Journal of Engineering Research and Application www.ijera.

com
ISSN : 2248-9622, PP 36-46

RESEARCH ARTICLE OPEN ACCESS

Fatigue Crack Growth Prediction of a Semi-Elliptical Surface

Crack in Pressure Vessel using AFGROW
Vinay K*, Manjunath S. B**
*(Post Graduate Student, Department of Mechanical Engineering,Dayananda Sagar College of Engineering,
Bangalore, Karnataka-560078, India.
** (Assistant Professor, Department of Mechanical Engineering,Dayananda Sagar College of Engineering,
Bangalore, Karnataka-560078, India.

ABSTRACT : Fracture mechanics is the field of mechanics concerned with the study of the propagation of
cracks in materials. The analysis of crack growth is one of the key problems in safety evaluation of industrial
components subjected to cyclic loading. Different approach for fracture mechanics are Linear Elastic Fracture
Mechanics, Elastic Plastic Fracture Mechanics and Dynamic time dependent fracture Mechanics. Linear Elastic
Fracture Mechanics (LEFM) method is used in present study mainly based on the assumption of small scale
yielding condition. This is expressed by means of two parameters, the stress intensity factor and the T stress. If
the loads are above a certain threshold, microscopic cracks will begin to form at the surface. Eventually a crack
will reach a critical size, and the structure will suddenly fracture. To predict the fatigue crack growth with
numerical approach, ASTM standard fracture test specimens viz., compact tension specimen, semi-elliptical
crack specimen and single edge notch specimen are simulated and its fatigue crack growth is predicted and
validated using analytical method. Further, the approach is applied to simulate and predict the fatigue crack
growth on an axial semi-elliptical surface crack in a section metallic pressure vessel using AFGROW.
Keywords– Crack length,Fatigue crack growth, Pressure vessel,Stress intensity factor, Semi-elliptical crack.
of structure design, the important aspect is the
I. INTRODUCTION calculation of the stress intensity factor.
Many investigations have shown that Yanyao Jiang et al. [1] presented an
sudden failures of aircraft components, pressure investigation on both standard and non-standard
vessels or pipeline systems might occur due to compact specimen to determine the fatigue crack
presence of surface cracks. Potential sources of these growth behavior of 7075-T651 aluminum alloy
cracks are material defects or geometric experimentally in normal environment condition.
discontinuities i.e. zones where stress increase The effect of the stress ratio on the crack growth was
happens. These zones, known as local stress studied with overloading and under loading. From
concentrations, are regions where the points with an the experiment they observed relationship between
extremely high magnitude of stresses could appear. da/dN and ∆K are practically independent of the
These points are areas where cracks are most often geometry and also the size of the specimen.
initiated and later propagate under cyclic loadings. SlobodankaBoljanovie [2] made an
Fatigue process consists of three stages, initiation investigation on estimating the fatigue crack growth
and early crack propagation, subsequent crack behavior on the finite plate having semi-elliptical
growth, and final fracture Due to previous reasons crack which is subjected to cyclic tensile loading.
the ability to assess the effects of thesedefects on The Stress intensity factor was obtained by applying
structural integrity under fatigue and fracture analytical and numerical methods. The analytical
loadings is of much practical significance. results were compared with experimental results and
it has shown good results.
The basic parameter that should be defined K. Ray et al. [3] presented a methodology
when formulating computational models is a shape to determine the fatigue crack growth rate curves
of the flaw i.e. initial crack. One of the most without integration of it. Exponential model has
common flaws found in structural components is a been used to predict the crack growth. The model
part-through surface flaw. These flaws could most provided a good agreement with experimental data. \
often be approximated and analyzed as a semi- P. Kannana et al [4] has carried out the
elliptical crack. For the assessment of fracture work on determining the leak pressure prior to
strength and residual fatigue life for defects failure, having axial semi elliptical crack with crack
contained in structures, or for damage tolerance length four times to that of thickness value which
analysis recommended to be performed at the stage represent a typical crack length of tested cylinder

National Conference on Advances in Mechanical Engineering (NAME) 2018 36 |Page

Department of Mechanical Engineering Jawaharlal Nehru National College of Engineering, Shivamogga
Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, PP 36-46

specimen. Theoretical results of fracture pressure

were validated with experimental results. With the
maximum plane strain fracture toughness, leak
pressure is obtained.

