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# What is the Fracture Toughness Master Curve?

Research into the fracture of ferritic steels in the ductile-brittle transition region has led to two important conclusions:

1. Scatter in fracture toughness data in the transition region follows a characteristic statistical distribution that is similar for all ferritic steels.
2. The shape of the fracture toughness vs. temperature curve in the transition range is virtually identical for all ferritic steels. The only difference between steels is the absolute position of this curve on the temperature axis.

Based on the above, an indexing procedure has been developed to provide a conservative lower-bound estimate of fracture toughness for ferritic steels (in particular nuclear grade pressure vessel steels), based on a reference temperature (RTNDT). The earliest example of this is the ASME reference curve (see TWI FAQ: How do I use the ASME reference curve to estimate the fracture toughness of ferritic steels?)

More recently, an alternative reference temperature (T0) has been proposed, based on the 'fracture toughness master curve'.

This statistical model is based on the micro-mechanisms of cleavage fracture. The fracture toughness at a fixed temperature in the transition region follows a 3-parameter Weibull distribution with a slope of 4 as shown below [ASTME1921-05] :

Where

 F= cumulative probability that failure of the specimen will occur at or before KJC B= specimen thickness in millimetres KJC= fracture toughness determined in a test specimen (critical J converted to the equivalent critical K) in MPa √m Kmin= threshold toughness, ASTM E1921 fixed Kmin at 20 MPa √ m (18.2 ksi √in) for ferritic steels K0= Weibull mean toughness, which corresponds to the 63rd percentile toughness for a 25-mm thick specimen

The reference temperature T0 used in this indexing procedure is defined as the temperature at which the median fracture toughness (F=0.5) is 100 MPa √m in a 25mm thick specimen.

Once the reference temperature T0 is derived from analysis of the experimental data, the temperature dependence of median toughness in the ductile-brittle transition region can be defined, as given below [ASTM E1921-05] :

KJc(median) = 30 + 70exp[0.019(T - T0 )] (MPa √m and °C)

The fracture toughness distribution can then be inferred through Equation 1 and the tolerance bounds - both upper and lower - can be calculated. Figure 1 schematically illustrates the fracture toughness master curve for a particular steel specimen with 25mm thickness.

It is worth noting that the Master Curve approach works best in the ductile-brittle transition region. It may not fit data in the lower shelf very well, and it is totally unsuitable for the upper shelf. As for the ASME reference curve, a cut-off at KJC = 220 MPa √m has therefore been imposed.

Validation studies have been undertaken on the fracture toughness master curve, comparing it with the original ASME reference curve (see TWI FAQ: What is the difference between the ASME reference curve and the fracture toughness master curve?). It has been suggested that the reference temperature T0 is the superior indexing parameter for fracture toughness of ferritic steels compared to the RTNDT approach [K Yoon etc.] ; the use of T0 as an alternative to RTNDT in ASME KIC -reference curve is described in ASME Case Code N-629, and in Annex L of BS 7910.

It is necessary to test between 6 and 10 valid specimens to define a value of T0, and TWI can carry out fracture toughness testing, and analysis to determine T0 to ASTM E1921 and BS 7910.

Fig.1. [T L Anderson2005]  Fracture toughness master curve. Taken from E 1921, 'Standard Test Method for Determination of Reference Temperature, T0, for Ferritic Steels in the Transition Range.' American Society for Testing and Materials.

## References

• T L Anderson: 'Testing and analysis of steels in the ductile-brittle transition region'. In 'Fracture Mechanics', 2005, 338-340.
• ASME Case Code N-629: 'Use of Fracture Toughness Test Data to Establish Reference Temperature for Pressure Retaining Materials Section XI, Division 1', ASME 2007.
• ASTM E 1921: 'Standard Test Method for Determination of Reference Temperature, T0 , for Ferritic Steels in the Transition Range.' Philadelphia, PA.
• K K Yoon: 'Fracture toughness data analysis using the master curve method'. WRC bulletin No. 486 Part 3.
• W He: 'TWI Frequently asked question: What is the difference between the ASME reference curve and the fracture toughness master curve?'
• W He: 'TWI Frequently asked question: How to use the fracture toughness master curve to estimate the fracture toughness of ferritic steels?'
• BS 7910: Guide to methods for assessing the acceptability of flaws in metallic structures’.