Observation of deformation twinning and martensitic transformation during nanoindentation of a transformation-induced plasticity steel

For the first time, deformation twinning and martensitic transformation were observed in retained austenite in a low-alloyed transformation-induced plasticity steel using nanoindentation in conjunction with electron backscattering diffraction and transmission electron microscopy. Dislocation glide, martensite formation and deformation twinning were correlated to pop-ins and deviation from linearity in the load-displacement curve. Deformation twinning was found to enhance the stability of retained austenite. This observation furthers our understanding of RA stability during straining of low-alloyed multiphase TRIP steel.

step size of 0.04 μm. The EBSD map in Fig. 1 was used for phase identification prior to nanoindentation. The ultra-microindentation system (UMIS) with a Berkovich diamond indenter was employed for nanoindentation. The peak load was chosen as 2 mN in order to study the deformation behaviour of RA as its stability in our steel is relatively high due to its high carbon content 2,7 . The load control was set to square root mode, including a gradual increase to the maximum value of 2 mN followed by unloading. Load and displacement data were recorded with a resolution of 75 nN and 0.05 nm, respectively. It is noted that the effect of grain boundaries and neighbouring phase on nanoindentation cannot be avoided in the present study due to the small RA grain size 17 . Following nanoindentation, a focused ion beam instrument (FEI Helios NanoLab G3 CX dual-beam) was used to cut lamellae from indented areas corresponding to the white square and circle in Fig. 1. The microstructure under the indentations was characterised using a JEOL JEM-ARM200F TEM operating at 200 kV. Data availability. The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.   Figure 2 shows the load-displacement curve of the RA indicated by the white square in Fig. 1. The pop-in like behaviour around 0.2 mN resulted from the initial contact of Berkovich diamond indenter with sample surface. The corresponding Hertzian elastic contact solution is as follows: 18

