Scholarly article on topic 'Numerical Study on Creep Rupture Behavior of SA533B Low-Alloy Steel'

Numerical Study on Creep Rupture Behavior of SA533B Low-Alloy Steel Academic research paper on "Materials engineering"

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{"Creep Relationships" / "Finite Element Method" / "High-temperature Behavior" / "Larson-Miller Parameter" / "Low-alloy Steel."}

Abstract of research paper on Materials engineering, author of scientific article — T.H. Kim, Y.-S. Chang

Abstract Time-dependent loads may significantly affect on structural integrity of RPV (Reactor Pressure Vessel) under severe accident conditions respecting to the core melting. Especially, creep rupture at the high-temperature should be regarded as an important phenomenon to cope with failure of the RPV lower plenum. In this paper, creep behavior of SA533B as a typical reactor material was assessed based on several creep relationships such as Bailey-Norton's power law, MGR (Monkman-Grant Relationship) and MMGR (Modified Monkman-Grant Relationship). Creep rupture test data were referred from experimental projects of OECD/NEA. Subsequently, corresponding parametric FE (Finite Element) analyses were carried out for various temperature and loading conditions, of which results were used to establish an enhanced creep rupture evaluation method combined with the well-known LMP (Larson-Miller Parameter) of the low-alloy steel.

Academic research paper on topic "Numerical Study on Creep Rupture Behavior of SA533B Low-Alloy Steel"

Available online at www.sciencedirect.com

ScienceDirect Procedia

Engineering

Procedia Engineering 130 (2015) 1755 - 1760 ;

www.elsevier.com/locate/proeedia

14th International Conference on Pressure Vessel Technology

Numerical Study on Creep Rupture Behavior of SA533B Low-

Alloy Steel

T.H. Kima, Y.-S. Chang3*

aDepartment of Nuclear Engineering, Kyung Hee University, 1732 Deokyeong-daero, Yongin-si, Gyeonggi-do 446-701, Republic of Korea

Abstract

Time-dependent loads may significantly affect on structural integrity of RPV (Reactor Pressure Vessel) under severe accident conditions respecting to the core melting. Especially, creep rupture at the high-temperature should be regarded as an important phenomenon to cope with failure of the RPV lower plenum. In this paper, creep behavior of SA533B as a typical reactor material was assessed based on several creep relationships such as Bailey-Norton's power law, MGR (Monkman-Grant Relationship) and MMGR (Modified Monkman-Grant Relationship). Creep rupture test data were referred from experimental projects of OECD/NEA. Subsequently, corresponding parametric FE (Finite Element) analyses were carried out for various temperature and loading conditions, of which results were used to establish an enhanced creep rupture evaluation method combined with the well-known LMP (Larson-Miller Parameter) of the low-alloy steel.

©2015 The Authors.PublishedbyElsevierLtd. Thisis an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of ICPVT-14

Keywords: Creep Relationships; Finite Element Method; High-temperature Behavior; Larson-Miller Parameter; Low-alloy Steel.

CrossMar]

1. Introduction

After the Fukusima nuclear power plant accident, failure of reactor vessel became a practical threat and necessity of more precise structural analysis increased. Among many severe accident strategies, the IVR-ERVC (In-Vessel Retention-External Reactor Vessel Cooling) has been considered as an effective one and several relevant analyses were performed [1]. However, there are uncertainties in high-temperature behavior, material properties, thermal loads, damage evaluations and so on as ever.

* Corresponding author. Tel.: +82-31-201-3323; fax: +82-31-204-8114. E-mail address: yschang@khu.ac.kr

1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of ICPVT-14

doi:10.1016/j.proeng.2015.12.205

LMP (Larson-Miller Parameter), which representatively used for damage evaluation, is very sensitive material-dependent parameter. It can be derived from various extreme conditions while lots of efforts are required. In the present study, with regard to accelerated testing [2], three creep relationships such as Bailey-Norton's power law, MGR (Monkman-Grant Relationship) and MMGR (Modified Monkman-Grant Relationship) are examined. Creep rupture test data are referred from experimental projects of OECD/NEA [3] and used in FE (Finite Element) analyses by general-purpose commercial program, ABAQUS [4], with user-subroutine CREEP. Finally, the LMP correlation of SA533B low-alloy steel is enhanced by comparing experimental and FE analysis data in the conservative perspective of structural safety.

