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Effect of dislocation transmutation on modeling hardening mechanisms by twinning in magnesium
Abstract
Textured hexagonal close packed double-lattice structures show stronger anisotropy than textured cubic structures. The reason lies behind the necessity to activate deformation twinning and hard slip dislocation modes. Although the mechanisms behind activation of dislocations with non-basal Burgers vectors are still not fundamentally understood, the effect of twinning on hardening presents the most substantial challenge to polycrystal plasticity modelers. The origin of the increasing strain hardening rate regime (Regime II) upon profuse twinning is still not fundamentally clear. Previous successful attempts to fit the stress–strain behaviors based on a Hall–Petch effect by twin segmentation had systemically led to discrepancies in predicting intermediate textures and/or twin volume fraction evolutions. A recent dislocation-based hardening rule incorporated into the Visco-Plastic Self-Consistent (VPSC) model allows slip and twinning to be physically coupled in the simulations. In this paper, we investigate hardening mechanisms in pure magnesium and apply a dislocation based formalism to model anisotropy. In contrast to magnesium alloys, we show that pure magnesium under large strains develops substantial multivariant twinning and multifold twinning. These twinning phenomena are accompanied by a marked grain refinement and blunting of former twin boundaries. This blunting suggests severe accommodation effects in the soft matrix that caused the twin boundary to lose coherency. Thus, multivariant and multifold twinning take place to accommodate further deformation, but the subsequent twin–twin interactions arise to contribute in material hardening. The strain path anisotropy related to the saturation stresses revealed major missing links for comprehending hardening by twinning and substantiated dislocation transmutation effect by twinning shear.
... The {1012} twin is observed when the crystal is strained parallel to c -axis forming tension twin or compressed perpendicular to c -axis forming extension twin [12]. The resulting stress-strain response depicts anisotropy between rolling direction (RD) (in-plane compression (IPC)) and normal direction (ND) (throughthickness compression (TTC)) magnesium sample loaded in tension or compression [13]. In RD compression, the texture is aligned to cause c -axis extension by compressing perpendicular to c -axis, activating basal slip systems along with profuse tension twinning that is hardly observed when compressing parallelly to c -axis [14]. ...
... Residual dislocations Transmuted dislocations Oppedal et al. [13] have used numerical and experimental (pure Mg) means to demonstrate the influence of transmutation mechanism on the sharp hardening observed in Regime II due to profuse twinning. A modified version of the dislocation density model [30] was used in VPSC by incorporating the twin storage factor (TSF) to manipulate the hardening behavior. ...
... Oppedal et al. were successfully able to reconstruct the hardening behavior for pure Mg in multiple compression loading paths signifying that mechanisms other than the Hall-Petch effects were at work. The excessive hardening in the twin compared to the parent matrix is not due to dislocation generation in the twin, but a result of the transmutation-induced latent hardening as dislocations multiplies within the twin [13]. In the case of through-thickness compression (TTC), where twinning is not dominant, the Hall-Petch effect has been able to provide satisfactory results but increasing the dislocation density in the twin using TSF has been able to rationalize the different saturation stress between TTC and in-plane compression (IPC). ...
Parsing the effect of slip-twin interactions on the strain rate and thermal sensitivities of Magnesium (Mg) alloys has been a challenging endeavor for scientists preoccupied with the mechanical behavior of hexagonal close-packed alloys, especially those with great latent economic potential such as Mg. One of the main barriers is the travail entailed in fitting the various stress−strain behaviors at different temperatures, strain rates, loading directions applied to different starting textures. Taking on this task for two different Mg alloys presenting different textures and as such various levels of slip-twin interactions were modeled using visco-plastic self-consistent (VPSC) code. A recently developed routine that captures dislocation transmutation by twinning interfaces on strain hardening within the twin lamellae was employed. While the strong texture was exemplified by traditional rolled AZ31 Mg alloys, the weak texture was represented by ZEK100 Mg alloy sheets. The transmutation model incorporated within a dislocation density based hardening model showed enhanced flexibility in predicting the complex strain rate and thermal sensitive behavior of Mg textures’ response to various mechanical loading schemes.
... where _ g 0 is set equal to the macroscopic strain rate; m ¼ 20 (Beyerlein and Tom e, 2008; Capolungo et al., 2009); s : P s is the resolved shear stress; t s cr is the critical resolved shear stress (CRSS). The evolution of CRSS of slip system s (t s cr ) with straining is determined by using a dislocation density based hardening law (Beyerlein and Tom e, 2008) that has successfully applied to simulation of the materials with strong anisotropy, such as magnesium (Capolungo et al., 2009;Oppedal et al., 2012;Brown et al., 2012;Ma et al., 2014). The dislocation populations of different modes are evolved explicitly with deformation and affected by temperature and strain rate through thermallyactivated recovery and debris formation. ...
... The slip resistance of stage IV was also reported to be significant only at low homologous temperatures (Kocks and Mecking, 2003), but the forming temperature is relatively high in the present case. Moreover, for the purpose of reducing the fitting difficulties as in the previous works (Oppedal et al., 2012;Ma et al., 2014), the effect of debris in stage IV is ignored here. The grain size or twin boundary effect t s HP is attractive to be considered in DRX simulation, as the dramatic grain size evolution should have an effect on the hardening curve. ...
... where c is the dislocation interaction coefficient, which ranges typically from 0.5 to 1.0 (Lavrentev, 1980). In this work, it is assumed that c ¼ 0:9 (Beyerlein and Tom e, 2008; Oppedal et al., 2012). b is the length of the Burgers vector associated with the slip mode, and m the shear modulus. ...
A straightforward approach integrating a visco-plastic self-consistent (VPSC) model with a phenomenological dynamic recrystallization (DRX) criterion is proposed for coupling simulation of hot deformation and accompanying DRX. The phenomenological DRX nucleation and growth criteria are embedded into VPSC through a dislocation density based hardening model. The approach is validated and demonstrated by simulating compression of polycrystal copper at various conditions. The key DRX characteristics of copper during hot deformation, in terms of mechanical response and microstructure evolution, are well reproduced and illustrated with the VPSC-DRX coupling simulation approach. Furthermore, a series of numerical studies on the hot deformation behaviors corresponding to different loading paths and initial textures are carried out to explore their effects on dynamic recrystallization and further demonstrate the capability of the proposed method. The innovation of current work is establishing a relatively simple crystal plasticity based DRX simulation method that incorporates crystal information, deformation modes and grain population, and realizes integrated computation of deformation, texture and DRX process.
... In crystal plasticity simulations of pure magnesium, Oppedal et al. [29] used a CRSS value of 181 MPa for {1 0 1 1} twinning compared to 11 MPa for basal a , 15 MPa for {1 0 1 2} twinning, 30 MPa for prismatic a , and 50 MPa for the very hard second order pyramidal c + a . In general, {1 0 1 1} twinning has a high Schmid factor in this loading orientation but because of its high CRSS, it is not expected to form at the relatively low saturation stress levels attained during tension normal to the basal fiber. ...
... Resolved Shear Stress (RSS) is commonly used to determine the likelihood of elevation of stress through slip or twins. The RSS is dependent on the Schmid factor (SF), 0 ≤ |SF| < 0.5, of slip or twin plane of interest and the applied stress (σ app ) of the material [29] ( Table 1 describes the RSS of possible slip and twin systems). With all variants of {1 0 1 2} tensile twins having near maximum SF values, all variants are equally likely to be present in the EBSD micro textures. ...
... Compression twins usually remain as thin and needle-like lamellae, a fact that was attributed to the low mobility of twinning disconnections due to the step height and complexity of atomic shuffling requirements [70]. The formation of compression twins is believed to occur at relatively high stress levels due to their very large CRSS [29]. Although compression twins and contraction twins are exactly of the same crystallographic nature, {1 0 1 1}[1 0 1 2], contraction twins in this study have been observed to nucleate at substantially lower CRSS, well below previously reported values in the literature when the c -axis was under compression, not contraction. ...
Through in situ electron backscatter diffraction (EBSD) experiments, this paper uncovers dominant damage mechanisms in traditional magnesium alloys exhibiting deformation twinning. The findings emphasize the level of deleterious strain incompatibility induced by twin interaction with other deformation modes and microstructural defects. A double fiber obtained by plane-strain extrusion as a starting texture of AM30 magnesium alloy offered the opportunity to track deformation by EBSD in neighboring grains where some undergo profuse {1 0 1 2} twinning and others do not. For a tensile loading applied along extrusion transverse (ET) direction, those experiencing profuse twinning reveal a major effect of grain boundaries on non-Schmid behavior affecting twin variant selection and growth. Similarly, a neighboring grain, with its ⟨c⟩-axis oriented nearly perpendicular to tensile loading, showed an abnormally early nucleation of {1 0 1 1} contraction twins (2% strain) while the same {1 0 1 1} twin mode triggering under ⟨c⟩-axis uniaxial compression have higher value of critical resolved shear stress exceeding the values for pyramidal ⟨c + a⟩ dislocations. The difference in nucleation behavior of contraction vs. compression {1 0 1 1} twins is attributed to the hydrostatic stresses that promote the required atomic shuffles at the core of twinning disconnections.
... Magnesium exhibits a tendency towards brittle behavior, associated with the presence of high twin volume fractions. Although magnesium's mechanical behavior is highly anisotropic owing to it's crystal structure, observed strength and elongation at failure is typically less than 240 MPa and 20%, respectively [51,83]. Magnesium and its alloys possess an HCP crystal structure which gives them an anisotropic behavior at the monocrystal level, resulting in a high load path and texture dependence seen in the mechanical behavior of polycrystal magnesium [82,13,22,47,28,26]. ...
... The work of [83] demonstrated that, rather than being caused by HP effects, this anisotropy could be the result of increased dislocation density inside the twin grains. Implementing a modified version of the dislocation density based hardening model of [11] in the viscoplastic self-consistent (VPSC) code (VPSC-7d from Los Alamos National Laboratory) the compression of rolled Mg with a highly basal texture along multiple compression loading paths were simulated. ...
... Implementing a modified version of the dislocation density based hardening model of [11] in the viscoplastic self-consistent (VPSC) code (VPSC-7d from Los Alamos National Laboratory) the compression of rolled Mg with a highly basal texture along multiple compression loading paths were simulated. By setting the contributions of HP mechanisms to zero, [83] showed that increasing the amount of dislocation density stored inside twin volumes by a Twin Storage Factor (TSF) recreated the characteristic hardening behavior across multiple load paths. This approach will be referred to as the TSF method in the following. ...
