Tensile Work Hardening Modeling of Precipitation Strengthened Nb-Microalloyed Steels

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THE metallurgical basis for thermomechanical processing of HSLA steels is the use of microalloying elements.[1–4] Strain-induced precipitation of niobium carbonitrides is able to delay austenite recrystallization during interpass times,[5–7] leading to the strain accumulation that enhances nucleation during c fi a transformation and final grain refinement.[8–11] Depending on the steel composition and the thermomechanical sequences applied to condition the austenite, some Nb can remain in solution at finishing temperature. In particular, it is expected that for sheet rolling, which involves a fast process, short interpass times at the finishing mill (~10 seconds) will not allow full precipitation of Nb. Precipitation of Nb remaining in solution after finishing rolling can take place in austenite. The MC precipitates exhibiting a ClNa type of lattice adopt a cube–cube orientation relationship with austenite. After transformation to ferrite, these precipitates become incoherent or follow a Kurdjumov–Sachs orientation relationship with the matrix. The solubility of Nb decreases about 20 times when passing from austenite to ferrite, which promotes precipitation either during or after transformation, as far as the appropriate conditions are fulfilled. Interphase precipitation takes place at temperatures above 973 K (700 C), particularly for slow transformation rates and high supersaturation of Nb.[12–14] Precipitation on the ferrite side of the austenite/ferrite transformation front

AMAIA IZA-MENDIA, DENIS JORGE-BADIOLA, and ISABEL GUTIE´RREZ, are with the CEIT and Tecnun (University of Navarra), Manuel de Lardizabal 15, 20018, Donostia-San Sebastia´n, Basque Country, Spain. Contact e-mail: [email protected] Manuscript submitted November 8, 2016. METALLURGICAL AND MATERIALS TRANSACTIONS A

leads to a semi-coherent precipitation, following only one of the three variants of the Baker–Nutting orientation relationship.[15] Homogeneous or general precipitation of NbC in ferrite is expected to give all the Baker–Nutting orientation relationship variants. The precipitation strengthening found in Nb-microalloyed steels is usually well described by Ashby–Orowan equation[16,17]: pffiffiffiffi fv x ln ; ½1 Dryp ðMPaÞ ¼ 10:8 6:125  104 x where fv is the volume fraction of the particles and x is the average precipitate diameter in micrometers. This equation, which applies to nonshearable particles, shows remarkable agreement when applied to low carbon microalloyed steels.[16] For shearable precipitates, the dislocations cut through the particles and the corresponding shear stress becomes a function of the critical force to break the particle, F.[18] The strengthening becomes highly dependent on the detailed interaction mechanisms between the dislocations and the obstacles (precipitates) and F becomes proportional to the particle size.[19] The result is that, independent of the interaction mechanism, for shearable particles, the critical resolved shear stress decreases for decreasing particle size. In the present work, the contribution of the pre