II. BENCHMARK
For benchmark or validation, three test
specimens are taken from journals paper of
references section of [1], [2] and [3] which are
compact tension, semi elliptical crack specimen and
single edge notch specimen. As it is necessary to
find stress intensity factor which represents the
stress state at crack tip which is very important Fig.2 Meshed model of compact tension specimen.
factor in fracture mechanics ANSYS workbench 17
is used for it.For better feasibility of modeling Boundary condition applied for compact
standard test specimens CATIA V5 is used. The tension specimen by applying fixed support at
standard test specimens were modeled in CATIA bottom of the hole and force applied at upper hole of
and then imported to ANSYS workbench. A stress the specimen, force applied is of 2700N as shown in
intensity factor result which is obtained from figure 3
ANSYS workbench is validated with the theoretical
results. The theoretical formulas used for validation
are again taken from same journals paper of stated
above reference section. Air Force Crack
Growth(AFGROW) software is used for finding the
fatigue crack growth of standard test specimens by
using geometrical similarity model which are inbuilt
in the AFGROW software.

1.1 Compact tension specimen

The specimen was modeled according to
the ASTM E647 method as shown in figure 1. Initial
crack length (an) was 3.54mm and thickness of Fig.3Boundary condition.
4.85mm and also edge radius (r0) of 0.80mm. The
material used for analysis is 7075-T651 aluminum Figure 4 shows the value of stress intensity
alloy. Young`s modulus is 71GPa and Poisson ratio factor of compact tension specimen, maximum value
is 0.33. is of 204.66MP mm and minimum value is of
133.25MPa mm.

Fig.4 Stress intensity factor of compact tension

Fig.1Dimension of compact tension specimen.
specimen.
Meshed model of compact tension
Theoretical validation of compact tension
specimen shown in figure 2 having element size
specimen is made by taking the expressions from the
5mm as global mesh. Hex20 (hexahedra) element is
journalpaper of reference section [1].
used near the crack tip. In order increase accuracy of
the result at the crack tip, the elements are increased
at the crack tip by decreasing the element size to
0.1mm at crack tip.
National Conference on Advances in Mechanical Engineering (NAME) 2018 37 |Page
Department of Mechanical Engineering Jawaharlal Nehru National College of Engineering, Shivamogga
Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, PP 36-46
P 2+ξ
K= 3 0.886 + 4.64ξ − 13.32ξ2 +
B W (1−ξ)2 1.2 Semi-elliptical crack
14.72ξ3−5.6ξ4 (1) The figure 7 shows geometry of semi
K= Stress intensity factor elliptical crack having length (L) 100mm, width (W)
P= applied load of the specimen is 50mm and thickness (t) is of
Crack length to width ratio (ξ) = a/w 10mm. The initial crack length along thickness and
a= Crack length width direction is 3mm. The material used for
w =Width analysis is 2219T851 aluminum alloy. Young`s
B= thickness modulus is 71GPa and Poisson ratio is 0.33.The
semi-elliptical crack specimen was modeled using
By substituting and simplification to main
CATIA without any crack inserted to the model, the
equation we get K= 206.96MPa mm and the crack is inserted in ANSYS workbench with the
difference (error) between theoretical value and selection of semi-elliptical (not a pre-meshed crack).
ANSYS result is of 1.11%. a/2b ratio is equal to 1, that is crack length in
Fatigue crack growth is determined using thickness direction (a) to the width direction(2b)
Air Force Crack Growth (AFGROW) software ratio is equal to 1.
which is subjected to load ratio of 0.1. Figure 5
shows the graph of crack length v/s number of cycle
up to failure and finial crack length along width
direction is of 0.0494m.Where da/dN is crack
growth rate and ΔK is stress intensity factor range.

Cr
ac
k
le
ng
th
in
m Number of cycle
Fig. 5 Crack length verses number of cycles.
Fig. 7Geometry of semi elliptical crack.

