Engineering Framework To Transfer The Minimum Fracture Toughness In The DBTT Region Between SE(B) And 1T CT Specimens

Toshiyuki Meshii; Kenichi Ishihara

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Structural Integrity

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Procedia Structural Integrity 2 (2016) 7)04-711

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21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy

Engineering Framework To Transfer The Minimum Fracture Toughneso In The DBTT Region Between SE(B) And 1T CT

Sp ecim ens

Toshiyuki Meshiia*, Kenichi Ishiharab

"Faculty of Engineering, University of Fukui, 3-t-1 Bunkyo Fukui, 910-8507, Japan b KOBELCO RESEARCH INSTITUTE, INC., 1-5-5 Takatsukadai, Nishi-ku, Kobe, Hyogo, 651-2271, Japan

Abstract

The test specimen size effect of fracture toughness Jc of the material in the ductile-to-brittle transition temperature (DBTT) region is known to not be iobored. One practical method was to use the 1-inch thicknes s (IT) compact tension (CT) test specimen to integrity assessment of cracked structure. To support this practice, a metho d to convert Jc obtained with other sized CT spec impns is pro'aided in ASTM El 921. On the other hand, a large number of fracture toughness test data have been collected for the single-nlge notched bend (SE(B)) rpecimens. In order to practic ally use the SE(B) test data in engineering application, it is essentiad eer converting Jr obtained from dii::lCTi;!n^ sized SE(B) specimen to the 1T CT rpecimen Jc. In this paper, an engineering framework is proposedto convert minimum Jc obtained from various sized SE(B) specimens to tire minimum )T CT specimen Jc. Tht approgch applies the mod)fied Rirchie-KhioOririce Ca-lcre criterion, which predicT )he onsnt oof tleavage fracture whenthe crack-opaniag e-s meo)ured ait a distance from the crack-tip equal to tous times the crack-tip opemngdisplar ement lit, denrted as <r22d, exceeds a critical value <r2ic, to the elastic-plastic finite element results. Id addition, this framework utilizes our recenl finding that the J when i722d reaches the critical value <r22c has o possibility to correspond to the minimum Jc for a specified specimen qoafigurarion and material. The proposed framework has an advantage on the point; that it requires only stress-rtgam curve as an experimental data. The validity of the framework was domonstrated through the experimenta1 results.

* Corresponding author. Tel.: +81-776-27-8468; fax: +81-776-27-9764. E-mail address: meshii@u-fukui.ac.jp

Peer-review under responsibility of the Scientific Committee of ECF21.

10.1016/j.prostr.2016.06.091

Keywords: fracture toughness; transition temperature; test specimen thickness effect; modified Ritchie-Knott-Rice failure criterion; elastic-plastic finite element analysys

Nomenclature

B Specimen thickness

E Young's modulus

J J-integral

Jc, JcFEA Fracture toughness and J obtained at the fracture load Pc via FEA

Js J obtained at converged cr22d

K, SIF corresponding to the fracture load Pc

Kmax Maximum stress intensity factor during precracking

Kjc = {EJJ(1-v 2)}12: Cleavage fracture toughness

M = (b00YS)/Jc

P, Pc Load and fracture load

P P 1 max J min Maximum and minimum force during precracking

PQ, Ps Conditional value in ASTM E399 and P corresponding to Js

T„ In-plane T-stress

Vg, Vll Crack mouth opening displacement (CMOD) and load line displacement

W Specimen width

a Crack length

bo = (W-a): Initial ligament size

P = Tw(nca)12/K

S Crack-tip opening displacement (CTOD)

V Poisson's ratio

P Initial blunted notch

OB, OBO True and nominal tensile strength

0YS, °YS0 True and nominal yield stress

O22 Crack-opening stress

O22C Critical crack-opening stress

°22d a22 measured at a distance from the crack tip equal to four times the crack-tip opening

displacement (CTOD) St at the specimen mid-plane

O22d0 Converged value of cr22d

1. Introduction

The test specimen size effect of fracture toughness Jc of the material in the ductile-to-brittle transition temperature (DBTT) region is known to not be ignored. One practical approach was to use the 1-inch thickness (1T) compact tension (CT) test specimen in structural integrity assessment of cracked structures (IAEA, 2009). To support this practice, a method to convert Jc obtained with other sized CT specimens is provided in ASTM E1921 (ASTM, 2010). On the other hand, a large number of fracture toughness test data have been collected for the single-edge notched bend (SE(B)) specimens. In order to practically use the SE(B) test data in engineering application, it is essential for converting Jc obtained from different sized SE(B) specimen to the 1T CT specimen Jc.

