Damage Analysis Of Welded Joints

Damage Analysis of Welded Joints

OMMI (Vol.3, Issue 3) December 2004 www.ommi.co.uk

MICROSCOPIC DAMAGE ANALYSIS OF WELDED JOINTS UNDER TYPE III AND TYPE IV CREEP FAILURE T.Igari1, F.Kawashima1, T.Tokiyoshi1, N.Nishimura and N.Tada2 1. Nagasaki R&D Center, Mitsubishi Heavy Industries, Ltd., Fukahori-machi 5-717-1, Nagasaki 851-0392, Japan 2. Faculty of Engineering, Okayama University, Tsushima-naka 3-1-1, Okayama 700-8530, Japan

Abstract The progress of microscopic damage in the grain boundaries of coarse-grain and fine-grain HAZs in welded joints of 2.25Cr-1Mo steel under creep, so-called Type III and Type IV creep damage respectively, was numerically simulated by combining a random fracture resistance model and the stress distribution under steady state creep. The randomness of both the grain size and the resistance of grain boundaries were considered for reproducing the gradual increase in the number density of creep cavities. The damage on the observable surface and that on the final failure surface were correlated for the prediction of the final failure time, on the basis of the effective section area of the welded joints. The proposed simulation method was applied to creep tests on welded joints and the creep burst test of an elbow subjected to internal pressure. Both the distribution of the number density of cavities and the final failure time were successfully reproduced. KEY WORDS: Type III, Type IV, creep damage, welding, 2.25Cr-1Mo steel, high-energy piping, numerical simulation, small defect, creep cavity.

1.

Introduction

Quantitative evaluation of creep damage is required in the heat-affected zones (HAZs) of welds in the main steam and reheat piping of fossil power boilers subject to internal pressure over a long duration [1]. Damage in the coarse-grain HAZ (Type III), and the fine-grain HAZ (Type IV), compose the main focus, with the latter, Type IV damage, being more important as the maximum damage occurs not on the surface but subsurface on piping. Figure 1 schematically illustrates the relationship between the number density of small defects and the creep-rupture time fraction, together with the progression of microscopic damage in the coarse-grain HAZ (CGHAZ hereafter) and the fine-grain HAZ (FGHAZ hereafter) at prescribed creep-rupture time fractions of 50%, 60% and 75%. In the Type IV damage mode, cavities or small defects with an average size of 10.5 µ m (the same size as the grain) initiate and coalesce together. In the Type III damage mode, on the other hand, cavities or small defects with an average size of 4 µ m initiate and coalesce on the boundary of grains with an average size of 50~200 µ m. In the final stage of creep rupture life, these defects grow into small cracks or crack-like defects, with a length of 0.1mm~1mm, throughout the wall thickness of the piping, and can lead to final failure of piping having a thickness of up to 100mm. Type III and Type IV damage, e.g. multi-site creep damage, is basically “initiation

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type”. However, it also has the characteristics of “growth type” in the final stage of creep life as the growth of crack-like defects, in the high stress region of the weld thickness, governs the final failure life of the piping. There are several approaches to Type III and Type IV creep damage, such as continuum mechanics employed with a stress-based time fraction or a ductility fraction for the material [2], damage mechanics on the basis of the effective stress reflecting the damage parameter[3], creep fracture mechanics using the C* parameter[4-7], and creep void mechanics assuming diffusion[8]. There is no method currently available, however, which can simulate both microscopic damage, such as the initiation and coalescence of the cavities, and the progress of macroscopic damage, such as the distribution of the cavities or the growth of the crack-like defects in the welded joints with stress redistribution. In this paper, the microscopic damage progression in the grain boundaries of CGHAZ and FGHAZ in the welded joints of 2.25Cr-1Mo steel under creep is numerically simulated, by combining the random fracture resistance model and the stress distribution under steady state creep. The randomness of both the grain size and the resistance of grain boundaries are considered to reproduce the gradual increase of the number density of creep cavities in the heat affected zone. A scheme, to correlate the number density of small defects on the observable surface with that on the final failure surface, is proposed for predicting the final failure life. The proposed simulation method is applied to the creep testing of welded joints and the creep burst test of an elbow subjected to internal pressure. The ability to simulate the distribution of the number density of cavities and the final failure time is discussed.

