An efficient constitutive model for room-temperature,low-rate plasticity of annealed Mg AZ31B sheet

Metals and alloys with hexagonal close packed (HCP) crystal structures can undergo twinning in addition to dislocation slip when loaded mechanically. The complexity of the plastic response and the limited extent of twinning are impediments to their room-temperature formability and thus their widespread adoption. In order to exploit the unusual deformation characteristics of twinning sheet materials in designing novel forming operations, a practical plane stress material model for finite element implementation was sought. Such a model, TWINLAW, has been constructed based on three phenomenological deformation modes for Mg AZ31B: S (slip), T (twinning), and U (untwinning). The modes correspond to three testing regimes: initial in-plane tension (from the annealed state), initial in-plane compression, and in-plane tension following compression, respectively. A von Mises yield surface with initial non-zero back stress was employed to account for plastic yielding asymmetry, with evolution according to a novel isotropic and nonlinear kinematic hardening model. Texture and its evolution were represented throughout deformation using a weighted discrete probability density function of c-axis orientations. The orientation of c-axes evolves with twinning or untwinning using explicit rules incorporated in the model.     

Twinning to slip transition in ultrathin BCC Fe nanowires

We report twinning to slip transition with decreasing size and increasing temperature in ultrathin <100> BCC Fe nanowires. Molecular dynamics simulations have been performed on different nanowire size in the range 0.404–3.634 nm at temperatures ranging from 10 to 900 K. The results indicate that slip mode dominates at low sizes and high temperatures, while deformation twinning is promoted at high sizes and low temperatures. The temperature, at which the nanowires show twinning to slip transition, increases with increasing size. The different modes of deformation are also reflected appropriately in the respective stress–strain behaviour of the nanowires.     

Surface nanocrystallization mechanism of a rare earth magnesium alloy induced by HVOF supersonic microparticles bombarding

A nanostructured surface layer with a thickness up to 60 μm was produced on a rare earth Mg-Gd-Y magnesium alloy using a new process named HVOF-SMB (high velocity oxygen-fuel flame supersonic microparticles bombarding). The microstructural features of the treated surface at various depth of the deformed layer were characterized by optical microscopy (OM), transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM) with an aim to reveal the formation mechanism. Results showed that three steps during grain refinement process were found, i.e., twinning dominates the plastic deformation and divides the coarse grains into finer twin platelets at the initial stage, stacking faults are generated and a number of dislocation slip systems are activated leading to the cross slips with increasing strain and strain rate, eventually high-density dislocation networks, dislocation cells and dislocation arrays are formed, which further subdivides the twin platelets and residual microbands into sub-microstructures. As a result, homogeneous nanostructure with a grain size of about 10-20 nm is formed through dynamic recrystallization in the topmost surface layer. Based on the experimental observations, a grain refinement mechanism induced by plastic deformation with higher strain rate during the HVOF-SMB treatment in the rare earth Mg-Gd-Y alloy was proposed.     

Physical-mechanical properties of Zr-(Re)-doped β-rhombohedral boron

Effect of doping with Zr(Re) on the structure and physical-mechanical properties of β-rhombohedral boron has been studied. In all specimens p-type conductivity was found. Internal friction and dynamic shear modulus of the specimens were investigated at frequencies of torsion oscillations (0.5-5 Hz) in the temperature range 80<T<1000 K. The increase of Zr(Re) concentration in the samples results in increase of their hole concentration, this increasing and shifting the observed IF maxima to lower temperatures; activation energy of the maxima and frequency factor of the relaxation processes decrease by 10-15%. Effects of change of the structure-sensitive properties observed in Zr-(Re)-doped boron are analyzed in view of changes of activation energy necessary for the motion of twinning boundaries and stacking faults.     

A lattice-based model of the kinetics of twin boundary motion

In this paper we derive a macroscopic kinetic law for twin boundary motion from a lattice dynamical model. The model is developed for compound and type-1 twins and it is explicitly illustrated for a Cu-Al-Ni shape memory alloy. The governing multiple-well energy is calculated using an effective interatomic potential; a Frenkel-Kontorowa type model is developed for the dynamics at the lattice scale; and a quasi-continuum approximation is used to determine the continuum-scale kinetics. The model predicts that compound twins in the Cu-Al-Ni shape memory alloy are an order of magnitude more mobile than type-1 twins which is consistent with experimental observations.     

Size effects on the martensitic phase transformation of NiTi nanograins

The analysis of nanocrystalline NiTi by transmission electron microscopy (TEM) shows that the martensitic transformation proceeds by the formation of atomic-scale twins. Grains of a size less than about 50 nm do not transform to martensite even upon large undercooling. A systematic investigation of these phenomena was carried out elucidating the influence of the grain size on the energy barrier of the transformation. Based on the experiment, nanograins were modeled as spherical inclusions containing (0 0 1) compound twinned martensite. Decomposition of the transformation strains of the inclusions into a shear eigenstrain and a normal eigenstrain facilitates the analytical calculation of shear and normal strain energies in dependence of grain size, twin layer width and elastic properties. Stresses were computed analytically for special cases, otherwise numerically. The shear stresses that alternate from twin layer to twin layer are concentrated at the grain boundaries causing a contribution to the strain energy scaling with the surface area of the inclusion, whereas the strain energy induced by the normal components of the transformation strain and the temperature dependent chemical free energy scale with the volume of the inclusion. In the nanograins these different energy contributions were calculated which allow to predict a critical grain size below which the martensitic transformation becomes unlikely. Finally, the experimental result of the atomic-scale twinning can be explained by analytical calculations that account for the transformation-opposing contributions of the shear strain and the twin boundary energy of the twin-banded morphology of martensitic nanograins.     