Another issue is a large scatter in Jc. This issue has been studied extensively (Beremin et al., 1983; James, Ford and Jivkov, 2014; Wallin, Saario and Torronen, 1984) and an engineering framework named master curve method (ASTM, 2010) seems to be widely accepted. However, master curve does not give a distinct procedure to convert Jcs between SE(B) and CT specimens, though master curve reference temperature difference of 10 oC is known (Wallin et al., 2001).

On the other hand, predicting the "lower bound" fracture toughness for a specific specimen configuration has been another interest. Chen et al. insisted that "it is necessary to distinguish the concepts of the lower bound

toughness or the lower boundary of toughness values from that of the scatter band of toughness. The former is a definite parameter determined by the specimen geometry and yielding properties, and the latter is statistical behaviour determined by the distribution of the weakest constituent (Chen et al., 1997)." We interpreted Chen's opinion as that at least lower bound Jc for a specific specimen can be predicted by running an elastic-plastic finite element analysis (EP-FEA) with a given stress-strain relationship and a failure criterion. For this failure criterion, we considered (4S, cr22c) criterion (Dodds et al., 1991), which predicts the onset of cleavage fracture when the crack-opening stress ct22, measured at a distance from the crack tip equal to four times the crack-tip opening displacement (CTOD) S, hereinafter denoted as cr22d, exceeds a critical value cr22c. This criterion was validated to explain the crack depth dependence on Jc (Dodds et al., 1991) and to explain the test specimen thickness effect on Jc (Lu and Meshii, 2014a, b, 2015; Meshii et al., 2015; Meshii et al., 2013; Meshii and Tanaka, 2010; Meshii et al., 2010). Through examination of the applicability of the (4 St, cr22c) criterion to the decommissioned RPV steel Jc database ranged with specimen thicknesses 8 to 254 mm (Meshii and Yamaguchi, 2016), we reached an idea (Fig. 1 left) that the convergence of cr22d for increasing load is necessary for fracture initiation, because critical value o-22c is equal to the converged value of cr22d. Considering the fact fracture always occurred after cr22d reached cr22c, it seemed that it seems that the minimum J that satisfy cr22d = cr22c corresponds to the lower bound fracture toughness observed for the specimen and the material considered. It was also considered that the existence of the lower bound J is consistent with Chen et al.'s opinion (Chen et al., 1997).

In this study, engineering method to predict the minimum Jc for a specimen type and thickness from only tensile test results is proposed (Fig. 1 right) and validated for 0.5T SE(B) and 1T CT specimen.

Fig. 1 Engineering framework to obtain minimum Jc for a specified specimen type; only stress-strain curve is required as an experimental data

2. Material selection

Considering tensile strength crBo and yield stress crYS0 ratio obo/ovso for EURO RPVs and Japan RPVs is equal to 1.3 and irradiation of material, S55C, which is known to be in the transition temperature region at around room temperature, is selected as examination object. The chemical contents of S55C were C: 0.55 %, Si: 0.17 %, Mn: 0.61 %, P: 0.015 %, S: 0.004 %, Cu: 0.13 %, Ni: 0.07 % and Cr: 0.08 %, respectively. The material was quenched at 850 °C and tempered at 650 °C.. Charpy impact test results and true stress-true strain curve, which is obtained from the tensile test, for EP-FEA are shown in Fig. 2 and Fig. 3, respectively. Mechanical properties of the test specimens are Young's modulus E equal to 206 GPa, Poisson's ratio vequal to 0.3, nominal yield stress crYS0 equal to 394 MPa and nominal tensile strength crB0 equal to 710 MPa.

-100 -75 -50 -25

1+ |a« 1»,

0 25 50 75 100 125 150 175 200 Tested Temperature 0C

Fig. 2 Charpy impact test results

« 450 0-, 2 400 b 350

^f* À

0 0.2 0.4 0.6 0.8 1.2

¡2 KM s

■1(H)

