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Experimental study on LBB behaviour of LMFBR pipe elbows
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International Journalof Fatigue
International Journal of Fatigue 30 (2008) 574–584
www.elsevier.com/locate/ijfatigue
Experimental study on LBB behaviour of LMFBR pipe elbows P. Nagapadmaja a
a,*
, V. Kalyanaraman
b,1
, S.R. Satish Kumar
b,2
, P. Chellapandi
c,3
Steel Structures Group, Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai 600113, India b Department of Civil Engineering, Indian Institute of Technology Madras, Chennai 600036, India c Reactor Engineering Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, India Received 8 September 2006; received in revised form 27 February 2007; accepted 4 March 2007 Available online 19 March 2007
Abstract The concept of leak before break (LBB) has now replaced the traditional design basis of a double ended guillotine break (DEGB) to design the piping systems for new generation of nuclear reactors. The LBB aims at the application of fracture mechanics principle to demonstrate that pipes are, in general, unlikely to experience DEGB without prior indication of leakage due to through the thickness crack. Pipe elbows are the most critical components in any piping system under earthquake loading. Three cyclic load experiments have been conducted on 90 elbows of two different diameters to investigate their fatigue crack growth and leak before break behavior. A detectable leak before break was observed in all the three pipe elbows tested. Details of this experimental study and the results are presented in this paper. 2007 Elsevier Ltd. All rights reserved. Keywords: Elbow; Fatigue; Fracture; Leak before break; Pipe; Surface crack
1. Introduction The service life of structural components may be governed by several modes of degradation and failure such as fatigue, excessive deformation, fracture, yielding, creep, stress rupture, corrosion, wear, erosion etc. Fatigue is one of the most dominant modes of failure and any undetectable flaw in the structure can propagate during its service life, which may become catastrophic in time Prashant Kumar, [11]. Liquid Metal Fast Breeder Nuclear Reactor (LMFBR) is a class of reactors, which uses generally liquid sodium as a coolant. As sodium reacts easily with air as well as water, failure of sodium carrying components such as
*
Corresponding author. Tel.: +91 9444229298; fax: +44 22575286. E-mail addresses: [email protected] (P. Nagapadmaja), [email protected] (V. Kalyanaraman), [email protected] (S.R. Satish Kumar), [email protected] (P. Chellapandi). 1 Tel.: +91 44 22574256; fax: +44 22575286. 2 Tel.: +91 44 22574287; fax: +44 22575286. 3 Tel.: +91 44 27480106. 0142-1123/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2007.03.003
pipes, piping vessels is catastrophic Bhoje, [2]. The concept of LBB is now widely used in nuclear power plants to obtain warning through cracks before sudden failures of these components. Nathwani et al. [9] has applied Ontario Hydro’s LBB approach to the Darlington nuclear generating station. Various experimental and analytical studies have been carried out in Indira Gandhi Centre for Atomic Research (IGCAR) and Bhabha Atomic Research Centre (BARC) and other institutes on LBB behavior of Nuclear Reactor components such as Tees Chellapandi et al. [4], steam generators Chellapandi et al. [3,5] and piping elbows Bhandari et al. [1], Chattopadhyay et al. [6], Delliou et al. [7] and Smete et al. [13] and shell nozzle junctions Ukadgaonker et al. [14]. LBB behavior is ensured by demonstrating three levels of safety against sudden fracture, which is called as defense in depth strategy Chattopadhyay et al. [6]. Level 1 safety is ensured by the use of ductile and tough materials due to their high resistance against catastrophic rupture. Level 2 safety is demonstrated by performing fatigue crack growth study of a surface crack in the zones of high stress and it is then shown that there is insignificant growth of this surface
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Nomenclature a c t Gi
crack depth semi-crack length thickness of the specimen strain gauge locations
crack during the entire life period of the reactor. In the demonstration of Level 3 safety, it is ensured that a surface notch created at the location of maximum stress develops into through the wall crack leading to detectable leak before failure under cyclic loading. LMFBR pipes are generally thin walled and elbows are critical. When a thin-walled, 90 elbow is subjected to inplane bending moment, due to ovalisation of the circular section into an elliptical one, introduces high through the wall thickness bending stress at the crown and a crack may initiate close to the crown. This crack tends to propagate under the action of cyclic loads that are likely to be imposed due to earthquake ground motions during the service life of a reactor, leading to failure of the elbow Prabhakaran and Venkat Raj [10]. The present experimental study involves the level 3 safety demonstration under combined internal pressure and in-plane bending of two different diameter piping elbows made of austenitic stainless steel that are to be used in 500 MWe Prototype Fast Breeder Reactor (PFBR) which is being designed at Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam. This paper presents the details of the experimental study and the results. 2. Test details 2.1. Test specimen Austenitic stainless steels Bhoje [2], are widely used in nuclear industries for key structural components such as reactor vessels and piping. The selection of austenitic stainless steels is made on the basis of their various desirable material properties such as combination of resistance to oxidation, corrosion and creep as well as weldability and high ductility. The material austenitic stainless steel type SS316 LN, which is used in the current study, is basically a type 316 stainless steel in which, the carbon content is lower than 0.03% and the nitrogen content is between 0.06% and 0.08%. It has minimum yield stress of 235 MPa, a Young’s modulus of 1.92 · 105 MPa and Poisson’s ratio of 0.3. Three specimens were tested, of which the first two were identical. The dimensions of the specimens are given in Table 1. Static analyses of the entire test specimen along with brackets were carried out using the finite element software,
Table 1 Test specimen details Description
Smaller diameter pipe elbows (Specimens 1 and 2)
Larger diameter pipe elbow (Specimen 3)
Internal diameter of the pipe (mm) Average thickness of the pipe at bend (mm) Radius of curvature of the centerline of the bend (mm)
400
800
12
12
600
1200
ABAQUS [8]. In order to increase the lever arm for loading; straight extensions of mildsteel were welded on either side of the pipe elbow. One thousand millimeter and five hundred millimeter straight extensions were attached to larger and smaller diameter pipe elbows, to minimize the effect of end conditions on the free ovalisation of the bend In order seal and pressurize the pipe circular end plates were welded to the elbow with extension. Features were provided in these end plates to create hinged end support at one end and attachment to the swivel head of a 100 tonne actuator at the other end (Fig. 1). Plate shell elements were used to model the elbow, straight extensions, cover plate and brackets. Table 2 shows the comparison of critical stresses under combined internal pressure and an actuator load corresponding to first yield at the critical location. The yield loads for smaller and larger diameter pipe elbows were 100 kN and 150 kN, respectively. This has been obtained after trying out different levels of discretisation of the pipe elbow. The final results correspond to 128 shell elements for smaller diameter pipe elbow and 256 shell elements for larger diameter pipe elbow along the circumference and 252 elements along the meridian of the pipe elbow. The stresses from the FEM models indicated that the maximum stress occurs on the outer surface at 45 along the bend and around 6.8 and 8 from the crown along the circumferential direction of the pipe for smaller and larger diameter pipe elbows, respectively (Fig. 2) towards the intrados of the bend in the elbow. A 10 mm long, 1 mm wide and 0.5 mm deep semi-elliptical notch was made on the outer surface along the meridinal direction at the critical location, using a shaped grinding wheel of 50 mm diameter.
