S.G. Roberts

The brittle-ductile transition in silicon

Experimental and theoretical studies of the brittle-ductile transition (BDT) of precracked single crystals of silicon are discussed. For a given strain-rate the temperature T c at which the BDT occ...

Measuring fracture toughness of coatings using focused-ion-beam-machined microbeams

Measuring the toughness of brittle coatings has always been a difficult task. Coatings are often too thin to easily prepare a freestanding sample of a defined geometry to use standard toughness measuring techniques. Using standard indentation techniques gives results influenced by the effect of the substrate. A new technique for measuring the toughness of coatings is described here. A precracked micro-beam was produced using focused ion beam (FIB) machining, then imaged and loaded to fracture using a nanoindenter.

The brittle-ductile transition in silicon. II. Interpretation

A dynamic crack tip shielding model has been developed to describe the brittle-ductile transition (BDT) of precracked crystals in constant strain-rate tests. Dislocations are emitted from a discrete number of sources at or near the crack tip. At the BDT the dislocations are emitted and move sufficiently rapidly to shield the most vulnerable parts of the crack, furthest away from the sources, such that the local stress intensity factor remains below KIc for values of the applied stress intensity factor K above KIc. Computer simulations of the dynamics of dislocation generation from the crack tip sources, assuming mode III loading, suggest that a sharp transition as observed in silicon is predicted only if generation starts at K ≡ K0 ≈ KIc, but then continues at K ≡ KN ≪ KIc. Dislocation etch pit studies reported by Samuels & Roberts (Proc. R. Soc. Lond. A 421, 1─23 (1989)) (hereafter called I) confirm that generation begins at K0 ≈ KIc. It is suggested that K0 corresponds to the value of K at which a crack tip source is nucleated by movement of an existing dislocation in the crystal to the crack tip. The model accounts quantitatively for the strain-rate dependence of the transition temperature Tc reported in I, and predicts a dependence of Tc on dislocation density, in qualitative agreement with (unpublished) experiments. Calcluations of the strees field around the crack tip of a semicircular precrack, suggest that the ends of the half loops emitted by crack tip sources undergo multiple cross slip to follow the crack profile. The predicted dislocation configurations agree with etch pit observations reported in I.

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

We have investigated the strain-rate dependence of the brittle-to-ductile transition (BDT) temperature in pre-cracked tungsten single-crystals and polycrystals. There is an unambiguous Arrhenius relationship over four decades of strain rate, giving an activation energy for the process controlling the BDT of 1.05 eV. This is equal to the activation energy for double-kink formation on screw dislocations, suggesting that their motion controls the brittle–ductile transition.

The strength of Al2O3/SiC nanocomposites after grinding and annealing

Alumina matrix nanocomposites containing about 5 vol.% SiC of < 100 nm mean particle size show a substantial increase in strength after machining and annealing. The final strength is controlled by the annealing process and achieves the same level after a coarse machining using 150-grit diamond as is achieved using a complex lapping and polishing sequence. In all cases the final anneal leads to an increase in strength The nanocomposite retains a significantly higher residual surface-compression stress level than an equivalent grai size alumina after machining. A remnant stress, of about 20% of the initial level, is retained even after 10 h annealing at 1250 C. Hertzian indentation and measurements of Rayleigh ave velocity show that the nanocomposite surfaces contain defects of smaller size and density than are found in equivalent aluminas. Annealing appears to result in healing of existing surface defects thus increasing the nanocomposite strength while leaving its toughness unchanged. The crack-healing mechanism is associated with a chemical process on the nanocomposite surface which has been tentatively identified as an oxidation leading to amorphous mullite formation.

Indentation plasticity and polarity of hardness on {111} faces of GaAs

Abstract Hardness measurements have been carried out as a function of temperature on {111} faces of n- and p-type GaAs. The plastic zone has been studied by observations of slip-line patterns on the surface and dislocation etch pit patterns in sections at different depths from the indentation surface. The nature of the plastic zone, the types of cracks observed, the recovery slip after removal of the load and the polarity in hardness have been explained in detail in terms of slip geometry, sense and type of slip expected, dislocation interactions and the known differences in velocities of As(g) and Ga(g) dislocations.

