Journal Papers


  DE A gas gun based technique for studying the role of temperature in dynamic fracture and fragmentation. Jones, D. R, Chapman, D.J, Eakins, D.E. J. Appl. Phys. 114, 173508, 2013. (doi)


        FE Effects of Crystallographic Orientation and Grain Morphology on Crack Tip Stress State and Plasticity. Kartal, M.E, Cuddihy, M, Dunne, FPE. Intl. Jnl. Fatigue. Vol 61, 46-58, 2014. (doi)
  BL Experimental and computational studies of ultrasound wave propagation in hcp polycrystals for texture detection. Lan, B, Lowe, M, Dunne, FPE. Acta Materialia. Vol. 63, 107–122, 2014. (doi)
  Paper Slip band-grain boundary interactions in commercial-purity titanium, Guo, Y., Britton, T.B. and Wilkinson, A.J.  Acta Materiala, 2014,
  FD Lan B, Lowe M, Dunne FPE, 2014, Experimental and computational studies of ultrasound wave propagation in hexagonal close-packed polycrystals for texture detection, ACTA MATERIALIA, Vol 63, 107-122, 2014doi:10.1016/j.actamat.2013.10.012
  Kartal Effects of crystallographic orientation and grain morphology on crack tip stress state and plasticity, Kartal, ME., Cuddihy, MA. & Dunne, FPE. International journal of fatigue, vol 61, no. 46-58, pp. 46-58, 2014, doi:10.1016/j.ijfatigue.2013.11.022


                    〈a〉 Prismatic, 〈a〉 basal, and 〈c+a〉 slip strengths of commercially pure Zr by micro-cantilever tests

〈a〉 Prismatic, 〈a〉 basal, and 〈c+a〉 slip strengths of commercially pure Zr by micro-cantilever tests, J Gong, TB Britton, MA Cuddihy, FPE Dunne, AJ Wilkinson, Acta Materialia, vol. 96, 249-257, 2015, doi:10.1016/j.actamat.2015.06.020 

Open Access

Micro to Macro: Predicting bulk properties from micromechanical test data

Understanding and improving the behaviour and properties of hexagonal Ti and Zr alloys is at the heart of the HexMat programme grant.  Collaborative work between members of the Oxford Micromechanics Group, (Jicheng Gong & Angus Wilkinson) andImperial College’s Engineering Alloys group (Ben Britton, Mitch Cuddihy & Fionn Dunne) has successfully shown that microscale mechanical tests can be used to predict bulk polycrystal properties even in the highly anisotropic hexagonal metal Zr.  Bend testing of micro-cantilevers 500 nm to 10 µm wide was used to establish the flow stresses of the predominate slip systems in pure Zr.  This required understanding the significant size effect on plasticity present at this scale.  These flow stresses were then used with no additional fitting parameters within crystal plasticity finite element modelling of polycrystal deformation.  When measured micro-textures were used to populate the simulations the predicted stress-strain response is in good agreement with bulk polycrystal compression tests.  The work is reported in Acta Materialia.

  Measurements of stress fields near a grain boundary: Exploring blocked arrays of dislocations in 3D

Measurements of stress fields near a grain boundary: Exploring blocked arrays of dislocations in 3D
Y Guo, DM Collins, E Tarleton, F Hofmann, J Tischler, W Liu, R Xu, AJ Wilkinson, TB Britton, Acta Materialia, vol. 96, 229-236, 2015
, doi:10.1016/j.actamat.2015.05.041 

Open Access

3D Mapping of Stresses near Blocked Slip Bands

A collaboration between the Oxford Micromechanics Group, (Yi Guo, Ed Tarleton, Dave Collins, Angus Wilkinson), the team at ID34 at the Advanced Photon Source (Jon Tischler, Wenjun Liu, Ruqing Xu),Felix Hofmann (Eng Sci – Oxford), and  Ben Britton (Imperial College London) has generated the first 3 dimensional mapping of local stress fields caused by slip bands impinging on grain boundaries.  The work appears in Acta Materialia.  The study uses the differential aperture X-ray microscopy (DAXM) method pioneered at APS extending our earlier HR-EBSD studies into the third dimension and probing below the sample surface.  The stress intensity variations along a given slip band and from band to band have been quantified at a level of detail never previously achieved.  The local hot spots in the stress field play a crucial role in controlling processes such as crack initiation and twin nucleation which limit material performance.  Such studies of fundamental micromechanics issues underpin development of improved microstructures and new alloys all of which are being pursued within the HexMat programme grant that seeks to improve future Ti alloys for jet engine and Zr alloys for nuclear fuel technologies.


