numerical research on crack growth behavior in

Abstract: The fatigue crack growth behavior in a T92superheat- er tube with crack of an Ultra-Super Critical boiler under the variable load operation was investigated using elastic-plastic-fracture mechanics finite element method, and then the fracture parameters were calculated. Numerical results revealed that boiler load had an effect on stress intensity factor K, and fatigue crack growth rate accelerated along with the increase of load variety amplitude，overpressure and overheat-ing. Finally, through Paris fatigue crack growth rate model obtained the a-lg(N) curve and da/dN-a curve, and the results indicated that the load variety amplitude, overpressure and overheating all influenced the turning point of fatigue crack growth, but the influence of the turning point of fatigue crack growth is different. Key words: ultra supercritical boiler; variable load; a-N curve; t92superheater tube; numerical simulation; fatigue crack growth

a crack length, mm C, m material constants in da/dN correlations with ΔK da/dN fatigue crack growth rate, mm/cycle E young’s modulus, GPa J J -integral, MPa·mm K stress Intensity factor, MPa·mm1/2 Kmax maximum stress intensity factor, MPa·mm1/2 Kmin minimum stress intensity factor, MPa·mm1/2 ΔK stress intensity factor range, MPa·mm1/2

N number of cycles, cycle Ni number of cycles to initiation, cycle Nf number of cycles to failure, cycle lg(N) number of cycles of loop logarithmic, cycle v Poisson’s ratio σs yield strength, MPa

In consideration of reduction in CO2 emission and energy

saving for thermal power plants, USC boiler units have been developed to meet the requirements. As is known to all, superheater tube is one of the most important part of the USC boiler unit. The life of the superheater tube has directly affected safe operation of the USC boiler. Thus, it is necessary to predict the life of the superheater tube to ensure its safety under the variety of working conditions. However, when the electric power plants are required to follow the demand or electrical net, so the USC boilers have to often change their loads, operating temperature and pressure to follow the demands of electricity need, and fatigue crack growth often occured in the superheater tube, which would lead to a short fatigue life of the superheater tube. The persistent strength method, isothermal method, linear extrapolation method and extrapolation parameters[1], [2], [3], [4], [5], and[6], were mainly used to predict the service life of the superheater tube in the USC boiler in the past. But a large number of experiments had shown that these methods for a non-defective materials had a certain precision at a high temperature when the time was less than one hundred thousand hours life[77].So, it could cause several times or even ten times error for a material with crack[7]. Hence, the above methods to predict the life of the superheater tube with crack were no longer suitable. Up to now, the study of an USC boiler superheater tube focused on the performance of T92mechanical properties and T92/HR3C dissimilar steel welded jonts[8],[9],and[10], T92/Super304H welding fracture location[11], creep failure of T92 and HR3C/T91[12]and[13], and microstructure structure of T92/HR3Cdissimilar steel welded joints[14],etc. But fatigue crack growth for a T92superheater tube containing crack of an USC boiler has rarely researched under the variable load operations. In view of this, the elastic-plastic-fracture mechanics was analysised by Finite Element Method(FEM), and then

1 Copyright © 2014 by ASME

Proceedings of the ASME 2014 Power Conference POWER2014

July 28-31, 2014, Baltimore, Maryland, USA

POWER2014-32015

through Paris fatigue crack growth rate model, the fatigue crack growth behavior of the T92superheater tube with crack of the USC boiler is researched under the variable load operations. The diameter size of the T92superheater tube is much smaller than its axial direction size, the strain-generating in the axial direction is so small, which can be ignored. The size of the initial crack depth is very short. In addition, the structure of the T92superheater tube, which bear the loads is a symmetry. Concluded from what has been discussed above, it can be simplified to a plane strain problem. For reason of simplicity, the T92superheater tube, which represents quarter of the cross-section structural specimen with a crack, is selected to be analyzed in this study, and the initial crack is located at the outer wall of aT92superheater tube with an outer diameter of 48.3 mm and a thickness of 7.82 mm. The finite element model was shown in Fig.1,and the material mechanical properties of T/P92(9Cr-1.8W-0.5Mo-Nb-V in wt%)[15]at different high temperatures were shown in Table 1.

