Table S1: Chemical Composition (Wt%) and Processing Parameters of the CASTRIP Steels

Table S1: Chemical composition (wt%) and processing parameters of the CASTRIP Steels investigated

Hot Rolling Coiling Specimen Nb C Mn Si N Temperature (°C) Temperature (°C)

Nb-free steel 879 544 0.001 0.034 0.93 0.2 0.008

0.041wt% Nb steel 895 647 0.041 0.036 0.87 0.21 0.007

0.084wt% Nb steel 897 567 0.084 0.031 0.83 0.2 0.006

Appendix A

Determination of solid solution strengthening in Nb-microalloyed CASTRIP® steels using the Fleischer approach

Strengthening by solid solution increases yield strength through increasing the stress required to move dislocations according to the following equation proposed by Fleischer (reference 21).

Where τ = yield strength increment of the steel; c = solute concentration (at.%) G = shear modulus of low carbon steel, 79,600 MPa εs = lattice strain due to the solute;

The lattice strain εs is due to the combined effect of the misfit and modulus mismatch and can be estimated by:

The parameter εb is a measure of the relative size mismatch between the solute and solvent

atom given the atomic radius for Nb and Fe is 0.143 nm and 0.124 nm respectively. εb can be estimated as the fractional change in lattice parameter per unit concentration of solute atom:

Where a is the lattice parameter and c is the solute concentration (at.%). εb is calculated to be 0.153.

The parameter εG represents the modulus mismatch strain can be estimated as the fractional change in shear modulus per unit concentration of solute atom: Where G is the shear modulus and c is the solute concentration (at.%). εG is calculated to be -0.444.

is defined as:

is calculated to be -0.363. β is taken to be 3. εs is calculated to be 0.822. The atomic percentage for 0.04 and 0.08 wt% of Nb in these steels is 0.068 and 0.14 at% respectively.

Using these values, 0.04 wt% Nb gives Δτy = 22.16 MPa while 0.08 wt% Nb gives Δτy = 31.71 MPa.