 Open Access
 Total Downloads : 1193
 Authors : Jatin M. Patel, Prof. Mitesh J. Mungla
 Paper ID : IJERTV3IS10041
 Volume & Issue : Volume 03, Issue 01 (January 2014)
 Published (First Online): 03012014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Crack Detection of Pipe Using Static Deflection Measurement Method
Jatin M. Patel#1, Prof. Mitesh J. Mungla#2
#1, #2 Mechanical department(Cad/Cam), Gandhinagar Institute of Technology, Gandhinagar Gujarat, India
Abstract
A method of detection of crack location based on measurement of deflection of long pipes under bending loads is presented in this work. Crack is considered to be crosssectional with straight front parallel to its diameter and perpendicular to the plane of deflection. The crack is modeled by a rotational spring whose stiffness can be determined using the linear elastic fracture mechanics approach. The identification of a single crack in a beam based on the damageinduced variations in the static deflection of that beam. Pipes supported like cantilever beams have been examined. The details of the method are presented. Experiments have been carried out using steel, aluminum and UPVC pipes to demonstrate the effectiveness of the method. Cracks were introduced by wirecut machining.
Keyword: Crack Detection in pipe, Static Deflection Measurement, Rotational spring model, TPSDM

INTRODUCTION
In several areas of civil and mechanical engineering, at present, real challenges arising for the control, maintenance and retrofitting of existing structures and machinery concern the diagnostic identification of damages. Pipe, one of the five leading transportation tools, plays an important role in petrochemical industry ,power plants, chemical plants, gas and oil transportation, etc.. Crack present in the component may grow during service and may result in the component failure once they grow beyond a critical limit. It is desirable to investigate the damage occurred in the structure at the early stage to protect the structure from possible catastrophic failures. Developing pipe testing technique can avoid or decrease accidents and is an important guarantee for the safety service of pipe. Many reasons, such as corrosion damage, fatigue, creep damage and erosion, lead to pipe damage. However, fracture is always the final failure form. Therefore, crack diagnosis of the pipe is the most significant problem in nondestructive testing.
There are various Nondestructive techniques (NDTs) available for the detection of the crack in the
structural and mechanical components. To this purpose, nondestructive testing is of great interest under several respects, because it can provide a direct assessment of integrity of structures during service or can be employed to assess the residual resistance of a structure after the occurrence of a strong seismic event. At present, multiple techniques, for instance, leakage magnet detection technology, ultrasonic detection technology, eddy detection technology and acoustic emission detection technique, have been widely used in identifying the crack. Nevertheless, these traditional non destructive testing technologies are of low efficiency, and require complex instruments. At the same time, they need to detect the tested objects point by point. They are efficient but time consuming, expensive and laborious, particularly for slender beam like components. Therefore, researcher proposed a new detection technique based on vibration, based on natural frequency, based on deflection measurement etc, which can improve detection efficiency so as to determine crack location and size. It also can be utilized in detecting pipe damage in service.

CRACK DETECTION METHODS
Basically Two types of methods are available for detection of crack in mechanical components. one is conventional method and second is non conventional method,

Conventional (NonDestructive Testing – NDT) methods

Leakage magnet detection technology

Ultrasonic detection technology

Eddy detection technology

Ultrasound acoustics based assessment techniques etc.


