Effects of bulk metastability on athermal deformation mechanisms

Materials with successfully utilized metastability for microstructure design include alloys undergoing spinodal decomposition, metallic glasses and crystal-glass composites, bulk TWIP and TRIP steels, shape-memory alloys and TRIP titanium alloys. In TWIP, TRIP, and quench-partitioning steels, face-centered-cubic (fcc) phase stability is typically tuned by adjusting Mn, Ni, C, N, Al, and Si content.^{Reference Dumay, Chateau, Allain, Migot and Bouaziz62–Reference Li, Ludwig, Savan, Springer and Raabe68} Interestingly, it was observed that a harmful impurity element such as H can also be used for metastability design—it reduces the stacking-fault energy in Ni and high-entropy alloys, for instance.^{Reference Luo, Li and Raabe69,Reference Luo, Lu, Fang, Ponge, Li and Raabe70}

Depending on the stacking-fault energy, or more generally, on the free energy difference between the matrix phase and the next available (stable or metastable) phase state accessible through athermal transformations, a wide variety of deformation mechanisms triggered under load can be observed. Among these are well-known effects such as formation of hexagonal-close-packed (hcp, ε phase) or body-centered-tetragonal (bct, α′ phase) martensite variants in an fcc host matrix phase or mechanical twin formation. Also included are planar slip-through dislocation core expansions, stacking faults, formation of crystallographic slip bands and their successive dynamic refinement, and partial dislocations, including formation of stair-rod dislocations or the recently observed bidirectional TRIP effect.^{Reference Lu, Liebscher, Dehm and Raabe71} This mechanism refers to the phenomenon of deformation-driven forward and reverse (bidirectional) martensitic transformation. It occurs when the stacking-fault energy approaches near-zero values and is realized for the fcc-hcp case by the forward and reverse motion of dissociated Shockley partial dislocations. Figure 3 gives an overview of this rich arsenal of athermal deformation mechanisms occurring in alloys with a metastable fcc matrix structure. The deformation mechanisms are roughly grouped as a function of the free energy difference between the matrix and the next stable or metastable phase. For many fcc alloys (γ), the most frequently occurring adjacent more stable phases are ε (hcp), α (bcc), and α′ (bct) phases. Therefore, in fcc alloys, the reduction in stacking-fault energy can be used as an approximate measure and guideline for designing alloys with desired metastability.

Figure 3.

Stacking-fault energy dependence and occurrence of specific deformation effects in metastable alloys with face-centered-cubic (fcc) matrix structure. More intense gray indicates a higher overall contribution to strain and microstructure kinetics. The stacking-fault ranges and associated deformation mechanisms were taken from several works. ^{Reference Grässel, Krüger, Frommeyer and Meyer6,Reference Bouaziz, Allain, Scott, Cugy and Barbier13–Reference Steinmetz, Japel, Wietbrock, Eisenlohr, Gutierrez-Urrutia, Saeed-Akbari, Hickel, Roters and Raabe16,Reference Choi, Sandlöbes, Malyar, Kirchlechner, Korte-Kerzel, Dehm, De Cooman and Raabe19,Reference Raabe, Tasan, Springer and Bausch44,Reference Pierce, Jimenez, Bentley, Raabe, Oskay and Wittig65} Note: hcp, hexagonal close-packed; bcc, body-centered cubic; bct, body-centered tetragonal; TRIP, transformation induced plasticity.

Of particular interest is the situation where the stacking-fault energy of fcc materials approaches near-zero values (e.g., Co close to its allotropic hcp-fcc transformation temperature, and in certain medium- and high-entropy alloys).^{Reference Lu, Liebscher, Dehm and Raabe71} In this case, the bulk matrix no longer has a preference as to which structure to assume. Local transformation events and microstructure scaling are then dominated by the specific barriers pertaining to the different types of lattice defects that carry the respective transformation mechanism. In these instances, the fcc and hcp phases can coexist and athermally transform into each other upon loading, even in a reversible fashion.^{Reference Lu, Liebscher, Dehm and Raabe71}

If a bcc/bct phase has a similar free energy, up to three of these phases can simultaneously occur, as has been observed in several stainless duplex steels and TRIP steels where the fcc phase athermally transforms into hcp regions and further into the bcc or bct phase, preferably at the intersection of two hcp bands.^{Reference Mahajan, Green and Brasen72–Reference Mahato, Shee, Sahu, Chowdhury, Sahu and Porter74} In some of these metastable alloys, deformation via athermal transformations leads to complex cascades of metastable transition states. Such effects have some phenomenological similarity with microstructure formation in spinodally decomposing alloys where gradual relaxation from an oversaturated and metastable matrix state can proceed sequentially through multiple transitional phase states.

