Elastic Viscoplastic Self-consistent Research Articles

Measuring texture-component-dependent stress of CuZn39Pb2 by neutron diffraction

Understanding the micromechanical behavior of polycrystalline material is pivotal for regulating its mechanical performance and widening its application. Taking advantage of its non-destructive nature, the neutron diffraction technique has been widely applied to investigate the micromechanical behaviors, usually at the resolution of grains sharing the same diffraction plane. This work employs a newly developed technic of the texture-component-dependent (TCD) in-situ neutron diffraction method to obtain the full strain/stress tensor of a textured CuZnPb alloy at the resolution of individual crystallographic orientation. The variation of the internal stresses and lattice strains over the grains that share the same diffraction plane has been successfully captured by the TCD method. According to the results of in situ neutron diffraction, Copper ({-1–1–2}<-1–11>) possesses the highest lattice stress while Cube ({010}<100>) and Goss ({110}<001>) bear the lowest stress of 370 MPa. In parallel, the micromechanical response of the texture components is modeled by the elastic visco-plastic self-consistent (EVPSC) model. The simulated results are in reasonable agreement with the corresponding experiments in loading direction, while the lateral stress exhibits some deviation. By crystal plasticity finite element modeling, the deviation is related to the neighbor grain which affect more significantly the lateral stress than the material parameters. The full tensor of stress within the individual crystallographic orientation measured by TCD method gives more insight into the crystal plasticity modeling.

Deformation behavior of nickel-based superalloys with bimodal γ′ size distribution studied by in-situ neutron diffraction combined with EVPSC modeling

Nickel-based superalloys with multimodal γ′ size distribution microstructure have been designed to employ in extreme environments due to their excellent mechanical performance. Whilst the effect of γ′ size on deformation mechanism has been studied before, little has been done to assess the deformation sequence and contribution to the load partition for different types of γ′ precipitates. In order to address this gap, this study focused on bimodal superalloys of GH4738 (containing the secondary and tertiary γ′ precipitates) and GH4720Li (containing the primary and tertiary γ′ precipitates) alloys. In-situ neutron diffraction assisted by a 2-site elastic-viscoplastic self-consistent (EVPSC) model was employed to elucidate the deformation mechanisms. The effects of different types of γ′ precipitates on the partitioning of interphase stress and the underlying mechanisms have been revealed. The findings indicated that bimodal superalloys exhibited distinct deformation behaviours compared to unimodal ones. Notably, premature load partitioning was observed in the microplasticity stage, attributable to Orowan looping for secondary γ′ precipitates or the emission of dislocations from the straight interface of primary γ′ precipitates. In the macroplasticity stage, considerable dislocations shear three types of γ′ precipitates, especially for the tertiary γ′ precipitates, which results in the decrease in the increment rate of interphase stress. These findings could contribute to a better understanding of deformation mechanisms in superalloys with multimodal γ′ size distributions and shine a spotlight on material design to modulate intergranular and interphase stresses.

Study on the Internal Stress and Thermal Anisotropy in Magnesium Alloys Using a Thermal Elastic Viscoplastic Self-Consistent Model.

A thermal elastic viscoplastic self-consistent model is utilized to examine the thermal stress induced by the thermal anisotropy of single crystals during heat treatments. This model considers temperature-dependent elastic constants and critical resolved shear stress associated with thermal dilation. Simulation results demonstrate that under cooling, the elastic lattice strain increases significantly when constrained compared to unconstrained cooling. The deformation mechanism observed under cooling with constraint resembles tension along the constrained direction at room temperature. Polycrystals offer more deformation mechanisms to accommodate thermal anisotropy compared to single crystals, resulting in lower applied stress at the constrained boundary. Among the various observed textures, the maximum amplitude of residual lattice strain follows the following order: rolled > extruded > random. Lower thermal anisotropy in the entire polycrystal structure leads to reduced internal stress. For a single crystal within aggregates, the {00.2} plane experiences tensile lattice strain, while the {10.0} and {11.0} planes undergo compressive lattice strain due to the greater contraction of single crystals along the <c> direction compared to the <a> direction during cooling.