Methods designed for incorporation into multiscale modeling polycrystals are presented in this work in two tasks. This work contains mesoscale methods for capturing the effects of both the interactions of slip dislocations encountering twin grain boundaries and the simultaneous growth of multiple twin grain volume fractions on mechanical hardening and texture evolution. These are implemented in a crystal plasticity framework using the Los Alamos viscoplastic self-consistent code, VPSC-7. Presented here, the effects of simultaneous growth in multiple twin variants on textural evolution is tracked using a Kalidindi-type twin volume transfer scheme. In Task 1, the implementation of this scheme in order to simulate the texture of Twinning Induced Plasticity steels (TWIP) subjected to Equal Channel Angular Pressing (ECAP) are summarized. In Task 2, the hardening effects of two types of interactions between slip dislocations and encountered twin grain boundaries, namely dislocation transmutation and dissociation, are captured by way of modifying the dislocation density based hardening model of [11]. Interactions of the first type are presented in a constitutive relation calculating the amount of dislocation density apportioned to a given slip system contained within the encountered twin volume fraction from each interacting slip system in the parent volume fraction. The amount transmuted from each interacting slip system described using the Correspondence Method, an on to mapping of slip systems in a parent grain to slip systems in considered twin grains. Interactions of the second type are then introduced into this constitutive relation as a disassociation parameter, the value of which is established by observations gleaned from the results of the molecular dynamics simulations of [8] and [53]. These methods are implanted to simulate the anisotropic hardening behavior of HCP magnesium under multiple load paths
... The CRSS for each deformation system varies from study to study, because it strongly depends on not only the material properties such as the microstructure, but also the strain path, as well as the model chosen [22]. The hardening laws of the CRSS for {1012} twinning is surmised to be one of the reasons for this, because it is considered constant in some studies [22,23] and decreasing [24] or increasing [25] in others. The properties of {1012} extension twins, such as active twin variants, are highly dependent on the strain path. ...
... According to the literature, the latent hardening parameters between the twin and the slip systems are usually given as h αβ = 1.2, and twins induce the hardening of the slip systems compared to the base material. This hardening is considered to come from twin boundaries acting as barriers to dislocation propagation [36] and dislocation transmutation [24]. Most simulations carried out using crystal plasticity models have also shown the effect of higher latent hardening coefficients for slips caused by {1012} twinning. ...
The purpose of this study was to develop a numerical material testing method applicable to hexagonal close-packed (hcp) materials that can predict complex material behavior such as biaxial test results from relatively easy-to-perform uniaxial tests. The proposed numerical material testing method consists of a physical model that represents the macroscopic behavior of the material and a means of determining the included crystallographic parameters using macroscopic experimental data. First, as the physical model, the finite element polycrystal model (FEPM) previously applied by the authors for face-centered cubic (fcc) materials was applied and modified for hcp materials. A unique feature of the FEPM is that it avoids the use of strain-rate-dependent coefficients, whose physical meaning is ambiguous, because the deformation analysis can be performed while automatically determining the activity of all slip systems. The applicability of FEPM to numerical material testing methods was verified in hcp materials through this study. Then, a material parameter optimization process was developed using a genetic algorithm (GA). The proposed method was validated using literature values of magnesium alloy AZ31. First, the proposed optimization process was performed on cast AZ31 using uniaxial tensile and compressive stress—strain curves as teaching data to confirm that the stress—strain curves for the biaxial state could be predicted. Then, the proposed method was applied to rolled sheet AZ31, where the pseudo-anisotropic crystal orientations generated by numerical rolling were used as initial values. The prediction of unknown material data showed that, even in the case of sheets, the crystallographic parameters could be reasonably determined by the proposed optimization process.
... The secondary twins and new slip traces are readily distinguished from the primary twins. Twin-twin and twin-dislocation interactions can promote high ductility [67][68][69]. Interaction of different twins causes large strain accommodation, inevitably contributing to a high strain hardening rate. Furthermore, it has been reported [68][69][70] that in alloys that exhibit twin-twin interactions, twinning nucleation rate is developed. ...
... Interaction of different twins causes large strain accommodation, inevitably contributing to a high strain hardening rate. Furthermore, it has been reported [68][69][70] that in alloys that exhibit twin-twin interactions, twinning nucleation rate is developed. While in alloys containing only a single twin variant, high twinning propagation occurs which improves mechanical properties. ...
Low stacking fault energy alloys often exhibit low ductility. However, sometimes these alloys show unusual mechanical behavior following specific processing parameters. In this study, a low stacking fault energy α+β brass was processed by equal channel angular pressing (ECAP) at 350 • C in 'route C' through three passes. Room temperature tensile testing showed that ductility, surprisingly, reached ~80%, whilst good tensile strength was maintained. Investigation of alloy microstructure revealed a combination of deformation mechanisms, including slip and twinning, accompanied by grain boundary serration and grain fragmentation. It is suggested that these deformation modes triggered these unexpected mechanical properties in this intrinsically brittle alloy. The required energy for discontinuous recrystallization was supplied after only one pass in the α phase, and three passes in the β phase, which then prompted good ductility. In order to study texture evolution, the macro-texture was measured. A high fraction of recrystallized grains and change in strain path fostered the development of Goss, Rotated Goss and Rotated Cube components in the α phase. While in the β phase {011}<111> and Goss components were dominant. Despite the high Schmid factor, Hall-Petch effects and work hardening led to increase of strength and hardness after the final pass.
... Additionally, k B is the Boltzmann constant, and ∆V represents the thermal activation volume. The slip resistance S α has its contributions from four distinct sources: the initial temperature associated S α 0 [28,29], Hall-Petch associated S α HP [30], forest dislocation density related S α f or [31], and substructure related S α deb [32], described by [6,33] ...
Medium manganese (medium-Mn) steel, one of the third-generation advanced high-strength steels (AHSS), delivers impressive mechanical properties such as high yield strength, ultimate tensile strength, and uniform elongation. One notable feature of medium-Mn steels is the presence of ultrafine-grained (UFG) austenite, achieved through phase transformation from the parent martensite phase during intercritical annealing. While, in general, UFG is considered a strengthening mechanism, the impact of UFG austenites in medium-Mn steel has not been fully studied. In this manuscript, we advance our previous work on crystal plasticity simulation based on the Taylor model to consider fully resolved high-fidelity microstructures and systematically study the influence of the UFG austenites. The original microstructure with UFG is reconstructed from a set of serial electron backscatter diffraction (EBSD) scans, where the exact grain morphology, orientation, and phase composition are preserved. This microstructure was further analyzed to identify the UFG austenites and recover them to their parent martensite before the intercritical annealing. These two high-fidelity microstructures are used for a comparative study using dislocation density-based crystal plasticity finite modeling to understand the impact of UFG austenites on both the local and overall mechanical responses.
... Thus, this mechanism should not be active during deformation based on the SF criterion. High SFs are observed for a prismatic slip, a pyramidal slip, c + a pyramidal I slip, and CT but their activities are hindered by their relatively high CRSS [48][49][50][51][52] . ...
A large number of anomalous extension twins, with low or even negative twinning Schmid factors, were found to nucleate and grow in a strongly textured Mg-1Al alloy during tensile deformation along the extruded direction. The deformation mechanisms responsible for this behaviour were investigated through in-situ electron back-scattered diffraction, grain reference orientation deviation, and slip trace-modified lattice rotation. It was found that anomalous extension twins nucleated mainly at the onset of plastic deformation at or near grain boundary triple junctions. They were associated with the severe strain incompatibility between neighbour grains as a result from the different a basal slip-induced lattice rotations. Moreover, the anomalous twins were able to grow with the applied strain due to the continuous activation of a basal slip in different neighbour grains, which enhanced the strain incompatibility. These results reveal the complexity of the deformation mechanisms in Mg alloys at the local level when deformed along hard orientations.
... The dislocation transmutation theory proposes that during the formation of extension twins, two basal 〈a〉 dislocations in the matrix can transmute into one 〈c +a〉 pyramidal dislocation and one sessile I 1 SF when the advancing twin boundaries swept on basal 〈a〉 dislocations in the matrix [27,[41][42][43][44]. As a result, the types of dislocation changed from basal dislocations to pyramidal ones inside twins. ...
... This hardening was considered to be provided by the twin boundary acting as barriers to dislocation propagation and dislocation transmutation. [31][32][33] In this study, a latent hardening modulus h αβ is defined as 1.3 for the pyramidal slip. 34 If the latent hardening moduli of pyramidal slip was set to h αβ = 1, the RD_C stress was 6.8% lower and the simulated 45 ○ _C flow stress was 6.9% Fig. 17, the stress-strain curves simulated with h αβ = 1.3 for the pyramidal slip were apparently higher than that simulated with h αβ = 1.0. ...
The mechanical anisotropy of the magnesium alloy AZ31B-O was investigated using the Viscoplastic-Self-Consistent (VPSC)-Twinning and Detwinning (TDT) model. The anisotropic behavior of the material under uniaxial strain was studied using five distinct sheet orientations. In order to investigate the mechanical behavior under uniaxial compression, four alternative specimen orientations were employed. The VPSC model with the TDT mechanism was used to simulate the uniaxial tension and compression experiments. For tensile strain, the magnesium alloy samples were mainly regulated by base slip and prismatic slip. In compression of magnesium alloy samples, it was dominated by basal slip and {10–12} twinning. In all compression specimens, the grain c-axes are parallel to the compression axis regardless of the initial orientation. The r-values under different uniaxial strain paths have been also predicted by using the VPSC-TDT model. The negative r-values under uniaxial compression along RD to TD were further explained. The contribution of {10–12} twinning to plastic strain and the extra hardening induced by {10–12} extension twinning were discussed in depth. This study confirms that the extra hardening induced by {10–12} extension twinning will perform an important function when the twin volume fraction reaches a degree of about 50% with the active pyramidal slip at the same time.
... Desirable as the lightest structural metals, hexagonal close packed Magnesium and its alloys are riddled with the complexity of their mechanical behavior. They possess a variety of slip (basal, prism, pyramidal) and mechanical twin systems [1] that are activated to different degrees depending on orientation distribution and load path [2][3][4]. Further, twin operation is unidirectional. The most commonly observed twin system, {101 ̅ 2}(1 ̅ 011) tensile twin, shows profuse activity only when the load sense favors its activity [5,6]. ...
A critical issue for light Magnesium alloys is their propensity for strain localization at the component scale, linked to peculiar twinning phenomenon. For the (c-axes-aligned) rolling texture, highly compact coordinated twinning bands (CTBs) form that, uniquely, have a singular plane of shear. Normally, where these bands emerge and progress are up to stochastic factors. Here, a cross-notched sample design is nominated to guide the bands of conjugate orientations into predetermined diagonal corridors and enforce their overlap at a prefixed location. The deformation fields in the Magnesium AZ31 sample are in-situ monitored with an advanced microscopic image correlation (micro-DIC) variant that has a unique combination of extreme field coverage (~1.5×10 5 grains), intragranular resolution (~10 2 data points per grain) and very high time-step resolution (0.05-0.1% nominal strain increments over the twin plateau). The latter allows investigating the emergence, advance, lateral growth, and interaction of CTBs with extreme detail over absolute and sequential micro-DIC strain maps. The sample design is successful in guiding the CTB formations into the designated corridors. CTB rudiments first make a cross connection across the sample followed by lateral expansion that proceeds until the corridor is roughly filled. This happens sequentially for the two diagonal corridors, forcing the second band to negotiate the first. The band strain is reduced by about 25% at the enforced overlap compared to the characteristic intensity it exhibits outside it (around 2.3%)-a direct measurement of the dilution of the strain activity of a CTB as it crosses another CTB. The uniqueness of this application in guiding severely anisotropic bands is contrasted with the micro-DIC fields of a transversely isotropic sample of the same material that is analogously put under a twin-dominated deformation.
