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.     

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.     

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.     

A dislocation-based constitutive law for pure Zr including temperature effects

In this work, a single crystal constitutive law for multiple slip and twinning modes in single phase hcp materials is developed. For each slip mode, a dislocation population is evolved explicitly as a function of temperature and strain rate through thermally-activated recovery and debris formation and the associated hardening includes stage IV. A stress-based hardening law for twin activation accounts for temperature effects through its interaction with slip dislocations. For model validation against macroscopic measurement, this single crystal law is implemented into a visco-plastic-self-consistent (VPSC) polycrystal model which accounts for texture evolution and contains a subgrain micromechanical model for twin reorientation and morphology. Slip and twinning dislocations interact with the twin boundaries through a directional Hall–Petch mechanism. The model is adjusted to predict the plastic anisotropy of clock-rolled pure Zr for three different deformation paths and at four temperatures ranging from 76 K to 450 K (at a quasi-static rate of 10⁻³ 1/s). The model captures the transition from slip-dominated to twinning-dominated deformation as temperature decreases, and identifies microstructural mechanisms, such as twin nucleation and twin–slip interactions, where future characterization is needed.     

室温下镁合金板循环塑性随动强化本构模型研究

本文在具有各向异性屈服强度和拉压不对称的CPB06屈服准则的基础上,建立了基于随动强化的循环塑性本构模型．通过引入滑移、孪晶以及去孪等不同变形模式下的背应力演化方程,对室温下镁合金板材异常循环硬化行为进行了模拟．选取了AZ31B-O和AZ31B两种镁合金板材,通过拉伸-压缩-拉伸(T-C-T)和压缩-拉伸(C-T)等不同加载路径下的部分实验曲线确定模型的参数,采用三次插值多项式建立了背应力参数与上一变形模式中累积的等效塑性应变（即预应变）之间的函数关系．使用本模型对剩下的实验曲线进行了预测,发现预测结果与实验结果有良好的一致性,说明了当前模型的正确性．     

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.     

Influence of deformation path on the strain hardening behavior and microstructure evolution in low SFE FCC metals

Following our recent studies of the influence of mechanical twinning on the strain hardening of low SFE FCC metals deformed by simple compression, the investigation was extended to two different deformation modes. These were plane strain compression and simple shear carried out on 70/30 brass, which exhibits only strain hardening, and on MP35N, a Co–Ni based alloy that also shows secondary hardening by deformation promoted precipitation. It was found that the magnitude of the primary strain hardening in both alloys, and the secondary hardening in MP35N, was dramatically reduced under simple shear compared to the other deformation paths. This reduced hardening in simple shear appears to be a consequence of the bulk of the deformation twins, and also the secondary hardening precipitates, forming on planes that were parallel to the primary {111} slip planes in this deformation path. These hypotheses are supported by deformation path change tests in which the shear samples that show low flow stress under continued shear, when subjected to simple compression showed a significant increase (jump) in the flow stress, reaching values that are similar to those of the alloy continuously compressed to the same equivalent strain. That is, the reduced strain hardening in shear deformation is due not to reduced twinning, but to the twins produced by shear providing only limited barriers to continued strain by simple shear. Shear banding was found to be more marked in plane strain compression than in simple compression after cold working, and particularly after the additional secondary hardening in MP35N.     

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.     

An experimental study of cyclic deformation of extruded AZ61A magnesium alloy

Thin-walled tubular specimens were employed to study the cyclic deformation of extruded AZ61A magnesium alloy. Experiments were conducted under fully reversed strain-controlled tension-compression, torsion, and combined axial-torsion in ambient air. Mechanical twinning was found to significantly influence the inelastic deformation of the material. Cyclic hardening was observed at all the strain amplitudes under investigation. For tension-compression at strain amplitudes higher than 0.5%, the stress-strain hysteresis loop was asymmetric with a positive mean stress. This was associated with mechanical twinning in the compression phase and detwinning in the subsequent tension phase. Under cyclic torsion, the stress-strain hysteresis loops were symmetric although mechanical twinning was observed at high shear strain amplitudes. When the material was subjected to combined axial-torsion loading, the alternative occurrence of twinning and detwinning processes under axial stress resulted in asymmetric shear stress-shear strain hysteresis loops. Nonproportional hardening was not observed due to limited number of slip systems and the formation of mechanical twins. Microstructures after the stabilization of cyclic deformation were observed and the dominant mechanisms governing cyclic deformation were discussed. Existing cyclic plasticity models were discussed in light of their capabilities for modeling the observed cyclic deformation of the magnesium alloy.     