576
P. Nagapadmaja et al. / International Journal of Fatigue 30 (2008) 574–584 NOTCH (8 DEGREES BELOW THE CROWN IN THE CIRCUMFERENTIAL DIRECTION)
A STUB COLUMN OF 1000 mm LENGTH
G17
00 10
00
12
G19
0
A 00
90˚
G20
80
PLATE OF SIZE 300 X 300 mm
G18
10
ISMC:[email protected]/m
PART D ACTUATOR PART C
ISMB : 450 @ 0.71 kN/m
PART E
PART B
SOLID BLOCK OF SIZE 75 X 130 mm
STRONG WALL
PART A 2927
3756 7660 G5, G6 G7, G8
G3, G4
G9, G10
G15, G16
G11, G12
8˚
G1, G2
G13, G14
All dimensions are in mm
45˚
SECTION A-A
Fig. 1. Plan of experimental Setup for Larger diameter pipe elbow.
Table 2 Critical stresses (in MPa) under combined internal pressure of 1 MPa and an actuator load corresponding to first yield Stresses (MPa) Outer von Mises Inner von Mises Outer longitudinal Inner longitudinal Outer hoop Inner hoop
Smaller diameter pipe elbow
Larger diameter pipe elbow
203.8 238.4 161.95
208.9 210.1 151.3
63.0
58.8
235 263.4
235 235.3
2.2. Test setup The elbows were supported in the horizontal plane and had hinges about the neutral axis at both ends. They were tested under a constant internal pressure of 1 MPa and cyclic bending moments by applying collinear force through the end hinges. The required bending moment was imposed on the specimen by applying a cyclic horizontal compressive force at one end of the specimen, using an actuator of 100 tonnes capacity and 250 mm stroke length (Fig. 3). The test specimens were filled with water and pressurized to 1 MPa using an air chamber and a zero air cylinder. The pressure gauge of 1% accuracy was connected to one of the pipe extension to check the applied pressure.
The applied pressure can be maintained even under leaked condition by means of an air chamber Chellapandi et al. [3,4], which was initially filled with air. The fluctuation of pressure in the elbow could be minimized by the flow of water from the pipe to the air chamber during loading and from the chamber to the pipe during unloading. Electrical resistance foil type strain gauges (of gauge length 5 mm) were used for the strain measurements. Six and eight strain gauges were kept around the midsection circumference of the elbow for the smaller and larger diameter pipe elbows, respectively (Fig. 3). Two strain gauges were kept at the two notch tips to identify the crack initiation and one gauge on each side of straight extensions to check the applied load. Orion Automatic Data Logging System was used to log the strain gauges data. This data was then transferred to a computer. The crack growth was monitored using the crack depth gauge Instruction Manual RMG 4015 [12], which works on the principle of potential drop across the crack. A quadripole probe is used in the crack depth gauge, where the outer poles pass current into the cracked specimen, while the potential drop is measured across the two inner poles. The voltage drop depends on the size and shape of the crack as it grows. Evenly spaced 2 mm graduations were made on the specimen surface for a length of about 25–40 mm on either side of the center of the notch. The crack growth was monitored by measuring the crack depth at various points along the length of the crack.
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577
Fig. 2. Finite element model and stress contour at yield (larger diameter pipe elbow).
material nonlinearity even before 0.2% offset yield stress. Hence the load was reduced during cyclic testing as given in Table 3. In the other two specimens, the loads were increased gradually in the first trial of static loading in order to avoid plastic deformation of the specimen other than at the critical location as given in Table 4. 2.3.2. Cyclic tests After performing a static test, cyclic load was applied on each of the specimen at a frequency of 0.5 Hz initially in the load range shown in Table 3. Static tests were performed at intervals of 2500 cycles of above loading up to crack initiation. The crack initiation was identified by the sudden increase in the strain and crack depth at the
Fig. 3. Experimental set up for larger diameter pipe elbow.
Table 3 Load and strain ranges Specimen
2.3. Test procedure 2.3.1. Static tests The bending moment in the elbow was varied by applying compressive force through the actuator. Initially static tests were performed and the experimental strain results were found to compare well with the numerical results. To ensure crack initiation and propagation in a reasonable number of cycles, it was decided to apply tensile strain ranges of 3000 and 5000 micro strains at the critical location for all the three specimens for crack initiation and propagation, respectively. In order to apply a strain range of about 3000 micro strains (above the elastic limit of strain 1225 micro strains), a load of 245 kN as calculated from the elastic finite element analysis was applied on specimen 1 at the first instance. This caused permanent plastic deformation and ovaling of the section of the elbow at 45 due to the
1 2 3
Crack initiation
Crack propagation
Strain range le
Load range kN
Strain range le
Load range kN
1580 2850 3000
0–160 0–90 0–340
2250 4000 4700
0–180 0–200 0–450
Table 4 Load ranges applied at different fatigue cycle numbers Specimen
Cycle numbers
Load ranges (kN)
1
0–29,300 29,301–30,700 0–18,500 18,501–27,500 0–20,000 20,001–25,000 25,001–39,300 39,301–49,500 49,501–50,000
0–160 0–180 0–190 0–200 0– 200 0–250 0–340 0–450 0–250
2 3
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Static tests were also carried out after leak for specimens 2 and 3. In the case of specimen 2, the test was continued till the maximum applied load of 200 kN was reached whereas in the case of specimen 3, the test was done only up to 250 kN, as it deformed too much and the specimen head interfered with supports before ultimate load could be reached due to plastic deformation.
notch tips. After crack initiation, static tests were performed at an interval of 500 cycles till the crack propagated through the thickness. The strain gauges as well as crack depth gauge readings were recorded during these static increase and decrease in the externally applied load, causing in-plane bending. The tests were further continued beyond the through the wall thickness cracking, till a detectable leak (more than 1 kg/h) was observed. The leak rate was not measured during the test because the pressure could not be maintained after the leak. However, the leak rate would definitely be more than 1 kg/h.
3. Test results and discussions Fatigue tests were conducted on two smaller and one larger diameter pipe elbows with a semi-elliptical notch at
Strain (micro strains)
3000
2000
G1 G2 G9
1000
FEA Yield load (100 kN)
0 0
20
40
60
80
100
120
140
Load (kN)
Specimen-1
Strain (micro strains)
2500 2000 G1
1500
G2 1000
G9 FEA yield load (100 kN)
500 0 0
25
50
75
100
125
150
Load (kN)
Specimen-2
Strain (micro strains)
1800 1500 1200
G1
900
G2 G9
600 FEA yield load (150 kN)
300 0 0
25
50
75
100
125
150
Load (kN)
Specimen-3 Fig. 4. Variation of static test strain gauge readings with load at critical location (Initial static test).