... However, twinning is a polar mechanism and ET only occurs when HCP crystal experiences tensile stresses along the c-axis [6]. When the HCP crystal is compressed along the c-axis, plastic deformation perpendicular to the basal plane has to be accommodated by 〈c + a〉 pyramidal slip and/or {1011} < 1012 > compression twins (CT) [7], that also need a very high CRSS (114 -185 MPa [8,9] [11]. Among them, experimental results have shown that the D38 variant is the most favorable one [11][12][13]. ...
The transformation of compression twins (CT) to double twins (DT) is studied in a dual-textured Mg-6.5%Zn(wt.) alloy during deformation along the extrusion axis. After 7.3% compression, 85% of CT are transformed to DT. This ratio drops to 22% and 36% during tension although the applied stresses and strains in tension were much higher. The Schmid factor of the actual DT variants was very low (and often negative) in tension and compression and could not explain the differences in DT activity. It is shown that the suppressed CT→DT transformation during tension is accompanied by the activation of 〈a〉 non-basal slip -rather than 〈a〉 basal slip- which presumably hinder the transformation because the dissociation of 〈a〉 basal dislocations is necessary to nucleate and grow extension twins in primary CT. These findings point out an effective strategy to suppress DT by activating 〈a〉 non-basal slip, which may be useful to design Mg alloys with high ductility.
... Desirable as the lightest structural metals, hexagonal close packed Magnesium and its alloys are riddled with the complexity of their mechanical behavior. They possess a variety of slip (basal, prism, pyramidal) and mechanical twin systems [1] that are activated to different degrees depending on orientation distribution and load path [2][3][4]. Further, twin operation is unidirectional. The most commonly observed twin system, {101 ̅ 2}(1 ̅ 011) tensile twin, shows profuse activity only when the load sense favors its activity [5,6]. ...
A critical issue for lightweight Magnesium alloys is their propensity for strain localization at the component scale, linked to peculiar twinning phenomenon. For the (c-axes-aligned) rolling texture, highly compact coordinated twinning bands (CTBs) form that, uniquely, have a singular plane of shear. Normally, where these bands emerge and progress are up to stochastic factors. Here, a cross-notched sample design is nominated to guide the bands of conjugate orientations into predetermined diagonal corridors and enforce their overlap at a prefixed location. The deformation fields in the Magnesium AZ31 sample are in situ monitored with an advanced microscopic image correlation (micro-DIC) variant that has a unique combination of extreme field coverage (~150000 grains), intragranular resolution (~100 data points per grain) and very high time-step resolution (0.05-0.1% nominal strain increments over the twin plateau). The latter allows investigating the emergence, advance, lateral growth, and interaction of CTBs with extreme detail over absolute and sequential micro-DIC strain maps. The sample design is successful in guiding the CTB formations into the designated corridors. Seed segments of CTBs first make a cross connection across the sample, followed by lateral expansion that proceeds until the corridor is roughly filled. This happens sequentially for the two diagonal corridors, forcing the second band to pass through the first. The band strain is reduced by about 25% at the enforced overlap compared to the characteristic intensity it exhibits outside it (around 2.3%)—a direct measurement of the dilution of the strain activity of a CTB as it crosses another CTB. The uniqueness of this application in guiding severely anisotropic bands is contrasted with the micro-DIC fields of a transversely isotropic sample of the same material that is analogously put under a twin-dominated deformation.
... Here,̇0 represents the reference strain rate associated with twinning, 0 represents the threshold resistance to twinning, represents the frictional drag resistance, and is the rate sensitivity exponent. We note that this is a rather simple representation of the crystallographic shearing rate due to twinning and several advanced constitutive models accounting for the twin nucleation and growth kinetics have been proposed [76][77][78][79][80]. ...
... Here,γ α 0t represents the reference strain rate associated with twinning, τ α 0t represents the threshold resistance to twinning, D α represents the frictional drag resistance, and m α is the rate sensitivity exponent. We note that this is a rather simple representation of the crystallographic shearing rate due to twinning and several advanced constitutive models accounting for the twin nucleation and growth kinetics have been proposed [76,77,78,79,80]. ...
This work presents an open source, dislocation density based crystal plasticity modeling framework, $\rho$-CP. A Kocks-type thermally activated flow is used for accounting for the temperature and strain rate effects on the crystallograpphic shearing rate. Slip system-level mobile and immobile dislocation densities, as well slip system-level backstress, are used as internal state variables for representing the substructure evolution during plastic deformation. A fully implicit numerical integration scheme is presented for the time integration of the finite deformation plasticity model. The framework is implemented and integrated with the open source finite element solver, Multiphysics Object-Oriented Simulation Environment (MOOSE). Example applications of the model are demonstrated for predicting the anisotropic mechanical response of single and polycrystalline hcp magnesium, strain rate effects and cyclic deformation of polycrystalline fcc OFHC copper, and temperature and strain rate effects on the thermo-mechanical deformation of polycrystalline bcc tantanlum. Simulations of realistic Voronoi-tessellated microstructures as well as Electron Back Scatter Diffraction (EBSD) microstructures are demonstrated to highlight the model's ability to predict large deformation and misorientation developement during plastic deformation.
... The CRSS for 〈c + a〉 pyramidal slip for Mg-Zn alloys is very high (200 -246 MPa according to micropillar compression tests and VPSC simulations [53,[57][58][59]) as compared with that for ET (18 -39 MPa for different Mg-Zn alloys according to micropillar compression tests and VPSC simulations [53,[57][58][59][60]). There are no data in the literature about the CRSS for CT in Mg-Zn alloys but the values for pure Mg from mechanical tests on single crystals and VPSC simulations are in the range of 114 -185 MPa [61,62]. Therefore, ET or CT are likely active during tensile or compressive deformation, respectively, of C-textured grains, in agreement with the experimental observations. ...
A dual-textured wrought Mg-6.5 Zn (wt.%) alloy with limited yield asymmetry (compressive yield strength / tensile yield strength: 0.90) is reported. Approximately 80% of the grains present the standard texture of wrought Mg alloys while the grain orientation is rotated by ≈ 90º perpendicularly to the c axis in the remaining 20%. The deformation mechanisms responsible for this behavior are analyzed on samples deformed in tension and compression up to different strains. Compressive deformation of the grains with the standard texture is accommodated by 〈a〉 basal slip and extension twinning while tensile deformation promotes 〈a〉 basal and non-basal 〈a〉 prismatic and 〈a〉 pyramidal slip, leading to the typical yield asymmetry. However, the rotated grains present the opposite (and much stronger) yield asymmetry because tensile deformation is absorbed by 〈a〉 basal slip and extension twinning while compression deformation requires 〈a〉 basal slip and compression twinning. Thus, the contribution of the 20% rotated grains to the overall mechanical behavior leads to (almost) similar values of the yield strength in tension and compression. This work provides a physical understanding of the deformation behavior of dual-textured Mg alloys, that can be used to develop novel dual-textured Mg alloys with limited yield asymmetry.
... At lower temperatures, while the basal slip is easy, extension and contraction of the ⟨c⟩ axis are difficult [4]. Due to this inability to initiate slip at room temperature, as well as the HCP lattices' low symmetry, deformation twinning is promoted rather than ⟨c + a⟩ slip [5,6]. ...
Magnesium (Mg) alloys exhibit poor room temperature ductility, which prohibits forming operations in cost-effective industrial settings and the use of these alloys in critical safety components. Profuse twinning in Mg alloys is widely associated with high strain path anisotropy and low material ductility. Twinning typically propagates across the grains through the autocatalysis phenomena in typical texture conditions. Twin–twin and twin–slip interactions often lead to high strain incompatibilities and eventually failure. One way to avoid such premature failure is to prevent the early nucleation of twins. This research tests a hypothesis that a strong yet ductile phase surrounding each individual grain in traditional polycrystals could inhibit twin accommodation effects and thus twin nucleation and autocatalysis mechanisms at grain boundaries. As a proof-of-concept for testing this hypothesis, sharply textured magnesium sheets plated with different materials were subjected to four-point bending to assess the potential of a surface/grain boundary barrier in limiting twinning extent. The results showed that Mg AZ31 alloy plated with zinc alleviated twin nucleation while improving the strength of the alloy.
... with D the drag stress (3400 MPa for prismatic slip [93] ), g the normalized stress-independent activation energy, k the Boltzmann constant, ˙ ε 0 a material value equal to 10 7 s -1 in Mg [94] , and b the Burgers vector (0.321nm in this case). Fixing T = 573 K, and leaving k 1 constant, Eq. (3.14) describes how at high temperatures the increase in strain rate produces a decrease in the rate of dislocation removal. ...
The strain rate (ε˙) and temperature (T) dependent mechanical response of single crystal magnesium (Mg) micropillars compressed along the [2¯110] direction (a-axis) is investigated from room temperature to 573 K and from 10⁻³ to 100 s⁻¹. The loading direction was chosen to disfavour basal slip activation by a low Schmid factor, allowing the investigation of the rate-sensitivities of extension twinning and prismatic slip. For T ≤ 423 K, the plasticity was governed by extension twinning for the entire range of the applied strain rates. At T > 423 K and for ε˙ ≤ 10 s⁻¹, extension twinning did not occur and a continuous plastic flow induced by prismatic dislocation mediated plasticity was observed: the twin to slip transition takes place due to the decrease of the critical resolved shear stress of non-basal slip. For ε˙ > 10 s⁻¹, however, the accommodation of the plastic deformation by activation of prismatic slip is not enough to match the applied deformation rate, favouring again deformation twinning. The first part of this work provides a complete overview of the mutual effects of T and ε˙ on the transition points of deformation modes in Mg at the microscale. In a second stage, the influence of thermal and kinetic contributions on the evolution of the flow stress leading to the slip to twin transition at 573 K has been assessed in more detail. Within the slip-dominated plasticity regime, this work provides a quantitative assessment of the increases in the saturation stress (stage III) with ε˙ at high temperature, showing how the strain-rate dependency of the dislocation generation rate in the pillar and escape rate at the free surfaces of the structure controls the stress evolution in Mg microcrystals.
... with D the drag stress (3400 MPa for prismatic slip [93] ), g the normalized stress-independent activation energy, k the Boltzmann constant, ˙ ε 0 a material value equal to 10 7 s -1 in Mg [94] , and b the Burgers vector (0.321nm in this case). Fixing T = 573 K, and leaving k 1 constant, Eq. (3.14) describes how at high temperatures the increase in strain rate produces a decrease in the rate of dislocation removal. ...
... Early studies on twin-twin interactions in hcp metals revealed the strong correlation between twin-twin interactions and strain hardening [20][21][22]. In addition, a study of tension-compression of single crystal Mg reported that twin-twin boundaries are critical to the retardation of detwinning, because of the unfavorable dissociation of twintwin boundary dislocations [23]. ...
