The effect of time-dependent twinning on low temperature (<0.25 ∗ Tm) creep of an alpha-titanium alloy

The low-temperature (less than one-fourth of the melting temperature) creep deformation behavior of hexagonally close-packed (HCP) α-Ti–1.6 wt.% V was investigated. Creep tests were performed at various temperatures between room temperature and 205 °C at 95% of the respective yield stress at the different temperatures. The creep strain rate was found to increase with increasing temperature. Scanning and transmission electron microscopy revealed that slip and unusually slow twin growth, or time-dependent twinning, are active deformation mechanisms for the entire temperature range of this investigation. The activation energy for creep of this alloy was calculated to identify the rate-controlling deformation mechanism, and was found to increase with increasing creep strain. At low strain, the activation energy for creep was found to be close to the previously calculated activation energy for slip. At high strain, the calculated activation energy indicates that both slip and twinning are significant deformation mechanisms. The appearance of twinning at high strains is explained by a model for twin nucleation by dislocation pileups.     

Multiscale modeling of the plasticity in an aluminum single crystal

This paper describes a numerical, hierarchical multiscale modeling methodology involving two distinct bridges over three different length scales that predicts the work hardening of face centered cubic crystals in the absence of physical experiments. This methodology builds a clear bridging approach connecting nano-, micro- and meso-scales. In this methodology, molecular dynamics simulations (nanoscale) are performed to generate mobilities for dislocations. A discrete dislocations numerical tool (microscale) then uses the mobility data obtained from the molecular dynamics simulations to determine the work hardening. The second bridge occurs as the material parameters in a slip system hardening law employed in crystal plasticity models (mesoscale) are determined by the dislocation dynamics simulation results. The material parameters are computed using a correlation procedure based on both the functional form of the hardening law and the internal elastic stress/plastic shear strain fields computed from discrete dislocations. This multiscale bridging methodology was validated by using a crystal plasticity model to predict the mechanical response of an aluminum single crystal deformed under uniaxial compressive loading along the [4 2 1] direction. The computed strain-stress response agrees well with the experimental data.     

A crystal plasticity theory for latent hardening by glide twinning through dislocation transmutation and twin accommodation effects

Imagine a residual glide twin interface advancing in a grain under the action of a monotonic stress. Close to the grain boundary, the shape change caused by the twin is partly accommodated by kinks and partly by slip emissions in the parent; the process is known as accommodation effects. When reached by the twin interface, slip dislocations in the parent undergo twinning shear. The twinning shear extracts from the parent dislocation a twinning disconnection, and thereby releases a transmuted dislocation in the twin. Transmutation populates the twin with dislocations of diverse modes. If the twin deforms by double twinning, double-transmutation occurs even if the twin retwins by the same mode or detwins by a stress reversal. If the twin deforms only by slip, transmutation is single. Whether single or double, dislocation transmutation is irreversible. The multiplicity of dislocation modes increases upon strain, since the twin finds more dislocations to transmute upon further slip of the parent and further growth of the twin. Thus, the process induces an increasing latent hardening rate in the twin. Under profuse twinning conditions, typical of double-lattice structures, this rate-increasing latent hardening combined with crystal rotation to hard orientations by twinning is consistent with a regime of increasing hardening rate, known as Regime II or Regime B. In this paper, we formulate governing equation of the above transmutation and accommodation effects in a crystal plasticity framework. We use the dislocation density based model originally proposed by Beyerlein and Tomé (2008) to derive the effect of latent hardening in a transmuting twin. The theory is expected to contribute to surmounting the difficulty that current models have to simultaneously predict under profuse twinning, the stress-strain curves, intermediate deformation textures, and intermediate twin volume fractions.     

