2. Literature Review -...

Ph. D. thesis on Study of Design Aspects of Expansion Joints with Metallic Bellows and their Performance Evaluation 27

2. Literature Review

Literature review is an important task for any research work. Various resources

are referred to collect basic information about the expansion joints. During this

phase theories from books and hand - books, previous work input by research

scholars, technical articles, research papers, etc are referred from various

libraries. Of- course various websites are also referred for the study. The review of

research papers gives idea about previous research work done, their

methodology, and it indicates the space / gap to proceed for the research work.

In the field of expansion joints very limited literature is available. Only few

technical books and hand books of piping includes about the expansion joints

which are used in the piping. But these references are limited up to the working

principle of expansion joints. No text or reference books include, design of

expansion joints, as this is a specialized area. But all authors are mentioning the

reference of standards developed by EJMA. Since major contribution in the design

of bellows expansion joint is given by Expansion Joints Manufacturers

Association (EJMA). EJMA has established the codes and guidelines for the

design of bellows expansion joints. These codes are available based on

membership of EJMA.

Looking to Indian industries establishment, very few manufacturers are involved in

development of expansion joints. Since the criticality of the components and risk

factors involved is high. For the design verification and performance estimation of

expansion joint for special areas requires on going research and testing facilities

development continuously in the infrastructural set up. Also financial investment is

considerable more. Hence only few industrialists are involved in the field of

expansion joints.

Some technical reference books and handbooks on piping include the background

of bellow expansion joints. Many technical research papers have been reviewed

and concise brief summary is formulated. During the research work and thesis

writing proper references are utilized and mentioned. The literature review

analysis and summary are as following.


2.1 Important Theory Books and Handbooks Review:

K P Singh and Alan I Soler; Mechanical Design of Heat Exchangers; Arcturus Publishers, Cherry Hill, NJ 08003, First edition, 1984. [B11]

A first mathematical idealized model and free bodies of elements of an expansion

joint was initiated by Koop and Sayre.[10] The expansion joint thus idealized has

three element types as shown in figure 2.1. They are main heat exchanger shell,

annular plate and Outer shell. Notice that the loading and internal stress resultants

are symmetrical with respect to the median transverse plane. The necessary

stress and deformation relationships for each element in the joint can be found

with required parameters.

Figure 2.1: Idealized geometry of bellows

They put comprehensive effort to determine the axial stiffness of flanged joints

analytically. They also conducted some experiments to verify their mathematical

model. Their model is based on classical plate and shell theory and its application

to pressure vessels. He derived the equation to evaluate the stresses developed

in the different elements of an expansion joints. They obtained good agreement

with experimental data. They have also prepared a computer program in which

analytical equations are coded. This method is more accurate and hence still it is

referred by many researchers.


Figure 2.2 : Free body diagram of bellows geometry

The research is extended by Wolf and Mains[28], to overcome the problem of

variations in geometry of bellows by modeling axis by series of narrow rings. An

alternative procedure is to equip a finite element program, capable of handling

symmetrically loaded axi-symmetric structures. Such a program FLANFLUE

has been developed for treating flanged and tube expansion joints. This method is

not widely accepted because it was purely numerical method.

The first comprehensive attempt to develop design guidelines for bellows design

is due to Anderson. Andersons work has been integrated into the standards of the

EJMA. Following relationships were developed using analytical approach

according to different segments of convolutions.

Inner shell: Circumferential stress, awE

m (2.1)

Longitudinal stress, a

Faxlm (2.2)

Annular Plate: Radial bending stress, 26

e

rr t

M (2.3)

Circumferential bending stress, 26

etM

(2.4)

Outer shell: Membrane hoop stress, bwE

m (2.5)

Longitudinal hoop stress, e

lw tF2 (2.6)


Where, Fax = Appl;ied axial force per unit circumference of shell

F2 = Reaction force per unit circumference in the outer shell

w = radial deflection of shell, lateral deflection of annular plate

a = Mean radius of inner shell

b = Mean radius of outer shell Conclusions:

The mathematical model developed by Koop and Sayre is based on classical

plate and shell theory; hence, it obtains good agreement with results of various

experiments carried out by them. These equations are integrated in the codes of

EJMA.

Reference: Koop S and Sayre M F; Expansion Joints for Heat Exchangers;

ASME Winter Annual Meeting, New York, 1952. [10]

Fatigue Life of Bellows:

As much of the stress in the expansion joint is of secondary and peak type,

calculated values in operating units exceeding the material yield strength are not

uncommon. Therefore, the primary design involves restricting the primary and the

local membrane stresses to occur within specified limits, and computing

cumulative damage factor.

M W Kellog Company [B12] presented the following formula for the fatigue life

estimation of bellows. The company uses Number of cycles (Ni) and Stress level

(Si) terminologies for stainless steel bellows which gives good agreement with the

published data.

Ni = 5.3

1600000

iS (2.7)

Using factor of safety of 2 on the stress range the designers are recommended to

use following relation to estimate fatigue life.

Ni = 5.3

800000

iS (2.8)

Above relationship is useful to designers to estimate the life cycles of stainless

steel bellows.

Reference: Kellog M W; Design of Piping Systems; Wiely ; 1956. [B12]


Low cycle fatigue:

Expansion joints are under going low cycle fatigue because of secondary and

peak type, stresses in operating units exceeding the material yield strength.

Therefore, the primary design should involve restricting the primary and the local

membrane stresses to occur within specified limits, and avoidance of premature

fatigue. Using such mathematical computations number of life cycle can be

predicted for the bellows.

Miners hypothesis for predicting the effect of cumulative fatigue based on

different stress cycles is the first initiative to consider cumulative damage of the

material because of low cycle fatigue.

In this paper the authors have suggested the following formula, which gives good

experimental agreement for steel, copper, nickel, stainless steel and titanium

material components.

Si = eiNCE

22/1 (2.9)

Where,

E = Youngs modulus of the expansion joint material at the operating temperature

e = Endurance limit for the expansion joint material

C = ln

RA%100100 (2.10)

RA is the reduction in area in the tensile test of a material.

Reference: Tavernelli, J F; and Coffin L F; Experimental support for Generalized

Equation Predicting Low Cycle Fatigue; Instorn Engineering Corporation;

Application Series M-3; 1959. [22]


Tavernelli and Coffin has extended the study on low cycle fatigue of bellows type

expansion joints. They have suggested to use similar relation. Langer B F has

proposed the following expression for the acceptable number of cycles Ni, at

stress range Si,

Ni = 2

2

2)(

%100100ln

4

SeSiKeSF

RAE

(2.11)

Where,

SF is the required factor of safety, and

Ke is stress/strain concentration factor at the material point under

consideration.

If a stress range Si exceeds three times the allowable stress or twice the yield

strength of the material, then Si should be increased by a factor Ke can be

thought of is plasticity correction factor.

Using this relationship of predicting number of cycles, ASME code gives plots of

Ni Si for several common materials of construction.

Reference: Langer B F; Design of Pressure Vessels for Low cycle Fatigue;

Journal of Basic Engineering; Vol. 84; No. 3; Sept. 1962. [11]

Extending the research of fatigue life cycle of bellows expansion joint, Anderson

analyzed the available data from fatigue tests on convoluted unreinforced bellows

and determined that pressure stresses have a definite effect on fatigue life. He

found the following equation to correlate a pseudo-stress S (psi) to cycle life N.

Log10 S = 6.24 0.236 Log10 N (2.12)

The above study has been referred by EJMA and they have established the

relationship to estimate the life cycles of bellows expansion joint. Andersons work

has been integrated into the standards of the EJMA.

Reference: Anderson W F; Analysis of stresses in bellows; U S Atomic Energy

Commission, Report No. NAA SR 4527 (1964). [11]


Handbook of Piping Design; G K Sahoo; New Age Publishers; 1998. [B6]

A pipeline designer has to make judicious layout planning providing for expansion

for a pipe line even in a confined space to avoid the problems arising out of a stiff

piping system. The author has suggested using expansion joint at following

circumstances.