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the critical section, subjected to bending cyclic loads along with a constant internal pressure of 1 MPa. The crack propagated through the thickness for all the three specimens and a detectable leak of more than 1 kg/h was observed before failure, satisfying the LBB criteria. The results obtained from the tests are presented and discussed below. 3.1. Variation of strain with load Before applying cyclic loading, all the specimens were statically tested to obtain the variation of strains with load, for increasing load ranges and these were compared with results obtained from linear elastic finite element analysis. Fig. 4 shows the variation of critical strain gauge readings with load during the static test at the beginning for all the three specimens. The straight lines corresponding to the respective gauge strain, obtained from theoretical elastic analysis using FEM are also plotted. The first yield load, as obtained from the finite element analysis for smaller and larger diameter pipe elbows, was 100 kN and
150 kN. But it can be observed from the figures that the curve becomes non-linear at load lower than the theoretical yield load for specimen 1 due to residual stresses due to initial test beyond yielding. However, the variation is linear in subsequent cycles. For the initial tests, the load vs. strain relationship is linear and nearly parallel to the theoretical load deformation line obtained from elastic finite element analysis up to yield limit, after which the strains increase at a faster rate. The experimental and numerical results compare well in the elastic range within 10%, except for some of the gauges whose strains are very small. The unloading curve is almost parallel to the elastic loading curve in most cases. There is residual strain on unloading due to loading beyond elastic limit. As the centerline of the bend is lifting up while loading due to ovalisation of the cross section, this cause a small bending of the pipe about the horizontal plane, as indicated by the strains in the meridinal direction below the centerline of the bend being slightly more than that above the centerline of the bend. No. of Load cycles
Load ranges
250
(0 - 200 kN)
(0 - 190 kN)
0 10000 13000 14500 15000 17000 18000 18500 19000 21000 24000 26000 27000
Load (kN)
200 150 100 50 0 0
25
579
50
75
100
125
150
Actuator displacement (mm)
Specimen 2 (0 - 200 kN) 500
(0 - 340 kN)
(0 - 250 kN)
Load ranges (0 - 450 kN)
No. of load cycles (0 - 250 kN)
0 2500
(0 - 400 kN)
25000
400 Load (kN)
39300-400 kN 39300-450 kN
300
40000 41500
200
43000 44000
100
45500 46500
0 0
50
100 150 200 Actuator displacement (mm)
250
47500 49500
Specimen 3 Fig. 5. Variation of actuator displacement with load at different fatigue load cycles.
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3.2. Variation of actuator force and displacement with number of cycles
is clear that there was a gradual increase in the residual plastic deformation in the elbow due to repeated application of the same load range up to detectable leak and rapid increase after detectable leak i.e. after 27,000 cycles for specimen 2 and 49,500 cycles for specimen 3. It is also clear that there is a small residual plastic deformation recovery after cyclic loading.
Fig. 5 shows the variation of actuator displacement with load during static test after various number of fatigue cycles for specimens 2 and 3. These displacement readings were not taken for the first specimen 1. From the figures, it
Load ranges
Strain (micro strains)
4000
(0 - 160 kN)
(0 - 180 kN)
3000 G1 G9
Crack initiation
2000
1000
0 0
5000
10000
15000
20000
25000
30000
35000
No. of cycles (N)
Specimen 1 Load ranges 6000
Strain (micro strains)
(0 - 190 kN)
(0 - 200 kN)
4500 G1 G2 G9
3000
1500
Crack initiation
0 0
5000
10000
15000
20000
25000
30000
No. of cycles (N)
Specimen 2 Load ranges
6000
(0 - 200 kN)
(0 - 250 kN)
(0 - 340 kN)
(0 - 450 kN)
Strain (micro strains)
5000 4000
G1 G3 G9
3000 2000
Crack initiation 1000 0 0
10000
20000
30000
40000
50000
No. of cycles (N)
Specimen 3 Fig. 6. Variation of static test strain gauge readings at critical locations with number of cycles.
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For specimen 2 it is seen that there was very little progressive plastification in specimen’s load deformation behaviour until crack initiation stage. Only thereafter some
581
residual plastic deformation can be seen at zero load. The load range had to be increased to 0–200 kN after 18,500 cycles to accelerate crack propagation. In specimen 3 there No. of Load cycles
16
0
12
19340
crack depth (mm)
21840 24340
8
26840 29340 4
30700
0 -16
-12
-8
-4
0 4 initial notch
8
12
16
Distance from the centre of the notch (mm)
Specimen 1 No. of Load cycles
24 20
crack depth (mm)
16 12 8 4 0 -24
-20
-16
-12
-8
-4
0
4
8
12
16
20
24
initial notch Distance from the center of the notch (in mm)
0 12500 13500 16500 18500 19500 21500 22000 24000 25000 26000 26500 27000 27500
Specimen 2 No. of load cycles
16
0 crack depth 12 (mm)
37500 39300 40500
8
41500 42500 43500
4
44000 44500 0 -16
-12
-8
-4
45500 0
4
8
12
initial notch Distance from the center of the notch (mm)
Specimen 3 Fig. 7. Crack profiles from experiments.
16
46500 47500 49500
P. Nagapadmaja et al. / International Journal of Fatigue 30 (2008) 574–584
wall little progressive plastification until crack initiation for a given load range and only after crack initiation (37,500 cycles) the load deformation behaviour showed progressive increase in plastic deformation.
12
3.3. Variation of strain with number of cycles
10
6 4 2 0 0
10000
20000
3.5. Variation of crack depth/crack length with number of cycles
30000
40000
50000
No. of cycles (N)
Fig. 8. Variation of maximum crack depth with number of cycles.
Specimen-1 Specimen-2 Specimen-3
3.4. Crack profiles
30
Crack initiation (Specimen-3)
40
Crack initiation (Specimen-1)
Crack initiation (Specimen-2)
50
Crack length,2c in mm
Fig. 7 shows the experimental crack profiles as obtained from the crack depth gauge measurement for the three specimens and the progression of the crack front as the number of cycles of loading increased. The crack profiles are almost semi-elliptical in shape. The crack growth rate is slow initially and later increases at a faster rate and finally the crack became a through-wall-crack. In the larger diameter pipe elbow close to the notch location, there were punched identification numbers on one side of the slit. As the crack grew from the tip of the notch, it coalesced with minor cracks developed at these marks after 45,500 cycles and the crack extended more in that direction. The final crack profiles are erratic due to improper contact of the probe and also due to the loss of contact between the two surfaces due to the through-the-thickness crack. For specimen 1, the through-wall-crack depth shown by the crack depth gauge was smaller than the wall thickness, because of large plastic deformation induced due to the application of heavier load before cyclic test. For all the three specimens, it is seen that the cracks progressed through the thickness before it spread wide along the surface to cause breaking thereby demonstrating LBB.
