## 2 Materials and Methods  
As-cast Fe-30.9 Mn-4.9 Al-4.5 Cr-0.4C and Fe-21.3 Mn-7.6 Al-4.3 Cr-1C low-density stainless steels were produced by melting compacted powders of pure elements that constitute the alloys in an electric arc furnace. The alloys were turned and melted three times to homogenize them. The chemical composition of the alloys was confirmed using an optical emission spectrometer. Thereafter, Thermo-Calc modeling was performed to predict the likely equilibrium phases in the alloys and the critical transformation temperatures. The amount of the alloying elements in mass percent was entered into the Thermo-Calc software using the TCFE8 thermodynamic database. X-ray diffraction (XRD) analysis was performed on the alloys using a Bruker D2 Phaser diffractometer. The XRD scan was performed at 20 angles of 10 to 90\({}^{\circ}\). The measurements were taken at ambient temperature using generator settings of 10 mA, 30 kV, and cobalt as the anode material. The XRD patterns were matched using PANAlytical software.  
For thermomechanical testing, the alloys were machined into rectangular test samples of 10 \(\times\) 10 \(\times\) 7 mm configurations before subjecting them to rectangular axial isothermal compression testing on a Gleeble 3500 thermomechanical simulator. A platinum-rhoum (R-type) thermocouple was then welded to the mid-span of the samples. Nickel paste and graphite foil were applied in between the tungsten carbide ISO-T anvils and the samples to minimize frictional effects on the flow curves. Figure 1 shows the thermomechanical processing schedule applied to the samples. Three deformation temperatures of 800, 900, and 1000 \({}^{\circ}\)C and two strain rates of 0.1 and 5.0 s\({}^{-1}\) for each temperature were used. These parameters were selected from previous studies [13; 14; 15] and were considered safe for the hot working of Fe-Mn-Al-C low-density steels. Prior to deformation, the samples were heated at a rate of 5 \({}^{\circ}\)C/s up to a reheating temperature of 1200 \({}^{\circ}\)C and then soaked for 120 s to achieve homogenization at the reheating temperature. Thereafter, the samples were cooled to the deformation temperature at a rate of 1 \({}^{\circ}\)C/s and held for 60 s before deformation. All the samples were deformed to a total strain of 0.5 followed by compressed air quenching. The stress-strain data were then captured and analyzed.  
For microstructural analyses, the deformed samples were sectioned into two halves parallel to the compression axis. One of each sample was mounted in an OPAL 410 mounting machine using a polyfast hot mounting resin. The mounted samples were then ground using an IMPTECH 201 grinding machine using silicon carbide abrasive paper of 800 to 2000 grit. They were polished with an alumina suspension and etched with Villella's reagent. Microstructural observation of the polished samples was performed using both optical and scanning electron microscopes (SEM). The undeformed samples were prepared following a similar procedure. The obtained micrographs were then compared to observe the microstructural evolution that each sample went through under different deformation conditions.  
To determine if there is a significant influence of deformation parameters on the hardness of the alloys, Vickers hardness testing was conducted using an FM 700 microhardness tester in accordance with ASTM E 92-17 [16]. The indentation was obtained by using a load of 500 gr and a dwell time of 15 s. An average hardness was computed from five measurements taken at random spots on each sample.