Non conventional Methods

Natural frequency method

Wavelet analysis

Modal (Vibration) Analysis

Finite element method of second generation wavelets

Static Deflection Measurement Method Low detection efficiency, require complex instruments, time consuming, laborious and expensive. Due to this listed limitations, there is scope of
alternative of conventional method for crack detection. Therefore, people proposed a new detection technique based on vibration, which can improve detection efficiency so as to determine crack location and size. It can be also utilized in detecting pipe damage in service.
The objective of this work is to detect crack in pipe conveying fluid also to identification of crack location and crack size with conveying fluid in pipe and supporting objectives are to develop efficient and reliable strategy for crack detection in pipe which is pressurized by conveying fluid.
S.S.Naik [1] has demonstrated static deflection measurement method for detection of crack in pipe concluded maximum errors in prediction of crack location is about 9% for both Al & M.S pipe and Rotational spring stiffness for steel it is higher than Al. and it is decreases with increases crack depth. Kaushar
H. Barad et al. [2] have been investigated detection of the crack presence on the surface of beamtype structural element using natural frequency. S.M. Murigendrappa et al. [3] have been investigated Experimental and theoretical study on crack detection in pipes filled with fluid. E.Douka et al. [4] have been investigated Crack identification in beam using wavelet analysis, The fundamental vibration mode of a cracked cantilever beam is analyzed using continuous wavelet transform and both the location and size of the crack are estimated. Junjie Ye et al. [5] have been investigated on Pipe crack identification based on finite element method of second generation wavelet, a new method is presented to identify crack location and size, which is based on stress intensity factor suitable for pipe structure. Salvatore Caddemi et al. [6] have been investigated on the identification of a single crack in a beam based on the knowledge of the damageinduced variations in the static deflection of the beam.
In case of static deflection measurement method for crack detection is experimentally validate easily compare to other methods also Deflection is easy to measure by dial gauges compare to natural frequency & wavelet methods and not require complex instruments like FFT analyzer, accelerometers etc.
Rizos et al. [7] have represented the crack as rotational spring in modal analysis for a cantilever
Figure 1. Crack Model by rotational spring
The modelling for the detection of crack in slender pipes is based on the assumption that crack introduces only local discontinuity in the slope at the crack location and a very small difference exists between the mode shapes of the pipes with and without a crack. [8] Therefore, a pipe containing a crack, for example in = 00 orientation, can be conveniently represented by two pipe segments connected by a rotational spring of stiffness Kt at the crack position shown in Figure 2.
Figure.2 Crack in vertical orientation and its representation by rotational spring
When the rotational spring is used to represent a crack, the spring acts as sink for the energy released due to the crack. This energy is equal to the difference in energies of pipes with and without crack. The spring stiffness Kt can be determined experimentally using deflection method or vibration method. For a cantilever beam with load acting at the free end,
2
K emptypipe
c
beam having a rectangular cross section as shown in Figure 1.
t P(
nc )
where P is load acting at the free end, Mempty pipe is the bending moment due to P at the crack section at a distance L2 from the support and, c and nc are the
deflections along the load line for pipes with and without crack respectively. This relation provides the basis for determination of variation of Kt with crack size by the deflection method. Thus, if Kt is known, crack size a/t can be obtained using these plots.[8]


MATHEMATICAL FORMULATION
The equation of deflection for a crackfree beam is given by [1]
d 2 y
Figure.3 Cantilever beam with crack and its
EI nc M dx2
(1)
representation using rotational spring
Since M = W(L – x ), using the boundary conditions
This gives
y = 0 at x = 0 and dy /d x = 0 at x = 0, the
WLx2 Wx3 M
x x L (10)
nc nc
yIIcr
2EI
x xc c
6EI K
following relations for slope and deflection respectively are obtained
Extra deflection y due to the presence of crack for
dy W
x 2
any point in the segment II, is given by
nc
c Lx
dx 6EI 2 c
(2)
y y
IIcr
ync
xc x L
(11)
Wx3
WLx2
It is noteworthy that y = 0 for all locations over the
ync 6EI
2EI
(3)
segment I. using equation (3) and (10)
y M x x x x L
(12)
For modeling a beam with a crack, it is split into two segments (Fig.3.1). Deflection of segment I can be found out by following the procedure adopted for
K c c
To solve for K and xc for an unknown crack, it is
crackfree beam earlier.
necessary to measure y at two locations say x1 and
That is,
x within the segment II. If y and y
are the
d 2 y
2 1 2
EI Icr M W (L x) dx2
(4)
measured data, then from equation (12)
Using the boundary conditions as y = 0 and dy/d x = 0 at x = 0, slope and deflection of the beam at x = x c are given by
y1
y2
r x1 xc
x2 xc
(13)
dyIcr Wxc 2L x
dx 2EI c
Px2
(5)
(6)
Alternatively,
x x1rx2
c 1 r
(14)
yIcr
c 3L xc
6EI
K can then be determined using equation (12)
Similarly for the segment II (Figure 3) the slope and deflection are obtained solving the following governing equation
K P(L xc )(x1 xc )
y1

P(L xc )(x2 xc )
(15)
d 2 y
EI IIcr M W (L x)
(7)
y2
dx2
There is a jump in slope at x = x c. That is
Equations (14) and (15) give the crack location and rotational spring stiffness respectively [1]
dyIIcr
dx
dyIcr M
dx K
(8)
The use of TPSDM can be also extended to study of crack extension problems. For such a study,
Further, the displacements are continuous
y y
(9)
measurements of static deflections corresponding to
two instances in time, say t1 and t2, will be essential.
IIcr
Icr
Let the crack lengths be a1 and a2 and the crack growth be a (= a2 – a1), corresponding to the time interval. Using the static deflection measurements, rotational spring stiffness, say K1 and K2, corresponding to crack
lengths a1 and a2, can be estimated. Finally, using variation of K with a/t obtained through the forward problem, a1 and a2 (and a in turn) can be estimated. Verification of this aspect can be the subject matter of an interesting study [1].
Determination of Rotational Spring Stiffness by Deflection Method
The rotational spring stiffness, K corresponding to a crack in a component can be found experimentally by the deflection method. The equation for rotational spring stiffness K is
M 2
K Pc
nc
(16)
Figure.5 Measurement of Static Deflection At two locations with and without crack
where M is bending moment at crack section and, c
and nc are the deflections along the load line for cracked and crackfree beam respectively. Equation

gives the basis to obtain a variation of K with crack size (a/t) (Figure 4)


