Origin of double-peak precipitation hardening in metallic alloys

Whereas conventional precipitation hardening is well-known to feature a single hardness peak, recently, double-peak precipitation hardening was observed, where the first peak hardness is higher than the second conventional one, thus offering a new approach to strengthen materials. Yet, classical precipitation strengthening models fail to predict such high strengthening in the early aging stage. In this work, molecular dynamics simulations were firstly performed to obtain a realistic dislocation-precipitate interaction law at the nano-scale, which was introduced into the discrete dislocation dynamics (DDD) method so as to investigate the precipitation hardening effects at the micro-scale. The DDD simulations correctly predict the double-peak hardening, namely, the critical resolved shear stress (CRSS) for a dislocation passing through a precipitate field first decreases, then increases, and finally decreases, as the precipitate radius r(p) increases. Then, a precipitate shearing model was developed, which agrees well with the DDD simulations and experimental observations. Based on the DDD simulations and theoretical analysis, the three CRSS regimes were found to be controlled by coherency strengthening (CRSS proportional to r(p)(-1/2)), chemical strengthening (CRSS and Orowan mechanism (CRSS proportional to -r(p)(-1)), respectively. Finally, a universal law for the inverse relation between the CRSS and precipitate size at the second, conventional peak was unveiled, while the first peak was found to occur favorably for rapid precipitation in the early aging stage. This work provides new insights into precipitation hardening in general and double-peak hardening in particular, which are of great importance for alloy design.