Bulk metastability alloy design for medium- and high-entropy alloys

Medium- and high-entropy alloys represent a material class particularly well suited for compositional tuning, with the aim to render them thermodynamically metastable. These alloys are amenable to adjusting the stacking-fault energy over a wide range, especially by dropping the entropy maximization rule, thus allowing access to a nearly infinite range of nonequiatomic compositions.^{Reference Gludovatz, Hohenwarter, Catoor, Chang, George and Ritchie26–Reference Li, Körmann, Grabowski, Neugebauer and Raabe46} As previously mentioned, we focus on high-entropy alloy concepts utilizing deformation-stimulated athermal transformations. In this context, several new materials were recently introduced where substantial strain hardening was observed due to athermal transformation of the metastable massive solid-solution matrix phase (Figure 4).^{Reference Li, Tasan, Pradeep and Raabe25–Reference Deng, Tasan, Pradeep, Springer, Kostka and Raabe28,Reference Li, Pradeep, Deng, Raabe and Tasan30–Reference Ma, Yao, Pradeep, Tasan, Springer and Raabe33} For example, the phase stability of high- and medium-entropy materials pertaining to the FeCrMnCoNi system, as well as interstitially doped high-entropy alloys,^{Reference Li, Tasan, Springer, Gault and Raabe75} can be well tuned by modifying the ratio among Fe, Mn, Ni, Cr, and Co. Beyond fcc phase-stability trimming, H was also observed to reduce the stacking-fault energy of certain high-entropy alloys with these solid-solution element ratios.^{Reference Luo, Li and Raabe69,Reference Luo, Lu, Fang, Ponge, Li and Raabe70} This effect opens up the opportunity to exploit this otherwise harmful impurity element for metastability tuning of alloys that are exposed to harsh hydrogen-containing environments.

Figure 4.

Relaxing the strict configurational entropy maximization rule and favoring instead nonequimolar mixtures opens up an immensely rich composition space for the design of metastable massive solid-solution alloys. This example shows a set of related Fe-Mn-Co-Cr high-entropy alloys with altered Mn/Fe ratio. The compositional adjustment reduces the stacking-fault energy, enabling introduction of several types of phase states and athermal deformation effects.^{Reference Li, Pradeep, Deng, Raabe and Tasan30} Red color in diffraction patterns (top) and in micrographs (bottom) indicates crystalline regions with face-centered-cubic (fcc) structure and cyan indicates hexagonal-close-packed (hcp) structure. Note: TWIP, twinning induced plasticity; TRIP, transformation induced plasticity.

Several studies on these alloy systems revealed that their prevalent deformation mechanisms change when reducing the stacking-fault energy from dislocation shear (≥50 mJ/m²) toward additional mechanical twinning (20 mJ/m² ≤ stacking-fault energy ≤ 40 mJ/m²), and further toward dislocation shear plus hcp martensite formation (stacking-fault energy ≤ 20 mJ/m²) (see Figures 3 and 4). Another interesting deformation phenomenon was recently observed when approaching the latter limit of near-zero stacking-fault energy in fcc high-entropy alloys, namely, a bidirectional transformation induced plasticity (B-TRIP) effect. This mechanism describes the joint occurrence of athermal forward transformation from an fcc matrix phase into an hcp nanolaminate structure and the partial dynamic reverse transformation back from hcp to fcc (Figure 5).

Figure 5.

In situ low-angle annular dark-field scanning transmission electron microscope observation of a bidirectional transformation induced plasticity effect in a composition-tuned metastable high-entropy alloy. The local strain increases from the top left corner image to the bottom right corner image.^{Reference Lu, Liebscher, Dehm and Raabe71} Note: hcp, hexagonal close-packed.

Similar athermal effects can be achieved in TiZrHf-based medium and high-entropy alloy systems when blending them with bcc stabilizing elements such as Nb, V, Ta, Mo, W, Cr, and Fe, rendering them metastable bcc alloys.^{Reference Senkov, Scott, Senkova and Miracle76–Reference Lei, Liu, Wu, Wang, Jiang, Wang, Hui, Wu, Gault, Kontis, Raabe, Gu, Zhang, Chen, Wang, Liu, An, Zeng, Nieh and Lu78} Athermal transformation sequences in such metastable bcc high- and medium-entropy alloys include formation of bcc twins, athermal bcc-to-hcp phase transformation, hcp twins, and omega phase formation. Chemical ordering and cluster formation may also play a role.^{Reference Zhang, Tasan, Lai, Dippel and Raabe57–Reference Lai, Tasan and Raabe61,Reference Senkov, Scott, Senkova and Miracle76–Reference Lei, Liu, Wu, Wang, Jiang, Wang, Hui, Wu, Gault, Kontis, Raabe, Gu, Zhang, Chen, Wang, Liu, An, Zeng, Nieh and Lu78}