2. Brief review of three relationships

2.1. Creep curves of SA533B low-alloy steel

Characterization of precise material property is the key in modeling and simulations. For this purpose, several creep properties of SA533B low-alloy steel are evaluated through a series of creep tests at SNL (Sandia National Laboratory) and CEA (Commission Energy Atomic) [3]. Among these test results, nine cases of constant load creep test data were selectively referred in data correlations by considering balanced test conditions and data availability. Table 1 summarizes creep test data that were obtained from different temperature and stress conditions [3]. Case numbers. 1 ~ 3 were conducted in SNL and curve numbers. 4 ~ 9 were conducted in CEA, respectively. Resulting creep curves can be decomposed into unclear or very short primary creep stage, well distinct secondary creep stage and accelerate tertiary creep stage in general.

Table 1. Creep test conditions.

Case no. Temperature(K) Minimum creep rate(h-l) Applied load(kN) Rupture time(h)

1 975 0.586 5.64 0.33

2 975 0.433 5.79 0.3

3 975 0.692 5.79 0.309

4 975(977) 0.094 13.70 0.83

5 975(963) 0.005 7.10 20.11

6 1,260(1,260) 0.097 4.20 2.76

7 1,260(1,263) 0.035 3.30 8.13

8 1,260(1,258) 0.204 4.20 1.21

9 1,260(1,266) 0.071 3.30 3.51

0 means actual temperature.

2.2. Bailey-Norton's power law

Bailey-Norton's power law is one of traditional approaches to correlating creep, which can be represented by

where, A(T) is a hypersensitive function of temperature, a is initial stress, t is time and exponent « is a constant to indicate the secondary creep rate or minimum creep rate.

s is obtained from experimental data by fitting an extension line of secondary creep stage. Here, the rupture time is also expressed to stress dependence of the power law form, as follows:

tr = A'(T )am (3)

tr is rupture time of creep specimen. Subsequently, by fitting trend line of experimental data, constants of power law form is determined as Table 2.

Table 2. Material constants from stress dependent power law form of SA533B creep test.

Temperature(K) A m A' m'

975 4.0E-12 5.642 2.00E+8 -5.017

1,260 1.0E-07 4.381 3.00E+6 -4.536

2.3. Monkman-Grant Relationship and Modified Monkman-Grant Relationship

MGR is a relationship between secondary or minimum creep strain rate, ¿s and rupture time, tr [5, 6].

s'm • t = C

cs V ^MGR

m log £s + logtr = log CMGR

MGR is known to be valid for most of the materials. However, modified relationship between creep strain rate and rupture time was proposed by Dobes and Milicka who considered the failure strain, sr [5, 6].

s m ■ t Is = C

cs v/cr MMGR

• (5)

mlog £ s + log (tr/ £r)

— logCMMGR

This relationship is called as MMGR, in which the constant C is independent of stress and temperature. Data scattering decreased in MMGR plot than MGR plot and also a coefficient of MMGR trend line (m'=0.97) follows more elaborately than that ofMGR (m=0.928) regardless of the temperature difference.

3. Numerical analysis of creep specimen

3.1. Analysis model and condition

Two types of creep test specimens adopted by SNL and CEA were considered because their geometrical details were somewhat different from each other. The SNL specimens were generated in accord with global standard [7], however, the CEA specimens were 30% larger approximately while almost geometries were proportional to the standard ones. By taking into account asymmetric conditions of the specimen, axi-symmetric models were constructed. Element type of CAX4R (A 4-node bilinear axisymmetric quadrilateral element) was employed in a general-purpose commercial program element library [4]. The numbers of elements and nodes of SNL FE meshes were 2,101 and 2,291, and those of CEA FE meshes were 5,690 and 6,020 respectively. As boundary conditions, the upper face of the FE model was fixed along the Z-direction, and a side point was pinned to the all directions. Material properties of the SA533B low-alloy steel are delineated in Fig. 1 [3].

-*-Youig's modulus -B-Yield strength

Thermal expansion coefficient

800 t.000 t.200 Temperature (K)

1,000 1,200 1,400 1,600

Temperature (K)

Fig. 1. (a) Mechanical properties; (b) Thermal properties of SA533B low-alloy steel.

3.2. Analysis method

Initial temperature conditions were predefined by a field option during the whole procedure. Constant load conditions were applied as STATIC - GENERAL step and practical creep effect was incorporated into VISCO step. In the VISCO step, steady-state loads were applied by considering constant-load condition. With regard to the creep constitutive law, time-dependent user-subroutine, CREEP was adopted to follow each creep curve reasonably.

Creep constants which were used in the user-subroutine are arranged in Table 3. As discussed previously, most of creep curves indicate unclear or very short primary creep stage, well distinct secondary creep curve and accelerate tertiary creep.

e = A^f + A^a1"2 tn

Therefore, accurate application of creep constitutive models for FE analysis which represent the entire creep curves are available.

Table 3. Constants of creep constitutive model.