Plastic flow stability of nanotwinned Cu foils

The plastic flow stability of nanotwinned Cu foils was investigated via room temperature rolling. Nanotwinned Cu, with an average twin thickness of 5 nm, exhibited stable plastic flow without shear localization or fracture, even at thickness reduction of over 50%. The retention of {1 1 1} fiber texture after rolling indicates insignificant out-of-plane rotation of the columnar grains and is interpreted in terms of a symmetric slip model. No significant change in the average twin lamellae thickness was seen even at thickness reduction of over 50%, suggesting that some twin boundaries were annihilated during deformation. The annihilation of very thin twins is a consequence of migration of twin boundaries due to the glide of twinning dislocations (disconnections) in the twin plane. The work hardening after rolling is correlated with the dislocation storage at twin boundaries.     

Modeling finite deformations in trigonal ceramic crystals with lattice defects

A model is developed for thermomechanical behavior of defective, low-symmetry ceramic crystals such as α$\alpha$-corundum. Kinematics resolved are nonlinear elastic deformation, thermal expansion, dislocation glide, mechanical twinning, and residual lattice strains associated with eigenstress fields of defects such as dislocations and stacking faults. Multiscale concepts are applied to describe effects of twinning on effective thermoelastic properties. Glide and twinning are thermodynamically irreversible, while free energy accumulates with geometrically necessary dislocations associated with strain and rotation gradients, statistically stored dislocations, and twin boundaries. The model is applied to describe single crystals of corundum. Hardening behaviors of glide and twin systems from the total density of dislocations accumulated during basal slip are quantified for pure and doped corundum crystals. Residual lattice expansion is predicted from nonlinear elasticity and dislocation line and stacking fault energies.     

A three-dimensional crystal plasticity model for duplex Ti–6Al–4V

A rate dependent crystal plasticity model for the α/β Ti–Al alloy Ti–6Al–4V with duplex microstructure is developed and presented herein. Duplex Ti–6Al–4V is a dual-phase alloy consisting of an hcp structured matrix primary α-phase and secondary lamellar α + β domains that are composed of alternating layers of secondary α laths and bcc structured residual β laths. The model accounts for distinct three-dimensional slip geometry for each phase, anisotropic and length scale dependent slip system strengths, the non-planar dislocation core structure of prismatic screw dislocations in the primary α-phase, and crystallographic texture. The model is implemented in the general purpose finite element code (ABAQUS, 2005. Ver 6.5, Hibbitt, Karlsson, and Sorensen, Inc., Pawtucket, RI) via a UMAT subroutine.     

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.     

Cyclic behavior of extruded magnesium: Experimental, microstructural and numerical approach

The present study aims at determining the influence of cyclic straining on the behavior of pure extruded magnesium. For this purpose, tensile, compressive and cyclic tests are performed (small plastic strains are applied (Δε^p/2 = 0.1% and 0.4%). Deformation mechanisms (slip and twin systems) have been observed by TEM and the different critical resolved shear stress (CRSS) have been determined. Based on microscopic observations, a crystal-plasticity-based constitutive model has been developed. The asymmetry between tensile and compressive loadings mainly results from the activation of hard slip systems in tension (such as 〈a〉 pyramidal and prismatic and 〈c + a〉 pyramidal glides) and twinning in compression. It is shown that basal slip is very easy to activate even for small Schmid factors. Numerical simulations reveal that untwinning in tension subsequent to compression must be considered to correctly fit the experimental S-shaped hysteresis curves. TEM observations indicate also intense secondary slips or twins inside the mother twins under cyclic conditions, so that twinning in compression and dislocation glide in tension are affected by cycling. The polycrystalline model allows to predict slip activities and twin volume fraction evolutions.     

Modelling the behaviour of polycrystalline austenitic steel with twinning-induced plasticity effect

A micromechanical model using the scale transition method in elastoviscoplasticity has been developed to describe the behaviour of those austenitic steels that display a TWIP effect. A physically based constitutive equation at the grain scale is proposed considering two inelastic strain modes: crystallographic slip and twinning. The typical organizations of microtwins observed in electron microscopy are considered, and the twin–slip as well as the twin–twin interactions are accounted for. The parameters for slip are first fitted on the uniaxial tensile response obtained at intermediate temperatures (when twinning is inhibited). Then, the parameters associated with twinning are identified using the stress–strain curve at room temperature. The simulated results in both macro and micro scales are in good agreement with experimentally obtained results.     

