineers and inspectors can prevent critical failure through
observation.
The two main techniques of studying failure are physical testing and computer
analysis. Traditional materials and structures have been tested in a lab, but this is time
consuming, costly, and subject to human error. With the increasing capacity of
computers and advanced finite element software, analytical testing has become more
popular. With computers, the same specimen or model can be run in various scenarios
multiple times with little time or effort. Also, more complex scenarios that are not
possible in a laboratory setting can be studied.
Basic finite element codes record the maximum stress, force, and other values in an
element with no regard for material limits. The codes have slowly advanced to allow for
progressive failures of elements. As the plastic stress is reached, the integration points
stress is set to zero and therefore they stop carrying load. This is more accurate of a
portion of the specimen failing. Once all integration points of an element fail, it can then
be removed from the model. This replicates the plasticity that actually occurs.
3
3. Theory
The stress-strain relationship for an elastic material is defined below where σ is
the stress, E is the elastic modulus, and ε is the strain.
{𝝈} = [𝑬]{𝜺}
Equation 1
The elastic modulus matrix is calculated as in Equation 2 where γ is Poisson’s
ratio.
[𝑬] =
𝑬
𝟏−𝜸𝟐
𝟏
[𝜸
𝜸
𝟏
𝟎
𝟎
𝟎
𝟎]
Equation 2
𝟏−𝜸
𝟐
Stresses can be calculated where their value is the same regardless of the
coordinate system, such as von Mises stress, σvm. Von Mises stress is generally used to
predict the onset of yielding in ductile materials. Von Mises stresses uses the general
stress axial, σ, and shear, τ, components as calculated with Equation 3 (5).
𝝈𝒗𝒎 =
𝟏
√𝟐
𝟐
𝟐
[(𝝈𝒙 − 𝝈𝒚 ) + (𝝈𝒚 − 𝝈𝒛 ) + (𝝈𝒛 − 𝝈𝒙 )𝟐 + 𝟔(𝝉𝟐𝒙𝒚 + 𝝉𝟐𝒚𝒛 + 𝝉𝟐𝒛𝒙 )]
𝟏/𝟐
Equation 3
In finite element theory, the results are calculated at every node or integration
point of an element. For example, for a C3D8R and C3D6R there are eight and six nodes
respectively. Each element may or may not be connected to another via the nodes. This
way each element is related to the next and the applied loads are carried through the
structure. Finite element codes represent every element and node in large matrices.
The progressive failure option sets an integration point to zero when a set stress
limit, the failure stress limit of the material, is reached. This places a zero into the
appropriate matrix in the finite element code. Physically, this means that this portion of
the element has failed and can no longer carry loads or stresses. Once all the integration
points of an element have been set to zero the element is deleted from the model.
Though, this option can be overridden. The loads and stresses must redistribute
themselves to other areas. Essentially that integration point has failed.
4
4. Methodology
Engineers rely on knowing the method of failure of materials in their design. Knowing
when and how a material will fail leads to a more efficient design and use of material.
ABAQUS/Explicit 11.0 helps analyze material failure by incorporating a progressive
failure element option into their software. In order to explore the progressive failure
feature, a simple test with accepted results was modeled. This model follows the ASTM
standard for a simple tension test.
The method of this study is the following:

CAD Model of Tension Specimen

Verification in ABAQUS/Standard 11.0 in Section 5.1

Increasing Failure in ABAQUS/Explicit 11.0 in Section 5.2

Analysis of Stresses
4.1 Model Geometry and Material Properties
The model geometry follows the criteria in ASTM Standard A770/A770M-03, “Standard
Specification for Through-Thickness Tension Testing of Steel Plates for Special
Applications” (6). A type 1 specimen represents a one inch thick piece of steel, called
the reduced section. This is held in place in the testing machine by two thicker ends, or
caps. Figure 1 shows the shape of the type 1 standard tension specimen. The values for
the symbols are given in Table 1.
Figure 1: Type 1 Standard Tension Specimen
5
Table 1: Type 1 Standard Tension Specimen Dimensions
Plate Thickness (t)
2.54 cm
Diameter (D)
0.889 cm
Radius (R)
0.635 cm
Length of Reduced Section (A)
4.445 cm
To simplify the model, only half of the specimen was modeled and symmetric
boundary conditions were applied to the edge. Figure 2 displays the modeled and
meshed specimen in ABAQUS CAE.
Figure 2: Tension Specimen Finite Element Model
The material of the model is HY-80, high strength steel. This is a common
material used in pressure vessels, heavy equipment, and large steel structures. It has a
high tensile strength, high ductility, and is weldable. Table 2 describes the material
properties of HY-80 steel (7).
6
Table 2: HY-80 Material Properties
Density
0.284 lb/in3
Elastic Modulus
30,000 ksi
Poisson’s Ratio
0.3
Tensile Strength
80 ksi
The other material property in the model was the stress-strain curve. This curve
tracks how much a material deforms as it reaches its yield stress and failure stress.