2.

Random Fracture Resistance Modeling for Low Alloy Steel

Taking a microscopic view of the creep damage of low alloy steel HAZ in Figure 1, each grain has a different size and only a few grain boundaries are characterized by small defects under the same macroscopic stress. This fact suggests the randomness of both the grain size and the fracture resistance of the grain boundaries. The random fracture resistance modeling of FGHAZ was already discussed by the authors for reproducing the gradual increase of the number density of creep cavities in the Type IV damage mode [9,10]. Here the random fracture resistance modeling of the Type III damage is discussed. Figure 2 shows a microstructure of FGHAZ and CGHAZ subject to tensile stress and the scheme of the random fracture resistance modeling. The hypothetical grain boundary line resulting in final failure is shown in the figure as a bold line. In this paper, the one-dimensional grain boundary line is considered as a projection of the two-dimensional grain boundary line for the purposes of simulation. One grain boundary, with an average size 10.5 µ m, is the unit for small defects in FGHAZ, and one cell, with an average size of 4 µ m on the grain boundary, is the unit of the small defects in CGHAZ. Taking FGHAZ as an example, each grain boundary on the line has a different length L and a different initial value of fracture resistance R0, which are probabilistically distributed, depending on the characteristics of the material. In the course of a creep process for t hours, the initial value of R0, for each grain boundary and facet, is decreased by a small defect initiation-driving force F, resulting in the fracture resistance in eq.(1):

Damage Analysis of Welded Joints

R = R0 – F t

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(1)

or the decreasing rate in eq.(2): dR/dt = - F

(2)

When the fracture resistance of a grain boundary becomes zero, the grain boundary becomes a small defect with a size of a, as shown in Figure 2(b). This defect increases the driving force in the neighbouring grain boundaries from F to (F+Ka), resulting in the increased rate in eq.(3): dR/dt = - (F+Ka)

(3)

where Ka is a small defect growth-driving force and K is a coefficient. In this paper, the initiation of small defects and the subsequent growth due to diffusion is modeled by the initiation-driving force F, and the growth of small defects after their size becomes large enough to be subject to fracture mechanics is modeled as Ka. The parameters to be determined in the random fracture resistance modeling of FGHAZ are as follows: (a) the distribution of the grain boundary length [L]; (b) the distribution of the initial value of fracture resistance [R0]; (c) the small defect initiation driving force F; and (d) the coefficient K of the small defect growth driving force. In the case of CGHAZ, the same modeling as FGHAZ is considered by using the grain boundary facet of the CGHAZ instead of the grain boundary in FGHAZ. The procedure for determining these parameters for FGHAZ on the basis of the test data and field data was discussed by the authors in the related paper [9,10]. A similar procedure was also applied to the CGHAZ, and the list of test data for determining the parameters for FGHAZ and CGHAZ is summarized in the related paper [9]. The results of parameter identification for FGHAZ are summarized as follows: the distribution of the grain boundary length [L] was determined as the normal distribution with a mean value of 10.5µm and a standard deviation of 5µm, on the basis of the microscopic observation of the FGHAZ; the distribution of the initial value of fracture resistance [R0] with a mean value of 0.5 and a standard deviation of 0.1607 was determined as shown in Figure 3(a) on the basis of the time history of the number density of small defects at the specific location of FGHAZ in the creep test of welded joint. The stress dependence of F, shown in Figure 3(b), was determined through a combination of the distribution [R0] and the microscopic observation of a point with a prescribed stress. K, as shown in Figure 3(c), was determined basically using the creep crack growth data of FGHAZ. The results of parameter identification for CGHAZ, on the other hand, are summarized as follows: the length of grain boundary was set as 50~200µm depending on the basis of the microscopic observation of the CGHAZ; the distribution of the initial value of fracture resistance [R0], with a mean value of 0.5 and a standard deviation of 0.1309, was rather flat when compared with FGHAZ, as shown in Figure 3(a). The stress dependence of F for CGHAZ was almost the same as for FGHAZ, as shown in Figure 3(b). K for CGHAZ was about twice that of FGHAZ, as shown in Figure 3(c).