Spatially confined metastability alloy design at decorated lattice defects

Segregation engineering is a concept that renders not the entire host matrix, but only certain regions or phases of an alloy metastable through a corresponding heat treatment and elemental partitioning.^{Reference Raabe, Sandlöbes, Millán, Ponge, Assadi, Herbig and Choi1–Reference Li, Raabe, Herbig, Choi, Goto, Kostka, Yarita, Borchers and Kirchheim5} For some engineering alloys, this approach is well established and has been applied to adjust the stability of adjacent mesoscopic phases such as in quench-partitioning, medium Mn, and duplex stainless steels. In such cases, several size and confinement effects apply. While composition-dependent stacking-fault energy, temperature, and strain rate are the most influential parameters for triggering athermal deformation mechanisms and their activation sequence, specific additional features can be tuned through local chemical partitioning, grain size, texture, and the dislocation substructure. When developing this concept further, it should be emphasized that compositional partitioning generally occurs not only among adjacent mesoscopic phases, but also between the bulk matrix and its lattice defects^{Reference Koyama, Zhang, Wang, Ponge, Raabe, Tsuzaki, Noguchi and Tasan48–Reference Kwiatkowski da Silva, Leyson, Kuzmina, Ponge, Herbig, Sandlöbes, Gault, Neugebauer and Raabe56} (Figure 1).

Such local chemical decoration effects at lattice imperfections such as dislocations, stacking faults, and grain boundaries can be readily engineered due to the self-organizing nature of the mean-field McLean or Fowler–Guggenheim isotherms.^{Reference Fowler and Guggenheim55} Isotherms are thermodynamic models describing element partitioning between a lattice defect and its adjacent matrix region. The McLean isotherm assumes statistical decoration without any chemical interaction among the segregating atoms. The Fowler–Guggenheim isotherm assumes interaction among the segregating atoms. Typical metallic microstructures represent an array of sinks for trapping solute elements. Each type of lattice defect provides a characteristic density of trapping states and an associated distribution of characteristic trapping energies as shown in Figure 1. When exposed to a heat treatment, the solute elements can redistribute among these multiple traps, which leads to characteristic chemical compositions at the different lattice defects. These individual local decoration states can then lead to individual local metastability states at the defects, capable of producing local phase states that can undergo athermal transformation when exposed to loads.^{Reference Koyama, Zhang, Wang, Ponge, Raabe, Tsuzaki, Noguchi and Tasan48–Reference Wang, Tasan, Ponge, Dippel and Raabe54,Reference Springer, Belde and Raabe79–Reference Belde, Springer, Inden and Raabe81}

Compositional adjustment of such local partitioning effects to lattice defects can be readily achieved by adjusting the corresponding heat treatments.^{Reference Raabe, Sandlöbes, Millán, Ponge, Assadi, Herbig and Choi1–Reference Kuzmina, Ponge and Raabe3} Figure 6 shows an example where such local chemical partitioning of Mn to the low-angle lath interfaces of a Fe–Mn-based cubic martensite was utilized to promote local metastable martensite-to-austenite reversion at these interfaces. These metastable nanolaminate layers undergo spatially confined transformation from austenite back to bcc martensite under mechanical fatigue loading (i.e., triggered by an approaching crack). This confined phase transformation can reduce the crack propagation rate through compressive stresses, crack branching, or blunting, an effect phenomenologically resembling the micromechanics of bone.

Figure 6.

(a) Partitioning of Mn to the low-angle lath interfaces of a Fe-Mn-based cubic martensite was utilized to promote local metastable martensite-to-austenite reversion at these interfaces. (b) Under mechanical fatigue loading, these metastable nanolaminate layers undergo confined transformation from austenite to martensite, (c) triggered by an approaching crack. (b[i]) Zoom-in of the crack in the Fe-Mn-based cubic martensite and (b[ii]) a crack in bone, revealing striking similarity between the two materials. (d) This local athermal transformation lends the material improved resistance to fatigue damage.^{Reference Koyama, Zhang, Wang, Ponge, Raabe, Tsuzaki, Noguchi and Tasan48}

Summary and conclusions

Thermodynamic phase metastability can be utilized to make metallic alloys stronger and more ductile, and the types of athermal transformation and accommodation plasticity mechanisms that are responsible were described here. We reviewed two types of approaches. First, we discussed mechanisms and examples of bulk metastability alloy design known from transformation and twinning-induced steels, Ti-alloys, and high-entropy alloys. Next, we showed how spatially confined metastability can be created by heat treatments in which elemental partitioning between the matrix and its lattice defects leads to local metastable phases, a concept also referred to as segregation engineering.

Three trends seem to be particularly promising for further work along these lines. First, bidirectional athermal transformation, occurring when the stacking fault energy approaches near-zero values, leads to an ongoing refinement of the microstructure down to the nanometer regime. This effect leads to a high density of interfaces and stacking faults, hence reducing the mean free dislocation path and thus providing high strength and ductility. A second opportunity in this field lies in the well-targeted segregation at lattice defects, exploiting their usually high density, with the aim to render them metastable and thus amenable for athermal phase transformation when mechanically loaded. A third goal in realizing metastable alloys should be directed at using less expensive alloying elements. Most of the currently developed metastable high- and medium-entropy alloys use expensive alloying elements such as Co and Ni. These could be replaced by much less costly elements, such as Mn, C, or N, which create similar thermodynamic trends.