An investigation into the effect of constraint on fracture parameters

  • Simon M Tonge

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


The fracture toughness of a material is a known material property which represents how resistant a material is to fracture. Numerical measures of fracture, for example the J-integral, enable the comparison of fracture toughness between materials. However, a component has a susceptibility to failure which is not only dependent on the fracture toughness of the material from which it is made. When an component cracks, at the tip of the crack a high stress region known as the plastic zone forms. In this region plastic yielding has occurred. The size of the component in question constrains this plastic zone and can partly determine the likelihood of an component failing. There are two types of constraint: In-plane constraint and out of plane constraint. In plane constraint depends on the length of uncracked solid material ahead of the crack tip. Out of plane constraint refers to the effect of the component thickness, which is its orthogonal size relative to the direction of crack propagation.
Parameters such as T-stress account for the effect of constraint on fracture. Assessment codes and procedures enable the estimation of the safety of a component by comparison to tabulated measurements of these parameters. No fracture assessment code or procedure currently accounts for the effect out of plane constraint on an component’s fracture toughness. Furthermore, theories accounting for in and out of plane constraint often involve using three parameters, for example K-T-Tz. In this thesis a single parameter to quantify both in and out of plane constraint is tested, φ. It is compared with Q another parameter that has been suggested to quantify both types of constraint.
It can be concluded that the parameter φ is a potential parameter to quantify both in and out of plane constraint. This is because φ is sensitive to both in and out of plane constraint. Q, conversely does not combine in and out of plane constraint consistently. To enable the use of φ in structural integrity assessment further work would be needed, which would involve the testing of steel specimens to strengthen the evidence for this method, by proving its applicability to other materials
Date of Award5 Dec 2023
Original languageEnglish
Awarding Institution
  • University of Bristol
SupervisorMahmoud Mostafavi (Supervisor)

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