Internal Elastic Strains of AZ31B Plate during Unloading at Twinning-Active Region

Magnesium alloys, being the lightest structural metals, have garnered significant attention in various fields. The characterization of inelastic behavior has been extensively investigated by researchers due to its impact on structural component performance. However, the occurrence of twinning in the absence of any applied driving force during unloading has lacked reasonable explanations. Moreover, the influence of deformation mechanisms other than twinning on inelastic behavior remains unclear. In this study, uniaxial tension and compression tests were conducted on hot-rolled magnesium alloy plates, and neutron diffraction experiments were employed to characterize the evolution of macroscopic mechanical response and microscopic mechanisms. Additionally, a twinning and detwinning (TDT) model based on the elastic visco-plastic self-consistent (EVPSC) model has been proposed, incorporating back stress to describe the deformation behavior during stress relaxation. This approach provides a comprehensive understanding of the inelastic behavior of magnesium alloys from multiple perspectives and captures the influence of microscale mechanisms. A thorough understanding of the inelastic behavior of magnesium alloys and a reasonable explanation for the occurrence of twinning under zero-stress conditions offer valuable insights for the precise design of magnesium alloy structures.

The role of Ca on the microstructure and tensile properties of Mg-Al-Zn-Ca alloys

Synergy between Ca and other alloying elements such as Al and Zn can modify the microstructure and mechanical properties of Mg alloys. In this work, we compared four extrusion alloys: Mg-6Al-2 Zn, Mg-6Al-2Zn-0.5Ca, Mg-6Al-2Zn-1.0Ca, and Mg-6Al-2Zn-2.0Ca (all in wt.%). Tensile properties were remarkably not improved with Ca addition. The underlying reasons were explored using in situ synchrotron X-ray diffraction, electron microscopy, and cyclic loading tests. It is found that solute Ca imposes a softening effect on Mg's slip systems. The slight increase of the yield strength by the formation of Al2Ca particles is fully offset by the reduced Al solute strengthening. Texture weakening and resultant ductility enhancement reported in Mg-Zn-Ca ternary alloys is largely compromised by the high amount of Al. Nevertheless, Al2Ca particles can enhance the materials’ strain hardening by inducing back stress. An elastic-viscoplastic self-consistent (EVPSC) model was employed to simulate the deformation of the four alloys. Discrepancies between the simulation results and the experimental measurements mostly occur in the microscopic level (e.g. lattice strains and dislocation density evolution), and the reasons will be discussed.

On the effect of detwinning during compressive deformation of martensitic NiTi: in situ neutron diffraction and micromechanical modeling

A combined experimental and computational effort was undertaken to provide insight into the microscopic deformation behavior of B19′ martensitic NiTi during compressive loading–unloading. In situ neutron diffraction experiment was performed under quasi-static compression on a modified Eulerian cradle, where orientations rotated 50° away from the loading axis were selected to capture the hkl reflections all the way during compression. A domino detwinning scheme was deducted and implemented in an elastic–viscoplastic self-consistent (EVPSC) model in order to interpret the experimental data and elucidate the deformation mechanisms. Predictions of the model adequately fit the in situ load–unload stress–strain curve and lattice strains. Validity of the model was also confirmed by validation against deformed texture and evolution of individual microstrains from published work. Effects of domino detwinning on the intergranular stresses were analyzed. Possible deformation systems during compressive load and unload processes, including detwinning, slip and deformation twinning, were thoroughly discussed by comparisons between simulations and experiments.

Modeling the micromechanical behaviors of Zircaloy-2 alloy under large deformation

The orientation distribution of grains (so-called texture) and its evolution almost decisively govern the in-service performance of a polycrystalline material, especially for materials with low crystallographic symmetry. As an important nuclear material, zirconium and its alloys have a hexagonal-close-packed (hcp) crystallographic structure and multiple plastic deformation mechanisms. Among them, deformation twinning, reorienting the basal poles 85.22°, could result in an abrupt and drastic change in the texture. As simulation plays a more and more important role in the design, manufacturing, and service of an end-product, a reliable twinning model is essential for zirconium alloys. Two twinning models, namely the Twinning and De-twinning (TDT) and Predominant Twin Reorientation (PTR) models, were implemented in an Elastic Viscoplastic Self-consistent (EVPSC) framework with the thermal effect accounted for. The EVPSC-TDT and EVPSC-PTR models were applied to study the deformation behavior of a Zircaloy-2 slab under different strain paths. A predictive capability of the two twinning models was assessed by both the macro-mechanical behavior of stress-strain response and Lankford coefficient and the micro-mechanical behavior of texture evolution in terms of both pole figure and texture coefficient. It was found that the TDT model exhibits superior performance to the PTR model, especially in predicting texture development.

