Keywords

1 Introduction

High-Mn austenitic steels have attractive mechanical and functional properties associated with characteristic plasticity mechanisms in the γ-austenite that has a face-centred cubic (FCC) structure. These include an extended dislocation glide, mechanical twinning, and mechanical martensitic transformation into ε-martensite with a hexagonal close-packed (HCP) structure and further to α’-martensite with a body-centred cubic or tetragonal (BCC/BCT) structure. Extensive research has been conducted on the deformation mechanism of high-Mn steels, particularly on the transformation- and twinning-induced plasticity (TRIP/TWIP) effects, which lead to the remarkable combination of high strength, ductility, and toughness.

Hereinafter, high-Mn austenitic steel is defined in a broad sense as the steel characterised by a high concentration of Mn, an initially fully austenitic phase state, and low-to-moderate stacking fault energies (SFEs). This category includes traditional Hadfield steels (Hadfield 1888), cryogenic high-Mn steels (Charles et al. 1981; Kim et al. 2015; Sohn et al. 2015), non-magnetic high-Mn steels, TRIP/TWIP steels (Grassel et al. 2000; Bouaziz et al. 2011; Cooman et al. 2018), high dam** Fe–Mn alloys (Wang et al. 2019; Shin et al. 2017; Jee et al. 1997), and Fe–Mn–Si-based shape-memory alloys (SMAs) (Sato et al. 1982; Otsuka et al. 1990). In most cases, steels contain other alloying elements, such as Cr, Ni, Al, Si, C, and N, and the concentration of Mn depends on the alloy system (e.g. 12–29 wt% in the case of binary Fe–Mn systems).

This article focuses on a design strategy for improving the tensile and fatigue properties of high-Mn steels from microstructural, thermodynamic, and crystallographic perspectives. Referring to the concept of ‘plaston’, a plastically deformed infinitesimal volume element, various plasticity mechanisms in high-Mn steels are visualised by the deformation of deltahedral (either tetrahedral or octahedral) models. These are the minimum volumetric units representing the atomic coordination in each phase. The extended dislocation glide of the γ lattice, mechanical γ twinning, and γ → ε martensitic transformation commonly involve the twinning shear of the deltahedrons as an elementary process, and the α’-martensite is associated with the Bain distortion of the deltahedrons.

Section 11.2 presents a brief review of the atomic rearrangement and the related dislocation-based models for the extended dislocation glide, mechanical γ twinning, and mechanical γ → ε martensitic transformation. In Sect. 11.3, the polyhedron models and their mutual transformations are systematically drawn for the four plasticity mechanisms, including the γ → α’ martensitic transformation, along with the former three. In Sect. 11.4, the design of the tensile properties of high-Mn steels is described, which considers the selection rule of the plasticity mechanisms, microstructure development, and strain hardening mechanisms. Structures developed at the intersection of crossing habit-plane variants of the planar deformation products are highlighted. The atomic rearrangement caused by the double shears is visualised with distortion or kinking of the deltahedron models. In Sect. 11.5, the design of the fatigue properties of high-Mn steels is described. The reversible back-and-forth motion of partials with the aid of the unidirectionality of the shear deformation of the deltahedrons plays an important role in these properties.

This article addresses only microstructural, thermodynamic, and crystallographic aspects of the plasticity mechanisms. It does not address the improvement of mechanical properties by grain refinement, precipitation, and interstitial atoms, all of which have been extensively studied, especially to improve the yield stress, which is a critical weak point of TRIP/TWIP steels. For these issues, review articles (Bouaziz et al. 2011; Cooman et al. 2018, 2012; Chowdhury et al. 2017; Zambrano 2018; Lee et al. 2017; Chen et al. 2017) or other chapters of this book can be referred.

