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The Type-II Twin Boundary (TB) is a critical interface in functional materials whose irrational Miller-index identity has recently drawn significant research interest. This study establishes general structural characteristics of the Type-II twin interface, utilizing TBs in Shape Memory Alloys (SMAs) - TiPd, TiPt, and AuCd - as study targets. It is shown how the irrational identity of each TB is explained by the Terrace-Disconnection (T-D) structural topology. It is proposed that the terrace is the rational-plane nearest to the irrational TB in the reciprocal space, having in- tegral Miller-indices of least magnitude. Crystallographic-registry on this terrace requires non- trivial coherence-strains. A novel kinematic-origin of the coherence-strain is proposed, coming directly from a transformation of the classical twinning deformation-gradient. This trans- formation revealed that the classical twinning-shear partitions into the coherence-strain and a new metric termed the “terrace-shear” . It is shown that the magnitude of shear relating the twin- structure to the matrix is the terrace-shear and not the twinning-shear, contrary to classical un- derstanding. Furthermore, the Burgers vector of the twinning disconnection is shown to be related directly to the terrace-shear. The energy of each Type-II interface is determined from ab initio Density Functional Theory (DFT) calculations. It is shown that the energy-minimal atomic- structure on the terrace requires determination of a “lattice-offset” that is non-trivial and un- known apriori. In summary, this study expounds on T-D topological structure of Type-II twin interfaces, establishing methods to identify rational terraces, coherence strains, ab initio planar TB energies and revealing a unique partitioning of the twinning-shear exhibited by this class of interfaces.
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Twinning stress of type I and type II deformation twins
Recent reports on highly mobile type II twin boundaries challenge the established understanding of deformation twinning and motivate this study. We consider the motion of twin boundaries through the nucleation and growth of disconnection loops and develop a mechanism-based model for twin boundary motion in the framework of isotropic linear elasticity. While such mechanisms are well established for type I and compound twins, we demonstrate based on the elastic properties of crystals that type II twin boundaries propagate in a similar way. Nucleation of a type I twinning disconnection loop occurs in a discrete manner. In contrast, nucleation of a type II twinning disconnection loop occurs gradually with increasing Burgers vector. The gradual nucleation of a type II disconnection loop accounts for the higher mobility of type II twin boundaries compared with type I twin boundaries. We consider the homogeneous nucleation of a disconnection loop, which is adequate for twinning in shape memory alloys with a low-symmetry crystal lattice. For the magnetic shape memory alloy Ni-Mn-Ga, the model predicts twinning stresses of 0.33 MPa for type II twinning and 4.7 MPa for type I twinning. Over a wide temperature range, the twinning stress depends on temperature only through the temperature dependence of the elastic constants, in agreement with experimental results.
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- Award ID(s):
- 1710640
- PAR ID:
- 10180410
- Date Published:
- Journal Name:
- Acta materialia
- Volume:
- 176
- ISSN:
- 1873-2453
- Page Range / eLocation ID:
- 211-219
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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null (Ed.)The structure of type II twins in 10M Ni-Mn-Ga is modeled using the topological method. This method predicts the same twinning parameters as the kinematic model of Bevis and Crocker. Furthermore, topological modeling provides mechanistic insight into boundary migration rates, the twinning stresses and their temperature dependence. A type II twin is envisaged to form from a precursor, which is its type I conjugate. Disconnections on the precursor k_1 plane align into a tilt wall, which, after the relaxation of the rotational distortions, forms the type II boundary parallel on average to the k_2 plane. The component defects may align into a sharp wall or relax by kinking into a less orderly configuration. Both interfaces can host additional glissile disconnections whose motion along a boundary produces combined migration and shear. The ease of motion of these defects increases with their core width, and this, in turn, decreases with increasing sharpness of the boundary. Some experimental evidence in other materials suggests that type II twins can reduce their interfacial energy by adopting a configuration of low-index facets, which reduces twin boundary mobility. Topological modeling suggests that such a coherently faceted structure is unlikely in 10M Ni-Mn-Ga, in agreement with the high mobility of type II twin boundaries.more » « less
