In 1994, Dunne was appointed as a Postdoctoral research associate in the Department of Mechanical Engineering, University of Manchester (UMIST), before being appointed a Research Fellowship at Hertford College, Oxford and the Department of Engineering Science, University of Oxford from 1996 until 2012. He became the dean of the department but moved to Imperial College London in 2012. He is an Emeritus Fellow of Hertford College, Oxford.
While in Oxford, Dune was part of the Materials for fusion & fission power program. He led the Micro-mechanical modelling techniques for forming texture, non-proportionality and failure in auto materials program at the Department of Engineering Science, University of Oxford between October 2011 and June 2012, when he moved the grant with him to the Department of Materials, Imperial College London from June 2012 until it ended in March 2015.
He also led the Heterogeneous Mechanics in Hexagonal Alloys across Length and Time Scales (HexMat) program, which was Engineering and Physical Sciences Research Council (EPSRC) funded at a value of £5 million between May 2013 and November 2018. Dunne was the director of the Rolls-Royce Nuclear University Technology Centre at Imperial College London. He is part of a £7.2 million program on Mechanistic understanding of Irradiation Damage in fuel Assemblies (MIDAS) that is funded by Engineering and Physical Sciences Research Council until April 2024
As of November 2022, Dunne is a Professor of Materials Science at Imperial College London and holds the Chair in Micromechanics and the Royal Academy of Engineering (RAEng)/Rolls-Royce Research Chair. He is also a Rolls-Royce consultant, and an Honorary Professor and co-director of the Beijing International Aeronautical Materials (BIAM).
Dunne's research focuses on computational crystal plasticity, discrete dislocation plasticity, and microstructure-sensitive nucleation and growth of short fatigue cracks in engineering materials, mainly Nickel, Titanium, and Zirconium alloys.