3.

Methodology for Combined Micro-Macro Creep Damage Analysis

A methodology for the simulation of microscopic creep damage progress in welded joints is summarized in Figure 4. Firstly the piping configuration is prepared, including inner and

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outer radius, welding groove and unevenness of the bead line. The elastic modulus and the creep strain rates of parent metal, weld metal, FGHAZ and CGHAZ are prepared, in order to obtain the stress distribution of the FGHAZ and CGHAZ through elastic-creep analysis of the welded joints. In the example in the next section, the length of a FEM element in a thickness of 40mm is taken as 1mm. Secondly one-dimensional grain boundary line is prepared on the basis of the random fracture resistance modeling through the wall thickness of FGHAZ and CGHAZ. The length of the grain boundaries for FGHAZ obeys the distribution [L], and the grain boundaries of CGHAZ are divided into cells with the length of 4µm. In one layer of FEM elements of the FGHAZ and CGHAZ through the wall thickness, thirty lines with a different initial resistance are prepared from the outer to the inner surface, for simulating the damage on the surface parallel to the stress axis. Thirdly the creep damage progress in each grain boundary/cell is calculated on the basis of the initial value of the fracture resistance and the initiation/growth-driving force, depending on the stress from FEM elastic-creep analysis. Simulation results give the time history of the number density of small defects, i.e. the progress of creep damage in the welded joint. The other viewpoint is the prediction of final failure time of the welded joints. Figure 5 shows the microstructure of CGHAZ, and shows the relation of stress axis and damage for several sectional surfaces. The surface A, B and C are respectively parallel surface, perpendicular surface to the stress axis and the projected surface from the final failure surface. The damage on the surface C can be larger than that on the sections parallel to, or perpendicular to, the stress axis, and this damage on surface C is considered to govern the final failure time. The number density of small defects on the one-dimensional line, η, was correlated to the damage on the surface A and C, on the basis of the simple rectangular crystal shape model as follows: FGHAZ : Damage on surface A: NA(x)= η(x) / (Lm)2, Damage on surface C: ω (x)= η(x), CGHAZ : Damage on surface A: NA(x)= η(x) / (c Lm) , Damage on surface C: ω (x)= η(x), where x, N, ω, Lm and c are respectively the coordinate in the thickness direction, the number density of small defects on the surface, the area fraction of small defects on the final failure surface, the average length of grain boundary and the average length of cell of CGHAZ, i.e. 4µm. The final failure surface is determined by joining the FEM elements with the maximum damage at each depth level x from the outer surface.

4.

Simulation Results of Welded Joints

4.1 Simulation of welded joint model test Figure 4 also shows both the configuration of the test specimen, with a rectangular section of 40mm x 40mm, and the FEM model, from which steady state stress under nominal stress of 392MPa at 898K was obtained under the plane stress condition using the SENSOR/NSAS code and eight-node elements. The reason for using the plane stress condition is to compare the prediction of the number density of small defects with the microscopic observation on the surface of the welded joint in Figure 4. There are two layers in the CGHAZ and five layers in the FGHAZ, respectively. The elastic stress in each material is the same, due to the common value of Young’s modulus, but the difference in the creep strain rate in each material causes

