M3 Precipitation Hardening

Topic

Second-phase particles precipitating within the metal—dispersed throughout the metallic matrix—block the movement of dislocations attempting to pass through; this very obstruction produces the precipitation hardening described by the model: the more difficult it is for a dislocation to traverse this dispersion of second-phase particles, the greater the additional mechanical strength provided by this hardening mechanism. Closer proximity between these second-phase particles—resulting in reduced inter-precipitate spacing—causes a moving dislocation to encounter them more frequently, thereby increasing the strength contributed by this hardening mechanism.

When these second-phase particles are sufficiently small and coherent with the surrounding matrix lattice, an encountering dislocation does not bypass them but instead cuts directly through, slicing them in two; this is the cutting mechanism, and the additional strength it provides depends on the extra energy required for the dislocation to create the new interface—or "misfit surface"—left within the particle upon cutting. Within this same cutting regime, if these small, coherent particles increase in size, the additional strength provided by the cutting mechanism also increases.

Conversely, when these second-phase particles grow too large or lose coherency with the surrounding matrix, the encountering dislocation can no longer cut through them; instead, it must bow out between adjacent particles until it completely bypasses each one, leaving behind a dislocation loop encircling every particle. This is the Orowan mechanism, and the additional strength it provides depends, in this instance, on the inter-precipitate spacing that the dislocation must bow through to pass. The fact that these large, non-shearable particles are closer together—with reduced spacing between precipitates—forces dislocations to bow more sharply to bypass each one, thereby increasing the additional strength provided by this Orowan mechanism.

Consequently, this model—based on the blocking of dislocation motion—implies the existence of a transition radius for these second-phase particles: a critical size at which it ceases to be easier for a dislocation to cut through the particles and becomes easier to bypass them. Below this transition radius, the cutting mechanism dominates, whereas above it, the Orowan mechanism prevails; thus, the maximum strengthening effect from precipitation hardening is achieved precisely when the second-phase particle size approaches this transition radius. Since the blocking of dislocation motion by second-phase particles is the dominant regime in heat-treatable aluminum alloys and superalloys, this model represents the most significant strengthening mechanism for these alloy families.

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