1. In a system where space is very limited for a conventional flexible piping

system;

2. Where pressure drop required is minimum;

3. Where the thermal stresses are excessive at the terminal equipment

connection;

4. Where initial layout planning is inadequate to allow for sufficient expansion;

5. Where it is required to check the mechanical vibrations;

6. Where it is impossible to align a pipe line exactly;

7. Where it is economical than a conventional piping system.

Calculation of Thermal expansion:

To calculate the number of convolutions as stated above, total expansion is

required to calculate. It can be calculated with following relationship.

Total expansion = 100

tL (2.13)

Where; = Coefficient of thermal expansion in mm/m/1000C.

L = Total straight length of pipe line between two fixed supports / anchors

t = temperature difference in 0C between max. and min. temperature.

The authors have provided the design guide lines for the bellows. The number of

convolutions should be as per following approximations.

Number of convolutions Total expansion

1 convolutions up to 10 mm





This approximation is only for axial movements of piping due to expansion and

contraction due to temperature.


Anchor force due to thermal expansion:

The force acting on the fixed points of a straight pipe line without any

compensator is calculated by considering the pipe line as a stiff member and

preventing the line against buckling according to following equation.

Force on anchor, Ft = t A (2.14)

Where, = Repetitive thermal stress of material for 10 temperature difference.

(25 kg/cm2 for carbon steel tubes)

t = Temperature difference between service temp. & erection temp. 0C

A = Cross section area of pipe material in cm2.

The total reaction force acting on fixed point supports are due to internal pressure,

stiffness of the bellow material, and frictional resistance of the pipe.

Reaction force due to internal pressure, Fp = )(4

2 Pdm (2.15)

Reaction force due to stiffness, Fs = z

cn (2.16)

Where, n = Movement of one bellow in mm without pre-stressing.

c = stiffness constant or spring constant in kg/mm.

z = number of sides of bellows, for one bellow, z = 2.

Reaction force due to frictional resistance of pipe moving over anchors/saddles

Fr = lW0 (2.17)

Where, 0 = frictional coefficient of steel on unmachined steel surface

(0.20.4)

W = Weight of pipe, water, and insulation kg/meter.

l = Effective length of pipe in meter.

The total reaction force = Fp + Fs + Fr (2.18)


2.2 Research Papers Review: J F Wilson; Mechanics of Bellows: A critical Survey; International Journal of Mechanical Science; Volume 26, No. 11/12, pp 593-605, 1984.[7]

Bellows are thin walled corrugated tubes designed for high flexibility when

subjected to longitudinal loads, internal pressure or bending moments. Many

researchers have contributed in the theoretical and experimental studies on

bellows. This paper is critical survey of some papers. The purpose of this paper

are in threefold: to summarize the theoretical values of E found in the literature for

various geometric configurations; to evaluate the mathematical models; and to

compare calculated and experimental values of E. In making these comparison,

the historical results, either in equation or graphical, are presented using non-

dimensional parameters. For each theory, either the modulus ratio E/E or a

flexibility parameter proportional to E/E., is expressed as a function of a minimum

number of non-dimensional qualities selected from list.

Considering bellow as beam model; Feeley and Goryl studied the stiffness of disc

type of bellow using beam theory to model the triangular or crimped-plate theory.

In which b/h < 1 and h/R


Plate cylindrical shell models: Haringx predicted the axial load vs deflection

behaviour of the rectangular shaped bellows. For this model the flexibility is

defined in a form consistent with the shell parameters b/E, h/R, t/R, , and .

22223

22

ln211/1)/1

43

'

RbRh

Rt

EE (2.22)

Shell models: Hamada et al employed a computer aided finite element method

to solve the thin shell equations for the mechanical behavior of the U shaped

bellows. Results were reported only for = 0.3 and for h/b in the range of 1.6

2.4. These correlations, recast to exhibit the flexibility as a function of the shell

parameter . Berliner and Vikhman reported experimental data on the flexibility of

four axial loaded, U shaped, steel bellows. They suggested the axial load vs

extension data, cast in terms of the flexibility parameter (E/E) (t/R).

Turner and Ford used shell theory based on an energy analysis to predict the

flexibility of the semicircular bellows and S shaped bellows. For a fixed and ,

the flexibility of these two geometries differs greatly, as is seen by comparing their

results. This paper is including with one experiment program carried out on the

polyethylene siphon bellows. The purpose is to compare the measured axial

stiffness to that predicted by the appropriate theories discussed previously.

Figure:2.3 Flexibility of U shape bellows


Hamada et al have employed the a computerized technique to evaluate thin shell

equations for mechanical behavior. They reported the results for = 0.3 and h/b

in the range of 1.6 - 2.4. This correlation recast to exhibit the flexibility as a

function of shell parameter , as shown in figure 2.3.

The theoretical and experimental results for this externally loaded bellows are

summarized below. The value of E is predicted by each of the three theories is

compared to the experimental value, Haringx theory shows the best agreement.

Table 2.1: Stiffness results from various theories

Bellow model Stiffness

F1/1 (lb/in)

Equivalent Modulus

E (psi)

Shell theory 40.9 229

Crimped-plate 34.0 191

Beam theory 27.1 152

Experiment 31.0 174

Conclusions: Based on the experiments performed herein and those found in the

literature, the most accurate predictor of E for crimped-plate theory and

rectangular bellows is the Haringx theory.

The Haringx theory accurately predicts E for U shaped bellows which are

approximated as rectangular bellows of the same average dimension.

For a particular bellows design, the flexibility is increases, when Poissons ratio is

decreases.


S. V. Narasimham et al; Stress analysis of V-shaped expansion joints under internal pressure; International journal of Pressure Vessels and Piping; Elsevier Science Ltd. 1997 [18]

A composite shell type, V- shaped expansion joint is analyzed for the membrane

and bending stresses induced in circumferential as well as meridian direction

under internal pressure loading. The V- shape geometry consists of four junctions

of different shapes. Each junction is composed of various shape combinations.

The four segments are made of the complete V shape of the expansion joint.

They are toroidal shell of positive curvature, conical shell, toroidal shell of negative

curvature and cylindrical shell.

Formulation of equations for the analysis is based on following small size

elements.

Junction A Junction C

H (toroidal + ve) = 0 H (conical) = - H (toroid ve)

V (toroidal + ve) = 0 M (conical) = - M (toroid ve)

V (conical) = V (toroid ve)

(conical) = (toroid ve)

Junction B Junction D

H (toroidal +ve) = H (conical) H (toroidal - ve) = - Q (cylindrical)

M (toroidal +ve) = M (conical) M (toroidal - ve)= -M (cylindrical)

V (toroidal +ve) = V (conical) V (toroidal - ve) = - V (cylindrical)

(toroidal +ve) = (conical) (toroidal - ve) = (cylindrical)

These segments are analyzed analytically for the stress evaluation. Using

established theories of all sections, FORTRAN program is prepared to evaluate

the stresses. It has been established that the meredional bending stress is the

maximum of four stresses for all geometries of the joint.


Figure 2.4 : Junction points showing resultant stresses

The computer programming is used to evaluate stress resultants and

deformations at several points on the V shaped joint. Varying different

geometrical parameters, the stress analysis was carried out for a total of eight

expansion joints. The results are achieved using FORTRAN computer program

and output taken in the tabular format.

Finally it is concluded that the results obtained from the analysis are found to be

general agreement with the earlier researchers like Sreeramulu, Takezono etc.

Conclusions:

A composite shell type, V- shaped expansion joint is analyzed for the membrane

and bending stresses induced in circumferential as well as meridian direction

under internal pressure loading. The geometry of V shape convolution is

segmented on four divisions. Each segment is analyzed mathematically and

computer programme is prepared to estimate the stresses. The results are

derived using FORTRAN computer program and output taken in the tabular

format. Finally, it is concluded that the results obtained from the analysis are

found to be general agreement with the earlier researchers.