Tet 10(Tetrahedron element) is used to

mesh the specimen having element size 1mm. Figure
da/
8 shows the boundary condition applied to specimen
dN by applying upper face of the specimen with the
in pressure of -100MPa and lower face is fixed.
m/c
ycl
e

ΔK in MPa m
Fig. 6 Crack growth rate.
Figure 6shows the crack growth of compact Fig. 8 Boundary condition.
tension specimen and graph is plotted log da/dN Figure 9 shows the value of stress intensity
verses log∆K for a load ratio of 0.1. factor for semi elliptical crack specimen having
National Conference on Advances in Mechanical Engineering (NAME) 2018 38 |Page
Department of Mechanical Engineering Jawaharlal Nehru National College of Engineering, Shivamogga
Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, PP 36-46

maximum value of 226.6MPa mm and minimum width direction. Figure 10 and 11 shows crack
value of 203.89MPa mm length for both thickness (A) and also for width
direction(C). Finial crack length along thickness was
0.01m and crack length along width direction was
0.0169m. Fatigue crack growth is determined by
using NASGRO equation.
Cr
ac
k
le
ng
th
in
Fig. 9 Stress intensity factor of semi elliptical m
specimen.
Number of cycle
Fig.10 Crack length along thickness verses number
Theoretical validation of semi elliptical
of cycles.
crack specimen is made by taking the expressions
from the journal paper of reference section [2].
Cra
πa
∆K = ∆S × Me (2) ck
Q
Where ∆S= applied Stress range len
Q =elastic shape factor gth
∆K = Stress intensity factor range in
a = crack length in the depth direction m
Me= correction factor
a a
Q = 1 + 1.47 × ( )1.64 ( ≤ 1.0) (3)
b b
b = crack length in the surface direction Number of cycle
b a Fig.11 Crack length along width verses number of
Me = [ M1 + ( Q − M1 ) × ( )p ]fw g (4) cycles.
a t
a
P = 2 + 8( )3 (5)
b The figure 12 shows the fatigue crack
a a
M1 = 1.13 − 0.1 , 0.02 ≤ ≤ 1.0 (6) growth of semi elliptical specimen having crack
b b
The term fw is the finite width correction factor length of 3mm in width direction and 3mm along
1 thickness direction.
fw = πb a
(7)
cos
w t

The expression for g is given by

a
g = 1+ (0.1+0.35( )2 )(1 − sinϕ) (8)
t
ϕ = 900
Where g = geometrical correction
da/
By substituting and simplification to main dN
equation we get K= 228.316MPa mm and the in
difference (error) between theoretical value and
m/
ANSYS result is of 0.7515%.From the ANSYS
result stress intensity factor is higher at crack end. cyc
So that crack propagation is higher along width le
direction than along thickness direction for the
above loading condition and geometrical dimension
of the semi elliptical crack specimen.
Fatigue crack growth of semi elliptical
specimen is determined with the load ratio of 0. The ΔK in MPa m
crack growth was seen in both the thickness and Fig.12 Crack growth rate.

National Conference on Advances in Mechanical Engineering (NAME) 2018 39 |Page

Department of Mechanical Engineering Jawaharlal Nehru National College of Engineering, Shivamogga
Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, PP 36-46

1.3 Single edge notch specimen Figure 15 shows the value of stress
The figure 13 shows single edge notch intensity factor for single edge notch, having
specimen geometry having thickness of 6.5mm and maximum value of 288.44MPa mmand minimum
initial crack length of 17.75mm. The material used value is 204.94MPa mm.
for analysis is 2024T3 aluminum alloy. Young`s
modulus is 73100MPa and Poisson ratio is 0.33. The
Model of single edge notch specimen was modeled
using CATIA with crack inserted in the model.
Crack is defined in ANSYS workbench with the pre-
meshed option.

Fig.15 Stress intensity factor of single edge notch

crack specimen.

From the reference section [3] journal

paper, theoretical validation of single edge notched
specimen is made.
F πa
K = f(g)× (9)
WB
a 𝑎
f(g) = 1.12-0.231×( ) + 10.55 × ( )2 − 21.72 ×
w 𝑤
𝑎 𝑎
( )3 + 30.39 × ( )4 (10)
𝑤 𝑤
Where F = applied force
a = crack length
w = width
B = thickness
Fig.13 Geometry of single edge notch crack. By substituting and simplification to main
equation we get K= 289.136MPa mm and the
Tet 10(Tetrahedron element) is used to difference (error) between thetheoretical value and
mesh the specimen having element size 1mm. The ANSYS result is of 0.2407%.
upper face of the specimen is applied with the
pressure of -21.3MPa (tensile loading) and lower Fatigue crack growth of single edge notch
face is fixed. In order to increase the accuracy of specimen is determined with load ratio of 0.1. The
stress intensity factor result element size near crack crack length verses number of cycles up to failure is
tip is reduced to 0.1mm so that element are more at shown along width direction and having finial crack
the crack tip. length of 0.039m.