Crack initiation (Specimen-3)
Crack initiation (Specimen-1)
8
Crack initiation (Specimen-2)
Crack depth, a in mm
Fig. 6 shows the variation of strain in the critical gauges during static tests carried out after increasing number of fatigue cycles. The strain gauge 3 (G3) for the specimen 1 had failed early during the test and hence the readings for the gauge 3 were not shown in the figures. As the strains at either notch tips are likely to be the same, the test was continued in this specimen and only G1 was monitored. There are increases in the strains corresponding to increase in the actuator load. Otherwise the strains remain almost the same until the crack initiates. The strains at the two notch tips increases rapidly at the time of crack initiation and the gauges (G1 and G3 for specimens 1 and 3, G1 and G2 for specimen 3) immediately thereafter failed (not indicated in the figure).
Specimen-1 Specimen-2 Specimen-3
wall thickness
582
20 10 0 0
10000
20000
30000
40000
50000
No. of cycles (N)
Fig. 9. Variation of crack length with number of cycles.
grows gradually in the depth and length directions. After the crack grew to nearly half the wall thickness, the crack growth was rapid and reached through the wall thickness within around 500 additional cycles. Leakage of water and rapid pressure drop followed when the crack has propagated through the thickness. Even after this, the specimen was able to sustain the load range for many cycles (nearly 500 cycles were applied). 3.6. Variation of crack aspect ratio with number of cycles
Fig. 8 shows the variation of maximum depth of crack with respect to the number of fatigue load cycles for the three specimens. Fig. 9 shows the variation of crack length with respect to the number of fatigue load cycles for the three specimens. The crack profile remains essentially constant until crack initiation stage. Thereafter the crack
Fig. 10 shows the variation of crack aspect ratio with respect to the number of cycles of fatigue loading. It is observed from the figure that initially the notch aspect ratio remained constant until crack initiation from the notch. Thereafter the aspect ratio increased gradually during
P. Nagapadmaja et al. / International Journal of Fatigue 30 (2008) 574–584
early with the increase in the relative crack depth during cycling up to a crack depth of about 10% of the thickness (a/t = 0.1) for specimen 1. After this, it increases linearly with a steeper slope to a through-wall-crack. For specimens 2 and 3, the crack aspect ratio increases linearly with the increase in the relative crack depth during cycling up to a crack depth of about 20% the thickness (a/t = 0.5). After this, it was constant up to 40% of the thickness (a/t = 0.4) and progressed rapidly in the depth direction to a through-wall-crack within 500 cycles after
Specimen-1 Specimen-2 Specimen-3
0.45
Crack initiation (Specimen-3)
Crack aspect ratio (a/c)
0.6
Crack initiation (Specimen-1)
Crack initiation (Specimen-2)
0.9 0.75
583
0.3 0.15
Table 5 Number of cycles for crack initiation/crack propagation
0 0
10000
20000
30000
40000
50000
No. of cycles (N)
Specimen
1 2 3
Fig. 10. Variation of crack aspect ratio with number of cycles.
No. of cycles For crack initiation
For crack propagation
Total
19,300 12,300 37,500
11,400 14,700 12,000
30,700 27,000 49,500
cycling until the crack penetrated to about half the thickness of the specimens. Thereafter the crack progressed rapidly in the thickness direction to through the wall thickness crack. The increase in the crack aspect ratio during cycling indicates that the crack grew faster in the depth direction than in the surface direction. However there are some portions where the crack grows proportionally in the surface and depth directions. The crack aspect ratio remained constant (from 17,000 to 25,000 cycles for specimen 2 and from 43,000 to 47,000 cycles for specimen 3, respectively). 3.7. Relative crack depth versus crack aspect ratio Fig. 11 shows the variation of crack aspect ratio (a/c) with relative crack depth (a/t) for all the three specimens. It can be observed that the crack aspect ratio increases lin-
Specimen-1 Specimen-2 Specimen-3 0.9
Crack aspect ratio, a/c
0.75 0.6 0.45 0.3 0.15 0 0
0.2
0.4
0.6
0.8
1
Relative crack depth, a/t
Fig. 11. Crack aspect ratio vs. Relative crack depth.
Fig. 12. Final through-wall-crack.
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40% of the thickness. This may due to the loading in the plastic range. However, additional test data is necessary to make any reasonable justification. The details regarding the number of fatigue cycles taken for crack initiation, propagation and total number of cycles are given in Table 5. Fig. 12 shows the final crack of specimens 1, 2 and 3, respectively. As the specimen 1 had deformed plastically before the cyclic test, results of this specimen are not considered in further studies. 4. Conclusions The following conclusions have been drawn from the experimental study: 1) In the three specimens tested under low cycle fatigue, a through wall crack and a detectable leak was observed before failure, justifying LBB assumption adopted in designs. 2) The experimental and numerical strain values compare well within 10% except for some of the gauges whose strains are very small. 3) The actuator displacement increases gradually for the same load range, under cyclic load, up to leak and rapidly after the leak. 4) Initially, the crack growth rate is more in the depth direction than in the surface direction. After about 1/7th the thickness, the crack started growing more in the surface direction than in the depth direction. And after about half the thickness, the crack grew rapidly to a through-wall-crack. 5) It is observed that there is not much increase in the strain due to repeated cycling. 6) The crack profiles are almost semi-elliptical in shape, as they grow under cyclic loading. 7) The test was continued further for another 500 cycles beyond through-wall-crack and it was observed that stable cyclic load behaviour was observed and that further growth of crack along surface direction was very small (about 1–2 mm).
Acknowledgement The work presented in this paper was sponsored by Indira Gandhi Centre for Atomic Research, Kalpakkam, India and the support is greatly acknowledged. References [1] Bhandari S, Fortmann M, Grueter L, Heliot J, Meyer P, Percie Du Sert B, et al. Crack propagation of LMFBR elbow. Nucl Eng Des 1986;91:107–19. [2] Bhoje VS. Fatigue crack growth study of semi-elliptical cracks in plates subjected to bending. Indian Institute of Technology Madras; 2002. [3] Chellapandi P, Chetal SC, Bhoje SB. LBB investigation of PFBR steam generator. PVP 2000:403. [4] Chellapandi P, Srinivasan R, Biswas A, Chetal SC, Bhoje SB. Leak before break investigation on sodium piping for prototype fast breeder reactor. In: Indo German Theme Meeting on Fatigue and Fracture Assessment of Pressure Retaining Components, February 2002, BARC. [5] Chellapandi P, Chetal SC, Bhoje SB. Leak before break assessment of PFBR components and piping. In: Indo-German Theme Meeting on Fatigue and Fracture Assessment of Pressure Retaining Components, February 2002, BARC. [6] Chattopadhyay J, Dutta BK, Kushwaha HS. Leak before break qualification of primary heat transport elbows of 500 M We Tarapur atomic power plant. Int J Pres Ves Pip 1999;76:221–43. [7] Delliou PL, Julisch P, Hippelein K, Bezdikian G. Analysis of a bending test on a full scale PWR hot leg elbow containing a surface crack. Nucl Eng Des 1999;193:273–82. [8] Hibbit, Karlsson, Sorenson. ABAQUS/CAE User’s Manual, Versions 6.4 and 6.5; 2003. [9] Nathwani JS, Kee BL, Kim CS, Kozluk MJ. Ontario Hydro’s leak before break approach: Application to the Darlington nuclear generating station A. Nucl Eng Des 1989;111:85–107. [10] Prabhakaran KM, Venkat Raj V. Closed form expression for plastic J-integral for an elbow with a through wall crown crack under opening bending moment. Int J Pres Ves Pip 2002;80:31–9. [11] Kumar Prashant. Elements of Fracture Mechanics. New Delhi: Wheeler Publishing; 1999. [12] Pruf. Instruction Manual RMG 4015 (Rev. 2.0a), Wupertal: Karl Duestch; 1997. [13] Smete P, Delliou PL, Ignacolo S. Fracture resistance of cracked duplex stainless steel elbows under bending with or without internal pressure. Nucl Eng Des 2000;197:155–68. [14] Ukadgaonker VG, Khairnar YD, Vaidya Pratichi, Chellapandi P. Leak before break analysis of shell nozzle junction of steam generator-part 1. Indian Inst Technol Bombay 1999.
