III. RESULTS AND DISCUSSION

The determination of the local mechanical properties of austenite and ferrite in duplex stainless steel mandates the ability to distinguish these phases without altering the surface. MFM scans of the indented area can assist us in separating the indentation results into groups based on whether the remaining indent lies in a magnetic domain (ferromagnetic ferrite), a nonmagnetic domain (paramagnetic austenite), or at the interface. Figure 1(a) shows the 75 × 75 μm² phase plot of the indented area extracted from the lift mode. Clear magnetic domains with their worm-like shapes can be easily distinguished in a plain nonmagnetic matrix (nonmagnetic to indicate paramagnetism of the phase, which does not affect the cantilever dynamics). Furthermore, among these domains, remaining indents can be observed. MFM manages to show the distribution of the ferromagnetic ferrite within the paramagnetic austenite without the need to perform any chemical etching steps.

FIG. 1.

MFM scans for duplex stainless steel. (a) A 75 × 75 μm² phase scan in lift mode for the area containing the nanoindentation grid. The ferrite domains are distinguished through the worm-like magnetic domains, while austenite is plain. Nanoindentation grid can be easily noticed as regular bright spots. (b) A scan for a small indentation grid at a slower scan speed for the area marked in (a). The indentations are almost indistinguishable. The bright spots in (a) are artificial due to abrupt variations in the surface altering tip dynamics. (c) Scan of a single indentation shows no variation of phase magnetic characteristics after deformation, and a sharp phase boundary is observed passing though the remaining indent.

It is interesting to notice that the remaining indents in the austenite matrix show bright spots that might support the idea that some magnetic characteristics of these indents are probed, affecting the tip dynamics. Having a closer look on a group of indents that demonstrated such behavior revealed an important explanation of such observation [see Fig. 1(b)]. When the scan size was reduced (∼20 × 20 μm²) along with the scan speed, the previously observed magnetic characteristics disappeared from the remaining indents. In fact, the effect of the remaining indents in the lift phase scan almost disappeared making it almost indistinguishable. To further verify this finding, an indentation located at an interface is scanned and the resulting image is shown in Fig. 1(c). The scan shows a clear boundary separating the two domains (ferrite and austenite) that extends inside the remaining indent. It is surprising that the deformation of the material under the indentation load has no visible effect of the separation between the two domains. Based on our finding, in our range of indentation, the plastic deformation in the austenite did not result in any martensitic transformation and the material kept its paramagnetic properties.

The explanation of the artificial magnetic characteristics of the remaining indents is as follows. Due to the elastoplastic properties of this steel, indentation resulted in the well-known phenomena of pileup. Although the topography of the sample was recorded in the first tapping stroke of the scan, the high scanning speed did not generate an accurate record of the surface. The large scan size also added to this deficiency. During the second stroke (lift mode), the tip was coming across these pileups. The tip hits these abrupt surface variations altering its dynamics and showing these artificial bright spots at the remaining indents. This is why, with a lower scan speed and a small scan size, these spots disappeared.

While the phase plots of MFM showed a strong contrast between the ferritic and austenitic domains in Fig. 1, an extra weak signal was noticed in the lower left corner of the scan. A clearer image of the lower left 17 × 17 μm² area is shown in Fig. 2. The topography map does not provide any information on the phases present, as shown in Fig. 2(b). On the other hand, the lift mode phase plot not only shows the expected strong magnetic signal of the ferritic domains but also a weak magnetic signal of extended periodicity connecting the ferritic domains. This buried magnetic signal indicates the presence of a hidden ferritic domain under the austenite phase. Our investigation of the spatial range of the magnetic forces above the surface (data not shown) indicated that the magnetic forces can alter the tip dynamics approximately 400 nm above surface. Consequently, we believe that the thickness of the austenitic layer is on the order of couple of hundreds of nanometers. This yielded an even greater effect on the force curves recorded in this region.

FIG. 2.

A topography and lift phase scans for the lower left corner of Fig. 1. (a) A topography scan showing the remaining indents with no information to the phases present. (b) A lift phase scan revealing a strong ferrite magnetic signal besides a weak periodic signal connecting the ferrite domains. This indicates that a buried ferrite layer is underneath the austenite. Points P1 and P2 show large values of F _max and W_u/W_t due to the effect of the strong buried ferrite influence.