On the torsional and coupled torsion-tension/compression behavior of magnesium alloy solid rod: A crystal plasticity evaluation

Extensive attention has been paid to magnesium (Mg) alloys considering their potential as lightweight structural materials. However, it is still challenging to process and manufacture Mg materials that carry high strength and good ductility. This issue mainly arises from a lack of understanding toward the anisotropic mechanical behavior of Mg alloys in response to large deformation in a multiaxial stress state, which is unavoidably in existence under various material processing routes. In this regard, we seek to understand the torsional and coupled torsion-tension/compression behaviors of a magnesium alloy subject to large-strain deformation. The elastic viscoplastic self-consistent (EVPSC) model, which incorporates the twinning-detwinning (TDT) scheme and takes a torsion-specific finite element (TFE) approach, was employed to illuminate the inhomogeneous and multiaxial features of the torsional deformation in the AZ31 Mg alloy subjected to free/fixed-end torsion and coupled torsion-tension/compression. Experimental validation was conducted by characterizing the mechanical responses of the torsional specimens under the loading paths of free-end torsion and coupled torsion-tension. Our model successfully captures the Swift effect along with the shear texture, which is hardly predicted by conventional constitutive models. In addition, our model reveals that twinning is nearly equally active under free-/fixed-end torsion, while twinning under coupled torsion-tension and torsion-compression is promoted and suppressed, respectively. The comparison between the simple shear and pure torsion by simulation demonstrates that the significant bulk stress existing within the torsional rod is ascribed to the strong interaction between the cylindrical elements in the EVPSC model. As a final thought, we believe that the TFE-EVPSC-TDT model not only highlights the inhomogeneous and multiaxial features underlying the torsional and coupled torsion-tension/compression behaviors of the Mg alloy solid rod, but more significantly, can be used as a numerical tool for designing/tuning gradient twinning structures that may lead to optimized properties of Mg alloys.

Grain-size effect on the deformation of Mg–3Al–3Sn alloy: Experiments and elastic-viscoplastic self-consistent modeling

Grain refinement can significantly change the tensile behavior of Mg alloys. The underlying mechanisms are unclear yet. Here we report that grain refinement of a Mg–3Al–3Sn (wt.%, AT33) alloy increases the yield strength (σ0.2) following the Hall-Petch law, while decreases the strain hardening exponent (h). Tensile stress-strain curves and lattice strain evolution of four rolled AT33 samples with different grains sizes (10–97 μm) can be simulated by an elastic-viscoplastic self-consistent (EVPSC) model that takes grain size into account. The key to the model's success is that it allows both the initial critical resolved shear stress (CRSS) and the dislocation nucleation coefficient of different slip modes to be functions of the grain size. The coarse-grained samples have higher dislocation nucleation coefficient due to concurrently formed deformation twins. The model predicts that prismatic slip is the dominant deformation mode in this AT33 alloy; pyramidal <a> and <c+a> slips are more active in coarse-grained samples than in fine-grained samples.

Prediction of Mechanical Behaviors of the Q & P980 Steel Under Different Temperatures and Strain Rates Using Crystal Plasticity Method

The martensitic transformation in quenching and partitioning (Q&P) steels is greatly influenced by loading conditions such as environmental temperature and loading speed, and thus impacts the macroscopic mechanical properties during the deformation process. Within this work, an elastic-visco-plastic self-consistent (EVPSC) framework coupling with phase transformation model is used to simulate the stress strain responses as well as the microstructure evolution of the multi-phases Q& P980 steel under uniaxial tension process. A temperature and strain rate dependent transformation kinetics is incorporated into the model and phase transformation behaviors of the Q& P980 steel under different temperatures (25°C∼100 °C) and strain rates (0.0002s-1∼2s-1) are successfully characterized. The corresponding stress strain responses under different loading conditions are predicted and compared with the experimental data.