International Journalof Fatigue
International Journal of Fatigue 30 (2008) 574–584
www.elsevier.com/locate/ijfatigue
Experimental study on LBB behaviour of LMFBR pipe elbows P. Nagapadmaja a
a,*
, V. Kalyanaraman
b,1
, S.R. Satish Kumar
b,2
, P. Chellapandi
c,3
Steel Structures Group, Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai 600113, India b Department of Civil Engineering, Indian Institute of Technology Madras, Chennai 600036, India c Reactor Engineering Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, India Received 8 September 2006; received in revised form 27 February 2007; accepted 4 March 2007 Available online 19 March 2007
Abstract The concept of leak before break (LBB) has now replaced the traditional design basis of a double ended guillotine break (DEGB) to design the piping systems for new generation of nuclear reactors. The LBB aims at the application of fracture mechanics principle to demonstrate that pipes are, in general, unlikely to experience DEGB without prior indication of leakage due to through the thickness crack. Pipe elbows are the most critical components in any piping system under earthquake loading. Three cyclic load experiments have been conducted on 90 elbows of two different diameters to investigate their fatigue crack growth and leak before break behavior. A detectable leak before break was observed in all the three pipe elbows tested. Details of this experimental study and the results are presented in this paper. 2007 Elsevier Ltd. All rights reserved. Keywords: Elbow; Fatigue; Fracture; Leak before break; Pipe; Surface crack
1. Introduction The service life of structural components may be governed by several modes of degradation and failure such as fatigue, excessive deformation, fracture, yielding, creep, stress rupture, corrosion, wear, erosion etc. Fatigue is one of the most dominant modes of failure and any undetectable flaw in the structure can propagate during its service life, which may become catastrophic in time Prashant Kumar, [11]. Liquid Metal Fast Breeder Nuclear Reactor (LMFBR) is a class of reactors, which uses generally liquid sodium as a coolant. As sodium reacts easily with air as well as water, failure of sodium carrying components such as
*
Corresponding author. Tel.: +91 9444229298; fax: +44 22575286. E-mail addresses: [email protected] (P. Nagapadmaja), [email protected] (V. Kalyanaraman), [email protected] (S.R. Satish Kumar), [email protected] (P. Chellapandi). 1 Tel.: +91 44 22574256; fax: +44 22575286. 2 Tel.: +91 44 22574287; fax: +44 22575286. 3 Tel.: +91 44 27480106. 0142-1123/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2007.03.003
pipes, piping vessels is catastrophic Bhoje, [2]. The concept of LBB is now widely used in nuclear power plants to obtain warning through cracks before sudden failures of these components. Nathwani et al. [9] has applied Ontario Hydro’s LBB approach to the Darlington nuclear generating station. Various experimental and analytical studies have been carried out in Indira Gandhi Centre for Atomic Research (IGCAR) and Bhabha Atomic Research Centre (BARC) and other institutes on LBB behavior of Nuclear Reactor components such as Tees Chellapandi et al. [4], steam generators Chellapandi et al. [3,5] and piping elbows Bhandari et al. [1], Chattopadhyay et al. [6], Delliou et al. [7] and Smete et al. [13] and shell nozzle junctions Ukadgaonker et al. [14]. LBB behavior is ensured by demonstrating three levels of safety against sudden fracture, which is called as defense in depth strategy Chattopadhyay et al. [6]. Level 1 safety is ensured by the use of ductile and tough materials due to their high resistance against catastrophic rupture. Level 2 safety is demonstrated by performing fatigue crack growth study of a surface crack in the zones of high stress and it is then shown that there is insignificant growth of this surface
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575
Nomenclature a c t Gi
crack depth semi-crack length thickness of the specimen strain gauge locations
crack during the entire life period of the reactor. In the demonstration of Level 3 safety, it is ensured that a surface notch created at the location of maximum stress develops into through the wall crack leading to detectable leak before failure under cyclic loading. LMFBR pipes are generally thin walled and elbows are critical. When a thin-walled, 90 elbow is subjected to inplane bending moment, due to ovalisation of the circular section into an elliptical one, introduces high through the wall thickness bending stress at the crown and a crack may initiate close to the crown. This crack tends to propagate under the action of cyclic loads that are likely to be imposed due to earthquake ground motions during the service life of a reactor, leading to failure of the elbow Prabhakaran and Venkat Raj [10]. The present experimental study involves the level 3 safety demonstration under combined internal pressure and in-plane bending of two different diameter piping elbows made of austenitic stainless steel that are to be used in 500 MWe Prototype Fast Breeder Reactor (PFBR) which is being designed at Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam. This paper presents the details of the experimental study and the results. 2. Test details 2.1. Test specimen Austenitic stainless steels Bhoje [2], are widely used in nuclear industries for key structural components such as reactor vessels and piping. The selection of austenitic stainless steels is made on the basis of their various desirable material properties such as combination of resistance to oxidation, corrosion and creep as well as weldability and high ductility. The material austenitic stainless steel type SS316 LN, which is used in the current study, is basically a type 316 stainless steel in which, the carbon content is lower than 0.03% and the nitrogen content is between 0.06% and 0.08%. It has minimum yield stress of 235 MPa, a Young’s modulus of 1.92 · 105 MPa and Poisson’s ratio of 0.3. Three specimens were tested, of which the first two were identical. The dimensions of the specimens are given in Table 1. Static analyses of the entire test specimen along with brackets were carried out using the finite element software,
Table 1 Test specimen details Description
Smaller diameter pipe elbows (Specimens 1 and 2)
Larger diameter pipe elbow (Specimen 3)
Internal diameter of the pipe (mm) Average thickness of the pipe at bend (mm) Radius of curvature of the centerline of the bend (mm)
400
800
12
12
600
1200
ABAQUS [8]. In order to increase the lever arm for loading; straight extensions of mildsteel were welded on either side of the pipe elbow. One thousand millimeter and five hundred millimeter straight extensions were attached to larger and smaller diameter pipe elbows, to minimize the effect of end conditions on the free ovalisation of the bend In order seal and pressurize the pipe circular end plates were welded to the elbow with extension. Features were provided in these end plates to create hinged end support at one end and attachment to the swivel head of a 100 tonne actuator at the other end (Fig. 1). Plate shell elements were used to model the elbow, straight extensions, cover plate and brackets. Table 2 shows the comparison of critical stresses under combined internal pressure and an actuator load corresponding to first yield at the critical location. The yield loads for smaller and larger diameter pipe elbows were 100 kN and 150 kN, respectively. This has been obtained after trying out different levels of discretisation of the pipe elbow. The final results correspond to 128 shell elements for smaller diameter pipe elbow and 256 shell elements for larger diameter pipe elbow along the circumference and 252 elements along the meridian of the pipe elbow. The stresses from the FEM models indicated that the maximum stress occurs on the outer surface at 45 along the bend and around 6.8 and 8 from the crown along the circumferential direction of the pipe for smaller and larger diameter pipe elbows, respectively (Fig. 2) towards the intrados of the bend in the elbow. A 10 mm long, 1 mm wide and 0.5 mm deep semi-elliptical notch was made on the outer surface along the meridinal direction at the critical location, using a shaped grinding wheel of 50 mm diameter.