ft û

20I2SSSC ^^ Tensile test no. 1 < > Tensile test no.2 j\ FËA input

0 10 20 30 40 JO 60 70 30 90 100

Fig. 3 True stress-true strain curve for EP-FEA

3. EP-FEA

The FEA model of the 0.5T SE(B) and 1T CT specimen used in the EP-FEA are shown in Fig. 4. Considering symmetry conditions, one quarter of 0.5T SE(B) specimen and 1T CT specimen containing a straight crack were analyzed, with appropriate constraints imposed on the symmetry planes, as illustrated in Fig. 4(a) and Fig. 4(b). An initial blunted notch of radius p was inserted at the crack tip. For all cases, 20-noded isoparametric three-dimensional (3-D) solid elements with reduced (2 x 2 x 2) Gauss integration were employed. The material behaviour in the FEA was assumed to be governed by the J2 incremental theory of plasticity, the isotropic hardening rule, and the Prandtl-Reuss flow rule. The piecewise linear total true stress-strain curve of the S55C steel shown in Fig. 3 was used in the EP-FEA. In the EP-FEA, the applied load P was measured as the total reaction force on the supported nodes, and each fracture load Pc was determined from that of each experiment result. The Jc simulated by the EP-FEA, denoted by JcFEA, was evaluated using a load-vs.-crack-mouth opening displacement diagram (P-Vg diagram), in accordance with ASTM E1820 (2006). Abaqus (2014) was used as the FEA solver.

Qwend=3

Symmetry plane

(a) 0.5T SE(B) (b) 1T CT

Fig. 4 EP-FEA model for (a) 0.5T SE(B) and (b) 1T CT

4. Result of EP-FEA

P-V diagrams obtained from EP-FEA are shown in Fig. 5. Solid line in the Fig. 5 shows V calculated from the elastic compliance given in ASTM E1820. Here, Ps is the load P corresponding to Js: the predicted minimum J, described later. As shown in Fig. 5, the linear slope of the FEA result was very close to the linear P-V relationship calculated from the equations given in ASTM E1820. It was also noted that Pss for 0.5T SE(B) and 1T CT are close to the deviation point from the linear slope.

The relationships between cr22 measured at on the x1 axis cr22d and JFEA calculated from P-V diagram for each load step are shown in Fig. 6. From Fig. 6, it is clear that cr22d shows convergence tendency for increasing JFEA. There is not a definite method to determine the convergence value of cr22d, i.e., cr22c, hence we applied the method described below, which could be effectively applied to 102 SE(B) specimens manufactured from steel from the decommissioned Shoreham RPV, was chosen. For the actual method for the convergence judgement, first, an /'-th cr22d defined as a22di and cr22d which obviously converged define as cr22d0. Sn is defined as below

and J at the value of Sn/Sn+1 is equal to 0.9999 is defined as Js: the predicted minimum fracture toughness. By using this method the values of Js were predicted 15.6 N/mm for 0.5T SE(B) specimen and 11.5 N/mm for 1T CT specimen as shown in Table 1.

15 12.5 10 N 7.5 5 2.5 0

/ □ FEA A Ps -ASTM

□ FEA A Ps -ASTM

Vg,FEA I™]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

VLL.IEA

(a) 0.5T SE(B)

(b) 1TCT

Fig. 5 P-V diagram obtained from EP-FEA compared with the iiaear relationship predicted by the elastic compliance given in ASTM E1820.

□ FEA AJs

1 5.6

0 10 20 30

10 50 60 70 J [N/mm]

□ FEA AJs

0 10 20 30

10 50 60 70 80 90 100 J [N/mm]

(a) 0.5T SE(B)

(b) 1TCT

Fig. 6 Convergence of cr22d measured at the specimen mid-plane with increasing J Table 1 Predicted minimum Jc: Js

0.5T SE(B) 1T CT

CT22d0 (MPa) 1633 1694

Js (N/mm) 15.6 11.5

The tendency that Js of 0.5T SE(B) is larger than that of 1T CT, which often appeared in the past experiences, was obtained.

5. Fracture toughness test

The dimensions of the fracture toughness test are shown in Fig. 7 and Fig. 8. Fracture toughness test was conducted in accordance with ASTM E1921. After inserting a fatigue crack into the specimen, the crack length a satisfied ASTM's requirement of a/W = 0.45 to 0.55; the crack length was in the range of 0.496 to 0.504.

Detail ef l)

Fig. 7 Dimensions of 0.5T SE(B) specimen

Fig. 8 Dimensions of 1T CT specimen

Precracking was performed with two discrete steps which satisfied the requirement of the standard that precracking can be performed by using at least two discrete steps. Fatigue precrack was inserted with loads corresponding to Kmax = 22 and 19 MPam12 for the 1st and 2nd stages, respectively, which satisfied the requirement of the standard 25 and 20 MPam12. For each discrete step, the reduction in Pmax for any of these steps was 18.7 %, which satisfied the suggestion if the standard the reduction in Pmax for any of these steps be no greater than 20 %. The maximum force Pmax and the minimum force Pmin ratio R = Pmm/Pmax was applied, and the load frequency was 10 Hz.

