Question 4 of 8: Strengthening Single Crystals; Directionally-Solidified Single-Crystal Superalloy Turbine Blades

Question 4: Strengthening Single Crystals; Directionally-Solidified Single-Crystal Superalloy Turbine Blades (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

4.1 — (a) Two strengthening methods for a single crystal of pure copper

A single crystal of pure, annealed copper has an extremely low yield strength (a few MPa) because dislocations glide almost unimpeded on its close-packed $\{111\}\langle110\rangle$ slip systems with essentially no obstacles present. Two well-established methods raise its strength substantially without changing the fact that it remains, or becomes, a useful engineering metal.

Method 1 — strain (work) hardening. Plastically deforming the crystal (rolling, drawing, forging) multiplies the dislocation density from an annealed value of roughly $10^6$–$10^8\ \text{m}^{-2}$ to $10^{14}$–$10^{15}\ \text{m}^{-2}$ or more. Because dislocations moving on intersecting slip systems cut through and entangle with one another (forest hardening), the flow stress rises with dislocation density through the Taylor relation $\tau=\alpha Gb\sqrt{\rho}$: each additional dislocation makes it progressively harder for the next one to glide. A cold-drawn copper wire can reach several times the yield strength of the same metal annealed, entirely without any change in composition, at the cost of reduced remaining ductility and the introduction of anisotropic (textured) properties.

Method 2 — solid-solution strengthening. Alloying with a soluble solute (e.g. zinc, forming a copper–zinc solid solution such as brass) introduces substitutional solute atoms whose size and/or modulus mismatch with the copper matrix creates local lattice strain fields. These strain fields interact elastically with, and impede the glide of, dislocations, raising the shear stress needed for slip roughly as $\Delta\tau\propto c^{1/2}$ (concentration to the one-half power, for most solute/mismatch combinations). Unlike work hardening, solid-solution strengthening does not consume the material's ductility as an intrinsic feature of the process itself, and the strengthening persists even after a full recrystallisation anneal (which removes work hardening entirely), because the solute atoms remain in solution regardless of the grain/dislocation structure.

(A third route, precipitation/age hardening, is not available to a single-phase pure metal or simple binary solid solution at all compositions, and grain-boundary/Hall–Petch strengthening is not applicable to a single crystal by definition since it has no internal grain boundaries — both are excluded here for that reason, though they are the dominant strengthening routes in most polycrystalline engineering alloys.)

4.2 — (b) Why turbine blades are cast as directionally-solidified single crystals

A conventionally cast, equiaxed polycrystalline nickel superalloy blade has grain boundaries running in every orientation through the highly stressed aerofoil, and at the blade's service temperature (typically 900–1100 °C at the highest-stressed sections) those grain boundaries are the weakest link in the microstructure for the two damage mechanisms that actually limit blade life: creep and thermal-mechanical fatigue.

1. Grain boundaries are the dominant creep-damage site at high homologous temperature. At $T/T_m\gtrsim0.5$ (readily reached in service), grain-boundary sliding and diffusional (Coble) creep along boundaries, together with cavity nucleation and growth specifically at grain boundaries (especially boundaries oriented roughly transverse to the principal stress, i.e. the centrifugal loading axis of a rotating blade), dominate the creep-rupture life. Removing grain boundaries entirely — growing the whole blade as one single crystal — eliminates this damage mechanism outright, rather than merely slowing it, which is why single-crystal blades achieve dramatically longer creep-rupture lives than even carefully grain-boundary-strengthened (e.g. boron/carbide-doped, columnar-grain directionally solidified) polycrystalline alternatives at the same stress and temperature.
2. Directional solidification aligns the surviving anisotropy favourably. The blade is grown from a chilled base through a steep, controlled axial thermal gradient so that dendrites (and, for the single-crystal process, one selected dendrite via a crystal selector) grow along the low-modulus $\langle001\rangle$ crystallographic direction, which is deliberately aligned with the blade's long (radial, centrifugally loaded) axis. FCC-based (and here, the $\gamma$/$\gamma'$ two-phase Ni-superalloy) elastic modulus is markedly anisotropic, lowest along $\langle001\rangle$; orienting the low-modulus direction along the principal stress axis reduces the thermal stress generated by the through-section temperature gradients the blade experiences every start–stop cycle (thermal stress scales with $E\Delta T$), directly improving thermal-mechanical-fatigue life, which single crystals could not exploit if grown in a random or equiaxed orientation.
3. The $\gamma$/$\gamma^\prime$ precipitation-hardening microstructure is retained and even improved. Removing grain boundaries does not remove the alloy's primary strengthening mechanism, coherent, cuboidal $\gamma^\prime$ (Ni$_3$(Al,Ti)) precipitates in the $\gamma$ matrix, which continues to provide the bulk of the high-temperature strength via Orowan/coherency strengthening exactly as in the polycrystalline alloy. Because no grain-boundary-strengthening additions (boron, zirconium, carbon, hafnium) are needed once there are no boundaries to strengthen, the single-crystal alloy composition is free to eliminate those elements, which in polycrystalline alloys depress the incipient-melting temperature; the resulting higher usable solution-heat-treatment temperature allows a more complete, more homogeneous $\gamma^\prime$ distribution to be achieved, which raises both creep and fatigue strength further still.