Results and Discussion
where P is the applied load, h is the corresponding depth of indentation, R i is the radius of the indenter tip (160 nm in present study) and E r is the effective Young's modulus of indentation. For an isotropic elastic material, the effective indentation modulus E r is given as:  deviates from the Hertzian elastic solution at the first pop-in, which indicates the transition from elastic to plastic deformation. In the elastic regime, the maximum shear stress (τ m ) is calculated as 18 : The initiation load of the first pop-in (0.48 mN) leads to a maximum shear stress of 16.0 GPa. This value is ~20% of the austenite shear modulus (76.8 GPa) at room temperature 21 , which is within the expected range for the theoretical yield strength of a crystalline material 22 . Thus, the first pop-in is likely due to the initiation of dislocation glide 11,12,19,[23][24][25] . Figure 3 shows the corresponding microstructures of the cross-section under the indent (Figs 1 (white square) and 2). As seen, the blocky RA in granular bainite partially twinned (upper-left selected area diffraction (SAD) in Fig. 3(a)) and partially transformed to martensite (lower-left SAD in Fig. 3(a) and fast Fourier transform in Fig. 3(d)). The SAD (lower-left inset) in Fig. 3(a) indicates Kurdjumov-Sachs (K-S) orientation relationship (OR) ({110} bcc //{111} fcc , 〈111〉 bcc //〈101〉 fcc ) between the RA and martensite located far away from the indentation. On the other hand, Nishiyama-Wassermann (N-W) OR ({110} bcc //{111} fcc , 〈001〉 bcc //〈101〉 fcc ) was observed between the RA (SADs in Fig. 3(a)) and martensite located just below the indentation (Figs 3(b, d)); in the more plastically deformed region. Both of these ORs were reported for TRIP steels 26 . In the present steel, only K-S OR was detected in previous studies 2,7 . The N-W OR observed here adjacent to the indentation may be due to the high local strain, leading to rotation from the K-S to N-W OR, as they only deviate from each other by 5.26°2 6 .
As suggested in refs 11,12 , the second pop-in in the load-displacement curve (at a load of ~ 1.3 mN in Fig. 2) can be ascribed to martensite transformation. This is likely due to the volume expansion (~ 3% in iron-carbon alloys 27 ) associated with the rapid diffusionless martensitic transformation process 11 . Here the observation of martensite under the indentation (Fig. 3) further supports the link between the second pop-in and martensite formation.
Of greater interest here is the non-linear part in the load-displacement curve (Fig. 2), as it has been seldom reported before. Based on the observed microstructures (Fig. 3), it is likely due to deformation twinning in RA. On one hand, contrary to martensitic transformation, deformation twinning in face-centred cubic (fcc) crystals is not associated with volume change 28 , and is a continuous process, not spontaneous like martensitic transformation. Thus, twinning is not expected to directly result in a pop-in. On the other hand, deformation twinning is associated with stress relaxation 28 , which in turn can lead to the observed deviation from linearity in Fig. 2. Figure 4(a) shows the load-displacement curve of the RA indicated by the white circle in Fig. 1. This area provides an example of deformation twinning in film RA between bainitic ferrite laths ( Fig. 4(b,c)) characterised using annular bright field STEM imaging (Fig. 4(d,e)) together with fast Fourier transform (Fig. 4(f)). K-S OR between film RA and bainitic ferrite lath is shown via the SAD inset in Fig. 4(b). Compared to blocky RA in granular bainite (Fig. 3), no martensite was observed in this area, and accordingly the load-displacement curve ( Fig. 4(a)) did not show the second pop-in associated with martensite transformation. Additionally, the non-linear part seen in Fig. 2 was not observed in Fig. 4(a); probably due to the formation of fewer deformation twins in this film RA. It is reiterated that the effect of the neighbouring bainitic ferrite laths on the load-displacement curve is unavoidable here due to the large applied load (2 mN) and the nano-sized film RA.
While deformation twinning typically occurs in low stacking fault energy austenitic steels, such as high manganese steels 29 , it has been rarely observed in RA in low-alloyed TRIP steel. Sugimoto et al. 15 . and Timokhina et al. 16 . reported deformation twinning in blocky RA after tensile loading of Fe-0.4C-1.5Si-1.5Mn-0.036Al (10% strain) and Fe-0.12C-1.77Si-1.39Mn-0.031Al-0.02Cr-0.005Cu (5% strain) TRIP steels, respectively. The present steel has similar chemical composition to refs 15,16 and the observed deformation twining is probably due to the relatively high carbon content in RA (~ 6.0 at. %, as measured by atom probe tomography 7 ) which significantly increases the stability of RA against martensitic transformation 10 .
The deformation twins divided the RA grains into sub-grains ( Fig. 4(d)), then each sub-grain developed its deformation substructure by dislocation glide. Consequently, higher strain was required to initiate martensitic transformation and the overall RA stability was enhanced. When the strain is sufficient, the RA sub-grains would sequentially transform to martensite one by one if their volume is sufficiently large to initiate martensite nucleation (a minimum (sub)grain size of 0.7 µm was reported in ref. 5 ). This behaviour was demonstrated by partial transformation of blocky RA to martensite (Fig. 3). The stepwise transformation manner may also contribute to the latter portion of the non-linear stage in the load-displacement curve (Fig. 2) as the small volume expansion associated with limited martensite formation would not be sufficient to result in a pop-in.
To verify the effect of twinning on RA stability, nine indents on blocky RA, which exhibited the second pop-in (indicating martensite transformation) but not the deviation from linearity (indicating no or very limited twinning), were used to estimate the onset load of martensite transformation and returned an average value of 0.93 ± 0.21 mN. However, when many twins were observed in blocky RA (Fig. 3), the onset load for martensite transformation was relatively larger (~1.3 mN in Fig. 2). These results underscore the enhancement of the overall RA stability by deformation twinning.

Conclusion
Nanoindentation and correlative TEM observations of blocky and film RA grains indicate that the plastic deformation of RA occurs in the sequence of dislocation glide, twinning and martensitic transformation. When all these mechanisms are operative, they correspond to the first pop-in, non-linear part and second pop-in in the load-displacement curve, respectively. Deformation twinning enhanced the overall stability of RA via the division of RA grain into sub-grains. Lastly, the absence of martensitic transformation in film RA further supports its higher stability compared to the blocky RA.