In fracture toughness test, the loading rate was controlled to be 1.2 MPam1/2/s, which is very small in the specified range of 0.1 to 2.0 MPam1/2/s. The test specimen temperature was maintained to be in the range of 20 + 1 °C for 30/(25/B)+15 minutes, which satisfied ASTM requirement of 20 + 3 °C and 30/(25/B) minutes.

Test results are summarized in Table 2. Here, in Table 2, / and 3 denotes the average and standard deviation of each value, respectively. 23/ % is a reference value intended to represent the magnitude of data scatter.

It is seen from Table 2 that 23// of KJc were in the range of 26.1 to 49.2 % for all the specimens. Considering that the guideline for 23/ given in ASTM E1921 for KJc is 56(1-20//) % and was in the range of 44.2 to 44.8 % for the data in Table 2, it was concluded that the scatter in the KJc data summarized in the table is acceptable. In addition, it can be said that a very small scatter in KJc was realized from the current test data. It is also seen that all of the test results were satisfied ASTM E1921 requirements of M > 30 (M = b0aYS/J: b0 is the length of specimen ligament Wa).

Table 2 Fracture toughness test results for S55C (20 °C)

B/W Serial No. 1 2 3 4 5 6 M 21 2E/m(%)

a/W 0.499 0.501 0.498 0.498 0.500 0.499 0.499 0.001 0.47

Pc (kN) 10.5 11.5 10.6 10.8 11.9 12.6 11.3 0.8 14.7

Kc (MPa m1/2) 56.4 61.8 56.7 57.5 65.0 67.9 60.9 4.8 15.8

Jc (N/mm) 29.4 66.3 39.6 41.2 94.8 96.4 61.3 29.2 95.4

KJc (MPa m1/2) 81.5 122.5 94.7 96.6 146.5 147.7 114.9 28.3 49.2

M 167.5 74.3 124.4 119.5 52.0 51.1 121.4 35.7 95.0

a/W 0.496 0.498 0.504 0.500 0.499 0.499 0.499 0.003 1.06

Pc (kN) 41.9 51.1 49.4 53.5 50.4 55.0 50.2 4.6 18.2

Kc (MPa m1/2) 71.4 87.7 86.3 92.4 86.8 94.6 86.5 8.1 18.8

Jc (N/mm) 25.2 44.5 43.2 53.8 44.0 55.2 44.3 10.7 48.4

KJc (MPa m1/2) 75.5 100.4 98.9 110.4 99.8 111.7 99.5 13.0 26.1

M 390.9 221.3 228.0 183.1 223.9 178.4 237.6 35.4 65.8

P-V diagram for experimental results and EP-FEA results are shown in Fig. 9(a) and (b). As shown in Fig. 9, the path of the P-V diagrams for experiment and EP-FEA are very similar regarding SE(B) and 1T CT either. It was also confirmed that Ps is smaller than Pc for all of the test results.

J 0.5T SF(B)~]

_ fea o

f r. A

JF Test no.

: M 2 A

g----3 □

/------^ %

FEA O P, * Test no. 1 o 2 A 3 □ 4 O 5 v 6 O

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.S V [mm]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Vu [mm]

6. Discussion

(a) 0.5TSE(B) (b) 1T CT

Fig. 9 Comparison of FEA and experimental P- V diagrams

In Fig. 10, Jcs obtained from experiment and Jss were compared. Here, p = Tu(naf12IK is the biaxiality factor, which represents the intensity of crack tip constraint.

0.5T SE(B)

□ Jexp ♦ Js

0jc(0.02)

Fig. 10 S55C fracture toughness test results Jc compared with the predicted minimum toughness Js

As shown in Fig. 10, it is read that all of the experimental Jcs for 0.5T SE(B) were larger than those for 1T CT. This was as expected, because of thickness and constraint difference. Js also predicted this tendency. Js predicted minimum observed toughness Jc conservatively for 91 % and 125 % for 0.5T SE(B) and 1T CT specimens,

respectively. Comparing with Jss with the master curve 2 % bound Jcs, denoted as Jc(002), Jss were close to, but smaller than Jc(002)s. From these results, though further studies are necessary, on the point that Js can reproduce the tendency of master curve 2 % bound Jc and Js was close to these 2 % bound values, it was concluded that proposed framework in this paper can predict the minimum Jc in an engineering sense. The framework has an advantage that Js can be predicted from only tensile test results.

7. Conclusion

In this study, engineering framework to predict the minimum Jc for a specimen type and thickness from only tensile test results was proposed and validated for 0.5T SE(B) and 1T CT specimen.

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Engineering Framework To Transfer The Minimum Fracture Toughness In The DBTT Region Between SE(B) And 1T CT Specimens Academic research paper on "Materials engineering"

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