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Elastic consideration of the precipitation in model alloys of maraging steels: theory and experimental validation

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Abstract

The unique combination of high strength and high fracture toughness in maraging steels is attributed to the precipitation of mainly two phases, Ni3Mo and Ni3Ti, in the soft bcc martensitic matrix. Experimentally, it is difficult to distinguish between these phases; moreover, the effect of each precipitating phase on the properties of the steel is ambiguous. In the present work, we tackle these questions by analyzing the elastic fields and elastic energy associated with each precipitating phase and their role in the determination of the shape and relative arrangement. Using a semi-analytic approach based on the solution of the equations of elasticity by Fourier transform, the elastic fields and elastic energy associated with each precipitate were calculated. The calculations show that the minimum self-energy of both precipitates is accomplished when the smallest crystallographic misfit lies parallel to the longest geometric axis. The combination of elastic energy and surface energy provides an explanation to the observed morphologies of the precipitates, each type having an elongated shape but with a different aspect ratio. According to the calculations, the minimum self-elastic energy associated with Ni3Ti coherent precipitate is 2.8-fold larger than the energy of Ni3Mo. This implies for a larger strengthening effect of the former, as was confirmed experimentally in model alloys, one without Mo and the other without Ti. The elastic model also predicts that elongated shape and the anisotropic misfit strains favor several vertical arrangements of both precipitates, as was also verified experimentally by transmission electron microscopy of aged model alloys.

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Notes

  1. The surface area of a thin plate is approximately \( 2\pi a_{1}^{2}, \) and the surface area of a thin rod is nearly \( 2\pi a_{2} c_{2} \). Assuming equal volumes, the surface area of the plate is larger than the area of the rod when \( a_{1} > \left( {\beta_{1} /\beta_{2} } \right)c_{2} \). According to Fig. 6b, the elastic energy of a rod with β 2 = 20 is equal to that of a plate with β 1 = 0.2. For this situation, the surface area of the plate is larger when a 1 > 0.01c 2, which is an obvious relation for precipitates in solids.

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Acknowledgments

The authors thank Mr. O. Omasi for the preparation of the model alloys. This study was supported by the joint IAEC-UPBC Pazy foundation.

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Authors and Affiliations

  1. Department of Materials Engineering, Ben Gurion University of the Negev, POBox 653, Beer Sheba, Israel

    M. Shmulevitsh, L. Meshi & R. Z. Shneck

  2. Nuclear Research Center, Negev, POBox 9001, Beer Sheba, Israel

    M. Shmulevitsh & M. Pinkas

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  1. M. Shmulevitsh
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  2. L. Meshi
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  3. M. Pinkas
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  4. R. Z. Shneck
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Correspondence to M. Shmulevitsh.

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Shmulevitsh, M., Meshi, L., Pinkas, M. et al. Elastic consideration of the precipitation in model alloys of maraging steels: theory and experimental validation. J Mater Sci 50, 4970–4979 (2015). https://doi.org/10.1007/s10853-015-9044-7

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  • DOI: https://doi.org/10.1007/s10853-015-9044-7

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