{101̄2} twinning occurs extensively in Mg to accommodate plastic deformation. With multiple active twin variants, twin–twin interaction occurs and this often forms twin–twin boundaries. In this work, the {112̄2} twin–twin boundary is studied using electron backscatter diffraction (EBSD) analysis and atomistic simulations. EBSD data show that many of the twin–twin boundaries align well with {112̄2} or {112̄6} planes. Further, atomistic simulations reveal dynamically the formation of {112̄2} boundary via the interaction of two non-co-zone {101̄2} twin variants. Moreover, the twinning mode of the {112̄2} boundary is found to be an extension twin with second undistorted plane of {112̄6}. In addition, the {112̄2} boundaries contribute significantly to the 60° 〈011̄0〉 peak in the misorientation histogram; they also play an essential role in the unique strong strain hardening under c-axis tension. Our findings are crucial for completing the twinning theories for Mg.
... where is the dislocation interaction coefficient usually assumed as 0.9 (Oppedal et al., 2012) and b is the Burgers vector. Elasticity isotropy is assumed and an effective shear modulus μ(T), varied only with temperature, is used here, considering the temperature dependence of μ is much greater than its dependence on shearing direction (Beyerlein and Tomé, 2008). ...
... Crystal plasticity is widely used to investigate deformation mechanisms in Mg alloys, including slip and twinning (Van Houtte, 1978;Tomé et al., 1991;Kalidindi, 1998;Staroselsky and Anand, 2003;Abdolvand et al., 2011Abdolvand et al., , 2015Fernández et al., 2011Fernández et al., , 2013Zhang and Joshi, 2012;Oppedal et al., 2012Oppedal et al., , 2013Wang et al., 2013aWang et al., , 2013bLiu and Wei, 2014;Ardeljan et al., 2015;Kabirian et al., 2015;Qiao et al., 2015Qiao et al., , 2016Lévesque et al., 2016;Hama et al., 2016Hama et al., , 2017Prasad et al., 2017;Feather et al., 2019). These models have successfully captured the anisotropic response of Mg alloys under various loading conditions. ...
The present work addressed the effects of heat treatment on the mechanical response of a WE43 Mg alloy using an integrated framework of SEM-DIC experiment and CPFE simulation. Both macroscopic responses including yield strength, ultimate strength, ductility, and microscopic responses, including local displacement and strain maps, were experimentally investigated. The focus of this work is to use the CPFE simulation as an integrated computational tool to study the effects of heat treatment. The CPFE framework was evaluated using the local fields of displacement and strain obtained from the SEM-DIC experiment rather than the conventional scheme of using macroscopic responses at different loading directions. Subsequently, the information which is available using CPFE, such as the critical resolved shear stress (CRSS) and relative slip activity, was used to study the effects of heat treatment on the response of WE43 Mg alloy. The contributions of different strengthening mechanisms on the CRSS were addressed. The results show that effects of heat treatment can be captured using the predominant mechanisms of the grain size effect and the influence of precipitates. Finally, it has been shown that classical Hall-Petch in which one constant can capture the size effects, should be modified. To do so, each deformation mode should have a unique Hall-Petch constant, which are calculated here for the WE43 Mg alloy.
... The initial value of ( ) 0 is calculated with respect to the value at room temperature as (9) and (10) in which, ( ) is the shear moduli related to the current temperature, the dislocation interaction parameter defined as 0.9 (satisfying the Taylor relationship [49]). This model does not consider latent hardening effects, as dislocation density evolution induced by latent hardening has been found to be small compared with that due to self-hardening in the alloy investigated in this study [50][51][52]. The latent hardening effects could be added by replacing the scalar with an interaction coefficient matrix as employed in Ref. [53]. ...
This manuscript presents the formulation, implementation, calibration and application of a multiscale reduced-order model to simulate a titanium panel structure subjected to thermo-mechanical loading associated with high-speed flight. The formulation is based on the eigenstrain-based reduced-order homogenization model (EHM) and further considers thermal strain as well as temperature dependent material properties and evolution laws. The material microstructure (i.e., at the scale of a polycrystalline representative volume element (RVE)) and underlying microstructural mechanisms are directly incorporated and fully coupled with a structural analysis, allowing concurrently probing the response at the structural scale and the material microscale. The proposed approach was fully calibrated using a series of uniaxial tension tests of Ti-6242S at a wide range of temperatures and two different strain rates. The calibrated model is then adopted to study the response of a generic aircraft skin panel subjected to thermo-mechanical loading associated with high-speed flight. The analysis focuses on demonstrating the capability of the model to predict not only the structural scale response, but simultaneously the microscale response, and further studies the effects of temperature and texture on the response.
A material’s ability to withstand high deformation rates without failure has a profound effect on many applications. Indeed, in modern industrial society, e.g., alternative energy sources (fusion reactors), automobile crashes, projectile impact, and deep-space exploration (meteoroid impact), structural metals often experience deformation rates of 103–104 s−1 or higher, which can lead to catastrophic failures due to loss in ductility. However, the effects of stress state combined with high strain-rate behavior on deformation mechanisms are still not fully explored. Therefore, this paper attempts to lay out a perspective of anomalous dynamic behavior observed in low-melting-temperature materials such as magnesium (Mg)-based alloys. In other words, the paper reviews research conducted on time-dependent dynamic behavior along with the multiaxial state of stress in Mg alloys.
Twins in crystal defect, one of the significant factors affecting the physicochemical properties of semiconductor materials, are applied in catalytic conversion. Among the catalysts serving for photocatalytic water splitting, Zn 1− x Cd x S has become a hot‐point due to its adjustable energy band structure. Via limiting mass transport to control the release rate of anions/cations, twin Zn 1− x Cd x S solid solution is prepared successfully, which lays a foundation for the construction of other twin crystals in the future. On twin Zn 1− x Cd x S, water tends to be dissociated after being adsorbed by Zn ²⁺ /Cd ²⁺ at twin boundary, then the fast‐moving electrons at twin boundary quickly combine with the protons already attached to S ²⁻ to form hydrogen. According to the theoretical calculation, not only the intracrystalline electron mobility, but also the extracrystalline capacity of water‐adsorption/dissociation and proton‐adsorption on the twin boundary are superior to those of the counterpart plane in defect‐free phase. The synthetic twin Zn 1− x Cd x S apparent quantum efficiency of photocatalysis water splitting for hydrogen reached 82.5% ( λ = 420 nm). This research opens up an avenue to introduce twins in crystals and it hopes to shed some light on photocatalysis.
The ductility of Magnesium alloys is often limited due to the strong basal texture. Initial attempts were made to reduce the intensity of the basal textures by adding rare earth(RE) elements. However, owing to the cost and scarcity of RE elements, alloys with calcium and tin were recently introduced. Among them, Mg-2Sn-2Ca alloys are the most promising, with high strength reported in the extruded condition. In this work, we report, for the first time, the mechanical properties of the alloy in the sheet form. In plane mechanical anisotropy in compressive behaviour is studied along with the detailed characterisation of texture, microstructure and the deformation twins in the material. Unlike strongly basal textured Mg alloys, deformation twinning was also observed in samples loaded along the normal direction as well. Crystal plasticity simulations were performed to confirm the slip and twin activity. Furthermore, a detailed analysis of deformation twins revealed that the so called Schmid twins accommodate strain by both twin growth and slip, whereas the non-Schmid twins accommodate the strain exclusively by crystallographic slip.
In this study, the role of twin-twin interactions on the distributions of local defects (e.g., dislocations) and stress fields in a magnesium alloy is investigated. A co-zone (101¯2)-(1¯012) tensile twin junction in a deformed Mg-3 wt.%Y alloy is analyzed using transmission electron microscopy (TEM). The results show that the morphology of the impinging (1¯012) twin is asymmetric, and the non-interacting boundary of the recipient (101¯2) twin is irregular. Detailed analysis of TEM images reveals that type-II pyramidal [1¯21¯3](12¯12) dislocations concentrate in the vicinity of the twin-twin junction site. The same 〈c + a〉 dislocations are also observed inside the interacting twin domains along with a few 〈a〉 dislocations. The 〈c + a〉 dislocations emanating from the impinging (1¯012) twin boundary have edge character and are extended with faults parallel to the basal plane. In contrast, the 〈c + a〉 dislocations connected to the recipient (101¯2) twin are predominantly screw orientation and compact. Elasto-viscoplastic fast Fourier transform based crystal plasticity calculations are performed to rationalize the observed twin morphology and local dislocation distribution. The model calculations suggest that the local stress fields generated at the junction site where the two twins meet are responsible for the experimentally observed concentration of 〈c + a〉 dislocations. The calculated stress fields are asymmetric with respect to the junction site, explaining the observed asymmetric morphology of the impinging twin. Overall, these findings show strong effects of twin-twin interactions on the distribution of dislocations as well as the evolution of the twinned microstructure and as such, can help advance understanding of twinning in Mg alloys and their effect on mechanical behavior.
This study investigated the formation mechanism of new grains due to twin–twin intersections in a coarse-grained Mg–6Al–3Sn–2Zn alloy during different strain rates of an isothermal compression. The results of electron backscattered diffraction investigations showed that the activated twins were primarily {101¯2} tension twins, and 60° <101¯0> boundaries formed due to twin–twin intersections under different strain rates. Isolated twin variants with 60° <101¯0> boundaries transformed into new grains through lattice rotations at a low strain rate (0.01 s⁻¹). At a high strain rate (10 s⁻¹), the regions surrounded by subgrain boundaries through high-density dislocation arrangement and the 60° <101¯0> boundaries transformed into new grains via dynamic recrystallization.
In this study, AZ31 Mg alloy sheet was pre-twinned at room temperature along the transverse direction (TD) to introduce {10-12} tensile twins. The uniaxial tensile experiment was conducted at 200 °C to investigate the dynamic recrystallization, twinning behaviors and mechanical response. The strain paths tilted angles of 0°, 15°, 30°, 45°, 60°, 75° and 90° in respect to the rolling direction (RD) on the RD-TD plane were considered. Results revealed that the strain path has significant effects on the microstructural evolution and mechanical response at warm temperature. When the strain path tilts were 0°, 15°, 30°, 45° and 60° with the RD, continuous dynamic recrystallization (CDRX) was the main mechanism to coordinate strain. The detwinning dominated the microstructural evolution but retarded by CDRX for the pre-twinned sample with a strain path angle of 75°. Detwinning and CDRX played an important role on the microstructural evolution in the pre-twinned sample when the strain path was tilted 90°. Additionally, the effect of CDRX on {10-12} twinning and three types of {10-12} tensile twin behaviors were discussed. Both strengthening and weakening effects were observed in pre-twinned samples.
Twin–twin interactions are an important component of the microstructural evolution of hexagonal close-packed metals undergoing plasticity. These interactions are prevalent because of the predominance of twinning due to limited easy slip modes. Despite their importance, the complexities of the atomic-scale behavior of interacting twins has limited robust characterization. Using interfacial defect theory, we developed a three-dimensional model of twin–twin interactions, double twinning and other complex interfacial reactions that occur between twins acting on different interface planes. Using molecular dynamics, {\({11\overline{2}2}\)} and {\({11\overline{2}1}\)} twins in titanium were activated and produced facets, twin–twin interactions and double twins that we characterized with our model. The results showed excellent agreement between the molecular dynamics results and the model. Surprisingly, some highly ordered and mobile boundaries can be produced by these complex reactions, which could provide important insights for higher scale models of plasticity.