Santoshi Igi, Hiroshi Katayama, Masanori Kawahara; Evaluation of mechanical behavior of new type of bellows with two directional convolutions; Journal of Nuclear Engineering and Design; Elsevier; 2000. [19]

Metallic bellows has to absorb regular and irregular expansion and contraction in

piping system. Bellows have difficulties such as the instability of deformations

under over pressurizing or large loading conditions, the instability to absorb

torsional deformations due to lack of flexibility in circumferential directions and

thirdly the difference in thickness between the crest and the root is unavoidable

due to manufacturing process by buldge forming. In order to solve these three

problems, a new type of bellows, so-called double convolution bellows, were

proposed.

Figure 2.5 : Conventional bellows Figure 2.6: New type of bellows

This new type of bellows has convolutions in two directions; the first convolutions

in the longitudinal direction are the same as conventional bellows; and the second

convolutions are added in the lateral direction. This paper presents a study on the

mechanical behavior of the new type bellows under different loading conditions.

For the single convolution bellow and double convolution bellow various tests

were carried out.

1. First cyclic axial loading test: This test is carried out with the help of MTS

1000 kN fatigue test machine at a rate of five cycles per minute. Cyclic

loads were controlled in a displacement control mode. Tests were

conducted under various levels of the displacement like 3.6, 9.1, 18.2,

36, 41 and 54.6 mm.


2. Internal pressure tests were carried out with gradually increasing inside

pressure of bellow. Here it is observed that uneven and inclined

deformation appeared in the SCB specimen, but did not appeared in the

DCB specimen.

3. Torsion tests were carried out with 10 kN m torsion test machine. Torsional

displacement was controlled in a twisting angle control mode. Tests

conducted until 100 in SCB and 250 in DCB. Here it is observed that the

torsional deformations are considerable absorbed at the lateral

convolutions at the root.

In all tests strains were measured by the strain gauge at the crest, the side wall

and the root of bellow. It is concluded that existence of second lateral convolutions

in DCB was effective to stabilize the deformation behaviors even under large

cyclic plastic loading and internal pressurizing. The new type bellows, has a

certain capacity to absorb torsional displacement by the effect of lateral

convolution at the root part.

Finally it is concluded that the new type of double convolution bellows, are

effective to stabilize the deformation behaviors even under large cyclic plastic

loadings. Root buldge is not fond in double convoluted bellows. Double

convolution bellows has certain capacity of torsional displacement by effect of

lateral convolution T the root part.

Final comparison of general behavior of SCB and DCB:

Table 2.2: Comparison of SCB and DCB

Parameter Conventional bellows Double convoluted bellows

Convolution Main circular convolution Main circular convolution & lateral / root convolutions

Thickness at crest Reduced Nearly equal to that of root

Instability in the deformation

Unstable deformation Stable: No instability

Design features Simple but less flexible More complex in shape but also more flexible

Torsion Less flexible More flexible

Fatigue Short life Longer life


Conclusions:

This paper suggests a new type of bellow, which has convolutions in two

directions; the first convolutions in the longitudinal direction are the same as

conventional bellows; and the second convolutions are added in the lateral

direction. Finally, it is concluded that the new type of double convolution bellows,

are effective to stabilize the deformation behaviors even under large cyclic plastic

loadings. Root buldge is not fond in double convoluted bellows.


C. Becht IV; Fatigue of bellows, a new design approach; International Journal of Pressure vessels and Piping- 77; Elsevier;2000. [2]

Fatigue is an important aspect of the design of metallic bellows expansion joints.

These components are subject to displacement loading which frequently results in

cyclic strains well beyond the proportional limit for the material. At these high

strain levels, plastic strain concentration occurs. Current design practice relies on

use of empirical fatigue curves based on bellows testing.

Author has considered different geometries of bellows with reference to two

parameters, QW and QDT. Various dimensions of bellows are assumed, modeled

and using COSMOS/M finite element program stresses are plotted on the graphs.

Then he plots the graphs for QW versus strain concentration developed. The

same results have been extended to stress range versus number of cycles. So,

concluded that consideration of strain concentration clarifies the fatigue data and

will permit greater accuracy in design of bellows for fatigue.

Two non-dimensional geometry parameters are

QW = q/2w (2.23)

QDT = q / [2.2(Dm tp)1/2] (2.24)

Where, q = pitch, w = convolution depth,

Dm = Mean diameter of bellows,

tp = bellows material thickness after thinning.

For un-reinforced bellows, QW parameter varies between 0.27 and 0.61 and QDT

parameter varies between 0.46 and 1.74. He has recommended that, QW should

be greater than 0.4 and QDT should be greater that 1.0 for minimum strain

development in the bellows material.


Figure 2.7 : Various Bellows Geometries

Author has extended the strain results for the estimation of fatigue life. The result

gives improved understanding of the fatigue life behavior, without going for

rigorous fatigue testing procedure. Normal procedure to estimate fatigue curve

needs number of testing, which makes procedure time consuming and also costly.

Figure 2.8 : Strain concentration versus QW

It is suggested that the consideration of strain concentration clarifies the fatigue

data and will permit greater accuracy in design of bellows for fatigue. Further,


improved understanding of bellows fatigue behavior may lead to a reduction in the

requirements for bellows fatigue testing to develop design fatigue curves.

Conclusions:

With reference to experiments conducted by it is recommended that QW should

be greater than 0.4 and QDT should be greater than 1.0 for minimum strain

development. Ha has also claimed that strain results are more accurate, and this

data may be further useful to estimate the fatigue life of bellows. This is better

approach estimation of fatigue life compared to rigorous testing.


Li Younnsheng; Fuzzy Amendment to the Hypothesis of linear Accumulation of fatigue damage for Expansion joints; International Journal of Pressure Vessels and Piping; Elsevier, Vol. 51; 1992 [13]

EJMA suggests the Miners hypothesis for the evaluation of fatigue life of the

expansion joints. Author has proposed amendment in the approach using Fuzzy

sets theory. First setup the subordinate degree equation of cyclic stress (s) with

the number of cycles (n). The contribution of each cyclic stress to the fatigue

damage of expansion joints is then put to fuzzy permutation according to the

Relative Hamming Distance. On this basis, an amendment to the Miners

hypothesis is derived. A sample example gives explanation about the Miners

hypothesis and amendment. The computation of accumulation of fatigue damage

in expansion joints tends to be more reasonable using newly suggested amended

approach.

The value of stress cycles of the expansion joint depends on various operating

parameters. Stress in intensity will be always higher when, the pipe flow is

initiated, halted and restart is taking place. Further higher intensity can be

developed in case of any sudden breakdowns. The stress intensities are always

lower while normal running of the plant. All stress intensities needs to be arranged

in decreasing order and than, estimate the number of cycles in each stress

category. By rearranging the stresses and number of cycles in decreasing order,

and than utilizing the same Minors hypothesis of cumulative damage factor, which

should be less than 1.

Figure 2.9 : Stress cycles of the expansion joint


Miners criteria: Usage factor, U = U1 + U2 + U3 + , (2.25)

Where, each usage factor, U1 = n1/N1 (2.26)

K1 =

m

ii

m

1

1

(2.27)

K2 = 112 / K , K3 = 113 / K , similarly Km = 11/ Km

Where = Relative Hamming Distance between stress cycles. This can be

calculated by suggested equations in the paper. Using these amendment

coefficients can be calculated.

Amended criteria: Usage factor = U = K1 U1 + K2 U2 + K3 U3 + , (2.28)

Where, K1, K2, K3 are amendment coefficients.