2 Plasticity Mechanisms in γ-austenite

The extended dislocation glide, mechanical γ twinning, and the mechanical γ → ε martensitic transformation proceed via shear displacement on the {1 1 1}γ planes, and their products commonly have a planar morphology with crystal habit on the {1 1 1}γ planes. The plated deformation products and the remaining γ-austenite form a lamellar structure. As an example of the lamellar structure, Fig. 11.1 shows a differential interference micrograph of the surface relief on an Fe–30Mn–5Si–1Al alloy, which was formed by the shear displacement of the pre-polished surface on a specimen plastically deformed to 3%. The banded surface relief is caused by the homogeneous shear associated with the mechanical γ → ε martensitic transformation, which is the predominant plasticity mechanism in this alloy. ε-Martensite bands are formed on a unique {1 1 1}γ plane in certain grains (e.g. A in Fig. 11.1), while ε-martensite plates on different {1 1 1}γ planes cross in the other grains (e.g. B in Fig. 11.1). The frequent appearance of the annealing twin boundaries, some of which are indicated by arrows in Fig. 11.1, is also a microstructural characteristic of high-Mn steels with low-to-moderate SFEs.

Fig. 11.1
figure 1

Optical micrograph of the surface relief on the pre-polished surface of tensile deformed Fe–30Mn–5Si–1Al alloy

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The shear-type atomic displacements associated with the planar plasticity mechanisms on the {1 1 1}γ planes are shown in Fig. 11.2. With respect to the first close-packed layer A, there are two possible second layers, B and C, with different relative atomic positions, as shown in Fig. 11.2a, b, respectively. The atomic positions on the third {1 1 1}γ layer indicated in Fig. 11.2c, d) represent two types of periodic stacking sequences of the close-packed layers, ABCABC or ABABAB, which correspond to the FCC and structures, respectively.

Fig. 11.2
figure 2

The stacking sequence of the closest packing atomic planes and their change by the shear displacement of the planes. a AB stacking unit, b AC stacking unit, c ABC stacking, d ABA stacking, e γ-austenite, f lattice slip, g γ twin, h ε-martensite, i extended dislocation glide, j mechanical γ twinning, and k mechanical γ → ε martensitic transformation

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Figure 11.2e–h shows the atomic arrangements in the γ-austenite and the three plastic deformation products, which are viewed from the [1 0 1]γ direction. The perfect dislocation glide (e → f) does not change the stacking sequence of ABCABC, as the atoms move to the next position of the same type, for example, C to C. Mechanical twinning (e → g) is the homogeneous shear displacement of atoms, which changes the atomic positions regularly (A → B, B → A, and A → C), and the stacking sequence changes from ABCABC to ACBACB, as shown in Fig. 11.2g. The resulting structure remains unchanged, whereas the crystallographic orientation is modified into a mirror-symmetric atomic arrangement with respect to the {1 1 1}γ plane. The γ → ε martensitic transformation (e → h) is a regularised shear displacement of atoms on the alternate {1 1 1}γ planes. The stacking sequence changes from ABCABC to ABABAB, as shown in Fig. 11.2h, accompanying the structural change from FCC to HCP.

Figure 11.2i–k shows the three plasticity mechanisms as the motion of partial dislocations of the type 1/6{1 1 1} <1 1 2>γ (Shockley partials). An extended dislocation in (e) consists of a few (leading and trailing) partials and stacking faults (SFs) between them. The passage of the extended dislocation causes a two-step atomic displacement from C to B and then to the next C, as shown in Fig. 11.2b, i. During this process, the stacking sequence of the SF changes locally to ABA. The mechanical γ twinning (j) and the mechanical γ → ε martensitic transformation (k) proceed via the regularised group motion of partials on every plane or on alternate {1 1 1}γ planes, respectively. In other words, they are regarded as the ordering of fully extended SFs.

Owing to the common elementary process consisting of the partial–SF units, the slip band, γ twins, and ε-martensite have similar morphological and crystallographic characteristics (plated form and crystal habit on the {1 1 1}γ plane), resulting in a generally high strain hardening capability. The selection of the plasticity mechanisms essentially depends on thermodynamic conditions, which determine the extension width of SF and the degree of ordering of SFs. However, when the plasticity mechanisms are competing thermodynamically, crystallographic orientation, and dislocation interaction can also affect the deformation microstructure.