The mechanical properties of an annealed commercially pure Ti plate were investigated. Tension and compression tests were made at room temperature, and EBSD was used to characterize the initial and deformed microstructures. The visco-plastic self-consistent model with an empirical Voce hardening law was used to reproduce the material behavior. Several self consistent schemes (SCS) were used, and the simulated twin volume fractions, textures and plastic anisotropy (r-values) were compared with experimental data. The hardening of slip modes by twinning were taken into account by latent hardening coefficients. Only the Tangent SCS allows reproducing perfectly all the stress-strain curves, but the latent hardening for prismatic slip by tension twinning must be higher in compression than in tension. It is found that under compression, tension twinning and prismatic slip compete and impede each other, so tension twinning dramatically increases the critical resolved shear stress (CRSS) of all slip modes, which is modeled by a strong latent hardening. But under tension, tension twins grow in undeformed matrix and slightly increase the CRSS for prismatic slip, resulting in a low latent hardening. The Tangent SCS can also reproduce better the r-values. The deformed textures predicted by all the SCS except Secant are similar. Simulations show that the CRSS for pyramidal <c+a> slip is higher than the CRSS for basal slip.
Twinning and detwinning behavior of a commercial AZ31 magnesium alloy during cyclic compression–tension deformation with a total strain amplitude of 4% (±2%) was evaluated using the complementary techniques of in-situ neutron diffraction, identical area electron backscatter diffraction, and transmission electron microscopy. In-situ neutron diffraction demonstrates that the compressive deformation was dominated by twin nucleation, twin growth, and basal slip, while detwinning dominated the unloading of compressive stresses and subsequent tension stage. With increasing number of cycles from one to eight: the volume fraction of twins at -2% strain gradually increased from 26.3% to 43.5%; the residual twins were present after 2% tension stage and their volume fraction increased from zero to 3.7% as well as a significant increase in their number; and the twinning spread from coarse grains to fine grains involving more grains for twinning. The increase in volume fraction and number of residual twins led to a transition from twin nucleation to twin growth, resulting in a decrease in yield strength of compression deformation with increasing cycles. A large number of -component dislocations observed in twins and the detwinned regions were attributed to the dislocation transmutation during the twinning and detwinning. The accumulation of barriers including twin boundaries and various types of dislocations enhanced the interactions of migrating twin boundary with these barriers during twinning and detwinning, which is considered to be the origin for increasing the work hardening rate in cyclic deformation of the AZ31 alloy.
To clarify the effect of twinning deformation on the work-hardening behavior of commercially pure titanium, the changes in the grain size and texture due to twinning deformation were investigated, along with the grain-size dependence of the work-hardening behavior. In specimens with an average grain size of 10 μm or less, twinning deformation was inactive, and the instantaneous work-hardening exponent (n = d(lnσ)/d (lnε)) was constant at approximately 0.2. For specimens in which twinning deformation occurred, the average grain size decreased and the texture changed with increasing strain due to twinning deformation, which resulted in an increase in the instantaneous n value. In the grain-size range at which twinning deformation did not occur, the smaller the grain size, the higher the rate of increase in the dislocation density and the greater the activity of 〈c + a〉-type dislocations, resulting in an increased strain hardening rate. Furthermore, the flow stress could be approximated using only the Bailey–Hirsh equation. The promotion of work hardening by twinning deformation can be mostly explained by the increase in the dislocation density increment rate, increase in the fraction of 〈c + a〉 dislocation due to grain refinement, and change in the Taylor factor due to the change in the texture.
Existence of tension – compression yield asymmetry is a serious limitation to the load bearing capablities of Magnesium alloys in a number of light weight structural applications. The present work is aimed at nullifying the tension to compression asymmetry problem and strain hardening anomalies in a Magnesium – Silver – Rare Earth alloy by engineering different levels of microstructural conditions via friction stir processing and post process annealing. The existence and extent of yield asymmetry ratio in the range of microstructural conditions was experimentally obtained through quasistatic tensile and compression tests. The yield asymmetry problem was profoundly present in specimens of coarse grained microstructures when compared to their fine grained and ultra fine grained counterparts. The impact of the microstructure and associated mechanisms of plasticity on the macroscopic strain hardening behavior was established by Kock – Mecking's analysis. Crystal plasticity simulations using Viscoplastic Self Consistency approach revealed the consequential role of extension twinning mechanism for the existence of yield asymmetry and anomalies in strain hardening behavior. This was especially dominant with coarsening of grain size. Electron Microscopy and characterization were conducted thoroughly in partially deformed specimens to confirm the predictions of the above simulations. The role of crystallographic texture for inducing the polarity to Tension – Compression yield asymmetry was corroborated. A critical grain size in Magnesium – Silver – Rare earth alloy was hereby established which could nullify influences of extension twinning in yield asymmetry ratio.
The effects of pre-existing {10–12} extension twins on the precipitation behavior of an extruded AZ80 material during aging and on its mechanical properties after peak aging are investigated. The material containing {10–12} twins—which are formed by compression before aging (twinned material)—has a finer grain size and higher dislocation density than the extruded material. Although the peak hardnesses of the twinned and extruded materials are almost the same, the time to reach the peak hardness is considerably shorter in the former material than in the latter (4 h and 24 h, respectively). In the twinned material, the high dislocation density of the {10–12} twins promotes continuous precipitation, which results in the formation of numerous fine Mg17Al12 precipitates within the twins in the early stage of aging. The formation of these continuous precipitates reduces the driving force for discontinuous precipitation, which consequently suppresses the formation and growth of coarse Mg17Al12 precipitates at the grain boundaries. Despite its shorter peak-aging time, the 4 h-peak-aged twinned material shows higher tensile strength and elongation than the 24 h-peak-aged extruded material. These higher mechanical properties of the former material are attributed primarily to the presence of more abundant fine continuous precipitates, which are effective in strengthening the material, and less abundant coarse discontinuous precipitates, which can act as crack initiation sites. These results demonstrate that the introduction of {10–12} twins into wrought Mg–Al-based alloys can accelerate the Mg17Al12 precipitation kinetics considerably and improve the strength and ductility of the peak-aged alloys simultaneously.
This paper reports a new {315}α″ type deformation twinning system, in adition to {130}<310>α″ in a full α″ Ti-23Nb (at. %) alloy. The {315}α″ twins were identified by trace analyses based on electron backscatter diffraction (EBSD) results, meanwhile ex-situ EBSD measurements showed that both {315}α″ and {130}α″ deformation twins transform into {332}β twins of the β parent phase after annealing at 573 K. The crystallographic correspondences between α″ twinning systems and {332}β twins have been analyzed theorectically, of which {315}α″/{332}β and {130}α″/{332}β correlated twins were confirmed experimentally. The calculations of twinning shear, shuffle and Schmid factor (SF) were carried out to survey the priority of occurrence of these α″ twins. It is concluded that the remarkable work-hardening and enhanced plasticity arise from both {315}α″ and {130}α″ deformation twinning in the present full α″ Ti-23Nb alloy.
{101¯2} twins were introduced into the magnesium (Mg) plate AZ31 via pre-rolling along its transverse direction. The plates, both with and without the pre-induced {101¯2} twins, were subjected to uniaxial tension along different directions. Using crystal plasticity modeling, we found that the strengthening effect of the pre-induced {101¯2} twins on the macroscopic flow stress primarily arised from the increased slip resistance caused by the boundaries, rather than the orientation hardening due to the twinning reorientation (although the latter did make its contribution in some specific loading directions). Besides, the pre-existing {101¯2} twins were found, by both experiments and simulation, to promote the activity of prismatic 〈a〉 and pyramidal 〈c + a〉 in the parent matrix of the material. Further analysis showed that the enhanced non-basal slip activity is related to the {101¯2} twin boundaries' low micro Hall-Petch slope ratios of non-basal slips to basal slip. With the critical resolved shear stress (CRSS) obtained from crystal plasticity modeling and the orientation data from EBSD, a probability-based slip transfer model was proposed. The model predicts higher slip transfer probabilities and thus lower strain concentration tendencies at {101¯2} twin boundaries than that at grain boundaries, which agrees with the experimental observation that the strain localization was primarily associated with the latter. The present findings are helpful scientifically, in deepening our understanding of how the pre-induced {101¯2} twins affect the strength and slip activity of Mg alloys, and technologically, in guiding the design of the pre-strain protocol of Mg alloys.
The mechanical properties of magnesium alloy AZ31 were investigated experimentally with visco-plastic self-consistent modeling. Tension, compression and plane strain compression (PSC) tests were performed along 3 directions of a hot rolled plate, and the material parameters input in the model were fitted with the uniaxial stress-strain curves. The critical resolved shear stress (CRSS) for tension twinning was modeled with a modified Voce hardening law first decreasing, and then increasing with strain, that could reproduce better the flow stress for twin-predominant deformation. Such CRSS evolution may better model twin nucleation, propagation and growth. Firstly simulations were carried out assuming latent hardening coefficients for slip by other slip systems equal to self-hardening. Then different heterogeneous latent hardening were used, whose values were based on dislocation dynamics simulations from the literature. This study shows that equal self and latent hardening can reproduce the stress strain curves and plastic anisotropy as well as heterogeneous mode on mode latent hardening. Discrepancies between simulations and experimental results from PSC are explained by an under-estimation of twinning for some PSC strain paths.
Compared to cold drawing, dieless drawing has shown great potential for manufacturing biodegradable Mg alloy microtubes due to the large reduction in area acquired in a single pass. However, owing to the local heating and local deformation, the deformation mechanism during dieless drawing is not clear, and thus causing difficulties in controlling the microstructure of dieless drawn tubes. For the purpose of acquiring a desired microstructure, in this study the deformation mechanism of ZM21 Mg alloy tube was clarified by conducting continuous observation of the microstructural evolution during dieless drawing. The results show that both SRX and DRX occurred during dieless drawing. SRX occurred before the plastic deformation to soften dieless drawn tubes. With increase of feeding speed, the deformation mechanism changed accordingly: (1) At the low-speed of 0.02 mm/s, the deformation mechanism was dominated by twin-slip sliding, during which {10–12} tension twins were generated inside grains to accommodate the plastic deformation by changing the crystal orientation. (2) At the intermediate-speed of 2 mm/s, a twin-DRX process related to {10–12} tension twin was observed, which was characterized by the generation of abundant {10–12} tension twins and the evolution of misorientation angle of {10–12} tension twins. Moreover, the transformation from twin-DRX to CDRX can be observed at the late stage of plastic deformation, which was attributed to the inhomogeneous conditions of dieless drawing. (3) At the high-speed of 5 mm/s, a CDRX process was observed, during which grain boundary sliding and grain tilting were observed, in addition to the gradual rotation of subgrains. These results show that during dieless drawing, DRX is not only a temperature-dependent phenomenon, but also influenced by the variation of feeding speed.
