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What is the normalisation method for obtaining R-curves?


The normalisation method is a technique that can be used to obtain a J R-curve in some cases directly from the force displacement curve recorded during a fracture mechanics test, together with initial and final crack length measurements from the specimen fracture surface. The normalisation method effectively provides a way to estimate the crack extension during testing when this cannot be determined experimentally. The method is most commonly used for cases where high loading rates are used, or when testing at high temperatures or in corrosive environments where the unloading compliance method for determining crack extension in impractical. It can also be useful when a material is more ductile than originally expected and an R-curve test would have been more appropriate than a single point test, but there is no more material for further testing.

The normalisation technique is explained in ASTM E1820 ‘Standard Test Method for Measurement of Fracture Toughness’. The procedure uses the data recorded as force versus displacement. Each force value is ‘normalised’ using a formula given in the standard for a particular specimen type and material properties. Each corresponding load line displacement value is also ‘normalised’ using another formula for the particular specimen type. The resulting normalised force versus displacement curve is plotted up to the maximum load, with an additional Final Data Point calculated using the final crack length instead of the initial crack length (used for all the other normalisation calculations).

A normalisation function of the form provided in the standard is then fitted to the normalised data points. Data points between the maximum load and the Final Data Point are then adjusted iteratively to fit onto the normalisation function curve, by adjusting the crack size for each data pair. This method therefore gives a curve for which the force, load line displacement, and crack length estimates are given for each data point throughout the whole test, and then the standard method for determining a J R-curve can be used.

The normalisation method cannot be used:

  • If the crack extension exceeds the lesser of 4mm or 15% of the initial uncracked ligament. If there is a large amount of crack extension in the test, the uncertainty in the derived plasticity function increases, which can lead to non-conservative J-R curves.
  • For large specimens in low toughness material where large crack extension can occur with little measurable plastic force displacement
  • For specimens with uneven fatigue crack fronts. This method relies heavily on accurate measurement of the load, displacement and crack length at the end of test.
  • If a test ends with unstable crack extension, the Final Data Point cannot be determined and the method cannot be applied.
  • For specimens other than standard geometry SENB and CT specimens with 0.45 ≤ a/W ≤ 0.7.

If the normalisation method is used to determine JIc, at least one additional confirmatory specimen must be tested at the same rate under the same test conditions. The normalisation function is used to determine the load line displacement corresponding to a 0.5mm crack extension, and the specimen is loaded to this extension during test. The specimen is then marked, broken open and the ductile crack extension measured. In order to validate the normalisation method, and hence the JIc value obtained, the measured crack extension shall be 0.5 ± 0.25mm.

TWI can carry out R-curve tests using the normalisation method, and can also apply this method to get an R-curve from historical single point test data.

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