For this reason, the Thomson tetrahedron (Fig. 11.3) is useful. The faces of the tetrahedron correspond to the {1 1 1}γ planes, and the edges of the tetrahedron correspond to the six <1 1 0> γ directions of the FCC structure. The corners of the tetrahedron are denoted by A, B, C, and D, and the midpoints of the opposite faces are denoted by α, β, γ, and δ. The planes opposite A, B, C, and D are denoted by a, b, c, and d, respectively, on the outer surface, and −a, −b, −c, and −d on the inner surface. The <1 1 2>γ Shockley partials are represented by Roman–Greek pairs (arrows from corner to mid-point). This enables us to discuss operational shears, their interactions, and the crystallographic orientation of the deformation products with respect to the crystallographic orientation of the γ-austenite, which is described in Sect. 11.4.

Fig. 11.3
figure 3

Notations of the Thomson tetrahedron

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3 Polyhedron Models for FCC Plasticity Mechanisms

Interstitial lattice sites in FCC, HCP, and BCC structures are generally visualised by either tetrahedrons or octahedrons, whose vertices are at the centre of neighbouring atoms. These polyhedron models are widely used to discuss the distribution of interstitial atoms and their transitions during phase transformations. They can be used as unit volume elements to entirely fill the lattice spaces instead of cubic or hexagonal unit lattices. In this section, we visualise the plasticity mechanisms as distortions of the polyhedron models. Here, the extended dislocation, γ twin, and ε-martensite can be composed of a regular tetrahedron, regular octahedron, and their twin-sheared products. The α’-martensite can also be visualised by the distorted tetrahedrons produced by the so-called Bain distortion of the γ-austenite.

Figure 11.4 presents the four-unit polyhedrons. Figure 11.4a shows the atomic arrangement in the γ-austenite, in which a regular tetrahedron and regular octahedrons are drawn as the unit volume elements. Eight such tetrahedrons and four such octahedrons are included in an FCC unit lattice. The ratios between the tetrahedron and octahedron in terms of volume, number density, and space occupancy are 1:4, 2:1, and 1:2, respectively. When an a/6 (1 1 1) [−1 2 −1]γ partial passes on the upper atomic layer in Fig. 11.2a, the regular tetrahedron and the regular octahedron are subjected to twinning shear. Hereinafter, we refer to the distorted tetrahedron and octahedron in Fig. 11.2b as the “twin-sheared” tetrahedron and octahedron. By this twinning shear, one side of the regular tetrahedron is extended from \(\left(\sqrt{2}/2\right)\)aγ to aγ, with the length of the other sides remaining unchanged, as shown in Fig. 11.2c, d. Note that the regular octahedron consists of four twin-sheared tetrahedrons, as shown in Fig. 11.2c, while the twin-sheared octahedron consists of two regular tetrahedrons and two twin-sheared tetrahedrons, as shown in Fig. 11.2d.

Fig. 11.4
figure 4

Four-unit polyhedrons. a Regular tetrahedron and regular octahedron in the γ-austenite, b twin-sheared tetrahedron and twin-sheared octahedron after a partial passage, c a twin-sheared tetrahedron inside the original regular octahedron, d mutual transformation between the regular tetrahedron and twin-sheared tetrahedron from the c state

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Using these four-unit polyhedrons, we can fill the FCC lattice, including the SFs, γ twins, ε-martensite (= HCP lattice), and partials. An SF is a monolayer consisting of twin-sheared tetrahedrons and twin-sheared octahedrons, most of which can be replaced with regular tetrahedrons and regular octahedrons with different orientations according to the interrelation between Fig. 11.2c, d. A γ twin can be built by stacking SF monolayers, while ε-martensite can be built by alternating stacking of the SF and γ monolayers. The partial is the boundary between the twin-sheared monolayer and the γ monolayer. Along the partial, the polyhedrons are elastically distorted to adjust the atomic displacement of a/6(1 1 1)[−1 2 −1]γ.

Figure 11.5 demonstrates the deformation of the polyhedrons associated with the γ → α’ martensitic transformation. The two regular tetrahedrons (a) are compressed in the 001 axis and stretched in the 100 and 010 axes (d) by the Bain distortion. The regular octahedron (b) is also distorted in the same manner (e). Hereafter, we refer to the distorted tetrahedron and octahedron in α’-martensite as the α-tetrahedron and α-octahedron, respectively. The twin-sheared tetrahedron residing in the regular octahedron (c) is transferred into the α-tetrahedron (f). Comparing Fig. 11.5e, f shows that the α-octahedron consists of four α-tetrahedrons.