The mechanical response and texture evolution of magnesium alloy during hot deformation are closely related to the heterogeneous meso-deformation. The improved Voce hardening law was developed and introduced into the crystal plasticity (CP) theory, and a reconstruction method of textured representative polycrystal was proposed. Three-dimensional crystal plasticity finite element model (3D-CPFEM) was established to meso-simulate the hot compression deformation of ZK61 Mg alloy. The influence of the temperature and strain rate on mechanical response was investigated, and the corresponding texture evolution and the texture transformation mechanism was revealed through meso-simulation. The results show that the 3D-CPFEM with the improved Voce hardening law and the initial texture characteristic can well predict the mechanical response and texture evolution under different temperatures and strain rates during hot compression of ZK61 Mg alloy. The basal plane texture of the ZK61 tubular blank is transformed into the basal fiber texture after hot compression, where the basal plane of grains is deflected gradually from the radial-axial plane to the radial-tangential plane. The texture transformation is attributed to two reasons, i.e., the orientation deflection of the grains with larger basal slip systems Schmid factor (SF) and the orientation retention of the grains whose c-axis tends to be parallel to the axial direction (AD) of the tubular blank. The change of the grain orientation corresponding to the basal plane texture component of the tubular blank has little contribution to the formed basal fiber texture.
The aim of present work is to develop a crystal plasticity modeling approach to integrate slip, dynamic recrystallization (DRX) and grain boundary sliding (GBS) for simulating the deformation behavior and texture evolution of magnesium alloys at high temperatures. Firstly, the deformation mechanisms of an AZ31B Mg alloy sheet at 300 °C were investigated by examining texture and microstructure evolution during uniaxial tension and compression tests. DRX refines microstructure at strains less than 0.2, and subsequently GBS plays a significant role during deformation process. A GBS model is developed to evaluate strain and grain rotation induced by GBS, and implemented into the polycrystal plasticity framework VPSC. The VPSC-DRX-GBS model can well reproduce the stress−strain curves, grain size, texture evolution and significant texture differences in tension and compression tests due to GBS. The calculated GBS contribution ratio in tension is obviously higher than that in compression due to easier cavity nucleation at grain boundaries under tension loading.
An extruded magnesium AZ31 magnesium alloy was processed by rotary swaging (RSW) and then deformed by tension and compression at room temperature. The work-hardening behaviour of 1–5 times swaged samples was analysed using Kocks-Mecking plots. Accumulation of dislocations on dislocation obstacles and twin boundaries is the deciding factor for the strain hardening. Profuse twinning in compression seems to be the reason for the higher hardening observed during compression. The main softening mechanism is apparently the cross-slip between the pyramidal planes of the second and first order. A massive twinning observed at the deformation beginning influences the Hall-Petch parameters.
Wrought magnesium and Mg alloys are characterized by a strong basal texture and several slip and twin modes activated at room temperature. These modes interact with each other, and the obstacles on each system associated with other deformation systems are empirically modeled via latent hardening coupling coefficients. {101‾2} tension twinning can be easily and largely activated, causing severe mechanical anisotropy and dramatic texture change. Twin nucleation and growth can also be influenced by slip-induced dislocations. To investigate how dislocations and twins affect {101‾2} twinning, a rolled magnesium alloy AZ31 was pre-deformed along different directions and reloaded in in-plane compression at room temperature. Elasto-visco-plastic self-consistent simulations including twinning, detwinning and secondary twinning show that the critical resolved shear stress for {101‾2} twinning is strongly increased by previous twins, moderately enhanced by basal and pyramidal slips, but additional prismatic dislocations have no effect on twinning. The present experiments and simulations demonstrate that latent hardening for {101‾2} by slip modes is much less than self-hardening.
A gradient nanostructured layer was prepared on the surface of Mg-8Gd-3Y alloys by severe shot peening (SSP). The microstructure evolution, residual stress distribution and mechanical property of the gradient nanostructured layer were systematically investigated by Rietveld refinement, transmission electron microscopy, and X-ray stress and hardness analyses. The results show grain sizes of the peened samples were 80–100 nm at the top surface and increased gradually with depth. The refinement process of Mg-8Gd-3Y alloys to nano size during SSP mainly involved three steps: i) introduction of deformation twinning and dislocations in grains with a large size, ii) subdivision of large grains into substructures by twin-twin interaction and dislocation cells interacting twins, iii) evolution of subgrains to nanograins by the dislocation-assisted lattice rotation. Simultaneously, high-level compressive residual stresses were induced with a maximum magnitude of −206 MPa. Besides, the surface roughness values obviously increased and several surface cracks were detected at the near surface, which might have detrimental effects on surface behavior. Owing to the microstructural improvement, the top surface of the peened Mg-8Gd-3Y alloy attained the maximum microhardness of 155 ± 5 HV, exhibiting approximately 2 times higher than the pristine alloy.
Magnesium alloy sheets usually has to be processed by warm forming, and change of strain path and evolution of microstructure can significantly influence their warm formability. Forming limit test for an AZ31B alloy sheet under strain path changes was configured and implemented, and the effects of strain paths and microstructure evolution on the forming limit diagram are investigated. The sheet was pre-strained under in-plane uniaxial, plane strain and biaxial tension loading paths at 150 °C, 200 °C and 300 °C, followed by hemispherical punch stretching experiments at the three temperatures using specimens extracted from the pre-strained samples. A crystal plasticity model that incorporates dynamic recrystallization (DRX) and annealing recovery was combined with the Marciniak-Kuczyński (M-K) approach to calculate the FLDs. The evolution of dislocation density during annealing in the pre-strained FLD test at 200 °C was evaluated, through which the predictions of pre-strained FLDs were considerably improved. The present work provides experimental as well as crystal plasticity based methods for evaluating warm formability of magnesium alloys influenced by temperature, pre-straining, DRX and recovery.
〈a〉dislocations on basal or prismatic planes and {112¯2} compression twins are commonly activated in deformed Titanium (Ti). In the present work, their interactions are investigated by both crystallographic analysis and atomistic simulations. For a three-dimensional {112¯2} twin, we firstly analyze seven possible twin boundaries (TBs) bonding two low index planes in matrix and twin. Next, we focus on the two lower energy boundaries, {112¯2}M/T∥{112¯2}T/M coherent twin boundary (CTB) and {1¯21¯1}M/T∥{12¯11¯}T/M. Depending on dislocation character and boundary type, we define four types of interactions between 〈a〉 dislocations and these TBs. Further, we predict possible dislocation reactions on/across TBs using crystallographic analysis according to the deformation compatibility and the change in elastic energy, such as twinning/detwinning of the primary twin, slip transmission and secondary twinning, for each type of interaction. Molecular dynamics (MD) simulations are then conducted for all interactions under pre-selected loadings in order to explore the dynamic process associated with each of these interactions and examine the predicted reactions. MD simulations predict that the interaction between 〈a〉 dislocations and some facets can lead to the formation of secondary twins and 〈a〉 dislocations on basal or prismatic planes in twins, and reveal the possibility of forming 〈c〉 and 〈c+a〉 dislocations in twins. Moreover, some of the possible reactions take place on lateral TBs other than CTBs.
Gas-gun experiments are carried out to study the mechanical properties and fracture behavior of a textured Mg-3Al-1Zn alloy under high strain rate. The impact direction (ID) is either perpendicular or parallel to crystallographic 0001 planes, referred to as ID∥〈c〉 and ID⊥〈c〉, respectively. Shock compression and spallation are achieved with different specimen-to-flyer plate thickness ratios. The Hugoniot elastic limits and spall strengths are estimated as 0.32–0.35 GPa and 0.9–0.92 GPa, respectively, showing weak anisotropy. The deformed specimens are characterized with scanning electron microscope and X-ray computed tomography. Abundant {101̄2} extension twins are activated and the strain hardening rate exhibits a sharp increase and then decrease for the ID⊥〈c〉 specimen, while a small number of twins are observed and the hardening rate decreases monotonically for the ID∥〈c〉 specimen. As a result of the anisotropic distribution of the β-Mg17Al12 phase, cracks are generally distributed in the mid-part and connected together for the ID⊥〈c〉 case, while the distribution of cracks in the ID∥〈c〉 specimen is relatively discrete along the ID and parallel to the rolling plane.
This paper is concerned with structural changes taking place in pure magnesium subjected to cold straining under heavy loading. It was shown that at T = 0.3 Tm (melting point), low temperature dynamic recrystallization (LTDR) developed in the material. During LTDR, the size of dynamically recrystallized grains was found to be strain dependent. A certain relationship was established between this dependence and the dominating deformation mechanisms. The causes of the strain dependence of the dynamic recrystallization parameters in magnesium are discussed. © 2018 Zeitschrift fuer Metallkunde/Materials Research and Advanced Techniques. All rights reserved.
In many polycrystals of less than cubic crystal symmetry, plastic deformation is dominated by twinning. In particular, we will treat the case of Zr and Zr alloys in detail. We propose a new method for modelling grain reorientation due to twinning, which is based on a Volume Fraction Transfer (VFT) scheme; the scheme is also applied to the slip modes. We find that this method predicts textures that are, when twinning is the dominant mode, considerably different from, and in better agreement with experiment than the conventional schemes which reorient an entire grain when some criterion has been met. Various combinations of slip and twinning modes and of the associated critical stresses are systematically investigated for the case of rolling, tension and compression of Zr alloys. A comparison of various predicted and experimental textures leads to the conclusion that twinning must, indeed, be controlling texture development.
The deformation in compression of pure magnesium and AZ31B magnesium alloy, both with a strong basal pole texture, has been investigated as a function of temperature, strain rate, and specimen orientation. The mechanical response of both metals is highly dependent upon the orientation of loading direction with respect to the basal pole. Specimens compressed along the basal pole direction have a high sensitivity to strain rate and temperature and display a concave down work hardening behavior. Specimens loaded perpendicularly to the basal pole have a yield stress that is relatively insensitive to strain rate and temperature and a work hardening behavior that is parabolic and then linearly upwards. Both specimen orientations display a mechanical response that is sensitive to temperature and strain rate. Post mortem characterization of the pure magnesium was conducted on a subset of specimens to determine the microstructural and textural evolution during deformation and these results are correlated with the observed work hardening behavior and strain rate sensitivities were calculated.
A new rate-dependent elastic–viscoplastic crystal plasticity constitutive model (CPCM) to simulate the large strain deformation in magnesium alloys is presented. The observed intragranular plastic deformation mechanisms of primary extension, primary contraction, and secondary extension (double) twinning are accounted for. The basal and non-basal slip systems in the parent grain, primary and double twins were also incorporated in the model. The crystallographic planes and directions of various slip and twinning systems are calculated. The slip-induced shear in the parent grain, as well as primary and secondary twinned regions are simulated. The twinning-induced shear from the primary and secondary twinned regions are also computed. In the model the texture evolution in the parent, as well as primary and secondary twinned regions are tracked. Separate resistance evolution functions for all the slip and twinning systems were considered. The interactions between various slip and twinning systems are accounted for in a comprehensive manner. Using the proposed CPCM, the plastic deformation in a magnesium single crystal in simple shear strain path is simulated. The contributions of various plastic deformation mechanisms to the macroscopic plastic deformation of the magnesium single crystal in this strain path are presented. The importance of identifying the active plastic deformation in a given strain path on a magnesium single crystal for a reliable model prediction was shown with an example.