Finally it is concluded that; due to consideration of the effect of each stress cycle

on the fatigue damage of expansion joints, the fuzzy revised formula of the

Miners criteria put forward in this paper remedies the short comings of Miners

criteria in this application.

Conclusions:

Author has presented a fuzzy amendment to the hypothesis of linear accumulation

of fatigue damage for expansion joints that relative Hamming distance between

stress cycles should be calculated and coefficients should be derived. These

coefficients are useful in the estimation of number of cycles of bellow. He has

proven this with an example.


Y. Ooka, S. Yoshie; Dynamic Buckling Characteristics of bellows under Pressure waves; International Journal of Pressure Vessels and Piping- 44; 1990 [29]

In the secondary piping of liquid-metal fastbreeder reactors (LMFBRs) in Nuclear

power reactors, bellows are employed in the piping. A bellow expansion joint is

effective for the thermal expansion of piping in a restricted space and for

achieving a compact design of plant layout. Among various aspects of the

structural design, buckling is one of the serious failure modes to be prevented. It is

known that bellows buckle under internal pressure owing to the uniqueness of

their geometry with high flexibility.

A series of dynamic buckling tests was conducted in a water loop by using slow

explosives to generate pressure waves, which simulate those in a sodium-water

reaction in a steam generator. It has been clarified that the buckling strength of

the bellows was seen to increase when the duration of the applied pressure wave

was shorter than a critical value. The concept of the pressure impulse was found

to be effective for evaluating the dynamic buckling behavior of bellows. For small

number of convolutions, the buckling mode is the root bulge type, which occurs at

the first convolution.

It has been concluded that the buckling strength of the bellows was seen to

increase when the duration of the applied pressure wave was shorter than a

critical value. In the case of a relatively small number of convolutions, the buckling

mode is the root-buldge type, which occurs at the first convolution. In case of large

number of convolutions, two kinds of buckling mode can occur depending on the

duration of the shock pressure waves.

For short duration of less than 10 ms, the root bulge mode can occur, which is

similar to that observed in the case of a small number of convolutions. On the

other hand, the column squirm mode can occur for a long duration, and this is

similar to static buckling.


Figure 2.10 Analytical model of bellow

Author has mentioned that the buckling strength of the bellows observed to

increase when the duration of the applied pressure wave was shorter than a

certain critical value.

Figure 2.11 Comparison of results

For small number convolution bellows, the buckling mode is root-buldge type,

which occurs at first convolution. In case of large convolution bellows, bellows

may fail due to shock pressure waves or root-buldge failure may occur depending

on the duration of shock pressure waves. Generally for a short duration of less

than 10 ms, the root-buldge mode can occur, which is similar to that observed in


the case of small number of convolution. On the other end, column-squirm mode

can occur for a long duration, and this is similar to static buckling.

Conclusions:

Certain experiments are conducted to study dynamic characteristics of bellows

under pressure waves. There can be longer pressure waves or shorter pressure

waves. The buckling strength of bellows is increases when the duration of

pressure waves is shorter than critical value. The buckling mode is the root buldge

type, which occurs at first convolution. The column buckling may occur for long

duration, which is similar to static buckling. For short duration pressure waves root

buldge mode failure can occur. A series of dynamic buckling test has been

conducted to study dynamic buckling characteristics.


Lu Zhiming, Tong Shuiguang, Qin Yi, Fang Deming, Gao Zengliang; In-plane instability tests of bellows subjected to internal pressure and deformation load; International journal of Pressure Vessels and Piping -

79; Elsevier; 2002. [14]

The in-plane instability of U - shaped bellows is analyzed. The in-plane critical

pressures of bellows which are subjected to zero, tensile and compressive

deformation are measured experimentally. The in-plane instability critical pressure

of bellows under compressive deformation is apparently lower than that under

zero deformation, and the in-plane instability critical pressure of bellows under

tensile deformation is higher than that under zero deformation.

According to the limit analysis criterion, the critical pressure of the bellows under

zero deformation is

P critical = 2

3

ht

Cm p

p

s (2.29)

While as described by EJMA standards, the limiting design pressure based upon

in-plane instability is

P critical = 2

4.1

ht

Cm p

p

s (2.30)

Clearly, the ratio of critical pressure to limiting pressure is approximately 2.2 under

zero deformation. This is factor of safety applied in the design procedure.

Several tests are conducted to find the in-plane instability behavior in bellows for

various test conditions. The test conditions are zero deformation, compressive

deformation and tensile deformation of bellows under critical pressure. Excessive

deformation is observed from the pressure gauge and limiting pressure values are

calculated using EJMA relations. S4 and S6 are the longitudinal bending stresses

developed due to pressure and deflection respectively.

Tests have been performed under the application of internal pressure. The tests

specimens were U shaped bellow expansion joint, made of stainless steel sheets.


Table 2.3: Results of in-plane stability tests

Load Specimen no. P critical (MPa) Deformation (e) mm

Bending stresses S4 + S6 (MPa)

1 3.9 0 376.7

2 3.2 -3.7 1466.0

3 4.8 3.7 1441.7

4 1.88 0 515.0

5 0.6 -4.0 892.0

6 1.35 0 752.0

7 0.75 -3.0 738.0

The results of critical pressure determined experimentally are shown in table 2.3,

and it is concluded that the in-plane instability critical pressure of bellows under

compressive deformation is much lower than that under zero deformation. Also

the in-plane instability critical pressure of bellows under tensile deformation is

much higher than that under zero deformation. Hence, for expected compressive

deformation bellows, probability of in-plane instability is much higher. By these

tests, effect of various axial deformations is assessed qualitatively.

Conclusions:

In this paper, authors have conducted several tests to find the in-plane instability

behavior in bellows for various test conditions. The test conditions are zero

deformation, compressive deformation and tensile deformation of bellows under

critical pressure. Excessive deformation is observed from the pressure gauge and

limiting pressure values are calculated using EJMA relations. The longitudinal

bending stress is exerting due to pressure and deflection both. It has been

concluded that the in-plane instability critical pressure of bellows under

compressive deformation is much lower than that under zero deformation. In

addition, the in-plane instability critical pressure of bellows under tensile

deformation is much higher than that under zero deformation.


N W Snedden; Analysis and Design guidance for the lateral stiffness of bellows expansion joints; Journal of Thin-Walled structure; Vol. 3; 1985. [16]

Thin walled bellows have been several failures in service due to the lateral

buckling of bellows under pressure. The paper offers guidance to avoid bellows

squirming and provides the design engineers with simple procedures for

evaluating the stability of a pressurized bellows subject to either small or large

lateral displacements. Equations are derived by using simple beam model into two

categories; first one is small deflection analysis and other large deflection

analysis.

There are numerous formulae in the literature for calculating the elastic axial

stiffness of a bellow. Haringx analysis made use of the theory of unsymmetrical

bending of circular plates. Hamada examined the bending flexibility of U shaped

convolutions and produced simple design charts for range of bellows dimension. A

mathematical formulation can be developed applying simple beam theory to

these relations and finally following relation is developed to evaluate lateral

stiffness of bellow.

Bellows elastic lateral stiffness 23 5612

lEIPfor

lP

lEIKl (2.31)

(small deflections)

The deformation of a bellow subject to combined internal pressure and lateral

loading is asymmetric about the mid point of neutral axis. Hence, the elasto-plastic

moment/angular deflection relationship can be derived by assuming initial value of

deformation. Author has suggested following equation to calculate lateral stiffness

of bellow.

Bellows elastic lateral stiffness 22sin2cos1

lEIPforl

nnlnllKl

(2.32)

(large deflections)


Figure 2.12: Small deflection model

From experiments it is proved that bellows elastic lateral stiffness is nearby

theoretical results. Finally design recommendations are made for design

engineers that if bellows design stresses are within elastic limit, the bellows lateral

stiffness should be determined using a specific equation, considering either

bellows axial compressive load 22lEIP or 2

2lEIP

Figure 2.13 : Large deflection model

In the event that the lateral load /deflection characteristic of the bellows should be

verified by experiment or using specific equations. It is also recommended that for

the bellows to remain stable, lateral stiffness Kl must exceed zero. It is also firmly

recommended that any bellows expansion joint whose failure could be


catastrophic should be adequately restrained to prevent excessive deformation

due to instability.