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stress redistribution in the structure in the course of creep. The redistribution of the equivalent creep strain by von Mises across the weld metal, CGHAZ, FGHAZ and parent metal is shown in Figure 6, where the creep strain in the FGHAZ, especially that in the element next to the base metal, showed the largest creep strain. The steady state stress distribution along the fine-grain HAZ line AB after 2000h at 898K is shown in Figure 7. Two kinds of stress, maximum principal stress and von Mises equivalent stress, are shown in the figure, in which the latter stress gives a flat distribution, and the former maximum principal stress in the wall thickness is higher than those of the surfaces. Discussion concerning the dominating stress in Type IV creep damage is ongoing, and experimental verification of multi-axial creep damage is still being conducted [11]. The maximum principal stress was adopted here because the higher damage in the subsurface than on the surfaces was well explained. The distribution of the number density of small defects through the wall thickness from the simulation is shown in Figure 7, at 3340h, 5840h and 8345h (rupture time) following the start of the creep test. The results from simulation consist of the average value of the thirty grain-boundary lines. The subsurface locations exhibit higher values of number density for small defects, and peak values increase over time. The time history of the number density of small defects from the simulation at point C in Figure 6 is shown in Figure 8, together with the observed results. In this figure, the microscopic views of the simulated result of small defects at 4800h and 6400h are displayed together with the results observed by microscope. Both the time history of the number density of small defects and the microscopic view from the simulation agree well with the observed results. The prediction of final failure time was performed, following the process shown above and determining the final failure surface. In this case, the generalized plane strain condition was used instead of the plane stress model used in the previous discussion. The bold line in Figure 9 shows the element in HAZ having the maximum damage at each depth level from the surface, and the final failure surface is the hypothetical surface linking these elements. Figure 10 depicts the distribution of the damage ω through the wall thickness, where ω considers the area fraction of the small defects on the final failure surface. The distribution of ω along the neighbouring FGHAZ and CGHAZ line through the wall thickness is also shown in the figure. The predicted final failure surface in the figure consists of FGHAZ, and this corresponds to the observation in the experiment. The effective stress in eq.(4) is given in Figure 11, showing the gradual increase due to the damage increase.

σeff = σσ/(1 - ω)

(4)

Through comparing σeff with the flow stress of the material, (σy + σB)/2, the final failure time almost coincided with the actual failure time 8345h. 4.2 Simulation of Actual Power-Piping Elbow In the related paper [9,10], the microscopic creep damage simulation was applied to the Type IV damage of a power-piping elbow in Plant B, having experienced 150,000h of operation under internal pressure of 17.4MPa at 848K. This elbow was made of 2.25Cr-1Mo steel, and had an outer diameter of 508mm, a thickness of 108mm and a longitudinal weld at the intrados. Microscopic inspection at the FGHAZ was carried out after this elbow was removed.

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Elastic-creep FEM analysis was also carried out, modeling a fourth of the pipe section as the generalized plane strain condition, and by considering the uneven bead line and the difference of creep rate of the four materials as indicated previously. Figure 12 shows photographs of the thickness section and the FEM mesh division with the same number of layers of the CGHAZ and the FGHAZ as the model in Figure 4. The steady state stress distribution from elastic-creep analysis and the distribution of the number density of small defects through the wall thickness of 108mm are also depicted in the figure. Simulation of the microscopic creep damage on the basis of the method in Sec.3 was carried out by setting the 30 lines of the one dimensional grain boundary in the FEM elements of the FGHAZ line DE in the figure. As shown in the figure, the distribution of the number density of small defects from the simulation agreed well with those from observation. The cause of discrepancy between simulation and observation in the subsurface thickness is considered as the scatter of observed results. The other example of application to the combined Type III and Type IV damage is the creep burst test of a thin-walled re-heater elbow that was taken out from the plant A [12], which was operated at 841K for 130,000h and tested at 923K under the same internal pressure as the actual operation. The similar FEM analysis was carried out following the actual operation and testing. The time history of the number density of small defects on the outer surface of the piping during the test was simulated and was compared with the observed results in Figure 13. Simulated results almost corresponded with the observed results in both FGHAZ and CGHAZ. The final failure surface consisted of the combined FGHAZ and CGHAZ, and this tendency corresponded well with the actual observation. The predicted final failure time in the test is 3200h and the actual failure time was 3000h. The combination of the simulation and the strength of material can be a potential tool for predicting the failure time of welded joints. Another perspective would be a method to predict damage in actual operating piping, where the precise observation of creep damage in the wall thickness is not obtained. The authors are thinking of installing the proposed simulation method in the risk-based-maintenance system [13] on the basis of the probabilistic treatment of material properties and loading conditions such as operated temperature and pressure.

5.