We experimentally and numerically investigated the effect of twinning on plasticity using an extruded rod-textured magnesium alloy. The rod-texture is a 〈101¯0〉-axis fiber texture that presents a fundamentally different anisotropy correlated to twinning with respect to the widely discussed c-axis fiber texture generated by clock rolling. We quantified a profuse {101¯2}〈101¯1〉 extension twinning along the extrusion direction (ED) that consumed the entire parent before the inflection point in the stress–strain behavior. However, under compression along the extrusion radial direction (ERD), the twinning model in the viscoplastic self-consistent formulation still predicts substantial extension twinning. However, in this case the stress–strain curve did not inflect, and Regime II hardening was absent. We demonstrate via EBSD analyses that the absence of Regime II hardening along the ERD was due to a non-Schmid effect by multivariant “stopped” twinning. The intersecting variants of stopped twins incurred twin–twin interactions that limited the twin growth. Profuse {101¯1}〈101¯2〉 double twinning occurs both under ED and ERD but peculiarly triggered earlier under ERD than under ED, so the Voce model under VPSC could not capture their effect. The complex networks of stopped twins in the ERD clearly negate a possible Hall–Petch effect on Regime II by twin segmentation, since otherwise Regime II would be more marked in the ERD. Rather, the stopped twins suggest preferential latent hardening within the twinned regions by parent dislocation transmutation upon their incorporation in the twins. In fact, since twin–twin interactions mitigate the growth rates of sweeping extension twin boundaries, dislocation transmutation could be limited to the extent that Regime II hardening will be eliminated.
In order to study the behavior of material under finite deformation at various strain rates, the responses of AZ31 Mg sheet are measured under uniaxial (tension and compression) and multiaxial (simple shear) loadings along rolling direction (RD), 45° to rolling direction (DD), 90° to rolling direction (TD), and normal to the sheet (ND) to large strains. The material exhibits positive strain rate sensitivity (SRS) at room and elevated temperatures; the SRS is more pronounced at high temperatures and lower strain rates. The r-value of the material under tensile loading at room temperatures is higher in TD at lower strain rate. Texture measurements on several failed specimens are reported under tension and simple shear after finite plastic deformation of about 20% equivalent strain. The as-received material exhibits a strong fiber with equal fractions of grains having the c-axis slightly tilted away from the sheet normal towards both +RD and −RD. Pole figures obtained after tensile loading along the rolling direction (RD) show that the texture of the material strengthens even at low strains, with c-axis perpendicular to the sheet plane and prism planes lining up in a majority of grains. However, the tensile loading axis along TD does not lead to similar texture strengthening; the c-axis distribution appears to be virtually unchanged from the virgin state. The pole figures obtained after in-plane compression along RD brings the c-axes of the grains parallel to the loading direction. The pole figures after simple shear loading show that the c-axis rotates to lie on the sheet plane consistent with a compression axis 45° away on the sheet plane.
Substructure development in polycrystalline magnesium compressed at different temperatures and strain rates was investigated by means of light microscopy, X-ray diffractometry (texture and line-broadening analysis), and in some cases also by TEM or SEM. The fracture of the specimens is accompanied by shear banding. Dynamic recrystallisation starting above RT must be taken into account. The experimental results reflect the interaction between twinning and dislocation slip during the deformation, which leads to significant texture changes.
The kinetics of glide at constant structure and the kinetics of structure evolution are correlated on the basis of various experimental observations in pure f.c.c. mono- and polycrystals. Two regimes of behavior are identified. In the initial regime, the Cottrell-Stokes law is satisfied, hardening is athermal, and a single structure parameter is adequate. With increasing importance of dynamic recovery, be it at large strains or at high temperatures, all of these simple assumptions break down. However, the proportionality between the flow stress and the square-root of the dislocation density holds, to a good approximation, over the entire regime; mild deviations arc primarily ascribed to differences between the various experimental techniques used. A phenomenological model is proposed, which incorporates the rate of dynamic recovery into the flow kinetics. It has been successful in matching many experimental data quantitatively.
An advancing deformation twin in α-iron may be preceded by slip dislocations, each of which moves on a {112} plane parallel to the habit plane of the twin. Such a dislocation moves on one out of every three {112} planes, thus causing shear which is homogeneous under the optical microscope. These slip dislocations are called "emissary dislocations". Their existence is postulated on the basis of energy considerations. Experimental observations on α-iron specimens deformed at low temperature reveal some phenomena which are adequately explained by this concept: twin-like markings may appear at the specimen surface, even though cross-sectioning shows that the twins that caused them did not reach the surface, and, similarly, sub-boundaries may be zigzagged in front of a twin that is still at a distance of the order of 106 interatomic spacings. It appears that the movement of emissary dislocations cannot be reversed by load reversal, which is in agreement with the reverse of the Bauschinger effect exhibited by the stress-strain curves. Pile-up theory explains satisfactorily the details of some emissary dislocation configurations; the theory permits calculation of the maximum applied stress from microscope observation. The result of such a calculation × 108 dyn/cm2 bears comparison with the maximum stress of 53 × 108 dyn/cm2 actually applied. After cross-slipping out of the region to be occupied by the advancing twin emissary dislocations lose their peculiar character and may glide back upon stress reversal. Some details of the theory are supported by electron microscope observation, and show that an alternative mechanism for the creation of emissary dislocations is improbable.
Hexagonal close-packed (hcp) metals show a deformation behavior, which is quite different from that of materials with cubic crystalline structure. As a consequence, rolled or extruded products of magnesium and its alloys exhibit a strong anisotropy and an unlike yielding in tension and compression. In this work, the microstructural mechanisms of deformation in pure magnesium are modeled by visco-plastic constitutive equations of crystal plasticity. Single crystals and textured polycrystals are analyzed numerically. By means of virtual mechanical tests of representative volume elements mesoscopic yield surfaces are generated. The linking of micro- and mesoscale provides a procedure for the simulation of the yielding and hardening behavior of arbitrarily textured solids with hcp structure such as extruded bars or rolled plates.
In this paper we present a critical review of the results of experimental and theoretical investigations of the dependence of the flow stress τ on the dislocation density ϱ in crystals of different lattice types (f.c.c., b.c.c., h.c.p.). It was found that the τ(ϱ) dependence is preferentially described by an equation of the type .The effects of different factors such as deformation, deformation rate, structural state and dislocation distribution type on τ(ϱ) are considered.Analysis of the available experimental data was carried out. It showed that (a) the various dislocation types contribute differently to the flow stress, (b) the value of the contribution is mainly determined by the energy gain value at pairwise dislocation interactions, (c) the value of the contribution is contained in the parameter α (the larger the energy gain at the pairwise dislocation interaction, the larger is the value of α, i.e. α is an interaction constant) and (d) in general the τ(ϱ) dependence should be written The available theoretical models of work hardening are discussed. In most of these models the energy gain factor is not taken into account. This makes the models insensitive to the type of dislocation interaction chosen and leads to identical calculated α values. The theories and models in which the energy gain is taken into account are more realistic as they show good agreement between the calculated and measured α values.The role of forest dislocations in the work hardening of metal crystals and their contribution to the short- and long-range flow stress components are discussed. In h.c.p. metal crystals with similar densities of primary and forest dislocations the contribution from the forest dislocations to flow stress and its long-range component were shown to be of most importance.
Magnesium alloy sheets have been extending their field of applications to automotive and electronic industries taking advantage of their excellent light weight property. In addition to well-known lower formability, magnesium alloys have unique mechanical properties which have not been thoroughly studied: high in-plane anisotropy/asymmetry of yield stress and hardening response. The reason of the unusual mechanical behavior of magnesium alloys has been understood by the limited symmetry crystal structure of HCP metals and thus by deformation twinning. In this paper, the phenomenological continuum plasticity models considering the unusual plastic behavior of magnesium alloy sheet were developed for a finite element analysis. A hardening law based on two-surface model was further extended to consider the general stress–strain response of metal sheets including Bauschinger effect, transient behavior and the unusual asymmetry. Three deformation modes observed during the continuous in-plane tension/compression tests were mathematically formulated with simplified relations between the state of deformation and their histories. In terms of the anisotropy and asymmetry of the initial yield stress, the Drucker–Prager’s pressure dependent yield surface was modified to include the anisotropy of magnesium alloy. The numerical formulations and characterization procedures were also presented and finally the correlation of simulation with measurements was performed to validate the proposed theory.
Experimental results are given of the dependence of work hardening parameters (critical shear stress, τc, work hardening coefficient, θA, and stage length ϵA at easy glide) in Mg crystals under basal slip on the density of pyramidal dislocations ϱf of various kinds. A relation between the kind of basal–pyramidal dislocation interaction is found and its effect on the above-mentioned hardening parameters is shown. The influence of interaction type depends on the quantity of energy gain in this interaction.]Russian Text Ignored].
Hexagonal materials deform plastically by activating diverse slip and twinning modes. The activation of such modes depends on their relative critical stresses, and the orientation of the crystals with respect to the loading direction. To be reliable, a constitutive description of these materials has to account for texture evolution associated with reorientations due to both dislocation slip and twinning, and for the effect of the twin boundaries as barriers to dislocation propagation. We extend a previously introduced twin model, which accounts explicitly for the composite character of the grain formed by a matrix with embedded twin lamellae, to describe the influence of twinning on the mechanical behavior of the material. The role of the twins as barriers to dislocations is explicitly incorporated into the hardening description of slip deformation via a directional Hall–Petch mechanism. We introduce here an improved hardening law for twinning, which discriminates for specific twin/dislocation interactions, and a detwinning mechanism. We apply this model to the interpretation of compression and tension experiments done in rolled magnesium alloy AZ31B at room temperature. Particularly challenging cases involve strain-path changes that force strong interactions between twinning, detwinning, and slip mechanisms.
Using transmission electron microscopy, the dependence of dislocation density, ϱ, on stress, τ, and strain, ϵ, has been studied in Mg crystals deformed by basal and pyramidal slips. It has been shown that for the slip systems investigated the dependence τ(ϱ) may be written in the form τ ∼ ΣiαiGibi√ϱi, where αi is the coefficient whose value takes account of the type of dislocation interaction appearing during deformation. The strain dependences for the rate of changing the density of different dislocations have been found. Based on the measurement data on the density of thin slip bands in the (0001) system, the density of basal mobile dislocations providing the onset of an easy glide stage has been estimated.
An in-depth statistical analysis using electron backscatter diffraction (EBSD) is carried out to expose statistical correlations between {} twinning and grain size, crystallographic orientation, grain boundary length, and neighbor misorientation in high-purity polycrystalline zirconium strained to 5% and 10% at 77 K. A strong correlation was found between the active twin variant and crystallographic orientation. The propensity of a grain to twin or not was found to be only weakly dependent on grain area and diameter. Within the population of grains containing twins the number of twins per grain noticeably increases with grain area, and twin thickness is found to be rather insensitive to grain size and orientation. A weak preference for twinning was found for smaller grain boundary misorientation angles. These and the other statistical results reported can improve theoretical treatments for twin nucleation in polycrystal models. The statistical methodology presented has general applicability for all twin types in a wide range of metals.
