TRIBHUVAN UNIVERSITY
INSTITUTE OF ENGINEERING
THAPATHALI CAMPUS
A PRESENTATION ON:
Study Of Research Articles & Summarization
Prepared By:
Sushil Chapai (076-MSEDM-19)
05/22/2021
1
Article - I
Finite element analysis to estimate burst pressure
of mild steel pressure vessel using RambergOsgood model
By:
Puneet Deolia*, deoliapuneet@ymail.com
Firoz A. Shaikh, firoz.shaikh@viit.ac.in
Vishwakarma Institute of Information Technology, India
05/22/2021
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1. Abstract
Pressure Vessel: A tank/container which holds fluid at pressure other than
atmospheric pressure.
Burst Pressure: Pressure at which vessel crack and internal fluid leaks
To numerically calculate burst pressure requires material curve.
Ramberg-Osgood equation: Describes the non-linear relationship between stressstrain, i.e. SN-curve in materials near their yield points.
This equation is especially applicable to metals that harden with plastic
deformation, showing smooth elastic-plastic transition.
FEA was applied in this research work to predict burst pressure using RambergOsgood equation and results are compared with results from elasto-plastic curve
and true SN-curve.
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2. Introduction
Mild steels have high energy absorbing capacity, toughness as well as good
weldability and inexpensive, so preferred in this work.
Aseer Brabin et al (2011) examined different existing predictive equations which
are used to predict bursting value of vessels.
Found that Faupel’s bursting pressure formula is simple and reliable in prediction
of burst pressure of thin and thick-walled steel cylindrical vessels.
Zheng and Lei (2006) presented new modified Faupel formula for calculating the
burst pressure.
Diamantoudis and Kermanidis (2005) found that theoretical formulas used for
evaluation of bursting value gives conservative results when compared with FEA
results.
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2. Introduction
Evans and Miller (2015) found that the non-linear FEA is required to evaluate
bursting value of vessels and requires material curve for FEA.
The required material curve can be generated using Ramberg-Osgood equation
(Kamaya, 2015).
Obtained results are compared with experimental results as well as theoretical
results obtained by modified Faupel formula.
Study was carried out on six made up of 20R (1020) material (Zheng and Lei,
2006)
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3. Study tools / CAD Model
Vessels modeled using commercial software of CATIA
Vessel dimension: 500 T/T length, varying ID and THK
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4. Methodology
Material: 20R (1020), Yield strength σ𝑦 =285 Mpa, Ultimate strength σ𝑢 =400 MPa
Strain rupture of 28% is considered for analysis
Ramberg-Osgood equation:
Where, ε = total strain, σ = stress, E = Young’s modulus of elasticity
Parameter n is simplification variable.
Where 𝑒𝑢𝑠 = uniform strain at max load at σ𝑢 .
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5. Finite Element Model
Commercial software Hyper-mesh was used for pre-processing and post
processing
Commercial software NASTRAN 2012 was used as solver.
Performed a static nonlinear FEA of vessels.
The shell element, Tria3 element type was used to mesh the model of vessels
which comprised of node count in range of 15,000 – 16,400 for all pressure
vessels.
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6. Loading and Boundary Condition
Internal pressure of 1 bar at first
Incremented in steps until stress induced in vessel exceeds ultimate tensile
strength of material.
Internal pressure at which induced stresses exceeds ultimate strength of material is
considered to be the burst pressure of the vessel.
Some nodes are identified in the models which were constrained to keep the
models in equilibrium in such a way that no reactions are observed at constrained
location.
This boundary conditions are applied to avoid singularity in FEM.
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7. Result and Discussion
Vessels of different size were analyzed
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7. Result and Discussion
Table shows a comparison of failure pressure estimated with test data.
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7. Result and Discussion
All six vessels showed a good correlation of analyzed burst pressure with test
pressure.
Figure shows a comparison of burst pressure failure of different vessel by
Ramberg-Osgood with the experimental data and modified formulae.
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8. Conclusions
Reasonable agreement is achieved between finite element results and experimental
results.
Analysing the result, Ramberg-Osgood material model shows better correlation
with the experimental as compared to the modified Faupel formula.
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9. References
Aseer Brabin, T., Christopher, T., Nageswara Rao, B., 2011. Bursting pressure of
mild steel cylindrical vessels. Int. J. Press. Vessels Pip. 88 (2—3), 119—122.
Diamantoudis, A.Th., Kermanidis, Th., 2005. Design by analysis versus design by
formula of high strength steel pressure vessels: a comparative study. Int. J. Press.
Vessels Pip. 82 (1), 45—50.
Evans, C.J., Miller, T.F., 2015. Failure prediction of pressure vessels using finite
element analysis. J. Press. Vessel Technol. 137 (5), 0512061—0512069.
Kamaya, M., 2015. Ramberg—Osgood type stress-strain curve estimation using
yield and ultimate strengths for failure assessments. Int. J. Press. Vessels Pip. 137,
1—12.