Fig.1 Finite element model of crack growth in a superheater tube

Table 1 Material properties for the T92superheater tube of T/P92 steel at different high temperatures Temperature/℃ 500 600 650 Yield strength σs/MPa 330 245 180 Elastic modulus E/GPa 152 98 85 Poisson's ratio v 0.3 0.3 0.3

PLANE183 is selected in this paper. Because it is well suited to modeling irregular meshes, and is often used for modeling stress concentrations or crack tip. During meshing, PLANE183element is initially generated circumferentially about, and radially away. The key-point, namely crack tip in this paper, which can use KSCON to list current status of concentration.

The stress and strain field at the crack tip is singularity, so, the division of the crack tip mesh needs strict requirements. For the reason that, subregion mesh is used, as shown in Fig.1. The area with crack is meshed using free meshing method, and the transition area and non-crack area are meshed using mapped meshing method. The feature size at the crack tip is from a/8 to a/10 or even less, a is the crack length, and the initial crack

length a is 0.1mm. Around the crack tip of the first lap there are16units, and in the non-crack area dividing the wall thickness there is 10 units. The mesh of transition area should be kept matching for the mesh of crack area. In order to improve the speed of computation in the premise of not affecting the result precision, the mesh of non-crack area may be slightly sparse.

Appropriate boundary conditions can improve the accuracy of result, and the boundary constraints should try to avoid redundant constraints or less constraint. The bottom line, excepting the crack line, is constrained the displacement of y-direction, and the line in the left side of the finite element model is constrained the displacement of x-direction, as showed in Fig.1

The T92superheatertube of a 1000MW USC boiler with an outlet steam parameters of26.25MPa and 603℃/605℃,was used for investigating. For an actual variable load operation of the USC boiler, the boiler parameters, including load, steam outlet temperature and internal pressure, are changing with time in-service. As an USC boiler loads changed under the range of 200MW to1000MW,, the internal pressure changed under the range of 10 MPato26.25MPa, and the steam outlet temperature changed under the range of 500℃to 605℃, as showed in Fig.2, where dot curve and triangular curve represents internal pressure and steam outlet temperature changing with time respectively.

Seven variable load operation conditions are analysised, as showed in Table2. Among of them, the condition(f) and condition(g)are with overpressure and overheating under the range of load changing from 500MW to1000MW,respectively.

Fig.2 The parameter-time curve in a cycle of load variation

Due to the steam outlet temperature and internal pressure are changed with time, using table parameters to apply the loads. NSUBST command in ANSYS can set the number of substeps load, and steam outlet temperature and internal pressure are defined as different table format %tabname% for the independent parameter, respectively, which can be easily implemented load changing with time. The internal pressure is applied on the finite element model (on lines) in the T92superheatertube inner wall, as shown in Fig.1, the steam outlet temperature is applied to all nodes in the finite element model. The elastic-plastic model is selected as Bilinear Isotropic Hardening, and then the structural stress field of elastic-plastic-fracture mechanics is analysised by FEM.

Time(t/s)

Tem

pera

ture

(T°C

)

0

100

200

300

400

500

600

700

Pres

sure

(P/M

Pa)

0

5

10

15

20

25

30

35

0 120 2520 3720 79607800540042003960

Boiler Load (MW)200 300 500 800 2003005008001000


Table 2 Different variable load operation conditions

Load Boiler Load range/MW

Pressure range /MPa

Temperature range/℃

(a) 200~500 10~15 500~550 (b) 500~1000 15~26.25 550~605 (c) 200~1000 10~26.25 500~605 (d) 30~500 10.5~15 510~550 (e) 500~800 15~25 550~580 (f) 500~1000 15~27.5 550~605 (g) 500~1000 15~26.25 550~620

Previous researches have shown that calculation of the fracture parameters by FEM for many practical applications were in good agreement with experimental results[16],[17]. The compact tensile specimens which had a theoretical solution to verify the correctness of the results, was selected to solve fracture parameters by FEM, and calculated results showed that FEM was feasible to calculate fracture mechanics parameters, with highly accuracy[18],[19]. However, the T92superheatertube subjected the steam outlet temperature and internal pressure at the same time, and two of them are changing with time. Therefore, to solve theT92superheatertube that bears the steam outlet temperature and internal pressure varying with time is more convenient by the numerical simulations. For this reason, FEM is used for the calculation of the fracture parameters under different variable load operation conditions in this paper.