Cr
ac
k
len
gth
in
m
Number of cycle
Fig.14 Boundary condition. Fig.16 Crack length verses number of cycle.
National Conference on Advances in Mechanical Engineering (NAME) 2018 40 |Page
Department of Mechanical Engineering Jawaharlal Nehru National College of Engineering, Shivamogga
 Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, PP 36-46

The figure 17 shows the crack growth rate thickness of 7.2mm and minor radius of crack is
of single edge notched specimen having crack length 5.4mm and major radius is 25.4mm. Length of
of 17.75. NASGRO equation was used to determine specimen is of 1400mm. The material used for
the fatigue crack growth. analysis is AISI 4130 steel. Young`s modulus is
205GPa and Poisson ratio is 0.32.
Since large dimension of geometry
involved in pressure vessel mainly in case of length,
taking in the mind of computational time involved in
meshing, computer configuration and also
da/d computational time involved in result extraction. It is
N in essential to use symmetry of model. The figure
m/c below shows symmetry of pressure vessel model.
ycle

Fig.19 Symmetry region 1.

ΔK in MPa m
Fig.17 Crack growth rate.

III. CASE STUDY on PRESSURE VESSEL

For the safe design of pressure vessel, Leak
Before-Break (LBB) is important phenomenon
required to prevent catastrophic failure of pressure
vessel. The catastrophic failure can happen without
Fig.20 Symmetry region 2.
the formation of through crack. So it is essentially
need to find the leak pressure for safe design of
pressure vessel. In present work semi-elliptical crack
length was taken as four times of thickness length,
since it represents a typical fatigue crack geometry
observed at failure location in fatigue tested
cylinders. In the present study, initially finding out
the fracture pressure through theoretical means and
thenfinding out stress intensity factor with
theoretical way than with ANSYS workbench also.
Fig. 21 Symmetry region 3.

Tet 10(Tetrahedron element) is used to

mesh the specimen having element size 1mm. Since
of symmetry boundary condition, we are applying or
restricting Z=0 and X = 0 as shown below and
applying pressure of 31.48N/mm2 on the internal
surface of pressure vessel.

Fig.18 Geometry of the model.

The figure 18 show diagram of axial semi

elliptical crack, having outer diameter 228.6mm and

National Conference on Advances in Mechanical Engineering (NAME) 2018 41 |Page

Department of Mechanical Engineering Jawaharlal Nehru National College of Engineering, Shivamogga
Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, PP 36-46

Fig. 22 Restricting along Z direction.

P ×R
𝜎𝑢 = b i (19)
t
σu= hoop stress of unflawed cylindrical vessel
Pb = bursting pressure of unflawed cylindrical vessel
Ri = inner radius of pressure vessel
t = thickness of pressure vessel
2 σ ys t
Pb = σys 2 − ln⁡
(1 + ) (20)
3 σ ult Ri
1
Fig. 23 Restricting along X direction. σ σ u ×(πa)2 ×M σf
(1 − m) × ( f )P + m + × −
σu фK F σu
Figure below shows the value of stress
1=0 (18)
intensity factor for pressure vessel, having maximum
KF, m and p are fracture toughness parameters
value of 4048.7MPa mm and minimum value is σys = yield strength of material (1097MPa)
2412.8MPa mm. σult = ultimate tensile strength of material(1180MPa)
By substituting and simplification
σf=468.30MPa.
P ×R
σf = f i (21)
t
Pf = failure pressure
By substituting and simplification
Pf =31.48235 N/mm2
πa
K max = σ × M (22)
ф2

K=4496.21 MPa mm
The difference (error) between theoretical
value and ANSYS result is of 9%..