Conclusions:

There are numerous formulae in the literature for calculating the elastic axial

stiffness of a bellow. This paper suggests methodology to design bellows

considering lateral stiffness. There can be two approaches, first for small

deflection and other for large deflection. Authors have suggested two separate

equations for small and large deflection analysis. This work is an analytical

approach of beam theory.


Blazej Skoczen and Jacek Skrzypek; Application of the Equivalent Column concept to the stability of Axially compresed bellows International Journal of Mechanical Science; Volume 34, No. 11, 1992. [1]

The concept of an equivalent column is adopted in order to examine the

bifurcation buckling of S shaped bellows. The overall buckling of axially

compressed bellows with axial force and internal pressure are considered, and

pre-buckling nonlinearities is investigated.

All earlier researchers have introduced the traditional Euler formula for the

evaluation of buckling load for equivalent column. This relationship is

P = 2

2

lIE

s (2.33)

Where, EI is bending rigidity and s is based on support condition.

S shape geometry of bellow is analyzed. A S bellow consist of a number of

identical, thin walled, rotationally symmetric shell segments linked along the axis

of the whole structure. A single segment is consists of two circular arcs of angle

. Thus, the geometry of the segment may be represented by fragments of a

torus. The numerical equations are developed for the deformation analysis.

Secondly the equivalent stability analysis is carried out. Nonlinear equilibrium path

is estimated and equation is developed for appropriate critical length of bellow is

for the deformed bellow. The original length may be replaced by the number of

segments. Hence critical bifurcation of buckling force versus the number of

segments for each kind of S shaped segment of a given original geometry and

acted upon by an internal pressure of a given magnitude.


Figure 2.14 : Evolution of Axial and Bending flexibilities along equilibrium path

for S shape segment ( = 900, 1000, 1200)

Conclusions:

The theory used, based on the geometrically non-linear relation, enables us to find

the bellows critical force or length for an arbitrary bellows.

For squat structures subject to axial load and moderate internal pressure either

bifurcation buckling or the complementary global in-stability phenomenon takes

place.

Over pressurization of the bellows may lead to the root bulge phenomenon.

However, it may also happen that the structure does not lose stability.


J. A. Brown and G. A. Tice; Containment penetrations Flexible metallic bellows: Testing, Safety, Life extension issues; Journal of Nuclear Engineering and Design; North Holland; Volume 145; 1993. [6]

The performance and long term operational integrity of containment systems and

components is being challenged by many of worlds nuclear plants. As time in

service increases, so does the likelihood of component failure due to long term

degradation. A suggestion is made in by observing trends in containment

degradation, potential weaknesses can be anticipated and corrected, minimizing

interruptions in operations, increasing safety and improving plants life extension

outlook. Paper discusses the laboratory examinations of bellows for determine

leak areas, local leakage rate. Crack growth from corrosion and fatigue

mechanisms are examined, and method for predicting useful life are discussed.

Local Leak Rate Testing (LLRT) of bellow:

The purpose of two ply bellow elements is to permit local leak detection through

monitoring of the annulus between the two plies. Initially LLRT discovered very

little, if any, leakage. Actually inert gas or air can be taken as test medium, which

will be introduced under pressure between the plies. Pressure decay rates or

make-up flow rates to maintain a specified pressure are than measured.

Acceptance criteria for these tests are based on a percentage of the maximum

allowable leakage rate at the calculated peak containment internal pressure.

When leakage in a two- ply bellows assembly is detected, it is initially unknown

which of the bellows elements are actually leaking. In order to determine if the

inner, outer or both bellows elements are leaking, a tracer gas is introduced into

the annulus and a sensitive detection system (mass spectrometer) is used. As

long as one of the plies remains intact, primary containment integrity is

maintained.

Authors gave following guidelines / recommendations with reference to results of

leakage test.

1. If a bellows LLRT result is above a minimum threshold, it would be locally

pressurized with helium. The outer ply would be tested for the presence of

helium as an indication of leakage through the outer ply, no further

inspection is required.


2. If helium leakage is detected through the outer ply, then inner ply would be

tested for the presence of helium. If there is no leakage from the inner ply,

then no further inspection is required.

3. If helium leakage is detected through both the inner and outer plies, then

the bellows protective cover is removed and the outer ply examined by dye

penetrant testing.

4. All crack indications would then be evaluated to estimate current and

projected leakage rates.

5. Those bellows failing to meet the established acceptance criteria would e

repaired or replaced.

6. Authors have suggested a flow chart in their paper for the testing,

evaluation and replacement of bellows. It includes following aspects in the

decision tress flow chart.

7. If LLRT method facility is exist, then it should follow, and decision can

made for the evaluation or replacement of bellow.

8. If LLRT test facility does not exist, then bellow should pressurize and

leakage should observe from outer ply.

9. If leakage do not observed, then pressurize between plies with helium and

sniff inner ply for leakage.

10. Next observation should be made after removal of guard cover and

pressurize between plies with air or helium.

11. Observe all flaws carefully.

12. Operate bellow for one/two cycles.

13. If bellow is operable, flaws are not much severe, than use it till further more

time and if, bellow is not operable, than replace it.

Life extension issues:

When determining whether given bellows elements are suitable for continued

service, or when evaluating appropriate corrective actions, a logical sequence of

actions and decision points can be constructed. Various repair techniques have

been investigated through prototype testing by researchers. Certain types of


defects like nicks and gouges can be successfully blended by mechanical grinding

to reduce notch effects, thus fatigue life of bellows can be improved by careful

servicing of bellows.

Conclusions:

This paper discusses about local leak rate test (LLRT) of two-ply bellows. The

purpose of two-ply bellow elements is to permit local leak detection through

monitoring of the annulus between the two plies. Initially LLRT discovered very

little, as any leakage starts very little rate. Actually, inert gas or air can be taken as

test medium, which will be introduced under pressure between the plies. Pressure

decay rates or make-up flow rates to maintain a specified pressure are than

measured. Acceptance criteria for these tests are based on a percentage of the

maximum allowable leakage rate at the calculated peak containment internal

pressure. Authors have discussed other life extension issues of bellows, and all

aspects are covered and explained by flow chart.


Y Z Zhu, H F Wang, Z F Sang; The effect of environmental medium on fatigue life for u-shaped bellows expansion joints; International Journal of Fatigue; Volume 28; Pg. 28-32; 2006.[30]

This paper is on experimental research on effect of environmental medium on

corrosion fatigue life of expansion joint. Presently austenitic stainless steel is

widely used in making bellows expansion joints in the industries. Because this

material has several good characteristics like high strength, weld, cold

deformation and oxidizing ability of heat restating.

A test set-up is designed and developed for the experimental study. It is basically

to determine fatigue life for bellows expansion joints, measuring instrument for

strain and electro-chemical system. The chemical compositions of the material are

charted. By using electro-chemistry test method, the relation curve of electric

potential versus the number of cycles is recorded by X-Y function recorder,

initiation and propagation of fatigue crack are monitored. Applying frequency of

strain cycling f = 5 cycles / min. displacement range = 4.15 mm, and strain

gauges of 1x1 are pasted on the central surface outside bellows, whose

distribution is shown in figure 2.15.

Figure 2.15: Set-up diagram for experimental work

In the same study, Finite Element Analysis is used evaluate strains at several

locations while the bellow expansion joint is loaded with similar displacement

range of = + 4.15 mm (axial tension) to = - 4.15 mm (axial compression).