Case no. Creep constants Ai ni mi A2 n2 m2

1 1.00E-06 1.16 1.00 9.00E-21 1.00E-06 6.390

2 1.90E-07 1.50 1.00 1.00E-20 1.30 5.605

3 2.30E-07 1.50 1.00 2.00E-18 0.50 5.370

4 7.00E-06 0.35 1.00 1.00E-45 0.50 12.445

5 1.00E-10 2.66 1.00 1.00E-90 1.30 17.975

6 3,00E-07 1.49 1.00 1.00E-80 0.01 19.835

7 1.00E-08 2.45 1.00 1.00E-90 3.00 16.900

8 2.30E-07 1.76 1.00 1.00E-28 1.50 6.922

9 1.50E-07 1.69 1.00 5.00E-30 0.23 6.880

3.3. Analysis results

Experimental data and FE analysis results were compared, and failure criteria was determined based on the failure strain obtained from experiments. Fig. 2 (a) ~ (i) shows the results of total nine analysis cases in plot of time and creep strain. All ofthe FE analysis results predicted the rupture time more conservatively than experimental data about 0.4 ~ 19.7%. As comparing these results and creep relationships in terms of rupture time, FE analysis shows

more reasonable results than creep relationships because not only secondary creep stage but also tertiary creep stage is considered in FE analysis by the user-subroutine while only secondary creep stage of creep relationships.

Generally, all of the FE analysis results follow the experimental creep curves up to secondary creep stage, however, slightly different in the tertiary creep stage. Because most of the differences started with a vicinity of a boundary between secondary and tertiary creep stage, the analytic differences according to consideration of necking of specimen is judged to be occurred.

Fig. 2. (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4; (e) Case 5; (f) Case 6; (g) Case 7; (h) Case 8; (i) Case 9 of FE analysis results. 4. Enhancement of damage evaluation method 4.1. Fundamentals of LMP

LMP models have been widely and preferentially used for creep damage evaluation in the nuclear industry. Typically, LMP is expressed as temperature and stress dependent form, as follows [1]:

LMP = T (C + log (tr)) (7)

log cr = A - B (LMP) (8)

where, T is the applied temperature (K), tr is rupture time, ct is initial stress and C is the material constant which calculated from a lot of constant stress creep tests.

4.2. Modification of LMP

For the damage evaluation, LMP was fitted with Eqs. (7) and (8). Because of limitation in data, constant C was referred as 16.238 and 10.598 according to the temperature field of under 1,050K and over 1,050K [2]. 1,050K is empirically determined as transition temperature of SA533B low-alloy steel [2]. However, fitting line of Eq. (7) which expressed as LMP-calculation differed from that of Eq. (8) which expressed as LMP-prediction and this difference was caused by LMP constants A and B.

Thereby, the LMP constants A and B are modified as A: 5.74 (from the previous value of 5.9121 for under 1,050K), A'\ 3.7 (from the previous value of 4.1849 for exceeding 1,050 K) andB': 1.70E-04 (from the previous value of 2.1165E-04 for exceeding 1,050 K). Thereby, differences between two fitting lines were absolutely eliminated by modifying LMP constants.

5. Conclusions

In this study, creep rupture test data of SA533B low-alloy steel were assessed based on several creep relationships and employed in FE analyses. The results were also used to enhance creep rupture evaluation method, from which the following conclusions were made.

(1) Existing LMP correlations of SA533B was enhanced based on FE analyses. While the differences with experimental data were ranged from 0.4% up to 19.7%, it will be reduced to reasonable if the appropriate analytical considerations are achieved.

(2) Provided a series of creep rupture tests of certain material are conducted, creep rupture evaluation with LMP correlation could be available for other reactor vessels made of different materials.

References

[1] T. H. Kim, S. H. Kim and Y. S. Chang, Structural assessment of reactor pressure vessel under multi-layered corium formation conditions, Nuclear Engineering and Technology 47 (2015) 351-361

[2] M. E. Kassner, Fundamentals ofcreep in metals and alloys 3rd edition 2015.

[3] L. L. Humphries et al., OECD Lower head failure project final report, Vol. 1 - integral experiments and material characterization (2002)

[4] ABAQUS user's manual, Ver. 6-13.1, Dassault systems (2013)

[5] C. Phaniraj, B. K. Choudhary, K. Bhanu Sankara Rao and B. Raj, Relationship between time to reach Monkman-Grant ductility and rupture life, Scripta Materialia 48 (2003) 1313-1318

[6] W. G. Kim, J. Y. Park, I. M. W. Ekaputra and M. H. Kim, Analysis ofcreep behavior of alloy 617 for use of VHTR system, Procedia Materials Science 3 (2014) 1285-1290

[7] American Society for Testing and Materials, E8-04 Standard test methods for tension testing ofmetallic material (2001)