Elastic-viscoplastic self-consistent modeling for finite deformation of polycrystalline materials

Anisotropic 1-site and 2-site self-consistent models are developed to describe the elastic-viscoplastic behavior of polycrystalline materials deformed to finite strains on the basis of rate-dependent crystallographic slip and a generalized Hill-Hutchinson self-consistent approach. The choice of rate-dependent constitutive law at single crystal level implemented in the models is discussed through fitting experimental data and calibrating viscous parameters. It is found that drag-stress type Norton law works well for the 1-site elastic-viscoplastic self-consistent (EVPSC) model while threshold stress type Norton law is suitable for the 2-site EVPSC model to assure that the viscoplastic inter-granular interaction is realistic. Both models have been verified by thoroughly fitting experimental data in literatures. For the 1-site EVPSC model, selected experimental data covers both macroscopic and microscopic mechanical responses of steels during deformation with a large range of strain rate from the quasi-static (10−4s−1) to the dynamic (~104s−1). For the 2-site EVPSC model, in situ neutron diffraction data of nickel-based superalloys with various microstructures was fitted. Both models generally fit the experimental data well. A comparison between the EVPSC and elastic-plastic self-consistent (EPSC) models on the prediction of lattice strains has also been made for both the 1-site and 2-site cases, which verifies the predictability on lattice strains of the newly developed EVPSC models. A validation of the homogenization approach for the EVPSC modeling has been performed, which confirms that the proposed EVPSC models are applicable for cubic structure materials with finite deformations. Our formulation of EVPSC modeling developed in this work shines a spotlight on the way of developing a multi-functional self-consistent model to predict both macroscopic and microscopic deformation behaviors of various polycrystalline materials under different loading rates of 10−4s−1~104s−1.

Twinning and detwinning behaviors of commercially pure titanium sheets

The mechanical behaviors of commercially pure titanium (CP–Ti) sheets under uniaxial and reverse loadings along various in-plane directions are investigated by crystal plasticity modeling together with experiments. The elastic viscoplastic self-consistent (EVPSC) crystal plasticity model, that incorporates an enhanced twinning and detwinning (TDT) scheme to consider multiple twinning modes, is employed for the crystal plasticity modeling. The in-plane anisotropic, the tension-compression asymmetric, and the unique work hardening behaviors of the CP-Ti sheets are ascribed to available deformation mechanisms. In addition to various deformation slips (e.g., prismatic, basal and pyramidal c+a slips), deformation twinning and detwinning of extension ({101¯2}) and contraction ({112¯2}) twinning modes are deliberated in particular. The effect of the mechanisms on the evolution of the stress strain relation, hardening rate, texture, relativity activities, and twin volume fractions, etc. is explored. It is found that twinning and detwinning of both extension and contraction twins, as well as deformation slips, affect significantly the behaviors of the CP-Ti sheets. The modeling results agree well with the corresponding experiments. The difference of the mechanical behaviors between the two sheets and the difference among various loading conditions are ascribed to the different combination of the operative deformation mechanisms, especially the contribution from twinning and detwinning of extension and contraction twins.

The origin of discontinuous yielding in Mg alloys under slip-dominated condition studied by in-situ synchrotron diffraction and elastic-viscoplastic self-consistent modeling

A discontinuous yielding was observed in the as-extruded Mg-7Gd-2Y-1Zn-0.6Zr (wt. %) alloy under uniaxial tension along the extrusion direction, which was eliminated by the peak-aging treatment. The deformation mechanisms of the as-extruded and peak-aged alloys were studied by in-situ synchrotron diffraction measurement and elastic-viscoplastic self-consistent (EVPSC) modeling. The in-situ synchrotron diffraction results suggest that the unpinning of basal dislocations from solute atmospheres causes the stress relaxation in the basal slip favored grains. The EVPSC modeling results indicate that the discontinuous yielding in the as-extruded alloy is associated with the interaction between basal dislocations and solute atmospheres. After peak-aging treatment, the interaction between basal dislocations and solute atmospheres is weakened due to the consumption of a number of solute atoms. Consequently, the discontinuous yielding is eliminated in the peak-aged alloy.