Holmquist did a series of tests of HY-80 steel at various temperatures and created the
curve in Figure 3. A table of values taken from the curve is in Table 3.
Figure 3: Stress-Strain Curve for HY-80 Steel at Various Temperatures (8)
7
Table 3: Stress-Strain Values for HY-80 Steel
Stress (ksi) Strain
100
0
102
0.007
109
0.02
116
0.039
123
0.05
131
0.065
138
0.09
144
0.138
138
0.18
133
0.20
In the test, the specimen was held at both ends and a force is applied in opposite
directions. In the model, the centers of the two caps are held in all six degrees of
freedom. The symmetric half of the model was also held to not allow displacement in the
x direction and rotation about the y direction. Doing this forced the elements to act as if
the rest of the specimen is adjacent to them, thereby simulating a complete specimen.
8
Figure 4: Finite Element Model Boundary Conditions
In order for the elements to zero out their stresses once failure had been reached,
two lines had to be added to the ABAQUS keyword file. The tension failure and shear
failure keywords can be seen in Appendix 8.1.
4.2 Analysis
The goal of this explicit finite element analysis was to stress the elements such that they
reach their failure stress and are subsequently deleted from the model. Since a wellknown test and material was used, a tensile strength of 80 ksi is given (7). Therefore, the
stress was monitored throughout the analysis to validate the model and the process.
The specimen was loaded in two ways: by forcing an opposing deflection at the caps
and by placing two opposing loads at the caps. The deflection load was used in
ABAQUS/Standard and the force was used in ABAQUS/Explicit in order to aid
convergence. The load was applied to induce failure throughout the reduction area. In
9
order to ensure that the model did not crash due to excessive deformation, the load was
applied with an increasing amplitude. The steps can be seen in Table 4.
Figure 5: Finite Element Loads
Table 4: Finite Element Model Load Ramping
Time Amplitude
0.0
0
0.01
0.2
0.02
0.4
0.03
0.6
0.04
0.8
0.05
1.0
10
Several iterations of the model were performed to examine how failure spread
across the specimen. Initially, the model was run without the element failure feature
turned on to examine the necking phenomenon often seen in testing. To apply the load in
this case, a forced deflection was applied to the caps.
After the model was verified, the load was continually increased until all
elements in the reduction area were observed to fail. Once the analysis was complete, the
model was post processed in order to find the maximum von Mises stresses. This value
was compared to the known tensile strength of HY-80 steel to confirm the accuracy of
the model.
11
5. Results
The model consisted of 2548 elements using a combination of C3D8R and C3D6R. The
elements were chosen because the reduced integration option would shorten the
computing time.
5.1 Model without Element Deletion (ABAQUS/Standard)
A total deflection of 0.21 inches was applied to the top and bottom of the specimen. As
shown in Figure 6, the specimen starts to neck in the center of the reduction area. This is
the same result that is seen in physical testing. This verifies that the model produces
realistic results. The maximum von Mises stress seen by the model was 179 ksi. The
fracture stress from Table 3 is 144 ksi. Since the stress in the model is above the fracture
stress the model is accurately representing the physical application.
Figure 6: Finite Element Model without Element Deletion Option
12
5.2 Model with Element Deletion (ABAQUS/Explicit)
For the analysis including the element deletion the load was ramped over the total
analysis time of 0.05 seconds. This avoided any errors in the analysis code due to
excessive failure in the specimen. It also enabled the program to save results showing
how the specimen was slowly loaded and then failed.
Figure 7 shows the specimen just before failure where the load applied is 425 kips.
The red in the fringe shows the high stress through out the reduction area while the end
caps are less stressed. The maximum von Mises stress is 133 ksi, just below the element
deletion threshold of 144 ksi.
Figure 7: Finite Element Model with Element Deletion Option Before Failure
Figure 8 is the specimen after the maximum von Mises stress has reached 144
ksi. As shown, the elements in the middle of the reduction area have started to fail at
their integration points. As that happens, the load must be carried by other elements.
13
Figure 8: Finite Element Model with Element Deletion Immediately After Failure
Figure 9 shows the specimen at the end of the 0.05 second explicit analysis. The
final maximum von Mises stress is 126 ksi. There are some indications of trouble with
the finite element solver in the lower portion of the model as seen by the dissentious
fringe. This could be resolved through adjusting the ramping and time limit of the
analysis.
This value is lower than the final von Mises stress for the ABAQUS/Standard
analysis without element deletion. Yet this analysis is more accurate to the physical
limitations of the material. It cannot carry load beyond the failure limit.
14
Figure 9: Final Finite Element Model with Element Deletion
15
6. Conclusion
Material strength and failure govern engineering design of structures. The goal of design
is to optimize the strength while reducing weight and cost. This pushes materials to their
limits and makes it important to know their failure behavior. This helps the engineer
schedule adequate inspections and the inspector recognize the manifestations of material
failure.