On the mechanistic basis of deformation at the microscale in hexagonal close-packed metals, TB Britton, FPE Dunne, AJ Wilkinson, Proceedings of the Royal Society A, vol. 471, 20140881, 2015,  doi:10.1098/rspa.2014.0881 

Open Access


Measurements of stress fields near a grain boundary: Exploring blocked arrays of dislocations in 3D, Y Guo, DM Collins, E Tarleton, F Hofmann, J Tischler, W Liu, R Xu, AJ Wilkinson, TB Britton, Acta Materialia, vol. 96, 229-236, 2015, doi:10.1016/j.actamat.2015.05.041

  Electron back scattering

The effect of pattern overlap on the accuracy of high resolution electron backscatter diffraction measurements, V Tong, J Jiang, AJ Wilkinson, TB Britton, Ultramicroscopy, vol. 155, 62-73, 2015, doi:10.1016/j.ultramic.2015.04.019


Microtexture Analysis of the Alumina Scale in Thermal Barrier Coatings, J. Am. Chem. Soc, M. Bai, E. Sarakinou, Y. Chen, A. D. Chandio, X. Zhao, M. Preuss and P. Xiao, pg 3639–3642, 2015, DOI: 10.1111/jace.13945

  dye The effect of grain size on the twin initiation stress in a TWIP steel, Rahman, KM, Vorontsov, VA, Dye, D, Acta Materialia, pg 247, 2015,

Characterisation of short fatigue cracks in titanium alloy IMI 834 using X-ray microtomography, T. Chapman, K. Kareh, M. Knop, T. Connolley, P. D. Lee , M. Azeem, D. Rugg, T. Lindley, D. Dye, Acta Materialia , VOL 99 , Pg 49 - 62, 2015, DOI: 10.1016/j.actamat.2015.07.069


Understanding the “blue spot” sodium chloride hot salt stress-corrosion cracking in titanium-6246 during fatigue testing at low pressure, Saunders, EA
Chapman, TP, Walker, ARM, Lindley, TC, Chater, RJ, Vorontsov, VA, Rugg, D, Dye, D, Engineering Failure Analysis, Pg 2, Vol 61, 2015,


A generalized spherical harmonic deconvolution to obtain texture of cubic materials from ultrasonic wave speed, Lan, Bo; Lowe, Michael J. S.; Dunne, Fionn P. E., Journal of the Mechanics and Physics of Solids, Volume 83, p. 221-242, 2015, 10.1016/j.jmps.2015.06.012


A spherical harmonic approach for the determination of HCP texture from ultrasound: A solution to the inverse problem, Lan, Bo; Lowe, Michael J. S.; Dunne, Fionn P. E., Journal of the Mechanics and Physics of Solids, Volume 83, p. 179-198, 2015, 10.1016/j.jmps.2015.06.014


In situ micropillar deformation of hydrides in Zircaloy-4, Weekes, H., Vorontsov, V., Dolbnya, I., Plummer, J., Giuliani, F, Britton, T.B., and Dye, D.  Acta Materialia (2015),


Environmentally assisted fatigue crack nucleation in Ti-6Al-2Sn-4Zr-6Mo, Chapman, TP, Chater, RJ, Saunders, EA, Walker, AM, Lindley, TC, Dye, D, Corrosion Science, Pg 87, 2015


Study of 3-D stress development in parent and twin pairs of a hexagonal close-packed polycrystal: Part I - In-situ three-dimensional synchrotron X-ray diffraction measurement, Abdolvand H, Majkut M, Oddershede J, Wright JP, Daymond MR, . Acta Materialia. 93:246-255, 2015, Doi

  polycrystals II

Abdolvand H, Majkut M, Oddershede J, Wright JP, Daymond MR. Acta Materialia. 93:235-245, 2015,  DOi 10.1016/j.actamat.2015.04.025


Strain Localization and Failure in Irradiated Zircaloy with Crystal Plasticity, T. Erinosho, F. P E Dunne, International Journal of Plasticity Vol 71, 2015,