Strain-Path Dependence of $$ \{ 10\bar{1}2\} $$ Twinning in a Rolled Mg–3Al–1Zn Alloy: Influence of Twinning Model

In magnesium and its alloys, $$ \{ 10\bar{1}2\} $$ tension twinning is an important deformation mode and is highly dependent on the strain path. Although the $$ \{ 10\bar{1}2\} $$ -twinning behavior has been extensively modeled, the effects of twinning models on the predicted results has seldom been compared. In this study, two typical twinning models, predominant twin reorientation (PTR) and twinning-detwinning (TDT), were chosen to simulate the $$ \{ 10\bar{1}2\} $$ twinning-predominant deformations of a Mg alloy AZ31 rolled plate, in compression along the transverse direction (TD-c) and in tension along the normal direction (ND-t), and the results were compared with experimental data. In addition to the strain-stress curves in the ND-t and TD-c, six other flow curves were used to determine the material-parameter inputs for the simulations with the elastic visco-plastic self-consistent (EVPSC) model. Compared with the PTR model, the TDT model permits better curve fitting and texture prediction. The PTR model cannot fit the TD-c and ND-t flow stresses simultaneously, whereas the TDT model can. The best-fit parameters for the two models are identical at low strains but diverge somewhat at high strains. The simulated twin volume fractions are similar in the two models, but the predicted textures are significantly different. The PTR model can only reproduce the texture at strains over 5 pct in the TD-c and cannot reproduce the deformed texture in the ND-t. In contrast, the TDT model can reproduce all the experimental textures. To fit both the compression and tension curves well, strong latent hardening of the critical resolved shear stress (CRSS) for $$ \{ 10\bar{1}2\} $$ twinning by other twinning systems (htt) is necessary. The htt favors the twin variant with the highest Schmid factor in compression. The htt increases the CRSS for all $$ \{ 10\bar{1}2\} $$ twinning systems in tension, but the CRSS for the dominant twinning system remains relatively low in compression.

Crystal Plasticity Modelling of Large Strain Behaviour of HCP Materials

In this paper, we first introduce various polycrystal plasticity models including the Visco-Plastic Self-Consistent (VPSC) model, the Elastic-Plastic Self-Consistent (EPSC) model, and the Elastic Visco-Plastic Self-Consistent (EVPSC) model, as well as twinning models including the Predominant Twin Reorientation (PTR) model and the Twinning and De-Twinning (TDT) model, with emphasizing on characteristic differences between these models. Then, we demonstrate that the EVPSC-TDT model is able to capture key features of large strain behaviour of HCP materials under various deformation processes including uniaxial tension and compression, simple shear, and torsion.

Study of slip activity in a Mg-Y alloy by in situ high energy X-ray diffraction microscopy and elastic viscoplastic self-consistent modeling

Slip activity from various slip modes largely determines the yield strength and ductility of Mg alloys. Solid solution elements in Mg can change the slip activity dramatically. In this paper, far-field high energy X-ray diffraction microscopy (FF-HEDM) is employed to study slip activity in a Mg-3wt%Y alloy during an in situ tensile experiment. The specimen was incrementally loaded up to 3% engineering strain along the rolling direction. At each load step, FF-HEDM data were collected to track the crystallographic orientation, center of mass, and stress tensor changes of nearly 1000 grains in the probed volume. By analyzing the change in orientation and stress tensor of individual grains at different load steps, it is possible to identify the activated slip systems and measure their critical resolved shear stress (CRSS) values. Prismatic slip and pyramidal I <a> slip are found to be very active in this alloy. The estimated CRSS values for basal slip, prismatic slip and pyramidal I <a> slip are 12 MPa, 38 MPa, and 36 MPa, respectively. These CRSS values were applied in a dislocation-based elastic viscoplastic self-consistent (EVPSC) model that successfully simulated the tensile stress-strain curve from the FF-HEDM experiment. The model also qualitatively predicted the crystal rotation in most of the selected grains, though it underestimated the internal stress and the magnitude of crystal rotation in these grains. Influence of solute Y on the strength and ductility of Mg alloys is discussed.