Stress Intensity Factor (SIF)K can be obtained through the displacement method, stress method, and also can be obtained by the relationship of J-integral and SIFK. The methods of displacement and stress require high precision mesh. However, the J-integral method，which has nothing to do with the path of integral, through a line integral around the crack tip of elastic-plastic region, avoids using very intensive mesh near the crack tip.

J-Integral is one of the most widely accepted parameters for elastic-plastic-fracture mechanics, and is applicable to both linear elastic and nonlinear elastic-plastic materials. In the plane state of J-integral is defined by:

sy

ut

xutyWJ y

yx

x dd

(1)

then, the relationship of J-integral and SIFK in plane stress conditions is written as:

EKJ

2

(2)

and in plane strain conditions is generally expressed as:

E

vKJ22 1

(3)

where, E is the elastic modulus, and v is the Poisson’s ratio.

The load is deemed as the equal amplitude when making periodic change in this paper. Thus, Stress Intensity Factor Range(SIFR)ΔK can be expressed as follow:

minmax KKK (4)

where, Kmax and Kmin is maximum and minimum stress intensity factor, respectively.

The fatigue crack growth rate of P92 (9C-r1.8W-0.5Mo- Nb-V inwt%) material, in accordance with the GB/T6398-2000《Metal Fatigue Crack Growth Rate Test Method, was tested under the different temperatures[20]. By selecting multiple data points, using the least squares method, fitting the P92 material fatigue crack growth rate material parameters C and mare showing in Table 3 at temperature of 450℃and 600℃. Table 3 P92 material parameters of fatigue crack growth test.

Temperature /℃ Material parameters C m

450 1.4186655E-8 2.96766 600 6.2597934E-8 2.69137

In order to improve the accuracy of the result, through five integral paths around the crack tip of the elastic-plastic region, the average result of the J-integral value is taken, then according the Eq.(3),and the SIFK is calculated.

Fig.3shows the SIFK changing at different boiler load in the same crack length a. As it can be seen from the figure, the boiler load has a major impact on SIFK, and the initial SIFK is affected by the different initial crack. High initial stress intensity factor means that, in the process of operation to increase load, the steam outlet temperature and pressure are relatively higher, and the high temperature leads to the decrease of the T92 material performance. It is easier to accelerate the accumulation of fatigue damage, and the fatigue crack growth life accordingly becomes shorter. At the crack length a=0.1mm, SIFK varies with boiler load change relatively flat, when the crack length a is more than 0.5mm, SIF K is accelerating when the boiler load is about 500MW,and then is flatting at 800MW.

According to Fig.4, under the same crack length a, the SIFRΔK in condition(b), (e), (f) and (g)is varing basically consistent, and is rising faster. It can be seen that the SIFRΔK changes more gentle in condition(a) and condition(d).And the range of the SIFRΔK is in the middle in condition(c), but its upward trend is also fast. So, it can be seen that the SIFRΔK is much more influenced by the load variety amplitude, overpressure and overheating. Through the data points in Fig.4,thepolynomial fitting relationship of seven kinds of load conditions between the SIFRΔK and crack length a can be got, as shown in Table 4. The


fitting coefficient R shows that the SIFRΔK an crack length a is correlated linearly.

300 600 900 1200 15000

3

6

9

12

15

18

Boilerloads/MW

K/M

Pa.

m1/

2

a=0.1mm a=0.3mm a=0.5mm a=0.8mm a=1.2mm a=1.5mm

Fig.3 SIFK at different boiler load

0.0 0.4 0.8 1.2 1.6 2.0 2.40

2

4

6

8

△K

/MPa.m

1/2

Crack lengtha/mm

load(a)load(b)load(c)load(d)load(e)load(f)load(g) Fitting curve

Fig.4 Relationship between ΔK and crack length a under operation of different range of boiler load variation

Table 4 Fitting relationship between SIFRΔK and crack length a

Load Fitting relationship

Fitting Coefficient R

(a) ΔK=0.03258+1.99809a-1.07543a2+0.32592a3 0.99442 (b) ΔK=0.08076+8.63954a-4.57427a2+1.25097a3 0.99513 (c) ΔK=0.65245+5.24250a-2.41882a2+0.74084a3 0.99953 (d) ΔK=0.33825+0.80591a-0.12729a2+0.12670a3 0.99712 (e) ΔK=0.19171+7.89060a-3.96879a2+1.11015a3 0.99616 (f) (g)