On rate-dependent polycrystal deformation: the temperature sensitivity of cold dwell fatigue, Z. Zhang, M. A. Cuddihy, F. P. E. Dunne, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, vol. 471, issue 2181, p. 20150214, 2015

  Wilkinson 2015

Analysis of Dislocation Densities using High Resolution Electron Backscatter Diffraction, Vilalta-Clemente, A., Jiang, J., Britton, B., Collins, D.M. and Wilkinson, A., 2015.  Microscopy and Microanalysis, 21(S3), p 1891, 2015. DOI:


Terry Jun

Local deformation mechanisms of two-phase Ti alloy, T-S Jun, G. Sernicola, F.P.E. Dunne, T. B. Britton, Materials Science and Engineering: A, Volume 649, 1 January 2016, Pages 39–47, 2016, doi:10.1016/j.msea.2015.09.016

The HexMat team recently published a new paper – ‘Local deformation mechanisms of two-phase Ti alloy’. This work presents effective experimental tools (SEM/EBSD + FIB + in-situ micropillar compression) to perform deformation tests within isolated microstructural units with precise morphologies, focussing on the role of α(hcp)/β(bcc) morphology in local deformation behaviour of dual-phase Ti alloy. The presence and morphology of the β phase can strikingly alter the apparent yielding point and work hardening response. High resolution in-situ observations of pillars particularly oriented for (apparent) single slip reveals that the morphology, even in tri-crystal samples, has a significant impact and directly affects mechanical performance. The paper including in-situ testing videos can be found at MSEA, Vol 649, 39-47, 2016 [doi:10.1016/j.msea.2015.09.016].

                    Assessment of residual stress fields at deformation twin tips and the surrounding environments

Assessment of residual stress fields at deformation twin tips and the surrounding environments, H. Abdolvand, AJ.Wilkinson, Acta Materialia,  vol. 105, 219-231, 2016 doi:10.1016/j.actamat.2015.11.036 

Open Access

A study of dislocation transmission through a grain boundary in hcp Ti-6Al using micro-cantilevers

A study of dislocation transmission through a grain boundary in hcp Ti-6Al using micro-cantilevers, R.Ding, J.Gong, AJ.Wilkinson, I.P.Jones, Acta Materialia, vol. 103, 416-423, 2016 doi:10.1016/j.actamat.2015.10.023

  Terry Paper 1

A nanoindentation investigation of local strain rate sensitivity in dual-phase Ti alloys Journal of Alloys and Compounds, Jun, T.S., Armstrong, D.E.J. and Britton, T.B., Journal of Alloys and Compounds, Volume 672, 5 July 2016, Pages 282–291, 2016,

In this paper we outline a range of nanoindentation studies to explore the importance of local strain rate sensitivity with respect to crystal orientations, chemical compositions and microstructures in real engineering alloys, Ti-6Al-2Sn-4Zr-xMo (x= 2 and 6). We clearly show that there is a striking change in rate sensitivity between these alloys, such that dwell sensitive Ti6242 has a grain orientation dependent rate sensitivity while dwell insensitive Ti6246 is a grain orientation independent. To our knowledge, rate sensitivity with respect to a grain orientation of dual-phase Ti alloys is for the first time reported and our findings are critical in dwell fatigue of titanium alloys and the explosion in scientific studies in this area matches the immediate industrial need to find a solution and further understanding. Our experimental approach presents new exciting insight into this important deformation mechanism, as well as opening up further studies of new alloy chemistries and heat treatments.

  Terry paper 2

Local strain rate sensitivity of single α phase within a dual-phase Ti alloy, Jun, T.S., Zhang, Z., Sernicola, G., Dunne, F.P.E., Britton, T.B. Acta Materialia, Volume 107, 1 April 2016, Pages 298–309,

In this paper we outline a range of in-situ micropillar deformation studies to explore the importance of local strain rate sensitivity of single α phase with respect to individual slip systems (i.e. <a>type basal and prismatic slip) in real engineering alloys, Ti-6Al-2Sn-4Zr-2Mo. This work presents new methodology and understanding, utilizing state-of-the-art micro-mechanical experiments to explore time sensitive deformation mechanisms in real alloys. In this work, we clearly show that there is a significant difference in rate sensitivity between slip systems, such that the prism slip has a strikingly higher strain rate sensitivity exponent (i.e. m value) than the basal. This has significant implications on fundamental deformation mechanisms and will trigger new research both at the atomistic and macroscopic lengthscales in order to understand the origins of this phenomena, as well as the consequences on component life.

