A non-local methodology for geometrically necessary dislocations and application to crack tips

A multi-scale approach to microstructure-sensitive thermal fatigue in solder joints

“…Three components of the GND tensor, namely the screw dislocation density, the tangent edge dislocation density and the norm dislocation density, are found from a singular decomposition of the Nye's tensor, whose details can be referred to the local methodology in (Xu, 2021). A scalar GND density is then given by the by L2-norm minimization of the three density terms (Cheng and Ghosh, 2015) as:…”

Synergistic coupling of thermomechanical loading and irradiation damage in Zircaloy-4

“…where τ i 0 is the intrinsic material CRSS (measured experimentally [22]), µ is shear modulus, ρ SSD is the density of statistically stored dislocations (SSDs), whose evolution is linear with plastic strain [23], ρ GND is the density of geometrically necessary dislocations (GNDs) [24], and ρ loop is the total density of dislocation loops, which form during irradiation. Temperaturedependant elastic-plastic properties [23] are also incorporated.…”

〈112̄0〉-orientation-dependent crack initiation in a titanium alloy under dwell fatigue

“…The mean geometrically necessary dislocation (GND) density with 〈 a 〉 type Burgers vectors in hard grains near soft/hard GBs was calculated from EBSD data with the same step size of 200 nm, and so the comparison of the GND density under the same conditions was statistically significant. The use of mean GND density 27 within the measurement region can substantially reduce the effect of extreme GND density values 28 and well reflect the trend of GND density variation. The GND density is obtained by determining the dislocation density tensor based on the relationship established by Nye, 29 and the primary calculation approach is provided by the work of Pantleon.…”