The MFM scans are further used to divide the nanoindentation force curves into three groups: austenite, ferrite, and interface as were previously outlined. As a preliminary investigation, the quantities that can be extracted directly from the force curves are compared, namely the force recorded at maximum depth F _max and the ratio between the elastic energy to the total energy W_u/W_t involved in the indentation experiment,Reference Cheng and Cheng¹⁷ where

(1)

Before further processing, Chauvenet’s criterion is applied on these quantities recorded for each group to eliminate any outliers. Figure 3 shows that there is indeed a difference in the properties of the force curves measured in each domain. Ferrite has higher maximum force and energy ratios than austenite, while the interface properties show intermediate results between the two domains. This provides the motivation to quantify the mechanical properties of these phases.

FIG. 3.

Maximum force recorded F _max and energy ratio W_u/W_t for each phase and for the interface. The plot shows that differences exist between the phases, implying differences in mechanical properties. The interface records intermediate values between the two phases.

It is interesting to find that two points in the interface group recorded significantly large force and energy ratio values and statistically were marked as outliers. These two points are marked P1 and P2 in Fig. 2(a). With the assistance of MFM scans, it is realized that these two points were highly affected by the buried ferrite domain by recording such high values.

The unloading section of the force curves contains information related to the elastic modulus of the phases. The procedure proposed by Oliver and PharrReference Oliver and Pharr^18, Reference Oliver and Pharr¹⁹ is used to estimate the contact area A _c and extract the values of the elastic modulus E according to the following relations:

(2)

(3)

where S is the slope of the unloading curve evaluated at maximum indentation depth. The value of β is 1.03. The value of Poisson’s ratio for steel is assumed to be 0.3. The contact area is evaluated at the contact depth h _c, where

(4)

The loading section of the force curves contains the plastic characteristics of the indented domain. The most straightforward quantity to estimate that is related to material plasticity is the domain hardness H, which is evaluated as

(5)

Figure 4 shows the elastic modulus values for each group of data. It is interesting to see that ferrite shows the highest elastic modulus of 199.5 ± 14.1 GPa, while the austenite showed the lowest with 183.9 ± 11.6 GPa. This agrees very well with the analysis performed by Moverare and Odén.Reference Moverare and Odén²⁰ The hardness values calculated in Fig. 4 demonstrate the same trend, with ferrite hardness being 3.75 ± 0.23 GPa and austenite hardness being 3.19 ± 0.16 GPa. We can see that ferrite supersedes the austenite in its mechanical properties both elastically and plastically. Moverare and OdénReference Moverare and Odén²¹ have explained that although ferrite is generally considered as the strong phase,Reference Siegmund, Werner and Fischer^8, Reference Fischer, Rammerstorfer and Bauer^22, Reference Siegmund, Werner and Fischer²³ duplex stainless steel samples might show the opposite behavior.Reference Inal, Gergaud, Francois and Lebrun²⁴ The reason behind this is the role that nitrogen plays in stabilizing the austenite phase and in acting as a planar glide promoter, which enhances the strength of austenite.Reference Moverare and Odén²¹ This complies with the fact that the nitrogen concentration in this particular sample is very low (<0.07%).Reference Solomon and Devine²⁵

FIG. 4.

The elastic modulus and hardness values estimated for each group. The ferrite supersedes austenite in both quantities showing that ferrite is the strong phase. The properties of the interface show to be a weighted average of the two phases with no predominant behavior.

The properties of the interface are calculated and result in intermediate values between the two phases (E = 189.7 ± 15.4 GPa and H = 3.42 ± 0.38 GPa) also seen in Fig. 3. In fact, interface boundaries have an important role in the microscale deformation of the two phases. Fréchard et al.Reference Fréchard, Martin, Clément and Cousty²⁶ studied the plastic deformation of this type of steel and identified activated slip systems in each phase. They noticed that ferrite grains showed delayed deformation with two main mechanisms. First, the pileup of austenite dislocations at the phase boundary induced dislocation generation in ferrite. Second, some ferrite grains were totally sheared by the dislocation traces of the surrounding austenite. For such BCC/FCC (body centered cube/face centered cube) system, the Kurdjumov–Sachs crystallographic relation must be satisfied: {111}_fcc//{110}_bcc and {011}_fcc//{111}_bcc for the dislocations to be able to be transferred from the austenite to ferrite. Serre et al.Reference Serre, Salazar and Vogt²⁷ showed similar behavior but also noticed new curved deformation bands in ferrite grains that were explained to appear by the incompatibility of the ferrite grain with the neighboring austenitic grains. In our localized deformation, the interface demonstrated to be a weighted average effect of properties between the two phases without a predominant behavior. The large indented area and the inability to control the precise location of interface indentation could not assist in better analyzing these regions.