ANSYS software is used for the analysis and 2 D axi-symmetry element is used

for the analysis. It is observed that the expansion joints stress distribution at

outside walls coincides with experimental results. Normal stress computed

according to elastic rule of material, equals to 765 MPa (tensile) to 720 MPa

(compressive) stresses.

Figure 2.16 : Location points for strain measurement

The maximum strain appears at corrugation peak 458 and the maximum meridian

strain range is 0.9663%.

Figure 2.17: Comparison of Results derived from FEA and test

Conclusions:

Existence of corrosive media will reduce fatigue life for metal bellows expansion

joints. The effect of environmental medium should be paid attention when dealing

with fatigue life for bellows expansion joints.

The location of corrosion fatigue cracks is the same as that of fatigue crack under

atmosphere, both of which are at the point of maximum stress. The corrosion

fatigue crack takes place at the side, which is exposed to the medium.


Kaishu Guan, Xingh Zhang, Xuedong Gu, Longzhan Cai, Hong Xu, Zhiwen Wang; Failure of 304 stainless bellows expansion joint; Engineering Failure Analysis; Elsevier; Volume 12;page 387-399; 2005. [8]

This paper is study on failure analysis of a bellow expansion joint of 304 stainless

steel. In includes a case study of a failed SS 304 bellow. The bellow joint serve as

a conduit for chemical pipe lines with liquid media containing wet H2S. The raw

material of bellow is cold rolled AISI 304L austenitic stainless steel sheet of 1.3

mm thickness. The pipeline is having diameter of 196 mm. The design

temperature of the pipe is 145-1550 C.

The study begins with careful examination of a failed bellow. The location and

condition of cracks are observed carefully. The main crack is along the

circumference, on the crest of the expansion joint. The crack dimensions are

measured. There is no indication of localized damage in the form of pits. No wall

thinning and plastic deformation is observed near the cracks, which reveals that

the failure is brittle fracture in nature.

Material composition, hardness, thickness study:

Material composition is carried out. The hardness measured at several locations

and analyzed. Thickness at various points is measured. Minimum thickness found

at crest of convolution.

Microstructure study: Microstructure examination is carried out at failure region.

Fractography of origination zone and propagation zone is made.

Corrosion products detection is made by Scanning electron microscope (SEM) /

EDS on different locations. The analysis indicated the presence of high sulphur at

failure region.

Conclusions:

Crack initiation and propagation results from stress corrosion cracking (SCC)

induced by wet H2S due to deformation induced martensite and cold work.

It is recommended that solution annealed treatment be carried out for austenitic

stainless steel after cold working in order to eliminate the strain induced

martensite and cold work hardening.


R Dworaicka; FEM-based verification of the PN - EN standard-based stress concentration factor for the drum - pipe joint of a boiler; Journal of Achievements in Materials and Manufacturing Engineering; Volume 37; Issue 1; Pg. 48-51; Nov. 2009.[17]

The aim of paper is to present the results of the comparative test between the PN-

EN 12952-3: 204/ Apr: 2005 standard and Finite Element Method analysis.

A drum pipe joint of a boiler made from alloy steel (15 NiCuMoNb5) is the object

of investigation. Stress concentration factor for cylindrical shells are standardized.

The stress concentration factor for the object can be selected from the graph as

2.815. The relative maximum stress in drum derived from pressure is calculated

from formula as

F tang = 45.8 MPa.

Figure 2.18: Stress Concentration factor for cylindrical shell

FEM is used to study similar analysis in the virtual environment by ANSYS

software. A model of the object is generated, and with normal practice of FEA

methodology of adding constraints, boundary conditions, results are derived.

Maximum stress tang. = 121.2 MPa

Maximum stress concentration factor derived from pressure equals to 2.64.


Conclusions:

The stress concentration factor can be determined by two methods. The first

being using standard curves established by PN-EN 12952-3: 204/ April 2005. The other method is virtual one by using ANSYS FEA software.

The stress concentration factor derived from standard is 2.81.

The stress concentration factor derived from FEA is 2.81.

The results are very close to each other.


V. F. Jakubauskas and D. S. Weaver; Transverse Natural Frequencies and Flow Induced Vibrations of Double Bellows Expansion Joints; Journal of Fluids and Structures; Volume 13; 1999. [24]

This paper considers the transverse vibrations of fluid-filled double-bellows

expansion joints. The bellows are modeled as a Timoshenko beam, and the fluid

added mass includes rotary inertia and bellows convolutions distortion effects.

The natural frequencies are given in terms of a Rayleigh quotient, and both

lateral and rocking modes of the pipe connecting the bellows units are considered.

The theoretical predictions for the first six modes are compared with experiments

in still air and water and the arrangement is found to be very good. The flow-

induced vibrations of the double bellows are then studied with the bellows down

stream of a straight section of pipe a 900 elbow. Strouhal numbers are computed

for each of the flow-excited mode resonances. The bellows natural frequencies

are not affected by the flowing fluid but the presence of an immediate upstream

elbow substantially reduces the flow velocity required to excite resonance.

Comparison of theory with Bernoulli Euler and EJMA

Table 2.4: Comparison of Frequency (Hz)

Mode Frequency (Hz) Air (P = 0) Frequency (Hz) Water (P = 0)

Experimental B- Euler EJMA Experimental B- Euler

w/o mf2

EJMA

Lateral 1 78.8 91.8 91.8 35 37.2 51.0

Rock 1 119 143 158 61 66 89.1

Experiments are conducted to obtain natural frequencies of bellows for

determining the limiting velocities for flow induced vibrations. The bellows used in

the above test were placed in a water tunnel for experiments with internal flow.

The double bellows were placed in a straight section of pipe for uniform flow and

then placed immediately down stream of a standard 900 elbow to determine the

effect of non-uniform flow.

The test results are plotted as vibration RMS amplitude response against mean

flow velocity for the cases of a straight pipe upstream and an elbow upstream of

the bellows, respectively.


The effect of internal pressurization is to reduce the natural frequencies nut,

practically speaking; this effect is not large and diminishes with increasing mode

number.

Internal flow has negligible effect in the natural frequencies of bellows.

The effect of an elbow directly upstream of a bellows is to significantly reduce the

mean flow velocity required to produce large amplitude flow induced vibrations.

The effect of rotary inertia, which is neglected in both the Bernoulli Euler and

EJMA approaches, is significant, especially for vibration in air.

Conclusions:

This paper considers the transverse vibrations of fluid-filled double-bellows

expansion joints. The bellows are modeled as a beam, and the fluid added mass

includes rotary inertia and bellows convolutions distortion effects. The natural

frequencies are given in terms of a Rayleigh quotient, and both lateral and

rocking modes of the pipe connecting the bellows units are considered. The

EJMA model substantially overestimated the transverse natural frequencies of the

bellows used in this study in both air and water. Fluid flowing through bellows is

expected to have a negligible effect on their natural frequencies, at least in most

practical applications. The effect of internal pressurization on bellows natural

frequencies is relatively small on the first transverse mode and decreases with

increasing mode numbers.


V. F. Jakubauskas and D. S. Weaver; Transverse Vibrations of Bellows Expansion Joints Part I : Fluid Added Mass; Journal of Fluids and Structures; Volume 12; 1998. [25]

This paper is about the results of an analysis of the fluid-added mass in bellows

expansion joints during bending vibrations. The added mass is shown to consist of

two parts, one due to transverse rigid body motion and the other due to distortion

of the convolutions during bending. The later component is neglected in EJMA

standard analysis (1980). It is shown to be important for relatively short bellows,

as are commonly used for expansion joints, and to become increasingly important

for higher vibration modes. In the present work distortion component has been

determined using Finite Element Analysis and results are presented in graphical

form for a typical range of bellows geometries.