Ordering and the micromechanics of Ti7Al, A. Radecka, J. Coakley, I.P. Jones, D.Rugg, T.C. Lindley and D. Dye, Materials Science & Engineering A, Volume 650, Pages 28–37, 2016
Influence of complex LCF and dwell load regimes on fatigue of Ti–6Al–4V,  P.O. Tympel, T.C. Lindley, E.A. Saunders, M. Dixon, D. Dye, Acta Mat, Vol 103, pg 77, doi:10.1016/j.actamat.2015.09.014
The Dislocation Mechanism of Stress Corrosion Embrittlement in Ti-6Al-2Sn-4Zr-6Mo, Chapman, Tamara P.; Vorontsov, Vassili A.; Sankaran, Ananthi; Rugg, David; Lindley, Trevor C.; Dye, David, Metallurgical and Materials Transactions A, Volume 47, Issue 1, pp.282-292, 2016. DOI: 10.1007/s11661-015-3181-0
Assessment of residual stress fields at deformation twin tips and the surrounding environments, H.bdolvand, Angus J. Wilkinson, Vol 105, Pg 216, 2016,
Rate sensitivity in discrete dislocation plasticity in hexagonal close-packed crystals, Z. Zheng, Daniel S. Balint, Fionn P.E. Dunne, Acta Materialia, Vol 107, Pg 17, 2016
  T Jun
Local strain rate sensitivity of single α phase within a dual-phase Ti alloy, T-S. Jun,, Z. Zhang, G. Sernicola, F.P.E. Dunne, T.B. Britton, Acta Materialia, Vol 107, Pg 298, 2016.
On the formation of adiabatic shear bands in textured HCP polycrystals, Z. Zhang, D.E. Eakins, F.P.E. Dunne, International Journal of Plasticity, Vol 79, Pg 196, 2016

Lattice strains at cracks in single crystal titanium : Elastic distortion and GND contributions. F. P E. Dunne, T. Erinosho, International Journal of Solids and Structures, Vol. 80, 01.02.2016, p. 237-245, 2016,


A nanoindentation investigation of local strain rate sensitivity in dual-phase Ti alloys, Jun, T, Armstrong, DEJ, Britton, TB, Journal of Alloys and Compounds, Vol 672, Pg 282, 2016


Insights into microstructural interfaces in aerospace alloys characterised by atom probe tomography, Materials Science and Technology, T. L. Martin, A. Radecka, L. Sun, T. Simm, D. Dye, K. Perkins, B. Gault, M. P. Moody & P. A. J. Bagot, Volume 32, Issue 3, Pg 232, 2016. DOI: 10.1179/1743284715Y.0000000132


Determination of Ti-6242 α and β slip properties using micro-pillar test and computational crystal plasticity, ZhenZhangTea-Sung JunT. BenjaminBrittonFionn P.E.Dunne, Journal of the Mechanics and Physics of Solids, 95, 393-410, 2016


Intrinsic anisotropy of strain rate sensitivity in single crystal alpha titanium, ZhenZhangTea-Sung,JunT. Benjamin BrittonFionn P.E.Dunne, Acta Materialia, 118, 317-330, 2016



Formation of very large ‘blocky alpha’ grains in Zircaloy-4, V. Tong, B. Britton, Acta Materialia, online 3rd March 2017


Effect of nanoscale α2 precipitation on strain localisation in a two-phase Ti-alloy, D.LuntT.BusoloX.XuJ.Quinta da FonsecaM.Preuss, Acta Materialia, 129, 72, 2017

DOI: 10.1016/j.actamat.2017.02.068


Microscopic strain localisation in Ti-6Al-4V during uniaxial tensile loading, D.LuntJ. Quintada FonsecaD.RuggM.PreussMaterials Science and Engineering: A, 680, 444, 2017

DOI: 10.1016/j.msea.2016.10.099


"Using transmission Kikuchi diffraction to characterise α variants in an α + β titanium alloy", Tong, V., Joseph, S., Ackerman, A.K., Dye, D., and Britton, T.B., Journal of Microscopy (2017)