Hardening evolution of AZ31B Mg sheet

The monotonic and cyclic mechanical behavior of O-temper AZ31B Mg sheet was measured in large-strain tension/compression and simple shear. Metallography, acoustic emission (AE), and texture measurements revealed twinning during in-plane compression and untwinning upon subsequent tension, producing asymmetric yield and hardening evolution. A working model of deformation mechanisms consistent with the results and with the literature was constructed on the basis of predominantly basal slip for initial tension, twinning for initial compression, and untwinning for tension following compression. The activation stress for twinning is larger than that for untwinning, presumably because of the need for nucleation. Increased accumulated hardening increases the twin nucleation stress, but has little effect on the untwinning stress. Multiple-cycle deformation tends to saturate, with larger strain cycles saturating more slowly. A novel analysis based on saturated cycling was used to estimate the relative magnitude of hardening effects related to twinning. For a 4% strain range, the obstacle strength of twins to slip is 3 MPa, approximately 1/3 the magnitude of textural hardening caused by twin formation (10 MPa). The difference in activation stress of twinning versus untwinning (11 MPa) is of the same magnitude as textural hardening.     

A Peierls criterion for the onset of deformation twinning at a crack tip

A criterion for the onset of deformation twinning (DT) is derived within the Peierls framework for dislocation emission from a crack tip due to Rice (J. Mech. Phys. Solids 40(2) (1992) 239). The critical stress intensity factor (SIF) is obtained for nucleation of a two-layer microtwin, which is taken to be a precursor to DT. The nucleation of the microtwin is controlled by the unstable twinning energyγ_ut, a new material parameter identified in the analysis. γ_ut plays the same role for DT as γ_us, the unstable stacking energy introduced by Rice, plays for dislocation emission. The competition between dislocation emission and DT at the crack tip is quantified by the twinning tendencyT defined as the ratio of the critical SIFs for dislocation nucleation and microtwin formation. DT is predicted when T>1 and dislocation emission when T<1. For the case where the external loading is proportional to a single load parameter, T is proportional to . The predictions of the criterion are compared with atomistic simulations for aluminum of Hai and Tadmor (Acta Mater. 51 (2003) 117) for a number of different crack configurations and loading modes. The criterion is found to be qualitatively exact for all cases, predicting the correct deformation mode and activated slip system. Quantitatively, the accuracy of the predicted nucleation loads varies from 5% to 56%. The sources of error are known and may be reduced by appropriate extensions to the model.     

Dislocation pile-ups in bicrystals within continuum dislocation theory

Within continuum dislocation theory the plastic deformation of bicrystals under a mixed deformation of plane constrained uniaxial extension and shear is investigated with regard to the nucleation of dislocations and the dislocation pile-up near the phase boundaries of a model bicrystal with one active slip system within each single crystal. For plane uniaxial extension, we present a closed-form analytical solution for the evolution of the plastic distortion and of the dislocation network in the case of symmetric slip planes (i.e. for twins), which exhibits an energetic as well as a dissipative threshold for the dislocation nucleation. The general solution for non-symmetric slip systems is obtained numerically. For a combined deformation of extension and shear, we analyze the possibility of linearly superposing results obtained for both loading cases independently. All solutions presented in this paper also display the Bauschinger effect of translational work hardening and a size effect typical to problems of crystal plasticity.     

TlCu5O(VO4)3 mit KCu5O(VO4)3‐Struktur – ein Thallium‐kupfer(II)‐oxidvanadat als Oxidationsprodukt einer Tl/Cu/V‐Legierung

TlCu₅O(VO₄)₃ with KCu₅O(VO₄)₃ Structure – a Thallium Copper(II) Oxide Vanadate as an Oxidation Product of a Tl/Cu/V Alloy Brown‐black crystals of the new oxide vanadate TlCu₅O(VO₄)₃ (triclinic, P1, a = 610.4(1) pm, b = 828.9(1) pm, c = 1075.3(1) pm, α = 97.70(1)°, β = 92.25(1)°, γ = 90.28(1)°, Z = 2) were obtained as a byproduct during the reaction of a Tl/Cu/V alloy with oxygen. The compound is isotypic with KCu₅O(VO₄)₃. All the crystals investigated were twins by non‐merohedry with [100] as the twin axis. The structure contains ladder shaped [Cu₁₀O₂₆]‐ribbons composed of edge‐ and corner‐sharing [CuO₅]‐polyhedra (tetragonal pyramids and trigonal bipyramids) and linked by vanadate groups. The thallium ions fill channels running along the a axis. No stereochemical activity of the thallium(I)‐lone pair is observed.