Modelling plastic zones and the brittle-ductile transition

Abstract

Many crystalline solids fail by cleavage at low temperatures and by plastic processes at high temperatures. In the transition region, cleavage failure occurs at stresses increasing with increasing temperature, reflecting a decrease in yield stress and a consequent increase of plasticity around the crack tip. Crack tip plasticity blunts the crack and shields it through the compressive stresses in the plastic zone. This competition between cleavage and plastic flow can be modelled in terms of the generation (from a source), motion and interaction of dislocations moving on the slip plane containing the crack tip, obeying a velocity-stress-temperature law. Assumptions have to be made about the criterion for cleavage fracture and the density and strength of dislocation sources. While the temperature range and strain-rate sensitivity of the transition depend on the velocity law, the form of the transition (sharp or gradual) depends on spacing of the dislocation sources and thus the transition is structure sensitive. Static equilibrium arrays of discrete dislocations have also been modelled and these are compared with continuum plasticity models of the plastic zone.

Strain-rate dependence of the brittle-to-ductile transition temperature in tungsten

“…Experimental studies on these materials have shown that the T BDT / strain rate behaviour follows an Arrhenius law with an activation energy equal to that for dislocation glide [2,5]. Dislocation-dynamics models of slip around crack tips and the elastic "shielding" of the crack tip by the active dislocations fit the experimental results to high accuracy [6]. In other materials such as TiAl [7], NiAl [8] and zirconia [9], an Arrhenius law for the BDT with a well-defined activation energy is found, but no data exist for comparison with the thermal activation parameters of dislocation glide.…”

“…The dislocation velocity / stress / temperature relation for a given material is a key input parameter for dislocation dynamics modelling of the BDT [6,23]. Currently the only dislocation velocity data available for tungsten are at room temperature and 77K [15], and thus derivation of a sound dislocation velocity law for the experimental temperature range used here is problematic.…”

Fracture Toughness Enhanced by Grain Boundary Shielding in Submicron-Grained Low Carbon Steel

“…This idea is called ''shielding effect'' due to dislocations. 28) summarised the BDT temperature of single crystal silicon from several groups and plotted ln(strain rate), ln _ " ", against reciprocal BDT temperature, 1=T BDT , showing that each line from the collected data exhibits the same angle of slopes in the ln _ " " -1=T BDT diagram but shows different interceptions of the lines with the axis of ln _ " ". This indicates that the activation energy for the BDT is constant over the whole results used, being independent from the shape or measure of the experiment, however, the BDT temperature depends on the way of the experiment.…”

HVEM/AFM Observation of Hinge-Type Plastic Zones Associated with Cracks in Silicon Crystals

“…Silicon crystals have been employed as a model substance to understand such dislocation process, since highly perfect crystals are obtainable and they exhibit a very sharp BDT. 1,2) When the BDT occurs to cause a steep increase of fracture toughness, a burst of dislocation multiplication takes place around the crack tip. However, TEM studies for such dislocation process in Si have been very limited so that the mechanism of the sharp BDT has been still unclear from the viewpoint of the dislocation theory.…”