EXPERIMENTAL WORK
Figure.4 Experimental arrangement for measurement of static deflection of cantilever beam
Slender aluminium and mild steel pipes of uniform diameter were considered for experiments. Geometric and material properties of these pipes are given in Table 1. In all, 26 specimens made of both aluminium and mild steel were used. These include one crackfree specimen of each material. For static deflection measurements, the specimens were tested in cantilever configuration with a span of 0.95 m, using a clamping fixture made specifically for this purpose.
Figure 4 shows the experimental setup for measurement of static deflection to facilitate determination of K.
Table 1. Geometric and material data of MS and Al

RESULT AND DISCUSSION
The prediction of crack location by TPSDM is in good agreement with the actual location for both aluminium and steel pipes for crack size in the range of 2080 % of the thickness when the crack is in 12 oclock position. The prediction of the rotational spring stiffness is also possible using the proposed method. The rotational spring stiffness reduces as crack size increases.[1]
Inputs
L (Length of Beam)
1000mm
H (Height of beam)
10mm
B ( Width of beam)
40mm
E (Young modulus)
2.0e11
Poison ratio
Load
100kg at 0.9 m distance
from fix end
Crack Width(b)
1 mm
Crack Depth(a)
5mm
Crack depth ratio (a/t)
5
X1 (measurement
location 1 from fix end)
400mm
X2 (measurement
location 2 from fix end
800mm
Outputs
D1 (Deflection at X1
location)
9.69027mm
D2 (Deflection at X2
location)
31.4235mm
Dcr1 (Deflection after
crack at X1 location)
10.2509mm
Dcr1 (Deflection after
crack at X1 location)
91.855mm
xc is crack location of
beam
395.6630mm
Table 2. Analysis of cantilever beam (ANSYS Software)
Parameter
L(m)
D0(m)
Di(m)
(Kg/m3)
E(GPa)
Steel
0.95
0.0378
0.0278
7.860
173.81
Al
0.95
0.04
0.0298
2.645
60.347
Table 3.Analysis of cantilever pipe (ANSYS Software)
Inputs
Material of pipe
Mild steel
Length of pipe
0.95m
Outer diameter of pipe
0.0378m
Inner diameter of pipe
0.0278m
Density of pipe
material
7.860kg/m3
Modulus of elasticity
for pipe material
173.81GPa
/td>
Force applied in Y
Direction
80N
Outputs
Deflection of
uncracked pipe
967.6 m
Deflection of cracked
pipe
987.19 m
Table 4. Result
Sr. No
Method
Deflection for uncracked pipe in m
Deflection for cracked pipe in
m
Error in
%
1
Deflection method
878
885.333
0.82%
2
ANSYS
Software
967.6
987.19
1.98%
Analysis of cantilever beam in ANSYS software for finding the deflection of two different locations in beam with and without crack. Based on this analysis, relative errors were calculated in crack location is 20.78%.
Comparison of two different methods for calculating the deflection in cantilever pipe is shown in above table 4. In Deflection Method [1] difference between the values of deflection of pipe with crack and without crack is 7.333 m while same data of pipe can be analyzed in Software, difference between the values of deflection of pipe with crack and without crack is 19.59 m. Based on that above data find the relative errors in deflection method and Ansys Software are 0.82% and 1.98 % respectively. This deflection method is validate compare with Ansys software because of the relative error is small between two method.
Figure.6 Deformation without Uncracked Cantilever Pipe
Figure.7 Deformation with Cracked Cantilever
Pipe

CONCLUSION
From the above results it can be concluded that:
Deflection method is validate with experimentally and ANSYS Software with relative error is 0.82% and 1.98% corresponding.
REFERENCES

S.S.Naik, "Crack detection in pipe using static deflection measurement", J.Inst.Eng.India Ser,93(3)(2012) 209215

Kaushar H. Barad , D.S.Sharma, Vishal Vyas, "Crack detection in cantilever beam by frequency method" .NUiCONE, Procedia engineering 51(2013) 770775

S.M. Murigendrappa, S.K. Maiti , H.R. Srirangarajan, "Experimental and theoretical study on crack detection in pipes filled with fluid", Journal of Sound and Vibration 270 (2004) 10131032

E.Douka , S. Loutridis , A. Trochidis, "Crack identification in beam using wavelet analysis", International Journal of solid s and structures 40(2003) 35573569

Junjie Ye, Yumin He, Xuefeng Chen, Zhi zhai, Youming wang, Zhengija He, "Pipe crack identification based on finite element method of second generation wavelet", Mechanical system and signal processing 24(2010) 379393

Salvatore Caddemi, Antonino Morassi, "Crack detection in elastic beams by static measurements", International Journal of Solids and Structures 44 (2007) 53015315

Rizos, P, Aspragathos, N., Dimarogonas, "Identification of crack location and magnitude in a cantilever beam from the vibration modes". Journal of Sound and Vibration 138, 381388

Sachin S. Naik and Surjya K. Maiti, "Special issues related to detection of circumferential crack at different orientation in pipe by vibration method", ICSV14(2007)