ΔK=0.01160+9.97471a-5.88897a2+1.66395a3 ΔK=0.21170+9.08817a-5.11032a2+1.39896a3

0.99916 0.99553

Δ Under different load operation, the Pairs model is used to predict fatigue crack growth rate, and the calculated results are shown in Fig.5. Seen from the Fig.5a),which shows the different load variation ranges influencing the fatigue crack growth rate. The fatigue crack growth rate is significantly greater under the condition(b) and (c) than condition(a), and the initial fatigue crack growth rate is also much bigger difference, condition(a) is less than condition(b) and (c). Fig.5b) shows the range of load changing from 200MW to

500MW, but the initial load is not the same. The initial load of 200MW is in the condition(a), and condition(d) is 300MW, the biggest difference is the initial fatigue crack growth. the initial fatigue crack growth under the condition(d) is about ten times of the condition(a). Fig.5c)shows the variable load operation of two different load range, it can be seen in the condition(e) which is not only much faster in rate of fatigue crack growth than the condition(d), but also higher in the initial fatigue crack growth rate. Fig.5d)shows the range of load changing fromthe500MW to 1000MW. Seen from that the fatigue crack growth rate is almost overlap compared with condition(b), and the initial fatigue crack growth rate are quite fast under overheating and overpressure. Thus, when the load is experienced from 500MW to 1000MW, the fatigue crack growth rate significantly increase. The smaller initial load is beneficial for lower initial rate of fatigue crack growth when the range of load is changed from200MW to 500MW.

0.1 1 1010-10

10-9

10-8

10-7

10-6

10-5

a) △K,MPa.m1/2

da/d

N,m

m/c

ycle

load(a)load(b)load(c)

0.1 1 1010-10

10-9

10-8

10-7

10-6

b) △K,MPa.m1/2

da/d

N,m

m/c

ycle

load(a)load(d)

0.1 1 1010-10

10-9

10-8

10-7

10-6

10-5

load(d) load(e)

c) △K,MPa.m1/2

da/d

N,m

m/c

ycle


0.1 1 1010-9

10-8

10-7

10-6

10-5

load(b) load(f) load(g)

d) △K,MPa.m1/2

da/d

N,m

m/c

ycle

Fig.5 Relationship between FCGR and SIFRΔ K under operation of different range of boiler load variation

In a general way, from the da/dN-ΔK curve and a-N curve, it was generally difficult to obtain the direct information on the three stages of the turning point of fatigue crack growth. Wang Pu et al. studied on the GH864 alloy crack inflection with a-lg(Ni/Nf) curve and da/dN-a curve, and this method was also applicable to other materials for fatigue crack growth analysis[21].To evaluate the turning point of crack propagation, a-lg(N) curve is studied in this paper. Fig.6 shows the a-lg(N) curve under different variable load operation. Seen from the Fig.6, a turning point in the a-lg(N) curve exists indifferent conditions, and the crack length a changes with the number of cycles beyond the turning point, fatigue crack growth rate accelerates rapidly. Under different conditions, the number of cycles to reach the same turning point is also different. The a-lg(N) curve shows mutations from plat that crack may be merged, so the turning point in a-lg(N) curve may be roughly defined as dividing point of crack initiation region to crack extension region. Table 5 gives the crack length a corresponding to the turning points that are estimated under the different operation conditions. According to Fig.6 and Table 5, the value of lg(N) to achieve the same crack length a is significantly different. The range of load variation is from 500MW to 1000MWin case ((b)、(c)、(e)、(f)、(g)).To achieve the same crack length a，it is faster than in case ((a)、(d))which the range of load variation is from 200MW to 500MW. Seen from the Table 5, the turning crack length (dividing of crack initiation region to crack extension region) under condition(a)is about 0.029mm.Compared with condition(d),w- hich indicates that when the range of load is changed from 200MW to 500MW, the turning crack length can be affected by the different of initial boiler load or average load. Under the load range of 200MW to 500MW,the big the initial boiler load, the faster the crack entering to crack extension region. See Fig.6d) and Table 5, comparison of condition(b), (f) and (g) shows that to achieve the same crack length a, the number of cycles under the condition(f) and (g) is less than under the condition(b), and the crack is advance about 0.016mminto the crack extension region under the condition(g).Meanwhile, to achieve the same crack length a, the number of cycles under the

condition(g)is less than under the condition(f).

