*3.5. Grain Size Effect*

As mentioned before, the structure is made of tempered and fresh martensite lathes from the first and second quench and bainite from the partitioning stage. So, the toughness of such structure is increased by a high density of the high angle boundaries created, because this kind of boundary acts as an obstacle for cleavage propagation, forcing the cleavage crack to change its microscopic plane of propagation in order to accommodate the new local crystallography [22,36,37]. In addition, the presence of coarse martensite laths leads to early strain localization, especially when they are in the vicinity of untempered martensite islands [38]. However, the complexity of the lath martensitic/bainitic structure makes the grain size measurement very difficult. For this reason, the region of martensite/bainite lathes with a determined crystallographic orientation is defined as a block [39]. Clusters of blocks form a packet when they share the same (111)γ, to which the corresponding (001)α is almost parallel [40]. Since the blocks and packages present high angle grain boundaries (>11◦), the toughness of the material might be influenced by their size [41]. In this study, the effective grain size of the martensite/bainite was determined from EBSD measurements, considering grain boundary misorientation ≥15◦. Figure 11 shows the inverse pole figure (IPF) superimposed on the image quality map (IQ) for the treated samples. Results shows that partitioning at a lower temperature (540 ◦C) leads to a refinement of the effective grain size (block packages), as can be noticed by the change in the color orientation. Kawata et al. [42] showed that the bainite block is coarsened by ausforming, especially for a higher temperature, by formation of preferred variants in a packet. In contrast, the same ausforming treatments refine the lath martensite block. In fact, packet size will

influence the ductile–brittle transition temperature (DBTT). As mentioned in Equation (1), DBTT (*T*) is inversely proportional to the root square of the distance between high-angle grain boundaries (*d*), where K is a constant [36]:

$$T = T\_0 - \mathbb{K}d^{-2}.\tag{1}$$

**Figure 11.** IPF + IQ picture from EBSD analysis of samples: (**a**) S(540, 5); (**b**) S(640, 50).

## **4. Conclusions**

The aim of this work was to investigate the reason for brittle fracture of the samples from a low-carbon, low-Si AHSS, which were post-weld heat-treated by the Q&P method around Bs temperature (640 ◦C). Their strength and ductility were the best in comparison with other samples partitioned at lower temperatures, i.e., 540 ◦C and 440 ◦C. Results shows that since Dc α is much higher than Dc <sup>γ</sup> carbon diffuses out from martensite and piles up behind the border of α /γ. The partitioning temperature controls the rate of carbon diffusion, but this amount at the α /γ border cannot reach the level necessary to stabilize austenite at 640 ◦C, while it can occur for a small area next to the border at 540 ◦C. Subsequently, this RA can contribute to eliminating the brittle fracture due to the TRIP effect and increasing the impact toughness.

STEM results of carbon replicas revealed that there are many more very small precipitates (<0.1 μm) in the sample partitioned at 640 ◦C; this can increase the strength of the material via precipitation strengthening mechanism. On the other hand, EBSD results showed much larger crystallographic packets in this sample, which can result in a lowering of the material strength. The increase of strength by precipitation strengthening and the decrease of the strength due to larger packet size will counteract each other so that the tensile test results of the samples partitioned at 640 ◦C are still good.

**Author Contributions:** Concept and design of experiments: F.F. and E.V.; Experiments, simulations, analysis of data and writing the original draft: F.F.; Experiments and revising the paper: M.A.G.; Supervision: E.V. and F.M.

**Funding:** This research was funded by Erasmus+: Erasmus Mundus Joint Doctorate (EMJD)-Advanced Materials Engineering-DOCMASE, grant number "2011-0020".

**Acknowledgments:** The support of the EUSMAT (European School of Materials) via the Ph.D. program 'DOCMASE' and Flavio Soldera is gratefully acknowledged by the authors.

**Conflicts of Interest:** The authors declare no conflict of interest.