The plastic deformation of non-homogeneous polycrystals

To describe the work hardening process of polycrystals processed using various thermomechanical cycles with isochronal annealing from 500 to 900 °C, a dislocation based strain hardening model constructed in the basis of the so-called Kocks–Mecking model is proposed. The time and temperature dependence of flow stress is accounted via grain boundary migration, and the migration is related to annihilation of extrinsic grain boundary dislocations (EGBD’s) by climb via lattice diffusion of vacancies at the triple points. Recovery of yield stress is associated with changes in the total dislocation density term ρ^T. A sequence of deformation and annealing steps generally result in reduction of flow stress via the annihilation of the total dislocation density ρ^T defined as the sum of geometrically necessary dislocations ρ^G and statistically stored dislocations ρ^S. The predicted variation of yield stress with annealing temperature and cold working stages is in agreement with experimental observations. An attempt is made to determine the mathematical expressions which best describe the deformation behaviour of polycrystals in uniaxial deformation.     

Crystal plasticity modeling of slip activity in Ti–6Al–4V under high cycle fatigue loading

Deformation micromechanisms of a Ti–6Al–4V alloy under fatigue loading at room temperature are studied using a three-dimensional crystal plasticity constitutive model. The model employs a minimum set of fitting parameters based on experimental data for Ti–6Al–4V. Single slip is strongly favored through a softening law that affects mainly the driving force for slip on the first activated slip system. Cyclic deformation behavior at the macroscopic scale and at the local scale of grains is analyzed through the simulation of 20 cycles of fatigue on a polycrystalline structure of 900 randomly oriented grains. The progressive activation of slip (basal, prismatic, and pyramidal) is analyzed and compared to experimental observations.     

Numerical modeling of formability of extruded magnesium alloy tubes

In this paper, a constitutive framework based on a rate-dependent crystal plasticity theory is employed to simulate the large strain deformation phenomena in hexagonal closed-packed (HCP) metals such as magnesium. The new framework is incorporated into in-house codes. Simulations are performed using the new crystal plasticity model in which crystallographic slip and deformation twinning are the principal deformation mechanisms. Simulations of various stress states (uniaxial tension, uniaxial compression and the so-called ring hoop tension test) for the magnesium alloy AM30 are performed and the results are compared with experimental observations of specimens deformed at 200 °C. Numerical simulations of forming limit diagrams (FLDs) are also performed using the Marciniak–Kuczynski (M–K) approach. With this formulation, the effects of crystallographic slip and deformation twinning on the FLD can be assessed.     

On the strain hardening and texture evolution in high manganese steels: Experiments and numerical investigation

We present a systematic investigation on the strain hardening and texture evolution in high manganese steels where twinning induced plasticity (TWIP) plays a significant role for the materials' plastic deformation. Motivated by the stress–strain behavior of typical TWIP steels with compositions of Fe, Mn, and C, we develop a mechanistic model to explain the strain-hardening in crystals where deformation twinning dominates the plastic deformation. The classical single crystal plasticity model accounting for both dislocation slip and deformation twinning are then employed to simulate the plastic deformation in polycrystalline TWIP steels. While only deformation twinning is activated for plasticity, the simulations with samples composed of voronoi grains cannot fully capture the texture evolution of the TWIP steel. By including both twinning deformation and dislocation slip, the model is able to capture both the stress–strain behaviors and the texture evolution in Fe–Mn–C TWIP steel in different boundary-value problems. Further analysis on the strain contributions by both mechanisms suggests that deformation twinning plays the dominant role at the initial stage of plasticity in TWIP steels, and dislocation slip becomes increasingly important at large strains.     