Modelling the threshold conditions for propagation of stage I fatigue cracks

Abstract Under near threshold conditions fatigue cracks often propagate along crystallographic slip planes with a marked mode II contribution to the loading, particularly when the crack is short. We present here a model for this stage I fatigue crack in which a mode II crack generates dislocations either through activation of a source ahead of the crack or through direct emission from the tip, and the motion and interaction of these dislocations are then simulated dynamically throughout the load–unload cycle. The crack is assumed to grow when cyclic displacement occurs at the crack tip, so that the condition that at least one emitted dislocation per cycle must return to the crack tip, allows the threshold cyclic stress intensity (Δ K th ) to be calculated. In accord with experimental data we find that Δ K th increases with decreasing load ratio. At high load ratio the fatigue threshold is best defined by the need for the cyclic stress intensity to exceed some critical value, while at low load ratio, the requirement is that the maximum stress intensity exceeds a second critical value.

Micro-mechanical measurements of fracture toughness of bismuth embrittled copper grain boundaries

Measuring the fracture properties of single grain boundaries has until now required macroscopic bi-crystals which are expensive and not always available. We describe a method for fracture testing using micro-cantilevers, manufactured using focussed ion beam machining and tested using a nanoindenter. We have used the method to measure the fracture toughness of selected grain boundaries in bismuth-embrittled copper. This technique is applicable to grain boundaries in other brittle polycrystalline samples for which large bi-crystals cannot be produced for conventional testing.

In situstudy of self-ion irradiation damage in W and W–5Re at 500 °C

In situ self-ion irradiations (150 keV W+) have been carried out on W and W–5Re at 500 °C, with doses ranging from 1016 to 1018 W+m−2 (∼1.0 dpa). Early damage formation (1016W+m−2) was observed in both materials. Black–white contrast experiments and image simulations using the TEMACI software suggested that vacancy loops were formed within individual cascades, and thus, the loop nucleation mechanism is likely to be ‘cascade collapse’. Dynamic observations showed the nucleation and growth of interstitial loops at higher doses, and that elastic loop interactions may involve changes in loop Burgers vector. Elastic interactions may also promote loop reactions such as absorption or coalescence or loop string formation. Loops in both W and W–5Re remained stable after annealing at 500 °C. One-dimensional hopping of loops (b = 1/2 ⟨111>) was only seen in W. At the final dose (1018W+m−2), a slightly denser damage microstructure was seen in W–5Re. Both materials had about 3–4 × 1015 loops m−2. Detailed post-irradiation analyses were carried out for loops of size ⩾ 4 nm. Both b = 1/2 ⟨111⟩ (∼75%) and b = ⟨100> (∼25%) loops were present. Inside–outside contrast experiments were performed under safe orientations to determine the nature of loops. The interstitial-to-vacancy loop ratio turned out close to unity for 1/2 ⟨111⟩ loops in W, and for both 1/2 ⟨111⟩ and ⟨100⟩ loops in W–5Re. However, interstitial loops were dominant for ⟨100⟩ loops in W. Re seemed to restrict loop mobility, leading to a smaller average loop size and a higher number density in the W-Re alloy.

Brittle-ductile transitions in polycrystalline tungsten

The strain rate dependence of the brittle-to-ductile transition (BDT) temperature was investigated in notched and un-notched miniature bars made of high-purity polycrystalline tungsten and in notched bars of less-pure sintered material. The activation energy, E BDT, for the process controlling the BDT in pure tungsten was equal to 1.0 eV both in un-notched and notched specimens, though the brittle–ductile transition temperature, T BDT, was ≈ 40 K lower at each strain rate for the un-notched samples, indicating that the activation energy, E BDT, is a materials parameter, independent of geometrical factors. The experimental data obtained from pure tungsten are described well by a two-dimensional dislocation-dynamics model of crack-tip plasticity, which is also discussed. For sintered tungsten, E BDT was found to be 1.45 eV; T BDT at a given strain rate was higher than in the pure tungsten by ≈ 90 K, suggesting that the BDT in tungsten is very sensitive to impurity levels.