In situ full-field characterisation of strain concentrations (deformation twins, slip bands and cracks) 
Keywords: Crack Propagation
finite element analysis
EBSD
EDXD
Electron microscopy
Crack tip
Ferrite
Slip band
Silicon
High angular resolution electron backscatter diffraction
Stress intensity factor
J-integral
Strain measurement
Fatigue crack growth
DIC
Deformation twinning

This thesis has developed novel methods to characterise the deformation field, in and ex situ, of strain concentrations (i.e., deformation twins, slip bands and cracks) using diffraction methods to map the local elastic deformation field, and calculate elastic strain energy release rate (J-integral) and stress intensity factors (SIFs) to parametrise the field under conditions of small-scale yielding.
To calculate the J-integral from an elastic strain field, the field was integrated to equivalent displacement to use the finite element formulation for high accuracy. The method was validated against two and three dimensional synthetic crack fields and then applied to strain fields measured using synchrotron energy-dispersive X-ray diffraction (EDXD) for a fatigue crack propagating in the heat affected zone (HAZ) of a welded bainitic steel. The integrated displacement field was then used to calculate the J-integral and mode I, showing a good agreement with the standard analytical solution and results obtained using displacement fields of the same crack measured using Digital Image Correlation (DIC). The parametrisation via the J-integral and SIFs was extended to use the finite element solver’s equivalent domain integration (EDI), and anisotropic elastic and elasto-plastic material properties.
The high-resolution electron backscatter diffraction technique (HR-EBSD) was employed to map the elastic strain field. The effect of the unknown deformation conditions at the electron backscatter reference pattern (EBSP0) were investigated to select an optimum EBSP0. The developed analytical techniques were then applied to study deformation twinning, slip band and crack local fields, in situ. First, an age-hardened duplex stainless steel (DSS) sample was deformed in tension, promoting plastic deformation by deformation twinning in the ferrite phase. The local in-plane strain fields ahead of a loaded deformation twin were measured, in and ex situ, and decomposed to the opening mode I and in-plane shear mode II SIFs. The analysis showed that the increase in twin lateral thickness correlates with mode I, while the elastic recovery when the load was removed was mainly in mode II.
By estimating the EBSP depth resolution using Monte Carlo (MC) simulation, the analysis was extended to the third dimension and applied to study, in situ, intragranular slip bands in the ferrite phase of an age-hardened DSS. The integrated displacement fields gave information about the in- and out-of- plane movement of the surface, which was decomposed to the three dimensional stress intensity factors, KI,II,III. This showed that constraint of the topological changes due to out-of-plane shear induces additional tensile stresses, and the ratio of mode II to mode III depends on the direction of the slip band Burgers vector relative to the observed surface.
Finally, a simplified method that did not rely on FE solvers to calculate the J-integral and SIFs was derived and used to investigate mixed-mode cleavage crack propagation in (001) single silicon crystal. The mixed-mode crack field was consistent with a constant maximum potential energy release rate (MPERR) criterion for crack propagation and the expected cleavage toughness of silicon.