Concluding Remarks

A simulation method for multi-site creep damage in the FGHAZ and CGHAZ of welds involving low alloy steel was proposed on the basis of combining elastic-creep FEM analysis and random fracture resistance modeling of the material. The results obtained are summarized as follows: (1) Micro-macro damage simulation in this paper could predict the time history and distribution of small defects in Type III and Type IV creep failure. (2) The combination of the micro-macro damage simulation and the strength of material, such as flow stress, can be a potential tool for predicting the final failure time of welded joints.

References

Damage Analysis of Welded Joints

1. 2.

3. 4. 5. 6.

7.

8. 9.

10.

11.

12.

13.

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Ellis, F.V. and Viswanathan, R., Review of Type IV Cracking in Piping Welds. ASME-PVP 380 (1998), pp.59-76. Yamauchi, M., Tokiyoshi, T., Chuman, Y., Nishimura, N. and Iwamoto, T., Creep Damage Evaluation Procedure of Weldments in High-Energy Piping. EPRI/DOE Conference on Advances in Life Assessment and Optimization of Fossil Power Plants. March 11-13, (2002). Hyde, T.H., Sun, W. and Williams, J.A., Creep Analysis of Pressurized Circumferential Pipe Weldments - A Review, J. Strain Analysis, Vol.38, No.1 (2003), pp.1-29. Webster, G.A. and Ainsworth, R.A., High Temperature Component Life Assessment, (1994), Chapman & Hall. Yatomi, M., Nikbin, K.M. and O’Dowd, N.P., Creep Crack Growth Prediction Using a Damage Based Approach, Int. J. Press. Vessels and Piping Vol.80, (2003), pp.573-583. Segle, P., Andersson, P. and Samuelson, L.A., Numerical Investigation of Creep Crack Growth in Cross-Weld CT specimens. Part I: Influence of Mismatch in Creep Deformation Properties and Notch Tip Location, Fatigue Fract. Engng. Mater. Struct., Vol.23(2000), pp.521-531. Tu, Shan-Tung, Interaction Behavior between Material Boundary and Crack Tip at High Temperature, Proc. 4th Japan-China Bilateral Symposium on High Temperature Strength of Materials, June 11-13, Tsukuba (2001), pp.111-118. Rice, J.R., Constraints on the Diffusive Cavitation of Isolated Grain Boundary Facets, Acta Metall., Vol.29, No.4, (1981), pp. 675-681. 9. Kawashima, F., Tokiyoshi, T., Igari, T., Shiibashi, A. and Tada, N., A Proposal on Creep Damage Analysis of Welded Joint of Low-Alloy Steel Considering Microscopic Damage Progress. J. Soc. of Mater. Sci., Japan, (in Japanese), Vol.52, No.6, (2003), pp.631-638. 10. Kawashima, F., Igari, T., Tokiyoshi, T., Shiibashi, A. and Tada, N., Micro-Macro Combined Simulation of the Damage Progress in Low-Alloy Steel Welds Subject to Type IV Creep Failure, To be published in JSME Int. Journal Ser. A, Vol.47 No.3 (2004). 11. Sakane, M. and Hosokawa, T., Biaxial and Triaxial Creep Testing of Type 304 Stainless Steel at 923K, IUTAM Symposium on Creep in Structures, Kluwer Academic Publishers, (2001), pp.411-418. 12. Nishida, H., Yukami, T., Watanabe, H., Yamauchi, M.,Tokiyoshi, T. and Fujita, M., Experimental Study of the Creep Burst Mechanism on Seam-Welded High-Energy Piping at Elevated Temperature, Trans. Japan Soc. Mech. Eng. (in Japanese), Vol66 No.645, A(2000)pp946-953. 13. Watanabe, D., Chuman, Y., Nishimura, N., Matsumoto, H., Tominaga, K., Sakata, F., Kuroishi, T., Development of the Risk-Based Maintenance Optimization System for Fossil Power Plants, To be presented at Fifth China-Japan Bilateral Symposium on High Temperature Strength of Materials, Xi’an, China, August 16-21, (2004)