IV. PARAMETRIC STUDY on PRESSURE

Fig. 24 Stress intensity factor of pressure vessel. VESSEL
1.4 Parametric study using ANSYS workbench
Theoretical validation of pressure vessel is Parametric study is made on pressure vessel
made by taking the expressions from the journal by varying pressure with fixed thickness of 7.2mm
paper of reference section [4].Than its value was till to the fracture pressure. The graph is plotted with
applied to stress intensity factor equation. stress intensity factor verses pressure as shown in
figure 25. After the point A sudden increase in the
a
q = 2+8( )3 (11) stress intensity factor was seen mainly because
c
a = Depth of surface crack pressure at a point A is nearer to the fracture
c = Length of surface crack pressure of the experimental results. With increase
c a of pressure, stress intensity factor also increases.
λs = × (12)
R i ×t t
Ri = inner radius of pressure vessel
t = thickness of pressure vessel
fs = (1 + 0.52 × λs + 1.29 × λ2s − 0.074 ×
λs3)12 for 0≤λs≤10 (13)
a
M1 = 1.13 − 0.1 × for a ≤ c (14)
c
2 a
ф = 1 + 1.464 × ( )1.65 for a ≤ c (15)
c
Φ2 = Crack shape factor
c a
Me = M1 + (ф × − M1 ) × ( )q (16)
a t
M = Me × Fs (17)
M = Magnification factor
Fracture strength equation is given as
Fig. 25Stress intensity factor verses pressure.

National Conference on Advances in Mechanical Engineering (NAME) 2018 42 |Page

Department of Mechanical Engineering Jawaharlal Nehru National College of Engineering, Shivamogga
Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, PP 36-46

The figure 26 shows stress intensity factor

verses thickness. The thickness variation is made
with fixed pressure of 25MPa which is nearly below Cra
the fracture pressure. The stress intensity factor
ck
decreases with increase in the thickness and reaches
to a minimum value, thereafter stress intensity factor len
does not decrease with increase in thickness which is gth
known as plain strain fracture toughness. With the in
help of plain strain fracture toughness it is possible m
to calculate the leak pressure.

Number of cycle
Fig. 27 Crack length verses number of cycle for
pressure of 14MPa.

da
/d
N
in
Fig. 26 Stress intensity factor verses thickness. m/
cy
1.5 Parametric study using AFGROW
cle
Parametric study is done on HY (higher
yielding material) 130 steel pipe material using
AFGROW. Same dimension are taken as earlier to
that of pressure vessel. Same variation of pressure
and thickness has been made as earlier to parametric
study. Since due to insufficient material data of
AISI 4130 steel material which is required for
AFGROW software as input, so material chosen was
HY 130 steel pipe which come under pressure vessel ΔK in MPa m
of NASGROW material data base file. Pressure Fig. 28 Crack growth rate for pressure 14MPa.
variation has been made on pressure vessel having
thickness of 12.2mm. For pressure of 22MPa there is
no crack length because of crack growth is less than
2.54e-15m.The below figures shows crack length Cr
verses number of cycle up to failure along the ac
thickness and length direction. Crack growths for k
the pressure of 14MPa, 18MPa and 22MPa with the
le
fixed thickness of 12.2mm. Load ratio taken
parametric study is of zero. ng
th
in
m

Number of cycle
Fig. 29 Crack length verses number of cycle for
pressure of 18MPa.

National Conference on Advances in Mechanical Engineering (NAME) 2018 43 |Page

Department of Mechanical Engineering Jawaharlal Nehru National College of Engineering, Shivamogga
Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, PP 36-46

Thickness variation has been made on

pressure vessel having fixed pressure of 25MPa. For
thickness of 12.2mm there is no crack length
because of crack growth is less than 2.54e-15m.
Cra
ck
da/ len
dN gth
in in
m/ m
cy
cle

Number of cycle
ΔK in MPa m Fig. 33 Crack length verses number of cycle for
Fig. 30 Crack growth rate for pressure 18MPa. thickness of 27.2mm.

Cr
ac
k da
le /d
ng N
th in
in m/
m cy
cl
Number of cycle e
Fig. 31Crack length verses number of cycle for
pressure of 22MPa.

ΔK in MPa m
Fig. 34 Crack growth rate for thickness 27.2mm.

da/
dN
in Cr
m/ ac
cyc k
le len
gth
in
m

ΔK in MPa m Number of cycle

Fig. 32 Crack growth rate for pressure 22MPa.

National Conference on Advances in Mechanical Engineering (NAME) 2018 44 |Page

Department of Mechanical Engineering Jawaharlal Nehru National College of Engineering, Shivamogga
Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, PP 36-46

Fig. 35 Crack length verses number of cycle for

thickness of 22.2mm

da
/d
N
in
da/ m
dN /c
in yc
m/ le
cyc
le

ΔK in MPa m
ΔK in MPa m Fig. 38 Crack growth rate for thickness 17.2mm.
Fig. 36 Crack growth rate for thickness 22.2mm.