576
P. Nagapadmaja et al. / International Journal of Fatigue 30 (2008) 574–584 NOTCH (8 DEGREES BELOW THE CROWN IN THE CIRCUMFERENTIAL DIRECTION)
A STUB COLUMN OF 1000 mm LENGTH
G17
00 10
00
12
G19
0
A 00
90˚
G20
80
PLATE OF SIZE 300 X 300 mm
G18
10
ISMC:[email protected]/m
PART D ACTUATOR PART C
ISMB : 450 @ 0.71 kN/m
PART E
PART B
SOLID BLOCK OF SIZE 75 X 130 mm
STRONG WALL
PART A 2927
3756 7660 G5, G6 G7, G8
G3, G4
G9, G10
G15, G16
G11, G12
8˚
G1, G2
G13, G14
All dimensions are in mm
45˚
SECTION A-A
Fig. 1. Plan of experimental Setup for Larger diameter pipe elbow.
Table 2 Critical stresses (in MPa) under combined internal pressure of 1 MPa and an actuator load corresponding to first yield Stresses (MPa) Outer von Mises Inner von Mises Outer longitudinal Inner longitudinal Outer hoop Inner hoop
Smaller diameter pipe elbow
Larger diameter pipe elbow
203.8 238.4 161.95
208.9 210.1 151.3
63.0
58.8
235 263.4
235 235.3
2.2. Test setup The elbows were supported in the horizontal plane and had hinges about the neutral axis at both ends. They were tested under a constant internal pressure of 1 MPa and cyclic bending moments by applying collinear force through the end hinges. The required bending moment was imposed on the specimen by applying a cyclic horizontal compressive force at one end of the specimen, using an actuator of 100 tonnes capacity and 250 mm stroke length (Fig. 3). The test specimens were filled with water and pressurized to 1 MPa using an air chamber and a zero air cylinder. The pressure gauge of 1% accuracy was connected to one of the pipe extension to check the applied pressure.
The applied pressure can be maintained even under leaked condition by means of an air chamber Chellapandi et al. [3,4], which was initially filled with air. The fluctuation of pressure in the elbow could be minimized by the flow of water from the pipe to the air chamber during loading and from the chamber to the pipe during unloading. Electrical resistance foil type strain gauges (of gauge length 5 mm) were used for the strain measurements. Six and eight strain gauges were kept around the midsection circumference of the elbow for the smaller and larger diameter pipe elbows, respectively (Fig. 3). Two strain gauges were kept at the two notch tips to identify the crack initiation and one gauge on each side of straight extensions to check the applied load. Orion Automatic Data Logging System was used to log the strain gauges data. This data was then transferred to a computer. The crack growth was monitored using the crack depth gauge Instruction Manual RMG 4015 [12], which works on the principle of potential drop across the crack. A quadripole probe is used in the crack depth gauge, where the outer poles pass current into the cracked specimen, while the potential drop is measured across the two inner poles. The voltage drop depends on the size and shape of the crack as it grows. Evenly spaced 2 mm graduations were made on the specimen surface for a length of about 25–40 mm on either side of the center of the notch. The crack growth was monitored by measuring the crack depth at various points along the length of the crack.
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577
Fig. 2. Finite element model and stress contour at yield (larger diameter pipe elbow).
material nonlinearity even before 0.2% offset yield stress. Hence the load was reduced during cyclic testing as given in Table 3. In the other two specimens, the loads were increased gradually in the first trial of static loading in order to avoid plastic deformation of the specimen other than at the critical location as given in Table 4. 2.3.2. Cyclic tests After performing a static test, cyclic load was applied on each of the specimen at a frequency of 0.5 Hz initially in the load range shown in Table 3. Static tests were performed at intervals of 2500 cycles of above loading up to crack initiation. The crack initiation was identified by the sudden increase in the strain and crack depth at the
Fig. 3. Experimental set up for larger diameter pipe elbow.
Table 3 Load and strain ranges Specimen
2.3. Test procedure 2.3.1. Static tests The bending moment in the elbow was varied by applying compressive force through the actuator. Initially static tests were performed and the experimental strain results were found to compare well with the numerical results. To ensure crack initiation and propagation in a reasonable number of cycles, it was decided to apply tensile strain ranges of 3000 and 5000 micro strains at the critical location for all the three specimens for crack initiation and propagation, respectively. In order to apply a strain range of about 3000 micro strains (above the elastic limit of strain 1225 micro strains), a load of 245 kN as calculated from the elastic finite element analysis was applied on specimen 1 at the first instance. This caused permanent plastic deformation and ovaling of the section of the elbow at 45 due to the
1 2 3
Crack initiation
Crack propagation
Strain range le
Load range kN
Strain range le
Load range kN
1580 2850 3000
0–160 0–90 0–340
2250 4000 4700
0–180 0–200 0–450
Table 4 Load ranges applied at different fatigue cycle numbers Specimen
Cycle numbers
Load ranges (kN)
1
0–29,300 29,301–30,700 0–18,500 18,501–27,500 0–20,000 20,001–25,000 25,001–39,300 39,301–49,500 49,501–50,000
0–160 0–180 0–190 0–200 0– 200 0–250 0–340 0–450 0–250
2 3
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Static tests were also carried out after leak for specimens 2 and 3. In the case of specimen 2, the test was continued till the maximum applied load of 200 kN was reached whereas in the case of specimen 3, the test was done only up to 250 kN, as it deformed too much and the specimen head interfered with supports before ultimate load could be reached due to plastic deformation.
notch tips. After crack initiation, static tests were performed at an interval of 500 cycles till the crack propagated through the thickness. The strain gauges as well as crack depth gauge readings were recorded during these static increase and decrease in the externally applied load, causing in-plane bending. The tests were further continued beyond the through the wall thickness cracking, till a detectable leak (more than 1 kg/h) was observed. The leak rate was not measured during the test because the pressure could not be maintained after the leak. However, the leak rate would definitely be more than 1 kg/h.
