Small-angle neutron scattering of multiphase secondary hardening steels

Abstract

Alloying secondary hardening steels with Ni and Al allows the precipitation of an intermetallic phase B2-NiAl in addition to the classical secondary carbides precipitation, adding up the advantages of both types of precipitation (Erlach et al. Mater Sci Eng A 429:96, 2006; Erlach et al. Int J Microstruct Mater Prop 3:373, 2008). Small-angle neutron scattering experiments were carried out to analyse the nanometric scale precipitation of a martensitic steel containing a double precipitation of carbides and intermetallic phase. The precipitates size, volume fraction and chemical composition for both carbides and intermetallic phases according to the tempering time were estimated and discussed. In addition, experimental cobalt-free grades containing a single precipitation or a double precipitation were manufactured and analysed. Relationship between measured tensile yield strengths and the nanometre-sized particles are suggested, showing that both populations of precipitates have a relevant impact on the mechanical properties.

Appendices

Appendix 1

The form factor of a gaussian distribution of ellipsoids defined by r _i , σ _i and ell _i (see “SANS experiments” section) has the following expression:

$$ |F_{\rm gauss}(q)|^2 = \frac{\int_0^{2r_i}{\frac{4\pi}{3} {\rm ell}_i r^6 \mathrm{e}^{- (r-r_i)^2/(2 \sigma_i^2)} |F_{\rm ell}(q)|^2 \mathrm{d}r}}{\int_0^{2r_i} {r^3 \mathrm{e}^{- (r-r_i)^2/(2 \sigma_i^2)} \mathrm{d}r}} $$

(16)

where F _ell is given by

$$ |F_{\rm ell}(q)|^2 = \int\limits_0^1{|F_{\rm sph}(q)|^2 \left(qr_i\sqrt{1+ x^2({\rm ell}_i^2- 1)}\right) \mathrm{d}x} $$

(17)

The form factor of a sphere of radius r _i is recalled:

$$ |F_{\rm sph}(q)|^2 = 9 \left( \frac{\sin qr_i - qr_i \cos qr_i}{(qr_i)^3} \right)^2 $$

(18)

Appendix 2

The shear modulus is considered as proportional to T _m a ⁻³ where T _m is the melting point and a the cubic root of the volume per atom. For the sake of simplicity, it has been considered that ${\mathrm{M_2C}}$ shear modulus was a linear combination of $\mathrm{Cr_2C}$ (75%) and $\mathrm{Mo_2C}$ (25%). Iron is used as a reference. The calculation of shear modulus of $\mathrm{Cr_2C}$ and $\mathrm{Mo_2C}$ with the parameters given in the Table 3 leads to a ${\mathrm{M_2C}}$ shear modulus of 108 GPa. Melting points were found in [33].

Table 3 Estimation of the shear modulus of ${\mathrm{M_2C}}$ carbides (bold) from their melting temperature and cubic root of the volume per atom