Fig. 11.5
figure 5

Polyhedron models for the Bain distortion during γ → α’ martensitic transformation. a Regular tetrahedrons in a γ unit lattice, b a regular octahedron in the γ unit lattice, c a twin-sheared tetrahedron inside the regular octahedron, d distorted tetrahedrons in a α’ unit lattice, e a distorted octahedron in the α’ unit lattice, f and a distorted tetrahedron inside the distorted octahedron

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4 Plasticity Mechanisms Under Tensile Loading

4.1 Selection Rule and Generation Processes

There are several transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM) research studies on the SF as the embryo of ε-martensite and γ twins (Bray and Howe 1996; Brooks et al. 1979a, b). In designing high-Mn austenitic TRIP/TWIP steels, the stacking fault energy of the γ-austenite (SFEγ) is used as an important indicator to predict the appearance of mechanical γ twinning and mechanical ε-martensitic transformation (Choi et al. 2020; Lee et al. 2019, 2018, 2010; Lu et al. 2017; Zambrano 2016; Das 2015; ** of SFs into ε-martensite proceeds approximately but irregularly (Brooks et al. 1979b). For the gradual growth of the ε-martensite, the thermodynamic stability of the ε-phase is an additional requirement. The Gibbs free energy difference associated with the γ → ε martensitic transformation and the SFEγ are interrelated via the following equation (Olson and Cohen 1976):

$$\Gamma =2\rho \left(\Delta {G}_{\mathrm{chem}}^{\gamma \to \varepsilon }+\Delta {G}_{\mathrm{mag}}^{\gamma \to \varepsilon }\right)+2{\sigma }^{\gamma /\varepsilon },$$
(11.1)

where Γ is the stacking fault energy of the austenite, ρ is the molar surface density of atoms in the (111) planes, \(\Delta {G}_{\mathrm{chem}}^{\gamma \to \varepsilon }\) is the chemical Gibbs free energy difference between the γ- and ε-phases, \(\Delta {G}_{\mathrm{mag}}^{\gamma \to \varepsilon }\) is the magnetic contribution to the Gibbs free energy differences, and \({\sigma }^{\gamma /\varepsilon }\) is the energy per surface unit of the (111) interface between the γ- and ε-phases. Equation (11.1) was developed based on the concept that the stacking fault is an ε-martensite embryo consisting of a double atomic layer, as shown in Fig. 11.5. There are three types of martensitic transformation paths, namely, γ → ε, γ → α’, and γ → ε → α’, depending on the Gibbs free energies of the phases, Gγ, Gε, and Gα.

Studies have attempted to obtain reliable SFEγ values. SFEγ can be determined by measuring the radius of the nodes of partial dislocations using TEM (Kim and Cooman 2011; Pierce et al. 2012), measuring the extension width with the TEM weak-beam method, measuring peak broadening in XRD (Tian et al. 2008; Balogh et al. 2006; Barman et al. 2014; Schramm and Reed 1975; Tian and Zhang 2009c), and by thermodynamic and first principles calculations (Zambrano 2016; ** alloy, Fe–15Mn–10Cr–8Ni–4Si, was developed based on the design concept described in this article and is currently used in some large-scale buildings (Sawaguchi et al. 2016).

6 Concluding Remarks

An attempt is made to describe the plasticity mechanisms in high-Mn austenitic steels in a relatively comprehensive manner, considering the distortions of polyhedron models. The selection rule of the plasticity mechanisms, microstructural development, and their effects on the tensile and fatigue properties are discussed in terms of microstructural, thermodynamic, and crystallographic aspects. The tensile and fatigue properties of coarse-grained and interstitial-free Fe–Mn–Si–Al alloys with different SFEγ values are shown as representatives. The effects of grain refinement, precipitation, and interstitial elements are excluded here. Nevertheless, some microstructural events, such as crossing shear reactions at the intersection of the different ε-martensite variants and reversible back-and-forth movement of Shockley, which are highlighted in this article, are of importance in designing mechanical and fatigue properties of high-Mn steels.