Physical testing of every material in a load situation is expensive and time
consuming. Therefore, many finite element software codes, such as ABAQUS/Explicit
6.11, offer a progressive failure element option. In an explicit finite element analysis,
when the stress at an element’s integration point reaches its defined maximum, the point
is set equal to zero. This is how progressive failure is modeled, which identifies more
realistically the areas of the model that fail and become ineffective at carrying stresses.
The progressive failure option also identifies the time the integration point fails for an
increasing load (4).
In order to study the progressive failure element option, a test with known and
verified results was chosen for analysis. ASTM A770/A770M-8, “Standard Specification
for Through-Thickness Tension Testing of Steel Plates for Special Applications”, is a
common test that has been performed on various types of materials. After establishing
that the model behaved as expected in ABAQUS/Standard, i.e. necking and high stress
in the reduction area, the model was put under tension with the tension failure defined as
the failure stresses.
The progressive failure option performed as expected. It accurately loaded the
specimen, indicating material failure in the reduction area. It accurate predicted that after
the tension failure limit was reached in the reduction area, that area would fail and the
load would be carried by the smaller sections at either end. The next step after this study
is to explore some of the other codes available that specifically model cracks and
calculate their stresses. Instead of removing the elements from the model, elements are
disconnected along the crack and then the stresses recalculated.
16
7. References
1. Rashid K. Abu Al-Rub, George Z. Voyiadjis. On the coupling of anisotropic
damage and plasitcity models for ductile materials. 2003, International Journal of Solids
and Structures 40, pp. 2611-2643.
2. Chang-Sik Oh, Nak-Hyun Kim, Yun-Jae Kim, Jong-Hyun Baek, Young-Pyo
Kim, Woo-Sik Kim. A finite element ductile failure simulation method using stressmodified fracture strain model. 2011, Engineering Fracture Mechanics 78, pp. 124-137.
3. Ellingwood, Baidurya Bhattacharya and Bruce. Continuum damage mechanics
analysis of fatigue crack initiation. 1998, International Journal of Fatigue 9, pp. 631-639.
4. DCS Simulia. ABAQUS 6.11 Analysis User's Manual. Abaqus 6.11 Documentation.
Providence : s.n., 2011, p. 22.2.8.
5. Robert Cook, David Malkus, Michael Pelsha, and Robert Witt. Concepts and
Applications of Finite Element Analysis. New York City : John Wiley & Sons, INC,
2002. ISBN: 0-471-35605-0.
6. ASTM International. Standard Specification for Through-Thickness Tension Testing
of Steel Plates for Special Applications. 2012, pp. A770/A770M-03.
7. Matweb. HY-80 Material Properties. [Online] [Cited: July 16, 2012.]
8. T.J., Holmquist. Strength and Fracture Characteristics of HY-80, HY-100, and HY130 Steels Subjected to Various Strains, Strain Rates, Temperatures, and Pressures.
Dahigren, VA and Silver Spring, MA : Naval Surface Warfare Center, Research and
Technology Department, 1987.
9. Robert Cook, David Malkus, Michael Pelsha, and Robert Witt. Concepts and
Applications of Finite Element Analysis. New York City : John Wiley & Sons, INC,
2002. ISBN: 0-471-35605-0.
17
8. Appendices
8.1 ABAQUS Keyword File
*Amplitude, name=Amp-1
0.,
0.,
0.01,
0.2,
0.04,
0.8,
0.05,
1.
0.6
**
** MATERIALS
**
*Material, name=HY-80
*Density
0.00073499,
*Elastic
3e+07, 0.3
*Plastic
100000.,
0.
102000., 0.007
109000., 0.02
116000., 0.039
123000., 0.05
131000., 0.065
138000., 0.09
144000., 0.138
138000., 0.18
133000., 0.2
*TENSILE FAILURE, ELEMENT DELETION=YES
144000
*SHEAR FAILURE, ELEMENT DELETION=YES
116000
** ---------------------------------------------------------------18
0.02,
0.4,
0.03,
**
** STEP: Explicit Load
**
*Step, name="Explicit Load"
*Dynamic, Explicit
, 0.05
*Bulk Viscosity
0.06, 1.2
**
** BOUNDARY CONDITIONS
**
** Name: BC-1 Type: Symmetry/Antisymmetry/Encastre
*Boundary
_PickedSet19, XSYMM
**
** LOADS
**
** Name: Load-2 Type: Body force
*Dload, amplitude=Amp-1
_PickedSet26, BY, -300000.
** Name: Positive Type: Body force
*Dload, amplitude=Amp-1
_PickedSet27, BY, 300000.
**
** OUTPUT REQUESTS
**
*Restart, write, number interval=1, time marks=NO
**
** FIELD OUTPUT: F-Output-1
**
*Output, field, variable=PRESELECT
19
**
** HISTORY OUTPUT: H-Output-1
**
*Output, history, variable=PRESELECT
*End Step
20