Figure 2.19 : Fluid added mass in bellows

(a) axial vibration (b) transverse vibration (c ) convolution distortion in bending

A theoretical model for the fluid added mass of bellows expansion joints

undergoing transverse vibrations is developed. The total fluid added mass per unit

length, mf is assumed to be comprised of two components; one associated with

rigid-body motion, mf1 and the second associated with convolution distortion, mf2.

Thus, mf = mf1 + mf2 (2.34)

Mathematical formulation is developed for mf1 and mf2.

The results are derived for various modes of vibrations, using Finite Element

Analysis.


Table 2.5 :Comparison of Frequency - with and without mass (Hz)

Mode No. EJMA standard Without mf2 EJMA standard

with mf2 % Difference

1 140 137 2.7

2 386 324 16.3

3 753 464 38.4

4 1252 535 57.3

For shorter bellows, the distortion component may be significant even in the first

mode of vibration.

For longer bellows, the distortion component effect may be small in the first mode

but is not negligible in higher modes.

Neglect of the distortion component of fluid added mass results in an

underestimation of the total bellows mass per unit length, and therefore, an

overestimation of true transverse natural frequencies of bellows.

Conclusions:

Normally all analysis of bellows is carried out neglecting mass of fluid of bellows.

Actually, it is an important aspect for shorter bellows; the distortion component

may be significant even in the first mode of vibration. For longer bellows, the

distortion component effect may be small in the first mode but is not negligible in

higher modes.


V. F. Jakubauskas and D. S. Weaver; Transverse Vibrations of Bellows Expansion Joints Part II : Beam Model Development and Experimental Verification; Journal of Fluids and Structures; Volume 12; 1998. [26]

Bellows are undergoing transverse vibrations due to various reasons. A

theoretical model for the transverse vibrations of bellows expansion joints is

developed. The model is based on Timoshenko beam theory and includes the

added mass effect of an internal fluid. An analytical expression for bellows natural

frequencies is developed in the form of a Rayleigh quotient and it is presented in

a way which is suitable for hand calculations.

Equivalent bending stiffness = E Ieq = 0.25 k p Rm2 (2.35)

Where, Ieq = equivalent moment of inertia,

k = stiffness,

p = pitch, and

Rm = mean radius

The results of first four transverse modes are compared with the experiments as

well as the predictions of the simplified analysis of the EJMA. While the present

analysis agrees well with experiments, the EJMA approach can be substantially in

error due to its neglect of rotary inertia and the convolution distortion component

of fluid added mass.

Experimental method:

A special fixture is designed for these experiments. The bellows frequencies were

obtained by measuring the bending strains near the convolution crown using two

small strain gauges. These gauges are located precisely 1800 apart on the

convolution so that, depending on their wiring in the bridge, they could be used to

separate axial from transverse vibration modes. The frequency spectra were

obtained using Fourier analyzer in the transient capture mode; two typical shock

excitation spectra. Results are shown in table 2.6.


Table 2.6: Comparison of Frequency Results (Hz)

Mode Frequency (Hz) Air (P = 0) Frequency (Hz) Water (P = 0)

Experimental B- Euler

EJMA Experimental B- Euler

w/o mf2

EJMA

1 202 344 345 112 141 140

2 337 919 923 210 388 386

3 475 1792 1810 289 761 753

4 606 2977 2992 363 1258 1252

It is concluded that rotary inertia must be included in the analysis of transverse

vibrations of bellows and that the convolution distortion component of fluid added

mass, while having a rather small effect on the first transverse mode, must be

included to obtain reasonable estimates of the higher transverse frequencies, at

least in most practical applications.

The EJMA model substantially overestimated the transverse natural frequencies

of the bellows used in this study in both air and water.

Fluid flowing through bellows is expected to have a negligible effect on their

natural frequencies, at least in most practical applications.

The effect of internal pressurization on bellows natural frequencies is relatively

small on the first transverse mode and decreases with increasing mode numbers.

The presence of a 900 radiuses elbow immediately upstream of a bellow can

substantially reduce the mean flow velocity required to excite bellows to

resonance.

Since theoretical calculations using Bernoulli Euler beam theory agree so well

with those of EJMA, it appears that the later must be based on such an analysis.

Conclusions:

Excellent agreement between the present theory and experiment tends to validate

the assumptions used in modeling the fluid added mass and the bellows as a

Timoshenko beam model.


EJMA model is safe (over estimated) the transverse natural frequencies of the

bellows used in this study in both air and water.


natural frequencies, at least in most practical applications. No effect was observed

up to a mean water velocity up to 10 m/s.

The effect of internal pressurization on bellows natural frequencies is relatively

small on the first transverse mode and decrease with increasing mode numbers.


T Saito, H Umeda, S Kanazawa, K Watashi & A Imazu; A Thermal Transient Test of an FBR Piping-Bellows Model; International Journal of Pressure Vessels and Piping; Volume 44; 1990. [21]

In this paper the design of the liquid metal fast-breeder-reactor (FBR)

components, a high degree of integrity at elevated temperatures is required. This

study of FBR main coolant piping containing bellows expansion joints has been

performed to cope with such requirements. Bellows needs special methodology

for the application in design of the fat-breeder-reactor (FBR) components.

Figure 2.20 : Configuration of piping-bellows models for thermal-transient test

The bellows expansion joints for FBR piping usually consist of bellows and

hardware structures that connect bellows and piping. The bellows are required to

absorb thermal deformation of the piping system and to withstand internal and

external pressures, seismic loading, and so on. Creep-fatigue tests by mechanical

loadings, buckling tests by internal and external pressures, and vibration tests of

the bellows have been conducted for the purpose of grasping the characteristics

of the bellows. For thermo-transient loadings, the bellows are a thin walled

uniform structure, so the thermal stress is generally small.

The thermal-transient test of the piping bellows models was conducted by using

thermal-transient test facility for structures (TTS). The piping bellows models were


subjected to cyclic cold and hot transients by sodium at constant flow rate. A cold

transient of 250 C, sodium flows in to the model for a period of 30 minutes, and a

hot transient of 600 C, sodium flows in to the model during a period of 150

minutes. The tests were continued for 427 cycles. Thermocouples of the alumel

chromel type were installed on the inner and outer surfaces of the models to

measure the temperature of sodium and metal in the models. The outputs of these

thermocouples were recorded by a data-acquisition system.

Evaluation of the creep-fatigue damage of the models of the bellows expansion

joints based on the guide was carried out with the results of thermal-elastic-stress

analysis. Creep-fatigue damage was calculated by evaluating the total strain

range in accordance with the procedure in the guide. The creep-fatigue damage

results in the Y and E shape junctions of bellows were evaluated by the axi-

symmetry analysis of the 900 section. The creep-fatigue in first and second Y

shaped junction was the most significant.

This paper describes the results of the thermal-transient test of the piping-bellows

models consisting of an internally pressurized type of bellows and an externally

pressurized type of bellows. The piping bellows were subjected to cyclic cold and

hot thermal transients by sodium in a temperature ranging from 2500 to 6000 C.

Heat transfer and thermal elastic stress analysis were carried out for evaluating

the creep-fatigue strength.

Conclusions:

The important issue in the design of the bellows expansion joints for thermal

loadings is the creep-fatigue of the hardware structures. A thermal transient test of

the piping bellows was conducted. These models were subjected to more severe

cyclic thermal transients than those of the plant condition. After destructive

examination, no cracking were found in particular structures of the piping-bellows

models, such as the Y shaped and E shaped junctions.

The sodium temperatures show the axi-symmetrical change in the vertical type

bellows model, with three dimensional changes in the horizontal type model. The

largest axial-bending stress occurs near the structural discontinuity in the Y

shaped junction. An evaluation of creep-fatigue damage based on the guide was

confirming the safety margins considered in the design of bellows.