Cra
ck
Cra leng
ck th
len in
gth m
in
m

Number of cycle
Number of cycle Fig. 39 Crack length verses number of cycle for
Fig. 37 Crack length verses number of cycle for thickness of 12.2mm.
thickness of 17.2mm.

National Conference on Advances in Mechanical Engineering (NAME) 2018 45 |Page

Department of Mechanical Engineering Jawaharlal Nehru National College of Engineering, Shivamogga
Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, PP 36-46

[6] Zhenyu Ding, Zengliang Gao, Chenchen Ma,

Xiaogui Wan, “Modeling of I + II mixed mode
crack initiation and growth from the notch”,
Theoretical and Applied Fracture Mechanics, 84,
2016, 129–139.
[7] Ashok Saxena , Federico Bassi , Kevin Nibur ,
da/ James C. Newman , “One single-edge-crack
dN tensionspecimensfortension-compression fatigue
in crack growth testing”, Engineering Fracture
Mechanics, 176, 2017, 343–350.
m/
[8] Behzad V, Farahani, Paulo J, Tavares, J Tavares,
cy Jorge Belinha, P.M.G.P. Moreira, “A Fracture
cle Mechanics Study of a Compact Tension Specimen:
Digital Image Correlation, Finite Element and
Meshless Methods”, 2nd International Conference
on Structural Integrity,5, 2017, 920-927.
[9] M. Benachoura, A. Hadjouia, M. Benguediabb, N.
Benachoura, “Effect of the amplitude loading on
fatigue crack growth”, Procedia Engineering, 2,
2010,121–127.
[10] Gao Yi , Tiantang Yu , Tinh Quoc Bui , Chunping
Ma, Sohichi Hirose, “SIFs evaluation of sharp V-
ΔK in MPa m notched fracture by XFEM and strain energy
Fig. 40 Crack growth rate for thickness 12.2mm. approach”, Theoretical and Applied Fracture
Mechanics ,89, 2017, 35–44.
V. CONCLUSION [11] Punit Aroraa, P.K. Singh, V Bhasin, K.K. Vaze
Predication of stress intensity factor and ,D.M. Pukazhendhi, P Gandhib, G. Raghava,
fatigue crack growth for standard test specimens has “Fatigue crack growth behaviour in pipes and
been carried out. Finite Element Analysis results are elbows of carbon steel and stainless steel
good argument with theoretical values. Case study materials”, 6th International Conference on Creep,
Fatigue and Creep-Fatigue Interaction, 55, 2013,
has been made on pressure vessel, Finite Element 703-709.
Analysis result is in good argument with theoretical
value. Parametric study is done on pressure vessel
on both using ANSYS workbench and AFGROW
software, which gives knowledge how stress
intensity factor varies with thickness and pressure
and also how crack length varies with the pressure
and thickness value.

REFERENCES
[1] Tianwen Zhao, Jixi Zhang, Yanyao Jiang, “A study
of fatigue crack growth of 7075-T651
aluminiumalloy”,International Journal of Fatigue,
30, 2008, 1169–1180.
[2] SlobodankaBoljanovic, “Fatigue Strength Analysis
of a Semi-Elliptical Surface Crack”, Scientific
Technical Review, 62(1), 2012, 10-16.
[3] J.R. Mohanty , B.B. Verma , P.K. Ray, “
Prediction of fatigue crack growth and residual life
using an exponential model”, International Journal
of Fatigue,31, 2009, 418-424.
[4] P. Kannana, K.S. Amirthagadeswaranb, T.
Christopherc, B. Nageswara Raod, “A simplified
approach for assessing the leak-before-break for
theFlawed pressure vessels”, Nuclear Engineering
and Design, 302, 2016, 20–26.
[5] J.C. Newman, I S Raju, “Stress Intensity Factor
Equations for Cracks in Three Dimensional Finite
Bodies Subjected to Tension and Bending Loads”,
Computational Methods in the Mechanics of
fracture, 1986.

National Conference on Advances in Mechanical Engineering (NAME) 2018 46 |Page

Department of Mechanical Engineering Jawaharlal Nehru National College of Engineering, Shivamogga