"Formation of very large ‘blocky alpha’ grains in Zircaloy-4", Tong, V. and Britton, T.B., Acta Materialia (2017)


Growth of {} twins in titanium: A combined experimental and modelling investigation of the local state of deformation, Guo, Y., Abdolvand, H., Britton, T.B., and Wilkinson, A.J., Acta Materialia (2017)


On cold dwell facet fatigue in titanium aero-engine components. M.A. Cuddihy, A. Stapleton,  S. Williams, F.P.E. Dunne.  Intl. Jnl. Fatigue. 97, 177–189, 2017. (Awarded the Rolls-Royce UTCs top paper prize, 2017)


Investigation of slip transfer across HCP grain boundaries with application to cold dwell facet fatigue, Zebang Zheng, Daniel S. Balint,  Fionn P.E. Dunne. Acta Materialia. 127, 45-53, 2017.


Microstructural heterogeneity in rate-dependent plasticity of multiphase titanium Alloys, Zhang, Z, Dunne, FPE. Jnl. Mech. Phys. Solids. 103, 199–220, 2017.


The effect of the beta phase on the micromechanical response of dual-phase titanium alloys, Ashton, PJ, JunTS, Zhang, Z, Britton, TB, Leen, SB, Dunne, FPE.  Intl. Jnl. Fatigue.  100, 1, 377-387, 2017.


Mechanistic basis of temperature-dependent dwell fatigue in titanium alloys, Zheng, Z, Balint, DS, Dunne, FPE.  Jnl. Mech. Phys. Solids. 107, 185–2, 2017.


Hydrogen in Ti and Zr Alloys: Industrial perspective, failure modes and mechanistic
understanding., TP Chapman, D Dye, D Rugg., Philosophical Transactions of the Royal Society of London A 375:20160418, 2017.


A new beta titanium alloy system reinforced with superlattice intermetallic precipitates.,,AJ Knowles, T-S Jun, A Bhowmik, NG Jones, TB Britton, F Giuliiani, HJ Stone, D Dye., Scripta Materialia 139:71-75, 2017.

Comment on An Experimental Study on Evolution of Grain-Scale Stress/Strain and Geometrical Necessary Dislocations in Advanced TA15 Titanium Alloy during Uniaxial Tension Deformation”, Thomas Benjamin Britton, Adv. Engineering Materials, 19, Np.6, 2017.

2018/ 2019


Quantification of strain localisation in a bimodal two-phase titanium alloy, D.Lunt, X.Xu, T.Busolo, J. Quinta da Fonseca, M.Preuss, Scripta Materialia, 145, 45, 2018

DOI: 10.1016/j.scriptamat.2017.10.012


Enabling high resolution strain mapping in zirconium alloys, D. Lunt, A. Orozco-Caballero, R. Thomas, P. Honniball, P. Frankel, M.P reuss, J. Quinta da Fonseca, Materials Characterization, 139, 355, 2018

DOI: 10.1016/j.matchar.2018.03.014


"Deformation behaviour of [001] oriented MgO using combined in-situ nano-indentation and micro-Laue diffraction", Bhowmik, A., Lee, J., Britton, T.B., Liu, W., Jun, T.S., Sernicola, G., Karimpour, M., Balint, D., and Giuliani, F., Acta Materialia (2018)


Slip transfer across phase boundaries in dual phase titanium alloys and the effect on strain rate sensitivity, Zheng, Z, Waheed, S, Balint, DS, Dunne, FPE.  Intl. Jnl. Plasticity.  104, 23-38, 2018.


Phase morphology, variants, and crystallography of alloy microstructures in cold dwell fatigue, Zhang, Z, Dunne, FPE. Intl. Jnl. Fatigue. 113, 324-334, 2018.


Slip transfer and deformation structures resulting from the low cycle fatigue of near-alpha titanium alloy Ti-6242Si., S Joseph, I Bantounas, TC Lindley, D Dye., International Journal of Plasticity 100:90-103, 2018.


The effect of oxidation on the subsurface microstructure of a Ti-6Al-4V alloy., PAJ Bagot, A Radecka, AP Magyar, DC Bell, GDW Smith, MP Moody, D Dye, D Rugg., Scripta Materialia 148:24-28, 2018


The mechanisms of hot salt stress corrosion cracking in titanium
alloy Ti-6Al-2Sn-4Zr-6Mo., S Joseph, TC Lindley, D Dye, EA Saunders., Corrosion Science 134:169-178, 2018; ArXiv preprint.