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.     

In situ neutron diffraction investigation of deformation twinning and pseudoelastic-like behaviour of extruded AZ31 magnesium alloy

In situ neutron diffraction has been used to investigate the deformation twinning and untwinning during cyclic uniaxial straining of hydrostatically extruded AZ31 magnesium alloy. The development of the internal stresses and microstructure in the polycrystalline alloy when twinning takes place is explained on the basis of the two pairs of parent {10.0}_||, {11.0}_|| and twin {00.2}_||, {10.3}_|| grain families. The experimentally observed pseudoelastic-like behaviour in stress–strain cycles is interpreted as being due to the activation of reversal twinning processes during loading–unloading cycles. It is proposed that the driving force for the observed untwinning is the existence of high tensile stresses in favourably oriented grains which result from significant twinning activity prior to unloading from the peak stress.     

Influence of single crystal orientation on homogeneous dislocation nucleation under uniaxial loading

Atomistic simulations are used to investigate how the stress required for homogeneous nucleation of partial dislocations in single crystal copper under uniaxial loading changes as a function of crystallographic orientation. Molecular dynamics is employed based on an embedded-atom method potential for Cu at 10 and 300 K. Results indicate that non-Schmid parameters are important for describing the calculated dislocation nucleation behavior for single crystal orientations under tension and compression. A continuum relationship is presented that incorporates Schmid and non-Schmid terms to correlate the nucleation stress over all tensile axis orientations within the stereographic triangle. Simulations investigating the temperature dependence of homogeneous dislocation nucleation yield activation volumes of ≈0.5- and activation energies of . For uniaxial compression, full dislocation loop nucleation is observed, in contrast to uniaxial tension. One of the main differences between uniaxial tension and compression is how the applied stress is resolved normal to the slip plane on which dislocations nucleate—in tension, this normal stress is tensile, and in compression, it is compressive. Last, the tension-compression asymmetry is examined as a function of loading axis orientation. Orientations with a high resolved stress normal to the slip plane on which dislocations nucleate have a larger tension-compression asymmetry with respect to dislocation nucleation than those orientations with a low resolved normal stress. The significance of this research is that the resolved stress normal to the slip plane on which dislocations nucleate plays an important role in partial (and full) dislocation loop nucleation in FCC Cu single crystals.     

The role of superdislocations for modeling plastic deformation of lamellar TiAl

The deformation behaviour of lamellar TiAl-alloys is investigated by means of micromechanical finite element simulations. For the simulations, a lower and an upper bound periodic unit cell representing the lamellar substructure are used. Crystallographic slip is described by continuum crystal plasticity. For the simulations, 16 individual ordinary, super, and twinning systems divided into three morphological slip modes are taken into account. The strength and hardening parameters of the slip systems are determined by comparison with experimental data from room temperature compression tests of poly-synthetically twinned (PST) crystals of TiAl. The effect of the yield stress of the superdislocations is investigated by systematic parameter variations. The results show that the general anisotropy of PST-crystals can already be described with a purely morphological classification of the slip systems. Superdislocations cause a slight tension–compression anomaly if the yield stresses are higher than for the ordinary and twinning systems.     

Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Lightweight magnesium alloys, such as AZ31, constitute alternative materials of interest for many industrial sectors such as the transport industry. For instance, reducing vehicle weight and thus fuel consumption can actively benefit the global efforts of the current environmental industry policies. To this end, several research groups are focusing their experimental efforts on the development of advanced Mg alloys. However, comparatively little computational work has been oriented towards the simulation of the micromechanisms underlying the deformation of these metals. Among them, the model developed by Staroselsky and Anand [Staroselsky, A., Anand, L., 2003. A constitutive model for HCP materials deforming by slip and twinning: application to magnesium alloy AZ31B. International Journal of Plasticity 19 (10), 1843–1864] successfully captured some of the intrinsic features of deformation in Magnesium alloys. Nevertheless, some deformation micromechanisms, such as cross-hardening between slip and twin systems, have been either simplified or disregarded. In this work, we propose the development of a crystal plasticity continuum model aimed at fully describing the intrinsic deformation mechanisms between slip and twin systems. In order to calibrate and validate the proposed model, an experimental campaign consisting of a set of quasi-static compression tests at room temperature along the rolling and normal directions of a polycrystalline AZ31 rolled sheet, as well as an analysis of the crystallographic texture at different stages of deformation, has been carried out. The model is then exploited by investigating stress and strain fields, texture evolution, and slip and twin activities during deformation. The flexibility of the overall model is ultimately demonstrated by casting light on an experimental controversy on the role of the pyramidal slip 〈c + a〉 versus compression twinning in the late stage of polycrystalline deformation, and a failure criterion related to basal slip activity is proposed.     

