Table 1 Summary of selected results on the influence of grain size on toughness and the BDT temperature. The results are contradicting; the issue remains unclear. The main objective of this paper is to harmonise the statements presented below, based on a dislocation dynamics model of crack-tip plasticity.

Toughness, K

Toughness increases with decreasing grain size, \(d\)

Mild steel; hot forged + heat treated; grain size range: 12–85 μm

K_IC-testing; single edge notched bend (SENB) samples

Curry and Kott³

α-β titanium alloy; heat treated to produce various grain sizes;

Charpy test geometry

Greenfield and Margolin⁴

Armco iron; grain size range: 40–1050 μm

J_IC-testing, single edge notched tensile (SENT) samples

Srinivas et al.^5,6

Toughness decreases with decreasing grain size, \(d\)

α-brass, cold rolled + recrystallised; grain size range: 10–175 μm

J-integral, compact tension samples

Werner⁷

Toughness is not affected by grain boundaries

α-iron, 55% rolling reduction + recrystallisation; grain size range: 28–200 μm

J-integral, compact tension samples

Werner⁷

Toughness passes through a minimum at a specific grain size

Tool steel; grain size range: 20–100 μm

K_IC-testing, linear-elastic fracture mechanics

Pecyna and Mazur⁸

Britt-to-ductile transition

BDT temperature decreases with decreasing grain size, \(d\)

Recrystallised tungsten wires (wires made by powder metallurgy); grain size range: approx. 1–5 μm

Tensile testing; samples unnotched

Seigle and Dickinson⁹

Recrystallised tungsten wires (wires made from melted tungsten); grain size range: approx. 10–50 μm

Tensile testing; BDT temperature was defined as the temperature which produces a 1% area reduction; samples unnotched

Campbell and Dickinson¹⁰

Rolled tungsten plates; dislocation density = constant; grain size range: 0.37–1.1 μm (in the normal direction)

K_IC-testing, linear-elastic fracture mechanics; single edge cracked tension (SECT) samples

Bonnekoh et al.^12,13

BDT temperature increases with a decreasing grain size, \(d\)

Tungsten, electron beam melted, swaged + recrystallised; grain size range: 200–1280 μm

Bend test; unnotched samples

Klopp and Witzke¹⁴

Recrystallised tungsten; grain size range: 200–1000 μm

Bend test experiments; samples unnotched

Gilbert¹⁵

BDT temperature is not affected by grain boundaries

Recrystallised tungsten; grain size range: 10–500 μm

Three-point bending tests; samples unnotched

Farrell, Schaffhauser and Stiegler¹⁷

Tungsten single crystal; tungsten rod material, hot deformed; 3 μm mean grain size (cross section)

Four-point bend testing, pre-cracked samples

Giannattasio and Roberts^18,19,20

BDT temperature reaches a maximum at an intermediate grain size

Tungsten; grain size was achieved by annealing above the recrystallisation temperature

Summary of bending and tensile tests performed on unnotched samples

Stephens²¹

Pure iron, cold rolling + recrystallisation; grain size range: 1–8000 grains per sq mm

Three-point bending test

Tahmoush et al.²²