Subscribe to our newsletter to receive the latest news and events from TWI:

Subscribe >
Skip to content

What is the relationship between the fracture toughness parameters K, CTOD and J?

   

Frequently Asked Questions

Fracture toughness testing standards for metallic materials (e.g. BS7448) measure toughness (the resistance of a material to fracture) in terms of the crack tip conditions (defined by K, CTOD, J) required to cause crack extension (or to reach a maximum force condition) in a standard specimen containing a fatigue precrack. Crack extension can be by fast brittle fracture or by stable crack growth, known as tearing. When particular validity criteria are met, the result can be expressed in terms of the plane strain fracture toughness, K Ic. Where critical conditions are achieved under elastic-plastic conditions, results are expressed in terms of critical CTOD and/or critical J.

The relationship between applied stress intensity (K I) and the applied crack tip opening displacement ( δI or CTOD) depends on the stress state and the work hardening behaviour of the material, but can be generalised as:

[1]
[1]
where:
  • m is a constant that depends on specimen geometry and work hardening behaviour. In general, m lies in the range 1 to 2
  • E'=E for plane stress, E'=E/(1- ν 2) for plane strain
  • σ Y is the yield strength of the material

The relationship between CTOD and J (toughness or driving force) can be similarly expressed as:

[2]
[2]

and that between K I and J as:

[3]
[3]

The general principle, when using values of K Ic, critical CTOD and critical J in defect assessment procedures (e.g. BS7910), is to follow consistent parameters throughout. Hence, if the toughness of the material is measured in terms of CTOD, applied conditions are also calculated in terms of CTOD. However, some defect assessment procedures require all fracture toughness results to be expressed in terms of an equivalent value of K. These are usually designated as K J or K CTOD to distinguish them from plane strain fracture toughness K Ic. For example, the European SINTAP procedure (1) recommends the use of the following equation for steel specimens:

[4]
[4]

where CTOD values have been derived from deeply notched bend specimens tested to BS7448 and

[5]
[5]

Reference

A Bannister: 'SINTAP - Structural Integrity Assessment Procedure for European Industry', Brite Euram Project BRPR-CT95-0024 Final Report, British Steel Swinden Technology Centre, UK, 1999.

For more information please email:


contactus@twi.co.uk