0.0

0.4

0.8

1.2

1.6

107 108 109

Turning point

load(a)load(d)

a) lg(N)

a/m

m

0.0

0.4

0.8

1.2

1.6

105 106 107

Turning point

b) lg(N)a/

mm

load(b)load(c)

0.0

0.4

0.8

1.2

1.6

105 106 107

load(b)load(e)

c) lg(N)

a/m

m

Turning point

0.0

0.4

0.8

1.2

1.6

105 106 107

Turning point

d) lg(N)

a/m

m

load(b)load(f)load(g)

Fig.6 Relationship between crack length a and number of cycles lg(N)under operation of different range of boiler load variation


Table 5 a/mm value corresponding to the turning point of a-lg(N) curve

load (a) (b) (c) (d) a/mm 0.3 0.251 0.267 0.271

N/cycle 3.511e-9 1.174e-6 9.43e-5 1.08e-9 load (e) (f) (g)

a/mm 0.251 0.251 0.267 N/cycle 1.114e-6 9.567e-5 8.21e-5

As proposed by Luc R et al.[22], da/dN was a function of the crack length a, and there was a large corelation between the da/dN and crack length a, and the fatigue crack growth of independent of time can be used to describe by Tomkins model[23], which considered that the fatigue crack growth rate was proportional to the crack length a. Fig.7 shows da/dN-a curve under different variable load operation. As it can be seen from the Fig.7,the turning point is not obviously, but an arc segment of da/dN-a curve has existed in the different load condition, namely the "transition region". And at the left of the transition region, da/dN and crack length a has a good linear relationship. That is to say that the crack growth rate is proportional to the crack length a. According to Fig.7, the turning point of extension region to fracture region by selecting the mid-point of the "transition region" is showed in Table 6. As can be seen from the Fig.7d) and Table 6, the turning point under the condition(f) and (g) is advanced into the fracture region, but the fatigue crack growth rate under the condition(f)is faster than under the condition(g).

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.0

5.0x10-7

1.0x10-6

1.5x10-6

2.0x10-6

load(a)load(d)

Turning point

Transition region

a) a/mm

da/d

N/(m

m/c

ycle

)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.0

3.0x10-5

6.0x10-5

9.0x10-5

1.2x10-4

1.5x10-4

1.8x10-4

Turning pointTransition region

b) a/mm

da/d

N/(m

m/c

ycle

)

load(b)load(e)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.0

3.0x10-5

6.0x10-5

9.0x10-5

1.2x10-4

1.5x10-4

1.8x10-4

c) a/mm

da/d

N/(m

m/c

ycle

)

Turning point

Transition region

load(b)load(c)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.0

6.0x10-5

1.2x10-4

1.8x10-4

2.4x10-4

3.0x10-4

Turning point

Transition regionda/d

N/(m

m/c

ycle

)d) a/mm

load(f) load(g) load(b)

Fig.7 Relationship between da/dN and crack length a under operation of different range of boiler load variation

Table 6 a/mm value corresponding to the turning point of da/dN-a curve

load (a) (b) (c) (d) a/mm 2.37 2.29 2.44 2.37 da/dN

/ mm/cycle 3.732e-7 3.908e-5 2.963e-5 4.268e-7

load (e) (f) (g) a/mm 2.29 2.11 2.26 da/dN

/ mm/cycle 3.794e-5 2.814e-5 3.686e-5

1) When the crack length a is 0.5mm, SIFK accelerates as the

boiler load is about 500MW,and then turns to constant at about 800MW.

2) The SIFRΔK is much more influenced by the load variety amplitude, overpressure or overheating.

3) The fatigue crack growth rate increases with the increase of load variety amplitude, overheating or overpressure. But under the range of load changing from 200MW to 500MW, the small initial load can reduce the initial rate of fatigue crack growth.

4) To achieve the same crack length a, the range of load changing from 200MW to1000MW or from 500MW to 1000MW, including the condition of overpressure and overheating, are much faster than the range of load changing from 200MW to 500MW. However, the influence of overpressure and overheating(500MW t0 1000MW) is


greater than the load variety amplitude(200MW to 1000MW).

5) The turning points which crack turns from initiation region to extension region, is much more influenced by the load variety amplitude, overpressure or overheating, but the influence of overheating is much larger; and the crack is from crack extension region to fracture region, which is much more influenced by overpressure or overheating, and the influence of overpressure is much larger.

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numerical research on crack growth behavior in

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