The β′ precipitates, which take 45.6% of the total precipitate volume in the peak-aged sample, contribute to the entire precipitation strengthening by only 31.6%.

We have, for the first time, separated the strengthening effect of the contribution from βʺ and βʹ precipitates, respectively, by an indirect approach based on high-precision measurements of volume fractions, number densities, sizes, proportions of the precipitates, their lattice strains, the composition and grain size of the matrix. The under-aged sample only contains nano-precipitates of the β″ type, while the peak-aged one contains nearly equal volumes of β″ and β′ precipitates. To clarify this, two samples of the same Al–Mg–Si alloy but with different aging states were prepared. The reason for this difference is not well understood. It is generally believed that β″ precipitates, rather than β′ precipitates, are the major strengthening precipitates in aged Al–Mg–Si alloys. The present results provide a universal framework for modeling and analyzing the strengthening behavior of oxide particle strengthened solid-solution alloys. Moreover, the optimal oxide size is found to maximize the oxide particle strengthening. The critical particle radius does not rely on the volume fraction of oxide particle, in good agreement with the previous work. The calculated results of our work agree well with the experiments, compared with that calculated from the classical oxide particle strengthening theory. Here, a unique predictive model, which considers not only the relative position between the dislocation slip plane and oxide particle center, but also the distribution effect of oxide particle size, is proposed to describe oxide particle strengthening. However, the prediction of the classical oxide particle strengthening model can be not well consistent with the experiments, especially in the transition region from the dislocation cutting mechanism to the Orowan mechanism. The addition of oxide particle would lead to a remarkable improvement in the mechanical properties in solid-solution alloys, due to their pinning effects for dislocation motion. After aging treatment at 650 ☌ for 2 h, the yield strength and tensile strength of the stainless steel was 705.6 MPa and 1002.3 MPa, the elongation and the relative magnetic permeability was 37.8% and 1.0035, respectively. The coarsening behavior of (Nb, V)(C, N) precipitates in the grain was analyzed, and the size of the particles precipitated after aging treatment at 650☌ for different time was calculated and studied. Meanwhile, coarse M23C6 was distributed at the grain boundary with chain shape, which was non-coherent with the matrix. When the aging temperature was beyond 650 ☌, the coarsening rate of (Nb, V)(C, N) particles increase rapidly and the coherent orientation between (Nb, V)(C, N) particles and the matrix was lost gradually.

During the aging treatment, the (Nb, V)(C, N) particles gradually precipitated in the grain, which were coherent or semi-coherent with the matrix. The steel was aged at 550–750 ☌ for 2 h after solution heat treatment at 1100 ☌ for 1 h. The effect of aging on the precipitates, mechanical and magnetic properties of Fe-21Cr-15Ni-6Mn-Nb low magnetic stainless steel were investigated.

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