We study two possible twin growth mechanisms in hexagonal close-packed (hcp) metals: a slip-assisted one, based on dislocation reactions at twin interfaces, and a slip-independent one, based on the direct activation of twin dislocations. A twin thickening rate law is developed to estimate the contribution of slip dislocations to twin growth in hcp crystals. Application of the model to Mg single crystals, and comparison with experimental data, suggests that twin thickening proceeds independently of slip.
We present in this work a visco-plastic self-consistent (VPSC) anisotropic approach for modeling the plastic deformation of polycrystals, together with a thorough discussion of the assumptions involved and the range of application of such approach. We use the VPSC model for predicting texture development during rolling and axisymmetric deformation of Zirconium alloys, and to calculate the yield locus and the Lankford coefficient of rolled Zircaloy sheet. We compare our results with experimental data and find that they are in good agreement with the available experimental evidence. We also compare the VPSC predictions with the ones of a Full Constraints approach and observe that they differ both quantitatively and qualitatively: according with the predictions of the VPSC scheme, deformation is accommodated mostly by the soft systems, the twinning activity is much lower, and fewer systems are active, in average, per grain. These results are a consequence of having accounted for the grain interaction with its surroundings, which is a crucial aspect when modeling plastically anisotropic materials.
Uniaxial compression test data were obtained from magnesium alloy AZ31B sheet material tested along three sample directions (rolling, transverse and normal direction) over the temperature range T = 22–250 °C. The yield point during in-plane compression is insensitive to temperature, up to 200 °C, suggesting that athermal mechanisms are responsible for yielding. The in-plane compression samples exhibit very low r-values, which provides another signature of significant twinning activity in magnesium sheet, in addition to the characteristic sigmoidal strain hardening curve. By varying the critical resolved shear strengths (CRSS) and hardening behaviors of the deformation mechanisms, it is possible to model the changes in the flow stress profile, the strain anisotropy, and texture evolution using a viscoplastic self-consistent polycrystal model. Notably, the CRSS values for basal slip were observed to be constant, while that of twinning increased slightly, and the CRSS values of thermally activated slip modes, i.e., prismatic and pyramidal 〈c + a〉 slip, decrease over the temperature range investigated. Because deformation twinning is observed to be significantly active over the entire temperature range, and the ductility improves markedly as the temperature is increased, it is concluded that twinning is not intrinsically detrimental to the ductility. However, the poor ductility during in-plane compression at the lower temperatures appears to be connected with the twinning reorientation since there is a very limited ability to accommodate c-axis compression.
The viscoplastic self-consistent model was used to interpret differences in the mechanical behavior of hexagonal close packed magnesium alloys. There are only subtle differences in the compression textures of magnesium and its solid solution alloys containing lithium or yttrium. However, the plane strain compression textures of the alloys showed an increasing tendency for the basal poles to rotate away from the “normal direction” towards the “rolling direction”. Texture simulations enabled these distinctions to be attributed to the increased activity of the non-basal 〈c+a〉 slip mode. The alloys had improved compressive ductilities compared to pure magnesium, and the increased c+a slip mode activity provides a satisfying explanation for this improvement, since it can accommodate c-axis compression within individual grains. Accounting for individual deformation mode hardening enabled the flow curves to be simulated and the anisotropic plastic response of textured wrought alloys to be mechanistically understood and predicted.
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.
The concepts of twinning shears and twinning modes are introduced. The early attempts to predict these features are presented. This is followed by a detailed discussion of the formal theories of Bilby and Crocker and Bevis and Crocker for predicting these elements. Their formalisms are applied to predict twinning modes in single lattice structures, superlattices, hexagonal close packed structure and other double lattice structures. Wherever possible the predicted modes are compared with those observed.The description of fully coherent, rational twin interfaces is presented, and the concepts of elementary, zonal, complementary and partial twinning dislocations are discussed. It is suggested that the irrational K1 twin interfaces may be faceted on the microscopic scale, and these facets may be coherent.Homogeneous and heterogeneous nucleation of twins are discussed. The growth of twins by the nucleation of twinning dislocations on planes parallel and contiguous to the coherent twin boundary is considered. Various dislocation models proposed for the formation of twins in b.c.c., f.c.c., diamond cubic, zinc-blende and h.c.p. structures are critically reviewed. In some cases the supporting experimental evidence is presented. Additionally, the effects of deformation temperature, imposed strain-rate, alloying and doping, prestrain, precipitates and second phase disperions on deformation twinning are discussed.Mechanistic details regarding the accommodation processes occurring at twins terminating within a crystal, slip-twin, twin-slip and twin-twin intersections are reviewed and are compared with the experimental results. The role of twins in the nucleation of fracture in materials is also considered.
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.
A large deformation viscoplastic polycrystal theory is formulated. It is restricted to loading conditions since elasticity is entirely neglected. The single crystal behavior is based on crystallographic slip, and the slip rate is a non-linear function of the resolved shear stress. The time independent plasticity is obtained as a limit when the rate sensitivity tends to zero. The polycrystal behavior is obtained from the single crystal constitutive relation by solving integral equations derived from the field equations. A self-consistent approach is developed, where each grain is assumed to be a single ellipsoidal inclusion in a homogeneous equivalent medium. An interaction formula is derived and the local strain rates are calculated by resolving a nonlinear system of equations. Applications to texture predictions in tension, compression, rolling and torsion are finally considered.
Simulating the forming of anisotropic polycrystals, such as zirconium, requires a description of the anisotropy of the aggregate and the single crystal, and also of their evolution with deformation (texture development and hardening). Introducing the anisotropy of the single crystal requires the use of polycrystal models that account for inhomogeneous deformation depending on grain orientation. In particular, visco-plastic self-consistent models have been successfully used for describing strongly anisotropic aggregates. As a consequence, using a polycrystal constitutive law inside finite element (FE) codes represents a considerable improvement over using empirical constitutive laws, since the former provides a physically based description of anisotropy and its evolution.In this work we develop a polycrystal constitutive description for pure Zr deforming under quasi-static conditions at room and liquid nitrogen temperatures. We use tensile and compressive experimental data obtained from a clock-rolled Zr sheet to adjust the constitutive parameters of the polycrystal model. Twinning is accounted for in the description. The polycrystal model is implemented into an explicit FE code, assuming a full polycrystal at the position of each integration point. The orientation and hardening of the individual grains associated with each element is updated as deformation proceeds. We report preliminary results of this methodology applied to simulate the three-dimensional deformation of zirconium bars deforming under four-point bend conditions to maximum strains of about 20%. A critical comparison between experiments and predictions is done in a second paper (Kaschner et al., Acta mater. 2001, 49(15), 3097–3107).
The new neutron time-of-flight (TOF) diffractometer HIPPO (High-Pressure-Preferred Orientation) at LANSCE (Los Alamos Neutron Science Center) is described and results for quantitative texture analysis of a standard sample are discussed. HIPPO overcomes the problem of weak neutron scattering intensities by taking advantage of the improved source at LANSCE, a short flight path (9 m) and a novel three-dimensional arrangement of detector banks with 1360 3He tubes, on five conical rings with scattering angles ranging from 2θ=10° to 150°. Flux at the sample is on the order of 107 neutrons cm−2 s−1. A large sample chamber (75 cm diameter well) can accommodate ancillary equipment such as an automatic sample changer/goniometer used in this study. This instrument was used to measure the texture of a round-robin limestone standard and extract orientation distribution data from TOF diffraction spectra with different methods (Rietveld harmonic method, Rietveld direct method, automatic fitting of individual peak intensities), and the results compare favorably. Also, there is good agreement with results obtained on the same sample measured at other facilities, but with greatly reduced measuring time for HIPPO.
A study of the mechanical response of Mg AZ31 when deformed under twinning dominated conditions is presented. In addition to the well-known rapid texture variation, neutron diffraction measurements reveal a ‘sense-reversal’ of the internal stress in the twinned grains. The latter is characterized experimentally and an elasto-plastic polycrystal model is extended in order to account for twin domain reorientation and associated stress relaxation. It is concluded that the texture variation due to twinning is sufficient to explain the observed macroscopic stress–strain response. However, the evolution of internal stresses in diffracting subsets of grains is complex and more challenging to explain. It seems to be strongly controlled by the order in which slip and twinning are activated, the stress relaxation associated with twin propagation, and neighbor constraint effects.
Hexagonal materials deform plastically by activating diverse slip and twinning modes. The activation of such modes depends on their relative critical stresses, and the orientation of the crystals with respect to the loading direction. For a constitutive description of these materials to be reliable, it has to account for texture evolution associated with twin reorientation, and for the effect of the twin barriers on dislocation propagation and on the stress–strain response. In this work, we introduce a model for twinning, which accounts explicitly for the composite character of the grain, formed by a matrix with embedded twin lamellae which evolve with deformation. Texture evolution takes place through reorientation due to slip and twinning. The role of the twins as barriers to dislocations is explicitly incorporated into the hardening description via geometrically necessary dislocations and a directional Hall–Petch mechanism. We apply this model to the interpretation of compression experiments, both monotonic and changing the loading direction, done in rolled Zr at 76 K.
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.
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.
An attempt is made here to explain the observed phenomena in the yielding and ageing of mild steel, described in two previous papers, in the general terms of a grain-boundary theory. On this hypothesis, a satisfactory explanation of the variation of the lower yield point with grain size may be developed. It is shown that strain-ageing must involve two processes: a healing of the grain-boundary films, coupled with a hardening in the grains themselves. A discussion of the possible nature of the grain-boundary film is also undertaken.
A generalized spherical-harmonic description of the texture for polycrystalline materials has been implemented in a multiple-phase/multiple-data-set Rietveld refinement code. It has been tested using two sets of neutron time-of-flight data taken from a standard calcite sample previously used for a round-robin study [Wenk (1991). J. Appl. Cryst. 24, 920-927] and has been shown to give similar texture results as those obtained from individual pole figures. Simultaneous refinement of the calcite crystal structure including anisotropic thermal parameters gives results essentially identical to a recent single-crystal X-ray study.
Massachusetts Institute of Technology. Dept. of Metallurgy. Thesis. 1966. Ph. D. Vita. Bibliography: leaves 37-38.
- H J Bunge
Bunge, H.J., 1982. Texture Analysis in Materials Science: Mathematical Methods. Butterworth.
The deformation characteristics of textured magnesium. Transactions of the Metallurgical Society of AIME 242
- E W Kelley
- Hosford Jr
Kelley, E.W., Hosford Jr., W., 1968a. The deformation characteristics of textured magnesium. Transactions of the Metallurgical Society of AIME 242, 654–661.
The deformation characteristics of textured magnesium
- E W Kelley
- W Hosford
Kelley, E.W., Hosford Jr., W., 1968a. The deformation characteristics of textured magnesium. Transactions of the Metallurgical Society of AIME 242, 654-661.
Slip and deformation twinning in magnesium
- P G Partridge
- E Roberts
Partridge, P.G., Roberts, E., 1964. Slip and deformation twinning in magnesium. In: Third European Regional Conference on Electron Microscopy,
Czechoslovak Academy of Sciences, pp. 213-214.