A continuum model for initiation and evolution of deformation twinning

Within continuum dislocation theory the plastic deformation of a single crystal with one active slip system under plane-strain constrained shear is investigated. By introducing a twinning shear into the energy of the crystal, we show that in a certain range of straining the formation of deformation twins becomes energetically preferable. An energetic threshold for the onset of twinning is determined. A rough analysis qualitatively describes not only the evolving volume fractions of twins but also their number during straining. Finally, we analyze the evolution of deformation twins and of the dislocation network at non-zero dissipation. We present the corresponding stress-strain hysteresis, the evolution of the plastic distortion, the twin volume fractions and the dislocation densities.     

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.     

U–6Nb shear stress relaxation in compression waves (IJP 585-AV)

When uranium alloyed with 6-wt% niobium (U–6Nb) is rapidly compressed in uniaxial strain experiments, shear stress is observed to relax with a characteristic time of 30 ± 7 ns. In shock wave experiments, this relaxation inhibits the development of an elastic precursor commonly seen in other materials. When U–6Nb is cold-rolled to pre-twin and significantly increase the density of dislocations in the material, stress relaxation effects are diminished suggesting that twinning causes relaxation in the un-worked material. Separate ramp wave compression experiments produce effects that agree with those observed in shock-loading experiments. A phenomenological model is introduced that allows accurate simulation of all experiments. Estimates of residual shear stress after relaxation are obtained.     

Orientation effects in nanoindentation of single crystal copper

Numerical simulations and experimental results of nanoindentation on single crystal copper in three crystallographic orientations [(1 0 0), (0 1 1) and (1 1 1)] using a spherical indenter (3.4 μm radius) were reported. The simulations were conducted using a commercial finite element code (ABAQUS) with a user-defined subroutine (VUMAT) that incorporates large deformation crystal plasticity constitutive model. This model can take full account of the crystallographic slip as well as the orientation effects during nanoindentation. Distributions of the out-of-plane displacements and shear stresses as well as shear strains were obtained for indentation depths of up to 310 nm. The experimental studies were conducted using an MTS Nano Indenter (XP) system from which the load–displacement relationships were obtained while the surface topography as well as the surface profile along a line scan of indents were obtained using a Digital Instruments (Dimension 3100) atomic force microscope (AFM). The top views of the indent pile-up patterns under the spherical indenter show two-fold, three-fold, and four-fold symmetries for the (0 1 1), (1 1 1), and (1 0 0) orientations, respectively. Attempt was made to relate the anisotropic nature of the surface topographies around the indents in different crystallographic orientations of the single crystal copper specimens with the active slip systems and local texture variations. A reasonably good agreement had been obtained on several aspects of nanoindentation between the experimental and numerical results reported in this investigation as well as similar results reported in the literature. Thus, material properties of single crystal copper can be determined based on an appropriate numerical modeling of the nanoindentation on three crystallographic orientations.     

Crystal plasticity-based forming limit prediction for non-cubic metals: Application to Mg alloy AZ31B

A viscoplastic crystal plasticity model is incorporated within the Marciniak–Kuczynski (M–K) approach for forming limit curve prediction. The approach allows for the incorporation of crystallographic texture-induced anisotropy and the evolution of the same. The effects of mechanical twinning on the plastic response and texture evolution are also incorporated. Grain-level constitutive parameters describing the temperature dependent behavior of hexagonal close packed Mg alloy, AZ31B, sheets at discrete temperatures are used as a first application of the model. A trade-off between significant strain hardening behavior at lower temperatures (∼150 °C), and significant strain rate hardening at higher temperatures (∼200 °C) lead to similarities in the predicted forming limits. The actual formability of this alloy depends strongly on temperature within this range, and this distinction with the current modeling is related to more localized instability-based failure mechanisms at the lower temperatures than is assumed in the M–K approach. It is shown that the strain path dependence in the strain hardening response is significant and that it influences the forming limits in a predictable way. For broader applicability, a means of incorporating dynamic recrystallization into the crystal plasticity model is required.