Unifying the effects of in and out-of-plane constraint on the fracture of ductile materials

SM Tonge, CA Simpson, C Reinhard, Thomas Connolley, AH Sherry, TJ Marrow, M Mostafavi

Research output: Contribution to journalArticlepeer-review


Effects of plastic constraint on the fracture of materials have been studied extensively. Often in such studies, the plastic constraint is divided into in-plane and out-of-plane directions and each treated separately. Such a separation adds considerable complexity to the engineering structural integrity assessment analyses. Despite previous suggestions for unifying the effects of constraint in a single parameter, the current engineering assessments have not been updated due to lack of direct experimental validation of such parameters. In this study, we directly measured the effects of in-plane and out-of-plane constraints, for the first time, in the form of plastic zone around the crack using advanced experimental techniques. The measurement of constraints in four specimens with different levels of in and out of plane constraints, allowed us to show and relate the interdependency of in and out of plane constraints. The tests were carried out using synchrotron X-ray tomography with in-situ loading. Attenuation contrast between the constituents of the metal matrix composite material used allowed the tomograms to be analysed using digital volume correlation which calculated the full-field displacement within the samples. The displacement fields were used via a finite element framework to calculate the energy release rate in the form of the J-integral along the crack fronts. The measured plastic zone sizes, dependant on the combined level of in plane and out of plane constraints, were used successfully to rank the J-Integral at fracture of the samples. It was therefore proved the level of plastic constraint can be quantified by using the size of the plastic zone as without separating it into two components thus simplifying the treatment of constraint in structural analyses significantly.
Original languageEnglish
Article number103956
Pages (from-to)1-16
Number of pages16
JournalJournal of the Mechanics and Physics of Solids
Publication statusPublished - Aug 2020


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