3. Test results and discussions Fatigue tests were conducted on two smaller and one larger diameter pipe elbows with a semi-elliptical notch at
Strain (micro strains)
3000
2000
G1 G2 G9
1000
FEA Yield load (100 kN)
0 0
20
40
60
80
100
120
140
Load (kN)
Specimen-1
Strain (micro strains)
2500 2000 G1
1500
G2 1000
G9 FEA yield load (100 kN)
500 0 0
25
50
75
100
125
150
Load (kN)
Specimen-2
Strain (micro strains)
1800 1500 1200
G1
900
G2 G9
600 FEA yield load (150 kN)
300 0 0
25
50
75
100
125
150
Load (kN)
Specimen-3 Fig. 4. Variation of static test strain gauge readings with load at critical location (Initial static test).
P. Nagapadmaja et al. / International Journal of Fatigue 30 (2008) 574–584
the critical section, subjected to bending cyclic loads along with a constant internal pressure of 1 MPa. The crack propagated through the thickness for all the three specimens and a detectable leak of more than 1 kg/h was observed before failure, satisfying the LBB criteria. The results obtained from the tests are presented and discussed below. 3.1. Variation of strain with load Before applying cyclic loading, all the specimens were statically tested to obtain the variation of strains with load, for increasing load ranges and these were compared with results obtained from linear elastic finite element analysis. Fig. 4 shows the variation of critical strain gauge readings with load during the static test at the beginning for all the three specimens. The straight lines corresponding to the respective gauge strain, obtained from theoretical elastic analysis using FEM are also plotted. The first yield load, as obtained from the finite element analysis for smaller and larger diameter pipe elbows, was 100 kN and
150 kN. But it can be observed from the figures that the curve becomes non-linear at load lower than the theoretical yield load for specimen 1 due to residual stresses due to initial test beyond yielding. However, the variation is linear in subsequent cycles. For the initial tests, the load vs. strain relationship is linear and nearly parallel to the theoretical load deformation line obtained from elastic finite element analysis up to yield limit, after which the strains increase at a faster rate. The experimental and numerical results compare well in the elastic range within 10%, except for some of the gauges whose strains are very small. The unloading curve is almost parallel to the elastic loading curve in most cases. There is residual strain on unloading due to loading beyond elastic limit. As the centerline of the bend is lifting up while loading due to ovalisation of the cross section, this cause a small bending of the pipe about the horizontal plane, as indicated by the strains in the meridinal direction below the centerline of the bend being slightly more than that above the centerline of the bend. No. of Load cycles
Load ranges
250
(0 - 200 kN)
(0 - 190 kN)
0 10000 13000 14500 15000 17000 18000 18500 19000 21000 24000 26000 27000
Load (kN)
200 150 100 50 0 0
25
579
50
75
100
125
150
Actuator displacement (mm)
Specimen 2 (0 - 200 kN) 500
(0 - 340 kN)
(0 - 250 kN)
Load ranges (0 - 450 kN)
No. of load cycles (0 - 250 kN)
0 2500
(0 - 400 kN)
25000
400 Load (kN)
39300-400 kN 39300-450 kN
300
40000 41500
200
43000 44000
100
45500 46500
0 0
50
100 150 200 Actuator displacement (mm)
250
47500 49500
Specimen 3 Fig. 5. Variation of actuator displacement with load at different fatigue load cycles.
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3.2. Variation of actuator force and displacement with number of cycles
is clear that there was a gradual increase in the residual plastic deformation in the elbow due to repeated application of the same load range up to detectable leak and rapid increase after detectable leak i.e. after 27,000 cycles for specimen 2 and 49,500 cycles for specimen 3. It is also clear that there is a small residual plastic deformation recovery after cyclic loading.
Fig. 5 shows the variation of actuator displacement with load during static test after various number of fatigue cycles for specimens 2 and 3. These displacement readings were not taken for the first specimen 1. From the figures, it
Load ranges
Strain (micro strains)
4000
(0 - 160 kN)
(0 - 180 kN)
3000 G1 G9
Crack initiation
2000
1000
0 0
5000
10000
15000
20000
25000
30000
35000
No. of cycles (N)
Specimen 1 Load ranges 6000
Strain (micro strains)
(0 - 190 kN)
(0 - 200 kN)
4500 G1 G2 G9
3000
1500
Crack initiation
0 0
5000
10000
15000
20000
25000
30000
No. of cycles (N)
Specimen 2 Load ranges
6000
(0 - 200 kN)
(0 - 250 kN)
(0 - 340 kN)
(0 - 450 kN)
Strain (micro strains)
5000 4000
G1 G3 G9
3000 2000
Crack initiation 1000 0 0
10000
20000
30000
40000
50000
No. of cycles (N)
Specimen 3 Fig. 6. Variation of static test strain gauge readings at critical locations with number of cycles.
P. Nagapadmaja et al. / International Journal of Fatigue 30 (2008) 574–584
For specimen 2 it is seen that there was very little progressive plastification in specimen’s load deformation behaviour until crack initiation stage. Only thereafter some
581
residual plastic deformation can be seen at zero load. The load range had to be increased to 0–200 kN after 18,500 cycles to accelerate crack propagation. In specimen 3 there No. of Load cycles
16
0
12
19340
crack depth (mm)
21840 24340
8
26840 29340 4
30700
0 -16
-12
-8
-4
0 4 initial notch
8
12
16
Distance from the centre of the notch (mm)
Specimen 1 No. of Load cycles
24 20
crack depth (mm)
16 12 8 4 0 -24
-20
-16
-12
-8
-4
0
4
8
12
16
20
24
initial notch Distance from the center of the notch (in mm)
0 12500 13500 16500 18500 19500 21500 22000 24000 25000 26000 26500 27000 27500
Specimen 2 No. of load cycles
16
0 crack depth 12 (mm)
37500 39300 40500
8
41500 42500 43500
4
44000 44500 0 -16
-12
-8
-4
45500 0
4
8
12
initial notch Distance from the center of the notch (mm)
Specimen 3 Fig. 7. Crack profiles from experiments.
16
46500 47500 49500
P. Nagapadmaja et al. / International Journal of Fatigue 30 (2008) 574–584
wall little progressive plastification until crack initiation for a given load range and only after crack initiation (37,500 cycles) the load deformation behaviour showed progressive increase in plastic deformation.