Zheng, C.-X., Lei, S.-H., 2006. Research on bursting pressure formula of mild
steel pressure vessel. Zhejiang Univ. Sci. A 7 (2), 277—281.
05/22/2021
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Article - II
A study on the sealing performance of bolted flange
joints with gaskets using finite element analysis
By:
M. Murali Krishna,
M.S. Shunmugam,
N. Siva Prasad*
Indian Institute of Technology Madras, India
05/22/2021
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1. Abstract
Gaskets play an important role in the sealing performance of bolted flange joints.
Complex behaviour due to nonlinear material properties combined with permanent
deformation.
Performed 3D-FEA of bolted flange joints by taking experimentally obtained
loading and unloading characteristics of the gaskets.
Analysis shows that the distribution of contact stress has a more dominant effect
on sealing performance than the limit on flange rotation specified by ASME.
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2. Introduction
Flanged joints with gaskets are very common in pressure vessel and piping
systems.
Prevention of fluid leakage is the prime requirement of flanged joints.
Taylor-Forge method, provides procedures for the design of flanged joints.
Joints, even designed with codes such as ASME, DIN, JIS and BS experience
leakage and this problem is continuously faced by industry.
Analysis complexities due to behaviour of the gasket material combined with
permanent deformation.
Another inherent problem with bolted joints is flange rotation and contact stresses.
The ASME code has made an attempt to correct this problem by adding a rigidity
constraint ‘J’ based on the fixed rotation.
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2. Introduction
Sawa et al. presented a mathematical model for determining the contact stress
distribution in a pipe flange connection based on the theory of elasticity, treating it
as an axisymmetric problem.
Bouzid and Derenne developed an analytical method considering the rotational
flexibility of the flange for determining the contact stresses in order to predict the
joint tightness.
In the present work, a finite element model for finding the contact stresses in a
gasket has been developed.
Nonlinearity and hysteresis of the gasket under various loading and operating
conditions are taken into account.
The influence of flange rotations on the sealing performance of different gasket
models with varying loading and operating conditions has been studied.
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2. Introduction
The increase in the axial bolt force
when the joint is subjected to an
internal pressure has also been
analysed.
Flange specifications in this work:
Raised Face Weld-Neck Flange
80 mm NPS, Class 600#,
ASME/ANSI B16.5, M20 size
bolts
Spiral-wound ring gaskets are
considered with material properties
at room temperature.
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3. Gasketed Joints Configuration and Material Properties
Geometry
of
the
flange, gasket and bolt.
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3. Gasketed Joints Configuration and Material Properties
The flange and the bolt material properties are assumed to be homogenous,
isotropic and linearly elastic
Materials for flanges and bolts are chosen as forged carbon steel
Flange material: (SA-105, Young’s modulus E = 195 GPa, Poisson’s ratio v = 0.3)
Bolt material: Chromium steel (SA-193 B7, E = 203 Gpa, v = 0.3)
Non linear behaviour of gasket
Each reloading curve is assumed to be identical with the unloading one for
simplicity of input data in FEA
FEA elements in ANSYS consider geometric and material nonlinearities and
membrane & transverse shear are neglected.
A load compressive mechanical test (LCMT) has been carried out for finding the
mechanical characteristics of gasket material.
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4. Finite Element Modelling
Descritized 3D-FE model was developed
These
joints
possess
geometric
characteristics which are symmetrical
about an axis.
90° segment model of joint was
considered in the analysis for an eight
bolt model.
Similarly, 60° and 72° segments are
considered for 6 and 10 bolt models
respectively.
SOLID 185 method was used for
generation of meshing in flange.
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4. Finite Element Modelling
Gasket was modelled with interface elements (INTER 195)
In-plane deformation and transverse shear were neglected.
Thus complete gasket behaviour is characterized by a pressure-versus-closure
relationship.
Pretension elements (PRETS 179) were used to model the load in a bolted joint.
The bolt and nut as clean cylindrical as model to avoid meshing difficulties.
Bolt and nut were treated as a single entity and flange ring was a separate entity.
Flange ring was modelled as a target surface (TARGET 170) as it is stiffer than
the bolt, and the bolt head face is modelled as the contact surface (CONTA 173).
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4. Finite Element Modelling
After carrying out convergence studies, the model was discretized with 24,396
solid, 192 interface, 160 pretension and 612 contact elements and a total of 32,642
nodes.
FEA consists of bolt pre-loading and pressure loading conditions.
The gasketed flange is analysed by considering internal pressure in addition to the
bolt pre-load.
Equivalent hydrostatic end force has been applied uniformly in the axial direction
at one end of the pipe and the other end has been fixed in the axial direction.
20 steps for each of the bolting-up and pressurized stages have been considered.
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5. Flange Rotation with the ASME Code
Angular rotation of a flange under the influence of bolt pre-load and reaction
forces is called flange rotation.
The ASME code has a rigidity index ‘J’ to check the flange rotation.
For RFWN flange it is 0.3°
Higher the internal pressure, lower will be the stress upon gasket.
ASME has specified minimum gasket stress required upon bolt pre-load in terms
of maintenance gasket factor ‘m’, and gasket seating stress ‘y’.