Damage Analysis of Welded Joints

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Number density of small defects (/mm2)

75%

50% 60%

Stress

Fine grain

10.5µm Coarse grain

0

100 Time/Rapture Time (%)

50∼200µm 50%

Fig.1:

4µm 60%

75%

Schematic view of damage progress

Stress

Small defects

Small defects

Observed surface Grain boundary model Simulation model

Initial

R dR dt

F+K F

(a) Coarse grain

Fig.2:

Initial

R dR dt

F+K F

(b) Fine grain

Random fracture resistance model

8

Damage Analysis of Welded Joints

Mean

Standard deviation

Coarse

0.5

0.1309

Fine

0.5

0.1607

Stress (M Pa)

30 20

10

1

Coarse ○：Conventional (φ6, □6) △：Plant A Fine ●：Model test (□20, □40) ▲▼：Plant A ■◆：Plant B

10 0

0 0.2 0.4 0.6 0.8 1 Fracture resistance of grain boundaries R o

10 0 17 .0

(a) Fracture resistance [R0]

17 .5 18 .0 18 .5 PLM=T{15.6-log10(F)}/1000

10

-2

923K

843K

Fine

10

-3

10

-4

10

-5

10

1

10 Stress (MPa)

(b) Small defect initiation driving force F Fig.3:

(c) Small defect growth driving force K

Identified material constants

Macro (FEM)

Micro

A

FGHAZ

CGHAZ

C

10.5μm

FEM moment 1mm

40mm

Parent metal

Cell 4μm

B

Weld metal HAZ

CG FG HAZ HAZ

Fig.4:

Outline of simulation model

Final fracture Final failure Cross section surface

Stress

C : Projected surface

A

Fig.5:

9

Coarse

19 .0

50μm∼200μm

Relative frequency (%)

Symbol

Small defect growth driving force K

10 2

50 40

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Observable surface and final failure surface

2

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12 W eld M etal

Equivalent Creep Strain (%)

10

1.75mm

CG HAZ

FG HAZ

Parent Metal

0.5mm

2.81mm

1.05mm

Point C

8 6

D

Fig.6:

Distribution of equivalent creep strain along line DE

Fig.7:

Simulated results of welded joint test specimen

E

4 2 0

3340hr 5840hr 40

40

Height (mm )

35 30

30

25

25

20 15 Principal

10

8345hr

35

C Height (mm )

A

E

D

C

20 15 10 5

5 Mises 0

0

5 Stress (MPa)

Number density of small crack (1/mm2)

B

0 0 2000 4000 6000 Number density of small defects (1/mm2 )

9000

○ M easured ● Simulated

(6400hr)

6000

3000 Rupture

0 0

Fig.8:

(4800hr)

0.1mm 4000 Time (hr)

8000

Observed

Simulation

Simulated results of number density of small defects (Point C)

Damage Analysis of Welded Joints

Weld M etal

H AZ

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Parent M etal

Distance from inner surface (mm)

A C

40

30

Effective stress of final failure surface (MPa)

Final failure surface of model test

20

Coarse1

15 10 5 0

Fig.10:

0 0.2 0.4 0.6 0.8 1 1.2 Area fraction of defects ω

ω distribution of model test

250 200 150 100 50 3

0 0

Fig.11:

Fine5

25

B

Fig.9:

Final failure surface

35

2

4 6 Time (hr)

8

×10 10

Effective stress of final failure surface of model test

11

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Weld metal HAZ Parent metal

0D

0D

Length from outer surface(mm)

D

Length from outer surface(mm)

D

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E

E

Section view

E

FEM model

2

Number density of small defects (1/mm)

Fig.12:

3

0

20 40 60 80 100

●■ Measured ○  Simulated

700 20 30 2 E0 Number density of cavity (1/mm ) 2 ss (MPa) Stress (MPa) Number density of small defects (1/mm )

10

Simulation results of plant B

×103 Simulation Observation Coarse1 □ Coarse △ Fine5 ● Fine ▲

2

1

0

0

1

2

×103

3

Time (hr)

Fig.13:

Number density of small defects on outer surface of Plant A

12