Twin-induced hardening in extruded Mg alloy AM30

The mechanical anisotropy of extruded Mg alloy AM30 was recently investigated, both experimentally and numerically (Oppedal et al., 2013 [1]). The authors highlighted the need to include cases of intermediate levels of twinning as a critical validation, in addition to the limiting cases where the contribution of twinning is dominant or negligible. However, further scrutiny of the results revealed that the experimental data employed in that study were still inadequate to constrain all necessary parameters in the crystal plasticity models. In particular, the parameters describing the prismatic slip mechanism were under-constrained. In the present study, additional experimental data were obtained to provide the necessary constraint. Based upon these experimental results, clearer conclusions can be drawn about the requirements of a crystal plasticity model, which must accurately account for strong tension-compression asymmetry as well as anisotropy in both strength and strain hardening behavior. In addition to the previously employed Viscoplastic Self-Consistent (VPSC) model, with the Predominant Twin Reorientation (PTR) scheme, the Elastic Visco-Plastic Self-Consistent (EVPSC) model, with the recently developed Twinning and De-Twinning (TDT) description, is applied to simulate the uniaxial response along arbitrary directions. It is demonstrated that accounting for the initial texture and calibrating the EVPSC-TDT model using uniaxial tension and compression along the extrusion direction permits prediction of the strength anisotropy and strain hardening behavior along arbitrary straining directions.

A micromechanical model for nano-metallic-multilayers with helium irradiation

Nano-metallic-multilayers (NMMs) have attractive irradiation-tolerant properties due to the high ratio of interfaces acting as effective sinks for irradiation-induced defects, like helium bubbles. The mechanical behaviour of NMMs can be affected by both interfaces and He bubbles, which is closely related to the layer thickness. In this work, the macroscopic mechanical behaviours of Cu/Nb multilayers with irradiation-induced He bubbles are explored by the crystal plasticity model (CPM) coupled with the elastic-viscoplastic self-consistent (EVPSC) method. At the microscale, hardening effects of He bubbles, interfaces and forest dislocations are evaluated by considering their influences on the critical shear resistance of dislocation movement. At the grain level, the equivalent mechanical properties of a composite grain consisting of different individual grains and interfaces are obtained by the Mori–Tanaka method. At the macroscale, the self-consistent scheme is adopted to predict the macroscopic mechanical behavior of NMMs which are made of composite grains. Numerical results of the proposed model match well with corresponding experimental data.

A crystal plasticity model based on transition state theory

A crystal plasticity model is developed whereby explicit connections with transition state theory and with the statistics of dislocation arrangements are simultaneously enforced. Leveraging theoretical work on diffraction line profile analysis, the model predicts the distribution of internal stress (or lattice strain) resulting from that of dislocations arrangements. In turn the internal stress distribution is used to predict the activation rate of dislocation unpinning while providing an explicit connection with experimental diffraction line broadening profiles. The newly developed model is implemented into an elastic viscoplastic self-consistent (EVPSC) framework and applied to the case of stainless steel. To clearly demonstrate the additional predictive capabilities of the model, the latter is used to predict the rate sensitivity, stress and strain relaxation, Bauschinger effect, temperature effects, and evolution of the mean and the standard deviation of the lattice strains. It is found that a single set of parameters provides good agreement between the predictions and the corresponding experiments.

On twinning and anisotropy in rolled Mg alloy AZ31 under uniaxial tension

The Elastic Visco-Plastic Self-Consistent (EVPSC) model, with the recently developed Twinning and De-Twinning (TDT) description, is applied to study the mechanical behaviour of hot-rolled Mg alloy AZ31 under uniaxial tension. Numerical results are compared to the experimental uniaxial tensile tests reported earlier by Chapuis et al. [29] for the out-of-plane directions of a thick plate along angles of α = 0°, 30°, 45°, 60° and 90° between the normal direction and longitudinal specimen axis. It is shown that accounting for the initial texture and calibrating the EVPSC-TDT model by using uniaxial tension tests along the rolling direction and normal direction permits prediction of the strength anisotropy and strain hardening behavior along all five tensile directions, i.e. for cases in which the contribution of twinning is dominating, negligible or intermediate.