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6. FEA Results
Flange rotation occurs due to eccentric
placement of gasket under bolt preload.
And, the gasket is subjected to a nonuniform contact stress due to this
rotation.
Figure shows the rotation of the flange
in terms of the axial displacements at
the bottom surface of the ring portion
along the radial direction for an
asbestos filled spiral-wound gasket
model for bolt pre-load of F = 30 KN
with different internal pressures (P = 0,
3, 5 and 10 MPa)
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6. FEA Results
It was observed that axial
displacements vary non-linearly in
the radial direction.
Another figure shows calculated
flange rotation with an asbestos
filled spiral wound gasket at
different bolt pre-loads and internal
pressures.
The rotation is large when the joint
is subjected to internal pressure.
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6. FEA Results
Table shows the flange rotation
for different spiral-wound gaskets
with eight bolts.
It was observed that the
calculated flange rotations were
well below 0.3°, as specified by
ASME.
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6. FEA Results
Stiffness of a gasketed joint is nearly equal
to the stiffness of the gasket, and the
variation of axial bolt force is influenced
by the stiffness of the gasket.
Figure below shows the variation of axial
bolt force with internal pressure for
different spiral-wound gaskets with 8 bolts
for an initial bolt pre-load of F = 30 KN.
It was observed that the increase in axial
bolt force is highest in the PTFE-filled
spiral-wound gasket due to its lower
stiffness and lowest for the graphite filled
spiral wound gasket.
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6. FEA Results
Table shows the increase in axial bolt force
for various spiral wound gaskets with
different loading and operating conditions.
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6. FEA Results
Figure shows the effect of bolt pre-load (30
KN) and internal pressure (0, 5, and 10 Mpa)
on the gasket contact stress distribution in the
radial direction.
It was observed that the contact stress was
compressive and decreases as the internal
pressure increases.
It was also found that the contact stress varies
form inner to the outer radius of the gasket
with 1-4% higher values at the outer radius.
It was observed that the variation of contact
stress on the gasket from the inner to the
outer diameter is higher in graphite-filled,
followed by asbestos and PTFE filled.
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6. FEA Results
Table shows the contact stress on various
spiral-wound gaskets at the inner and outer
radial positions for different bolt pre-loads
and internal pressures.
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6. FEA Results
Lower contact stress at inner radius of gasket is vulnerable to leakage.
Figure shows the variation of contact stress with internal pressure for and asbestos
filled spiral-wound gasket with 8 bolts at different bolt pre-loads.
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6. FEA Results
The intersection of the contact stress line and residual stress (ASME) line gives
the limiting internal pressure for a given bolt pre-load.
Table shows maximum allowable internal pressures to maintain the minimum
contact stress to avoid leakage for 6, 8 and 10 bolt models, respectively, on various
spiral wound gaskets with different bolt pre-loads.
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6. FEA Results
These
tables
show
the
corresponding flange rotation
for different loading conditions
and the values are well below
0.3° as specified by the ASME
code.
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7. Conclusions
Three types of gaskets namely AF, GF and TF spiral-wound gaskets were
considered to determine the sealing performance of these gaskets.
The distribution of gasket contact stress is observed to be non-uniform across the
gasket width with higher values at the outer radius.
Results show that leakage in the flanged joint may occur even if the flange
rotation is well below the value of 0.3°.
The increase in axial bolt force with increase in internal pressure is found to be
highest in TF spiral-wound gaskets and least for GF spiral-wound gaskets.
Variation in contact stress distribution in the radial direction is found to be highest
in GF spiral-wound gaskets and the least for TF spiral-wound gaskets.
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8. References
Taylor F. Modern flange design, G+W Taylor–Bonney Division, Bulletin 502,
Edition VII, 1978.
Sawa T, Higurashi N, Akagawa H. A stress analysis of pipe flange connections. J
Pressure Vessel Technol 1991; 113: 497–503.
Sawa T, Ogata N, Nishida T. Stress analysis and determination of bolted preload
in pipe flange connections with gasket under internal pressure. J Pressure Vessel
Technol 2002; 124: 385–396.
Bouzid A, Derenne M. Analytical modeling of the contact stress with nonlinear
gaskets. J Pressure Vessel Technol 2002; 124: 47–53.
ASME/ANSI B 16.5–1988, Specifications for plate flanges. New York: American
National Standards Institution.
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8. References
Bickford JH. An introduction to the design and behaviour of bolted joints. 2nd ed.
New York: Marcel Dekker Inc.; 1990.
Bickford JH. Gaskets and gasketed joints. New York: Marcel Dekker Inc.; 1998.
Murali Krishna, M. Finite element analysis and optimization of bolted flange
joints with gasket, MS thesis, Indian Institute of Technology Madras, 2005.
ANSYS User’s Manual, theory reference. Canonsburg, USA: ANSYS Inc.; 2003
ASME. Boiler and pressure vessel code, section VIII, Division I. New York:
American Society of Mechanical Engineers; 1995.
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Thank you!
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