Characterizing solute hydrogen and hydrides in pure and alloyed titanium at the atomic scale., Y Chang, AJ Breen, Z Tarzimoghadam, P K¨urnsteiner, H Gardner, A Ackerman, A Radecka, PAJ Bagot, WLu, TLi, EA J¨agle, MHerbig, LT Stephenson, MP Moody, D Rugg, D Dye, D Ponge, D Raabe, B Gault., Acta Materialia 150:273-280,


The kinetics of primary alpha plate growth in titanium alloys., AK Ackerman, AJ Knowles, HM Gardner, AN Nemeth, I Bantounas, A Radecka, MP Moody, PAJ Bagot, RC
Reed, D Dye, Submitted to Acta Materialia, 2018


Interface characteristics in an + titanium alloy., AK Ackerman, VA Vorontsov, I Bantounas, Y Zheng, T McAuliffe, WA Clark, HL Fraser, D Rugg, D Dye., Submitted to Scripta Materialia, 2018


Atomic scale analysis of grain boundary deuteride growth front in Zircaloy-4, A.J.Breen, I.Mouton, W.Lu, S.Wang, A.Szczepaniak, P.Kontis, L.T.Stephenson, Y.Chang, A.K.da Silva, C.H.Liebscher, D.Raabe, T.B.Britton, M.Herbig, B.Gault, Scripta Materialia, 156, 42, 2018.


The effect of pressure on hy- drogen solubility in Zircaloy-4, HE Weekes, D Dye, JE Proctor, D. Smith, C. Simionescu, TJ Prior, MR Wenman., submitted to Journal of Nuclear Materials, 25 June 2018.

arXiv 1806.09657.


Dislocation interactions and crack nucleation in a fatigued near-alpha titanium alloy, S Joseph, TC Lindley, D Dye. International Journal of Plasticity 110:38-56, 2018.


Quantitative investigation of micro slip and localization in polycrystalline materials under uniaxial tension, Zhang, Z, Lunt, D, Abdolvand, H, Wilkinson, AJ, Preuss, M, Dunne, FPE, Intl. Jnl. Plasticity. 108, 88-106, 2018.


A microstructure-sensitive driving force for crack growth, Wilson, D, Zheng, Z, Dunne, FPE,  Jnl. Mech. Phys. Solids. 121, 147-174, 2018.


Rapid measurement of volumetric texture using resonant ultrasound spectroscopy, Lan, B, Carpenter, M, Gan, W, Hofmann, M, Dunne, FPE, Lowe, MJS, Scripta Materialia. 157, 44-48, 2018.


Understanding thermal alleviation in cold dwell fatigue in titanium alloys, Zheng, Z, Stapleton, A, Fox, K, Dunne, FPE, Intl. Jnl. Plasticity. In press, 2018.


Direct volumetric measurement of crystallographic texture using acoustic waves, Bo Lan, T. B. Britton, Tea-Sung Jun, Weimin Gan, Michael Hofmann, Fionn P.E. Dunne, Michael J.S. Lowe, Acta Materialia. 159, 384-394, 2018.


Microstructural effects on strain rate and dwell sensitivity in dual-phase titanium alloys, Waheed, S, Zheng, Z, Balint, D, Dunne, FPE, Acta Materialia. 2019


The effect of cooling rate and grain size on hydride microstructure in Zircaloy-4, Ruth Birch, Siyang Wang, Vivian S. Tong, T. Benjamin Britton, Journal of Nuclear MaterialsVolume 513, January 2019, Pages 221-225


Exploring new space in pattern indexing with methods launched from an astronomical approach, Britton T, Tong V, Hickey J, Foden A, Wilkinson A. (2018). Journal of Applied Crystallography, 2019


Rapid electron backscatter diffraction mapping: Painting by numbers. Tong V, Knowles A, Dye D, Britton T. (2019).  Materials Characterization.


Variable temperature micropillar compression to reveal basal slip properties of Zircaloy-4. Wang S, Giuliani F, Britton T. Scripta Materialia, 2019


A mechanistic modelling methodology for microstructure-sensitive fatigue crack growth. Wilson D, Dunne F. Journal of the Mechanics and Physics of Solids (2019).