**Nomenclature**


#### **Appendix A. Limitations and Challenges Associated with the In Situ Tensile Test Methodology**

Before the in situ tensile tests, the specimens were metallographically polished (OPS). Since the deformed surface of the test specimens was later to be analyzed with digital image correlation software, the test specimens were etched for 5 s in a 3% Nital solution to achieve the required surface contrast. The experiment revealed that only non-deformed inclusions were found on the surface of the specimens, while non-metallic sulfide inclusions with an elongated shape were in the middle of the specimens examined. For further tests, the specimens were ground to a thickness of 0.6 mm and then polished and etched. Since the specimens were very thin, manual grinding was not possible because it was not possible to avoid deviations in the thickness of the specimens. A conventional embedding mass was not suitable for specimen preparation because there was a high risk of damaging the specimens when detached from the embedding mass therefore It was decided to use the embedding mass Technovit-5071 as shown in Figure A1. A special feature of this embedding mass was that the specimens could be dissolved after processing by dissolving the embedding mass in acetone when heated to 30 ◦C.

**Figure A1.** Specimens after polishing in Technovit-5071.

Within the scope of this work, an attempt was made to generate a special pattern [7] on the specimen surface for the digital image correlation program with the help of polystyrene latex beads with a diameter of 0.095 μm. However, due to the previous etching, it was difficult to achieve an even distribution on the surface, as all the beads accumulated in the

resulting depressions (Figure A2). The available DIC systems, such as VEDDAC, GOM, and VIC-2D, have therefore not made a flat closed evaluation possible. Therefore, the procedure with balls was not pursued in further investigations. The focus was placed on a special etching of the specimen surface with the application of the "InLens" module.

The method for the deposition of SiO2 nanoparticles on the specimen surface was as follows:


**Figure A2.** Example of the accumulation of polystyrene latex beads in the deep spots created by etching.

As part of this work, various tests were also carried out to create contrasts on the surface of the specimens. To achieve the desired contrast, different etching times of 2 to 15 s were used (Figure A3).

**Figure A3.** Example of a microstructure surface with different etching times: (**a**) 2 s, (**b**) 5 s, (**c**) 15 s.

Various scanning electron microscope modules such as SE (Figure A4a) and "InLens" (Figure A4b) were used.

**Figure A4.** Example of a microstructure surface using different modules: (**a**) SE, (**b**) "InLens".

Different contrast values were used in the settings of the electron beam microscope (Figure A5a contrast = 49%, Figure A5b contrast = 52%).

**Figure A5.** Example of a microstructure surface at different contrasts of SEM: (**a**) contrast = 49%, (**b**) contrast = 52%.

#### **Appendix B. Local Mises Strain Measurement**

The von Mises strain at the meso plane was calculated using a scale in the areas studied (Figure A6). On each surface of the undeformed specimen, three points were selected so that one point was common; they formed two identical straights, and there was an angle of 90◦ between these straights.

**Figure A6.** Account length of the selected area used to calculate mesoscale plane-strain for the tensile specimen (11K).

The strain was calculated using the following formula:

$$\mathcal{D}\_1 = \ln \frac{a}{a\_0} = \frac{1}{2} \ln \frac{a\_1^2 + b\_1^2 + \sqrt{\left(a\_1^2 + b\_1^2\right)^2 - 4a\_1^2 b\_1^2 \sin^2 \delta}}{2a\_0^2} \tag{A1}$$

$$\mathcal{O}\_2 = \ln \frac{a}{a\_0} = \frac{1}{2} \ln \frac{a\_1^2 + b\_1^2 + \sqrt{\left(a\_1^2 + b\_1^2\right)^2 - 4a\_1^2 b\_1^2 \sin^2 \delta}}{2a\_0^2} \tag{A2}$$

$$\mathcal{Q}\_{\overline{v}} = \frac{2}{\sqrt{3}} \sqrt{\mathcal{Q}\_1^2 + \mathcal{Q}\_2^2 + \mathcal{Q}\_1 \mathcal{Q}\_2} \tag{A3}$$

As a result of the tests, the meso deformation in the long inclusion in the tensile specimen was calculated. The results of meso-scale deformation are presented in Table A1.

**Table A1.** Change in the length of the account of the selected area and angle at the meso plane for the tensile specimen.


The tests yielded the stress–strain diagram shown in Figure A7. The diagram shows that the range of plastic deformation started at 300 MPa. The maximum tensile strength achieved was 462 Mpa, and the breakage of the specimen began at a stretch of 7.9%

**Figure A7.** Stress–strain diagram of the tensile specimen.

Based on the data obtained, diagrams were created to compare the meso deformation and micro deformation in different areas of the study with the names of the selected areas (Figure A8). A diagram has also been created to compare macro and micro deformation (Figure A9).

**Figure A8.** Marking and numbering of measuring points (**a**) around non-metallic inclusions; (**b**) within non-metallic inclusions.

The diagram in Figure A9 shows that the intensity of micro deformation is significantly higher compared to macro deformation at the points far from the pearlite grains.

**Figure A9.** Comparison of meso deformation and micro deformation.

#### **Appendix C. Local Strain Measurement Overlaid on SEM Micrographs**

The frame by frame evolution of local strain distribution around (left) and within (right) the MnS inclusion is presented in Figure A10 from 1.6% to 7.75% global true strain.

**Figure A10.** *Cont*.

**Figure A10.** Local strain measurement overlaid on SEM micrographs.