Crystallographic orientation and size dependence of tension-compression asymmetry in molybdenum nano-pillars

Uniaxial tension and compression experiments on [0 0 1] and [0 1 1] oriented molybdenum nano-pillars exhibit tension-compression asymmetry, a difference in attained stresses in compression vs. tension, which is found to depend on crystallographic orientation and sample size. We find that (1) flow stresses become higher at smaller diameters in both orientations and both loading directions, (2) compressive flow stresses are higher than tensile ones in [0 0 1] orientation, and visa versa in [0 1 1] orientation, and (3) this tension-compression asymmetry is in itself size dependent. We attribute these phenomena to the dependence of twinning vs. antitwinning deformation on loading direction, to the non-planarity of screw dislocation cores in Mo crystals, and to the possibly lesser role of screw dislocations in governing nano-scale plasticity compared with bulk Mo.     

Micromechanical quantification of elastic,twinning, and slip strain partitioning exhibited by polycrystalline,monoclinic nickel–titanium during large uniaxial deformations measured via in-situ neutron diffraction

We draw upon existing knowledge of twinning and slip mechanics to develop a diffraction analysis model that allows for empirical quantification of individual deformation mechanisms to the macroscopic behaviors of low symmetry and phase transforming crystalline solids. These methods are applied in studying elasticity, accommodation twinning, deformation twinning, and slip through neutron diffraction data of tensile and compressive deformations of monoclinic NiTi to ~18% true strain. A deeper understanding of tension–compression asymmetry in NiTi is gained by connecting crystallographic calculations of polycrystalline twinning strains with in situ diffraction measurements. Our analyses culminate in empirical, micromechanical quantification of individual elastic, accommodation twinning, deformation twinning, and slip contributions to the total macroscopic stress–strain response of a monoclinic material subjected to large deformations. From these results, we find that 20–40% of the total plastic response at high strains is due to deformation twinning and 60–80% due to slip.     

Texture evolution via combined slip and deformation twinning in rolled silver-copper cast eutectic nanocomposite

In this work, a silver-copper (Ag-Cu) nanocomposite with 200 nm bilayer thickness and eutectic composition was rolled at room temperature and 200 °C to nominal reductions of 75% and higher. Initially the material had a random texture and {1 1 1} bi-metal interface plane. X-ray diffraction measurements show that the Ag and Cu phases developed the same brass-type (or ‘alloy-type’) rolling texture regardless of rolling reduction and temperature. Transmission electron microscopy analyses of the nanostructures before and after rolling suggest that adjoining Ag and Cu layers maintained a cube-on-cube relationship but the interface plane changed after rolling. Polycrystal plasticity simulations accounting for plastic slip and deformation twinning in each phase were carried out to explore many possible causes for the brass-type texture development: twinning via a volume effect or barrier effect, Shockley partial slip, and confined layer slip. The results suggest that the observed texture evolution may be due to profuse twinning within both phases. Maintaining the cube-on-cube relationship would then imply that neighboring Ag and Cu crystals twinned by the same variant and on a twin plane non-parallel to the original interface plane. Explanations for this unusual possibility for Cu are provided at the end based on the properties of the Ag-Cu interface.     

孪生诱发塑性对V-5Cr-5Ti合金应变硬化行为的影响

钒合金(V-Cr-Ti)作为潜在重要的聚变反应堆用结构材料, 近年来受到广泛的关注. 为了研究 V-5Cr-5Ti 合金不同应变率压缩下的应变硬化行为, 特别是孪生对塑性变形的影响, 以位错密度和孪晶演化为基础, 建立了该合金的应变硬化模型. 模型中考虑了孪晶中的位错滑移对材料塑性应变的贡献. 模拟结果表明, 由于孪生诱发塑性, 从而使动态压缩时的位错密度小于准静态加载时的, 这使得 V-5Cr-5Ti 合金在动态压缩时的应变硬化率比准静态加载时的小. 当孪晶形成后, 位错滑移引起的塑性应变率随应变增大而增大, 并逐渐接近加载应变率, 而孪生引起的塑性应变率则随应变增大而减小.