Modelling the upper yield point and the brittle–ductile transition of silicon wafers in three-point bend tests

Fracture transitions in iron: Strain rate and environmental effects

“…It should be noted that a fundamental relationship exists between K Ic and G Ic , such that G Ic 5 K Ic 2 /E, where E is the elastic modulus. Roberts and Hirsch 11 have shown nearly a factor of three times change in fracture toughness with a change in strain rate of an order of magnitude. Similarly, a drop in K Ic of tungsten by a factor of two was observed by Gumbsch 5 with an order of magnitude increase in stress-intensity loading rate.…”

“…This would include test temperature and applied strain rate (or stress-intensity rate). The basis for such an analytical model was taken from a previous study wherein the dislocation mobility approach of Roberts and Hirsch 10,11 was adopted with a slight variation. 17 This was originally done to evaluate a fracture toughness K Ic size effect that had been largely measured on silicon nanoparticles and nanopillars of less than about 500 nm in diameter.…”

“…This was later compared with soft transitions (more gradual) in metallic systems. 4,5 Over the following three decades various dislocation nucleation [6][7][8] and dislocation velocity [9][10][11] controlled approaches using discretized dislocation statics and dynamics were put forth. Although it is unclear whether dislocation nucleation or propagation controls the DBTT in a given material, the two processes have been suggested to be correlated and may in fact be viewed as a singular mechanism from the standpoint of thermal activation.…”

“…Although it is unclear whether dislocation nucleation or propagation controls the DBTT in a given material, the two processes have been suggested to be correlated and may in fact be viewed as a singular mechanism from the standpoint of thermal activation. For example, Roberts and Hirsch 11,12 have proposed that dislocation velocity is key to the magnitude of dislocation shielding that can take place. They calculate that the ability to emit subsequent dislocations from a crack-tip or an external source depends on the previous dislocation moving far enough away from the crack tip.…”

Modeling a linear electric molten zone in a silicon ribbon

“…The second derivative of the temperature profile, which is relevant for the generation of strained induced residual stress, peaks precisely in the same region, thus well above the critical temperature for the brittle-ductile transition. 19 Since the current concentration mechanism produces a steeper temperature profile near the molten zone, the use of radiative power will lead to an increased average temperature of the sample thus leading to higher convective and radiative losses. This is clearly seen in Table II which shows the radiative and electric power input required to produce a 1 mm molten zone in (i) an electric molten zone with only a small radiative contribution, (ii) using the base operation parameters, and (iii) a pure optical molten zone.…”