To achieve a better insight and attempt to glean more information concerning the plastic properties of the phases, the force curves were used to estimate the yield strength Y and hardening exponent n of the phases. Dao et al.Reference Dao, Chollacoop, Van Vliet, Venkatesh and Suresh²⁸ utilized dimensional analysis to relate material plastic properties to measurable quantities from the force curves. They provided a reverse algorithm that can estimate Y and the n of the indented material. Their set of empirical equations was solved and the results are plotted in Fig. 5.

FIG. 5.

Plastic properties of the three groups namely Y and n. Austenite and ferrite have similar yield strength, while the hardening exponent for ferrite is slightly lower than ferrite. The values are in very good agreement with the literature.Reference Solomon and Devine²⁵ This does not contradict what was seen in the hardness values as explained by Cheng and Cheng.Reference Cheng and Cheng¹⁷

The values of Y of the three groups lie in the range of 370 MPa. This value agrees very well with the values reported in Solomon and DevineReference Solomon and Devine²⁵ for the yield strength of bulk samples. The n value reported in Solomon and DevineReference Solomon and Devine²⁵ is 0.2, which is less than the range obtained in this study of 0.25. It is noted that Dao et al.Reference Dao, Chollacoop, Van Vliet, Venkatesh and Suresh²⁸ discussed the uniqueness and accuracy of the algorithm and demonstrated that the solution is unique given that n < 0.3 or Y/E _r < 0.03. Our material properties lie within these limits. On the other hand, the algorithm suffered from high sensitivity in predicting Y and n.Reference Gouldstone, Chollacoop, Dao, Li, Minor and Shen²⁹ Still, their values were estimated with reasonable accuracy compared to experiments,Reference Dao, Chollacoop, Van Vliet, Venkatesh and Suresh²⁸ especially when averaging several experimental indentation results. The error in n is expected to be larger due to its magnitude, numerical accuracy, and the uncertainties in the dimensionless functions.

While the trend observed previously in the hardness data can be seen in the hardening behavior of the three groups, the Y behavior shows no significant differences among the different domains. It is instructive to analyze the plasticity results using the dimensional analysis performed by Cheng and Cheng.Reference Cheng and Cheng¹⁷ TaborReference Tabor³⁰ used slip line field analysis for indentation in a rigid plastic solid using a frictionless rigid wedge, coming to the conclusion that H and Y are related where H = 3Y. However, for most metals, strain hardening results in an increase in yield strength of the material and consequently the plastic strain will vary across the deformed region. TaborReference Tabor³⁰ suggested to modify the relation into H = 3Y ₀, where Y ₀ is the uniaxial flow stress at some specified strain value. On the other hand, Cheng and ChengReference Cheng and Cheng¹⁷ showed that H/Y is not constant for a large range of material properties. Furthermore, they showed that H depends on E, Y, and n, where the strain hardening has its greatest effect at small values of Y/E. Comparing the Y values to the H values of this duplex stainless steel, we find that H ∼ (8–10)Y, in very good agreement with what Cheng and ChengReference Cheng and Cheng¹⁷ demonstrated at Y/E ∼ 0.002 and n ∼ 0.25. In summary, ferrite demonstrates higher elastic modulus and strain hardening than austenite, while they both have very similar yield strength. The difference observed in the values of H between the two phases is real and is a consequence to the elastic and hardening differences between them.

It is worth mentioning that thermal stresses are generally introduced in duplex stainless steel during cooling due to the difference in thermal coefficients of expansion between the two phases.Reference Johansson, Oden and Zeng⁷ Trying to simulate them from cooling modeling, the experimental values of residual stresses demonstrate smaller values than what simulations expect.Reference Siegmund, Werner and Fischer^8, Reference Siegmund, Werner and Fischer²³ Johansson et al.Reference Johansson, Oden and Zeng⁷ argued that plastic deformation and creep might be the reason for causing stress relief. Such stress relief is also anisotropic based on sample processing and texture.Reference Johansson, Oden and Zeng⁷ Furthermore, Johansson et al.Reference Johansson, Oden and Zeng⁷ demonstrated that although residual stresses increase in the initial elastic loading, they start decreasing during plastic deformation. Given these findings and knowing that nanoindentation causes highly localized deformation, we would argue that such stresses, despite not being included in our analysis, would not have a significant influence to invalidate the results.