Principal Research Results

Proposal of Rational Determination of Fracture Toughness Lower-Bound
Curves by Master Curve Approach
Background
The “Master Curve ＊ 1” gives the relation between the median of fracture toughness and temperature in ductile-brittle transition temperature region. The procedure to determine the Master Curve is provided in the current ASTM standard. CRIEPI has
conducted a series of fracture toughness tests for typical Japanese reactor pressure vessel (RPV) steels with various specimen sizes andshapes, and has ascertained that the Master Curve approach can be well applied to them. Considering the substitution of the alternative lower-bound curves based on the Master Curve approach for the recursive KIc curves in the present codes, the statistical characteristic should be well incorporated into the determination of the lower-bound curves. The current ASTM standard provides the procedure to identify the lower-bound curves, however, it is semi-empirically addressed without sufficient consideration on statistical reliability.

Objectives
Thist study aims to propose a rational determination method of fracture toughness lower-bound curves based on the MasterCurve approach;Principal Results
1. Proposal of a rational determination method of lower-bound curves
Lower-bound curve is derived by the following two steps (see Fig. 1);(a) Determine a confidence limit curve by reducing the Master Curve so that the confidence limit curve can envelop the variation of
the fracture toughness, and(b) Determine a lower-bound curve by shifting the confidence limit curve upward in temperature upon considering the uncertainty of
the reference temperature ＊ 2.
The current ASTM standard does not take account of the effect of sample size in the determination of the confidence limit curve,
and semi-empirically gives the shift adjustment in the determination of the lower-bound curve. By resolving these issues, a new
method to determine the rational lower-bound curves was proposed with well-defined meaning on their statistical reliability (seeTable 1).
2. Verification of the proposed method
The lower-bound curve based on the proposed methods could conservatively envelop the fracture toughness data for RPV
steels (see Fig. 2). Thus the adequacy of the proposed method was verified.

Future Developments
Based on the results, a Master Curve evaluation procedure using less and smaller specimens will be further developed,
which can coexist with the present surveillance program.
Main Researcher: Naoki Miura,Senior Research Scientist, Irradiation Embrittlement Research Unit, LWR Plant Life Management Project
Reference
N. Miura, et al., 2008, “Applicability of Small Specimens to the Evaluation of Master Curve Fracture Toughness for Japanese Reactor
Pressure Vessel Steels”, Technical Report Q07304 (in Japanese)
N. Miura, et al., 2008, “Proposal of Rational Determination of Fracture Toughness Lower-Bound Curves by Master Curve Approach”,
Technical Report Q07305 (in Japanese)＊1：The variation of the fracture toughness for ferritic steels in the transition range can be described by the Weibull distribution based on theweakest link theory. Consequently the relation between the median of fracture toughness and temperature can be expressed by an inherentcurve.
＊ 2：The temperature corresponding to the fracture toughness of 100 MPa-m1/2 on the Master Curve. The reference temperature is a unique index
to identify the location of the Master Curve.

96

5. Nuclear

Fracture toughness

Master Curve(Median of fracture toughness)
Confidence limit curve(Enveloping fracture
toughness variation)(b)(a)
Lower-bound curve(Considering reference temperature uncertainty)
Temperature

Fig.1 Schematic Derivation of Lower-Bound Curves−(a) Determine a confidence limit curve by reducing the Master Curve−−(b) Determine a lower-bound by shifting the confidence limit curve upward in temperature−

Table 1 Comparison of Determination of Lower-Bound Curves
Based on Current ASTM Standard and Proposed Method

ASTM standard

Confidence limit
curve
determination

Proposed method
Using reducing factor as function
Using constant reducing factor forof sample size and confidence
infinite sample size
levelLower-bound curve Determine semi-empirical shiftdetermination
adjustment

Determine shift adjustment
considering statistical distributionof reference temperature

Fracture Toughness, MPa-m 1/2

250
Lower-bound by ASTM
standard (semi-empirical)

200

150
Experimental Data
100

Lower-bound by proposed
method (theoretical)

50

0-100-80-60-40-20020

406080100

Temperature - Reference Temperature,

Fig. 2 Typical Comparison between Experimental Fracture Toughness Data and Lower-Bound Curves−experimental data were obtained from about 100 SFVQ1A specimens with the thickness of 10 to 100 mm−975