12
3.3. Variation of strain with number of cycles
10
6 4 2 0 0
10000
20000
3.5. Variation of crack depth/crack length with number of cycles
30000
40000
50000
No. of cycles (N)
Fig. 8. Variation of maximum crack depth with number of cycles.
Specimen-1 Specimen-2 Specimen-3
3.4. Crack profiles
30
Crack initiation (Specimen-3)
40
Crack initiation (Specimen-1)
Crack initiation (Specimen-2)
50
Crack length,2c in mm
Fig. 7 shows the experimental crack profiles as obtained from the crack depth gauge measurement for the three specimens and the progression of the crack front as the number of cycles of loading increased. The crack profiles are almost semi-elliptical in shape. The crack growth rate is slow initially and later increases at a faster rate and finally the crack became a through-wall-crack. In the larger diameter pipe elbow close to the notch location, there were punched identification numbers on one side of the slit. As the crack grew from the tip of the notch, it coalesced with minor cracks developed at these marks after 45,500 cycles and the crack extended more in that direction. The final crack profiles are erratic due to improper contact of the probe and also due to the loss of contact between the two surfaces due to the through-the-thickness crack. For specimen 1, the through-wall-crack depth shown by the crack depth gauge was smaller than the wall thickness, because of large plastic deformation induced due to the application of heavier load before cyclic test. For all the three specimens, it is seen that the cracks progressed through the thickness before it spread wide along the surface to cause breaking thereby demonstrating LBB.
Crack initiation (Specimen-3)
Crack initiation (Specimen-1)
8
Crack initiation (Specimen-2)
Crack depth, a in mm
Fig. 6 shows the variation of strain in the critical gauges during static tests carried out after increasing number of fatigue cycles. The strain gauge 3 (G3) for the specimen 1 had failed early during the test and hence the readings for the gauge 3 were not shown in the figures. As the strains at either notch tips are likely to be the same, the test was continued in this specimen and only G1 was monitored. There are increases in the strains corresponding to increase in the actuator load. Otherwise the strains remain almost the same until the crack initiates. The strains at the two notch tips increases rapidly at the time of crack initiation and the gauges (G1 and G3 for specimens 1 and 3, G1 and G2 for specimen 3) immediately thereafter failed (not indicated in the figure).
Specimen-1 Specimen-2 Specimen-3
wall thickness
582
20 10 0 0
10000
20000
30000
40000
50000
No. of cycles (N)
Fig. 9. Variation of crack length with number of cycles.
grows gradually in the depth and length directions. After the crack grew to nearly half the wall thickness, the crack growth was rapid and reached through the wall thickness within around 500 additional cycles. Leakage of water and rapid pressure drop followed when the crack has propagated through the thickness. Even after this, the specimen was able to sustain the load range for many cycles (nearly 500 cycles were applied). 3.6. Variation of crack aspect ratio with number of cycles
Fig. 8 shows the variation of maximum depth of crack with respect to the number of fatigue load cycles for the three specimens. Fig. 9 shows the variation of crack length with respect to the number of fatigue load cycles for the three specimens. The crack profile remains essentially constant until crack initiation stage. Thereafter the crack
Fig. 10 shows the variation of crack aspect ratio with respect to the number of cycles of fatigue loading. It is observed from the figure that initially the notch aspect ratio remained constant until crack initiation from the notch. Thereafter the aspect ratio increased gradually during
P. Nagapadmaja et al. / International Journal of Fatigue 30 (2008) 574–584
early with the increase in the relative crack depth during cycling up to a crack depth of about 10% of the thickness (a/t = 0.1) for specimen 1. After this, it increases linearly with a steeper slope to a through-wall-crack. For specimens 2 and 3, the crack aspect ratio increases linearly with the increase in the relative crack depth during cycling up to a crack depth of about 20% the thickness (a/t = 0.5). After this, it was constant up to 40% of the thickness (a/t = 0.4) and progressed rapidly in the depth direction to a through-wall-crack within 500 cycles after
Specimen-1 Specimen-2 Specimen-3
0.45
Crack initiation (Specimen-3)
Crack aspect ratio (a/c)
0.6
Crack initiation (Specimen-1)
Crack initiation (Specimen-2)
0.9 0.75
583
0.3 0.15
Table 5 Number of cycles for crack initiation/crack propagation
0 0
10000
20000
30000
40000
50000
No. of cycles (N)
Specimen
1 2 3
Fig. 10. Variation of crack aspect ratio with number of cycles.
No. of cycles For crack initiation
For crack propagation
Total
19,300 12,300 37,500
11,400 14,700 12,000
30,700 27,000 49,500
cycling until the crack penetrated to about half the thickness of the specimens. Thereafter the crack progressed rapidly in the thickness direction to through the wall thickness crack. The increase in the crack aspect ratio during cycling indicates that the crack grew faster in the depth direction than in the surface direction. However there are some portions where the crack grows proportionally in the surface and depth directions. The crack aspect ratio remained constant (from 17,000 to 25,000 cycles for specimen 2 and from 43,000 to 47,000 cycles for specimen 3, respectively). 3.7. Relative crack depth versus crack aspect ratio Fig. 11 shows the variation of crack aspect ratio (a/c) with relative crack depth (a/t) for all the three specimens. It can be observed that the crack aspect ratio increases lin-
Specimen-1 Specimen-2 Specimen-3 0.9
Crack aspect ratio, a/c
0.75 0.6 0.45 0.3 0.15 0 0
0.2
0.4
0.6
0.8
1
Relative crack depth, a/t
Fig. 11. Crack aspect ratio vs. Relative crack depth.
Fig. 12. Final through-wall-crack.
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40% of the thickness. This may due to the loading in the plastic range. However, additional test data is necessary to make any reasonable justification. The details regarding the number of fatigue cycles taken for crack initiation, propagation and total number of cycles are given in Table 5. Fig. 12 shows the final crack of specimens 1, 2 and 3, respectively. As the specimen 1 had deformed plastically before the cyclic test, results of this specimen are not considered in further studies. 4. Conclusions The following conclusions have been drawn from the experimental study: 1) In the three specimens tested under low cycle fatigue, a through wall crack and a detectable leak was observed before failure, justifying LBB assumption adopted in designs. 2) The experimental and numerical strain values compare well within 10% except for some of the gauges whose strains are very small. 3) The actuator displacement increases gradually for the same load range, under cyclic load, up to leak and rapidly after the leak. 4) Initially, the crack growth rate is more in the depth direction than in the surface direction. After about 1/7th the thickness, the crack started growing more in the surface direction than in the depth direction. And after about half the thickness, the crack grew rapidly to a through-wall-crack. 5) It is observed that there is not much increase in the strain due to repeated cycling. 6) The crack profiles are almost semi-elliptical in shape, as they grow under cyclic loading. 7) The test was continued further for another 500 cycles beyond through-wall-crack and it was observed that stable cyclic load behaviour was observed and that further growth of crack along surface direction was very small (about 1–2 mm).
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