Slip bands in metals
[5] Slip-bands can be simply viewed as boundary sliding due to dislocation glide that lacks (the complexity of ) PSBs high plastic deformation localisation manifested by tongue- and ribbon-like extrusion.
[clarification needed] This is different to slip-bands that is a planar stack of a stable array that has a strong long-range stress field.
[13] PSB and planar walls are parallel and perpendicularly aligned with the normal direction of the Critical resolved shear stress, respectively.
Fisher et al. [18] proposed that SBs are dynamically generated from a FrankβRead source at the specimen surface and are terminated by their own stress field in single crystals.
[23] Dislocation activity assists the growth of austenite precipitates and provide quantitative data for revealing the stress field generated by interface migration.
Steps can be created on the free surface as a consequence of the tendency for dislocations to follow one another along a glide path, of which there may be several in parallel with each other in the grain concerned.
The appearance of such bands, which are sometimes termed βpersistent slip linesβ, is similar to that of those arising from cyclic loading, but the resultant steps are usually more localised and have lower heights.
The parallel lines within individual grains are each the result of several hundred dislocations of the same type reaching the free surface, creating steps with a height of the order of a few microns.
The elastic strains describe the stress concentration ahead of the slip band, which is important as it can affect the transfer of plastic deformation across grain boundaries.
[5][33] To properly characterise slip bands and validate mechanistic models for their interactions with microstructure, it is crucial to quantify the local deformation fields associated with their propagation.
The conservation laws of elasticity related to translational, rotational, and scaling symmetries were derived initially by Knowles and Sternberg [36] from the Noether's theorem.
[37] Budiansky and Rice[38] introduced the J-, M-, L-integral and were the first to give them a physical interpretation as the strain energy-release rates for mechanisms such as cavity propagation, simultaneous uniform expansion, and defect rotation, respectively.
[39] That work paved the way for the field of Configurational mechanics of materials, with the path-independent J-integral now widely used to analyse the configurational forces in problems as diverse as dislocation dynamics,[40][41] misfitting inclusions,[42] propagation of cracks,[43] shear deformation of clays,[44] and co-planar dislocation nucleation from shear loaded cracks.
[45] The integrals have been applied to linear elastic and elastic-plastic materials and have been coupled with processes such as thermal [46] and electrochemical [47] loading, and internal tractions.
[48] Recently, experimental fracture mechanics studies have used full-field in situ measurements of displacements [49][50] and elastic strains [51][50] to evaluate the local deformation field surrounding the crack tip as a J-integral.
General definitions of the PeachβKoehler configurational force (πππ) [52] (or the elastic energy-momentum tensor [53]) on a dislocation in the arbitrary π₯1, π₯2, π₯3 coordinate system, decompose the Burgers vector (π) to orthogonal components.
π½π = β« πππ ππ ππ = β«(ππ ππβ ππ π’π,π) ππ π½ππ₯ = π ππ π½π, π,π,π=1,2,3 where π is an arbitrary contour around the dislocation pile-up with unit outward normal ππ, ππ is the strain energy density, ππ = πππ ππ is the traction on ππ, π’π are the displacement vector components, π½ππ₯ is π½-integral evaluated along the π₯π direction, and π ππ is a second-order mapping tensor that maps π½π into π₯π direction.
This vectorial π½π-integral leads to numerical difficulties in the analysis since π½2 and, for a three-dimensional slip band or inclined crack, the π½3 terms cannot be neglected.