Kazuyuki Tsukimori, Takuya Yamashita, Koji Iwata, Akira Imazu; Development of FBR piping bellows joint in Japan; Journal of Nuclear Engineering and Design; Elsevier; Volume 155; 1995. [9]

Fast Breeder Reactor (FBR) is essential for the nuclear power centers. The cost

of the FBR is very much high. To reduce the cost is one of the major factors in

FBR design. In FBR systems long and winding route of piping systems can be

shortened and simplified, sharp reduction of in related apparatus, equipment and

reactor building etc. can be expected. The use of bellows joint, which possess

good ability to absorb thermal expansion, is one of the best means of shortening

the piping system.

In the present paper authors have proposed the structural concept of bellows,

which can fit to FBR.

Figure 2.21 : Structure of FBR piping bellows joint

Authors have reviewed on the technical aspect, the essential factors required

to show the feasibility of FBR piping bellows joints are classified roughly

according to following categories.

1. Development of practical strength evaluation methods to realize rational

designs.

2. Assurance of quality reliabilities through standards.

3. Establishment of the safety logic for accidents supposed in the FBR design.

They have recommended an internally pressurized and gimbal type bellows joint

in FBR. Generic parts of the bellows joint are also suggested. Two shell structures


(two ply) supporting the end of the bellows, and ring-pin structures connecting

them, control the directions of movement of the bellows. The main structural

characteristics are as follows.

Double bellows structure (double ply) is proposed for safety point of view.

Branching of the axial cross-section shape of shell structures designed to be thin

and smooth so as to endure the thermal transient load caused by the sudden

change in sodium temperature. Nozzles for sampling gas are set up in order to

detect the leakage rapidly caused by failure of bellows. Lungs are attached to

hardware in order to set displacement gauges for monitoring the movements in

operation.

It is concluded that Design criteria similar to those for piping components, strength

evaluation methods for creep-fatigue, progressive deformations, and buckling etc.

for bellows have been developed in order to realize the design by analysis.

Two proto type bellows were manufactured and installed in the high temperature

sodium loop and operated long term in various conditions. This trial operation

showed the functions and durability needed for FBR piping bellows joints.

In order to investigate the potential for safety, crack propagation tests and

dynamic tests by impulse pressure have been implemented. From these tests, it

has been shown that rapid catastrophic failure of bellows never occurs, even if

under excessive loading.

Conclusions:

It is concluded that the prospect of applying bellows joints to FBR piping has

basically been confirmed and a frame work of design rules has been constructed

in a system of design by analysis.


2.3 Overall conclusions of Review study:

Review study is carried out on all above mentioned research papers on bellows

type expansion joints. All researchers have contributed in various areas of

expansion joints. Review comments are made by dividing papers in groups. The

groups are formulated as study on stress analysis, stability criteria, fatigue life,

and vibration analysis.

2.3.1 Papers on Stresses Analysis

Strain concentration or values of strain developed at the junctions may use

for the stress analysis of bellows. This approach gives accurate results.

The values of strain concentration can extend (utilize) for fatigue analysis of

bellows. This will lead to reduction in requirement for bellows fatigue testing

to develop design fatigue curves.

The flexibility is main desirable parameter of bellows expansion joint. The

material possesses certain modulus of elasticity, but the actual elasticity is

much higher because of its geometric features. Some researchers have

developed relations to evaluate actual flexibility of bellows.

In case of V shaped convolution of bellows, the maximum stress is

occurred at the ends of conical shell. This stress is becomes critical for the

design in case of axial load as well as internal pressure loading. The

location of maximum stress can be obtained by superimposing the two

solutions.

The stress analysis of bellows is based on main assumption that the bellow

is considered as beam model, shell model based on strength of material,

plate model, plate cylindrical shell models or shell model.

A new type bellow, DCB with two directional convolutions was developed

and certain mechanical tests were carried out and results are compared

with single convolution bellow. Existence of second lateral convolutions in

DCB was effective to stabilize the deformation behaviors even under large

cyclic plastic loadings and internal pressurizing. Additionally the new DCB

has certain capacity to absorb torsional displacement by the effect of lateral

convolution at the root part. However, due to manufacturing difficulties

industries do not adopt this concept.


2.3.2 Papers on Stability Analysis

The bellows are loaded with internal pressure as well as thrust force of

inside flowing fluids. True buckling analysis should include both loadings.

The buckling strength of bellows is depends on pressure waves intensities.

The bellow will possess a critical pressure value for buckling failure. If the

pressure wave intensity is shorter than critical value, it will be as static

loading type. The failure occurs from root buldge area. While pressure

intensity is more than critical value, column squirm will occur.

It is conclude that the in-plane instability critical pressure of bellows under

compressive deformation is much lower than that under zero deformation.

In addition, the in-plane instability critical pressure of bellows under tensile

deformation is much higher than that under zero deformation. Finally, the

in-plane stability is critical during compression mode of bellows.

It is recommended that the bellow should remain stable, lateral stiffness Kl

must exceed zero. Additionally, It is also recommended that any bellows

expansion joint whose failure could be catastrophic should be adequately

restrained to prevent excessive deformation due to instability. The

instability pressure can be derived using given relationships and which

should be avoided for better functioning of bellows.

The concept of an equivalent column is adopted in order to examine the

bifurcation buckling of S shaped bellows. The overall buckling of axially

compressed bellows with axial force and internal pressure are considered,

and pre-buckling nonlinearities is investigated.

Over pressurization of the bellows may lead to the root bulge phenomenon.

However, it may also happen that the structure does not lose stability.


2.3.3 Papers on Fatigue life Analysis

Bellows under go low cycle fatigue during its working. The number of life

cycle may calculate using Miners hypothesis as suggested in EJMA

standards. The number of life cycles depends on stress intensity of each

cycle and their number of occurrences.

M W Kellog Company presented the following formula for the fatigue life

estimation of bellows. The company uses Number of cycles (Ni) and Stress

level (Si) terminologies for stainless steel bellows which gives good

agreement with the published data. (Refer equation 2.7)

Expansion joints are under going low cycle fatigue because of secondary

and peak type, stresses in operating units exceeding the material yield

strength. Therefore, the primary design should involve restricting the

primary and the local membrane stresses to occur within specified limits,

and avoidance of premature fatigue.

Langer B F proposed the following expression for the acceptable number of

cycles Ni, at stress range Si. (Refer equation 2.11 )

Anderson analyzed the available data from fatigue tests on convoluted

unreinforced bellows and determined that pressure stresses have a definite

effect on fatigue life. He found the following equation to correlate a pseudo-

stress S (psi) to cycle life N. (Refer equation 2.12 )

The purpose of two-ply bellow elements is to permit local leak detection

through monitoring of the annulus between the two plies. Initially LLRT

discovered very little, as any leakage starts very little rate. Actually, inert

gas or air can be taken as test medium, which will be introduced under

pressure between the plies. Pressure decay rates or make-up flow rates to

maintain a specified pressure are than measured.

The effect of environmental medium should be paid attention when dealing

with fatigue life for bellows expansion joints. Existence of corrosive media

will reduce fatigue life for metal bellows expansion joints.


2.3.4 Papers on Vibrations analysis


natural frequencies, at least in most practical applications. No effect was

observed up to a mean water velocity up to 10 m/s. The effect of internal

pressurization on bellows natural frequencies is relatively small on the first

transverse mode and decrease with increasing mode numbers.

A thermal transient test of the piping bellows was conducted. These models

were subjected to more severe cyclic thermal transients than those of the

plant condition. After destructive examination, no cracking were found in

particular structures of the piping-bellows models, such as the Y shaped

and E shaped junctions.

Bellows can be used in Fast Breeder Reactor (FBR) piping, in nuclear

application. Certain design rules should be followed for this special

application.


2.4 Areas for further Research work:

In view of above study, further investigations are felt to be required in the following

areas of expansion joints.

1. Analysis of design parameters: The designers should aware about all the

geometric parameters and design features of expansion joints.

2. Investigation of stability of bellows: Excessive internal pressure may

cause a bell

2. Literature Review -...

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