Scale law of complex deformation transitions of nanotwins in stainless steel

Understanding the deformation behavior of metallic materials containing nanotwins (NTs), which can enhance both strength and ductility, is useful for tailoring microstructures at the micro- and nano- scale to enhance mechanical properties. Here, we construct a clear deformation pattern of NTs in austenitic stainless steel by combining in situ tensile tests with a dislocation-based theoretical model and molecular dynamics simulations. Deformation NTs are observed in situ using a transmission electron microscope in different sample regions containing NTs with twin-lamella-spacing (λ) varying from a few nanometers to hundreds of nanometers. Two deformation transitions are found experimentally: from coactivated twinning/detwinning (λ < 5 nm) to secondary twinning (5 nm < λ < 129 nm), and then to the dislocation glide (λ > 129 nm). The simulation results are highly consistent with the observed strong λ-effect, and reveal the intrinsic transition mechanisms induced by partial dislocation slip.

Coactivation of twinning and detwinning occurs in the NTs with λ < 5 nm, and the NTs with λ = 2 -3 nm contribute the highest ratio. The standard deviation of the evaluated λ is 0.5 nm.    Figure 4 The statistical diagram of the deformation behaviors. 14 microzones are observed through in situ TEM tests, where 7 observed zones contain the NTs with λ < 5 nm, 5 observed zones have the NTs with 5 nm < λ < 129 nm, and 2 observed zones are the twins with λ at the submicrometer scale. The standard deviation of the λ is 20 nm for the upper limit of 129 nm and 0.5 nm for the lower limit of 5 nm.
The statistical results exhibit that 80% of NTs (5 observed zones with λ < 5 nm) occur coactivated twinning and detwinning under a 70 o TB orientation angle to loading direction. 100% of NTs (2 observed zones with λ < 5 nm) exhibit detwinning and the subsequent martensite transformation under a 9 o TB orientation angle to loading direction. Among the 5 observed zones containing NTs with λ = 6 -129 nm, secondary twinning occurs with a frequency of 80%. In the left 2 observed zones, dislocation motion is active in the NTs with λ at the submicrometer scale.    dislocations are called as the 60° system. When α 1 = 30° for leading and α 2 = -30° for trailing partials, these dislocations are defined as the screw system 2 . According to the Thompson tetrahedron illustrating the possible slip planes in FCC crystal, the mixed dislocation and screw dislocation contribute to the deformation twinning 3 . The 60° system is associated with the mixed dislocations. Therefore, these two kinds of dislocation systems are easy to nuclear a twinning deformation in the nanocrystalline Inner boundaries

Inner boundaries Twin boundaries
Twin boundaries Note that the movement of leading and trailing partials as well as the stacking fault are all driven by the applied stress . Thereby, when CD moves a distance , the work done by the applied stress can be expressed as: . (1) From the dislocation theory, the increment of dislocation line energy can be achieved, where is the absolute length of leading partial , is approximated as the width of the defined region , and is as the magnitude of a lattice dislocation . is the Poisson ratio. is the shear modulus. is the angle between a Burgers vector and the dislocation line, such as α 1 and α 2 shown in Supplementary Figure 12. Let's define the angle to be positive when the angle rotates anticlockwise from the dislocation line.
Then, the critical twinning stress could be determined according to the relation of , given as: . (3) Here, for 60° system of dislocations, and for screw system.
for 60° system of dislocations, and for screw system. On the other hand, when C'D' moves a distance, , the work done by the applied stress is given as: , (4) and the reduction of stacking fault energy is , where is the intrinsic stacking fault energy. Otherwise, the increased dislocation line energy of lattice dislocation can be derived as: . (6) According to the energy balance between the work done by the applied stress, the energy change in the dislocation segments and stacking fault plane, the critical trailing stress can be given as: .
Here, for 60° system of dislocations, and for screw system. Moreover, the balance between the work done by the applied stress and the increment of dislocation line energy leads to the determination of the critical detwinning stress, given as: .
The behavior of twinning deformation demands the critical twinning stress lower than the critical trailing stress and local stress, and the detwinning deformation occurs only when the critical detwinning stress is smaller than the local stress. Here, it should be pointed out that the 60°system and screw system are two types of classic dislocation system for deformation twinning. While the dislocation in a grain is most likely a mixed nature 2 , therefore, it is difficult to separate and probe the 60° dislocation and screw dislocation in TEM tests during deformation twinning.
Another important issue is how to determine the maximum local stress in NTed metals, which must be greater than the critical twinning/detwinning stress for twinning/detwinning behaviors. A dislocation density-based plastic model has been developed in our previous work to describe the grain size and twin spacing-dependent mechanical properties of the NTed metals 5 . On the basis of this plastic model, the local flow stress in a unit of twin lamellae (Supplementary Figure 13) can be expressed as: , where and are the empirical constant and the Burgers constant, respectively.
is the dislocation density in the interior crystal, and is local dislocation density in the twin lamellae, given as ,