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null (Ed.)A plane-displacement diagram showing the four twinning elements, planes and directions, is fundamental to the classical theory of twinning. One aspect of the classical theory of type I and II twinning is shown to be inapplicable when the twin rotation is large. We employ the topological model with certain nonlinear characteristics to deduce a modified set of twinning elements. For twinning associated with a small rotation, both the classical theory and the topological model for type I and II twinning are shown, which give the same set of twinning elements. However, only the topological model is applicable for the large rotation case. As for the classical model, the twin plane in the type II twinning case is irrational unless it, and the type I twin is compound. Often, this irrational plane is close to a low-index orientation for a given orientation relationship. Then it can be favorable for the interface to break up into low-index, rational facets, separated by disconnections. This occurs without changing the orientation relationship. We apply the topological model to describe both the irrational type II twins and faceting in NiTi. The results agree with TEM observations.more » « less
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Aliabadi, Ferri MH; Soboyejo, Winston Wole (Ed.)This article is mainly concerned with summarizing the recent discoveries in the deformation physics of shape memory materials with special emphasis on (1) the need to develop fundamental understanding of twinning, slip, shear/shuffle at atomic scales, martensite twin boundary topologies, atomic stacking and stable/metastable fault structures in shape memory materials, and (2) factors that result in performance degradation and accumulation of residual strains leading to fatigue and fracture. The fundamental understanding has benefitted from ab-initio modeling of atomic-electronic structures and the fault energetics of stable/metastable crystal structures. Especially, the slip phenomenon during nucleation of martensite needs further elaboration, as it exercises a strong influence on hysteresis, functional and mechanical degradation of the shape memory alloys Finally, we discourse on studies of fatigue and fracture of shape memory alloys from the literature and outline efforts to explain the complex experimental trends with respect to fatigue thresholds and nucleation. It is in the fatigue area where advancing the understanding of cycle by cycle accumulation of the irreversibilities, the strong orientation dependence of slip resistance (i.e., non-Schmid behavior), complex evolution of elastic moduli, strain sensitive evolution of interfaces with terrace-disconnection energy minimal nanostructures, and asymmetric stress-strain response will lead to the development of a comprehensive model. In the case of fracture, continuum models employ LEFM concepts and the results need corrections for martensite-induced tractions which are rather complex with localized variants. Overall, deeper scientific activities, with potential use of lattice scale theories and ab-initio based empirical atomic potentials, are paramount to advance the field to the next level.more » « less
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null (Ed.)Stress-strain responses and twinning characteristics are studied for a rolled AZ31B magnesium alloy under three different stress states: tension along the normal direction (NDT), compression along the rolled direction (RDC), and torsion about the normal direction (NDTOR) using companion specimens interrupted at incremental strain levels. Tension twinning is extensively induced in twinning-favorable NDT and RDC. All the six variants of tension twin are activated under NDT, whereas a maximum of four variants is activated under RDC. Under NDTOR, both tension twins and compression twins are activated at relatively large strains and twinning occurs in a small fraction of favored grains rather than in the majority of grains. Secondary and tertiary twins are observed in the favorably-orientated grains at high strain levels. Deformation under each stress state shows three stages of strain hardening rate: fast decrease (Stage I), sequential increase (Stage II), and progressive decrease (Stage III). The increase in the hardening rate, which is more significant under NDT and RDC as compared to NDTOR, is attributed to the hardening effect of twin boundaries and twinning texture-induced slip activities. The hardening effect of twin boundaries include the dynamic Hall-Petch hardening induced by the multiplication of twin boundaries (TBs) and twin-twin boundaries (TTBs) as well as the hardening effect associated with the energetically unfavorable TTB formation. When the applied plastic strain is larger than 0.05 under NDT and RDC, the tension twin volume fraction is higher than 50%. The twinning-induced texture leads to the activation of non-basal slips mainly in the twinned volume, i.e. prismatic slips under NDT and pyramidal slips under RDC. The low work hardening under NDTOR is due to the prevailing basal slips with reduced twinning activities under NDTOR.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.actamat.2019.07.004
