Viscoplastic Self-consistent Simulations Research Articles

A Residual Stress-Based Model for Viscoplastic Self-Consistent Simulation of Cold-Sprayed Al6061

A Residual Stress-Based Model for Viscoplastic Self-Consistent Simulation of Cold-Sprayed Al6061

Unique deformation mechanisms of extruded Mg–Y-Sm-Zn-Zr alloy

In present work, the effect of C texture, with the c axis of grains aligned parallel to extrusion direction (ED), on the deformation modes during tension in extruded Mg–Y-Sm-Zn-Zr alloy was investigated. The results indicated that both the extension twins and pyramidal <c+a> dislocations were activated, whereas basal <a> and prismatic <a> dislocations remained dormant during the early stages of tension. With the increase in tensile strain, the number fraction of extension twins increased continuously and rotated their orientation towards the direction perpendicular to ED. Meanwhile, the prismatic slip was activated in the newly orientated grains exhibiting a deviation angle >60°with respect to ED based on the intragranular misorientation axis (IGMA) analysis. Additionally, Viscoplastic self-consistent (VPSC) simulation confirmed that the activation of pyramidal <c+a>, prismatic <a>, extension twin, coupling with the suppression of basal <a> slip attributed to the highest critical resolved shear stress (CRSS) of basal <a> dislocation. Further analysis by TEM revealed that the precipitation of LPSO and γ′ on the basal plane of Mg, along with the increased volume fraction of extension twin actively obstructed the movement of <a> dislocations, consequently elevating the critical resolved shear stress (CRSS) in basal <a> slip.

A dislocation density-based crystal plasticity constitutive model: comparison of VPSC effective medium predictions with ρ-CP finite element predictions

This work presents a dislocation density-based crystal plasticity constitutive model for glide kinetics, strengthening and dislocation density evolution, implemented in the effective medium-based visco-plastic self consistent (VPSC) framework and the spatially resolved, ρ-CP crystal plasticity finite element framework. Additionally, a distribution of intragranular stresses is introduced in the VPSC framework, instead of the conventionally used mean value of grain stress for effective medium calculations. The ρ-CP model is first calibrated to predict the mechanical response of a bcc ferritic steel with an initial rolled texture. The same set of constitutive model parameters are then used in VPSC to predict the aggregate stress–strain response and total dislocation densities. For these VPSC simulations, the interaction parameter governing the interaction between the grain and the effective medium in the Eshelby inclusion formalism, and a scalar parameter representative of the distribution of intragranular stresses within a grain, are used to calibrate the VPSC predictions in order to match the predictions of the ρ-CP model. A parametric study is performed to understand the effect of these two parameters on the VPSC predictions. Further, simulations are also performed for a random untextured polycrystal to identify the corresponding VPSC simulation parameters for predicting a similar response as the ρ-CP model. The novelty of the work is in the same set of constitutive models and associated parameters have been implemented in VPSC and ρ-CP to predict similar aggregate stress–strain response and total dislocation densities. This finite element-calibrated effective medium crystal plasticity approach reduces the computational time by at least two orders of magnitude and represents an advance towards the development of multiscale crystal plasticity modeling tools.

A viscoplastic self-consistent analysis of tensile anisotropy and tension-compression asymmetry in rare-earth magnesium alloy

The anisotropy and tension-compression asymmetry of rare-earth magnesium (Mg-RE) alloys have attracted significant attention. In this study, the room-temperature tensile anisotropy and tension-compression asymmetry of the extruded Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy were investigated utilizing techniques such as optical microscopy (OM), electron backscatter diffraction (EBSD), and viscoplastic self-consistent (VPSC) modeling. Among the tensile samples, the T0 sample (with axis parallel to extrusion direction) exhibits the greatest tensile yield strength (TYS) of 270 MPa and ultimate tensile strength (UTS) of 336 MPa, the T45 sample (with axis inclined at a 45° angle to extrusion direction) and T90 sample (with axis perpendicular to extrusion direction) exhibit lower TYS and UTS. The C0 sample shows a slightly greater compressive yield strength (CYS) of 290 MPa. The ratio of TYS/CYS is approximately 1.07. This study significantly adjusts the VPSC hardening parameters through the Schmid factor of deformation mechanisms in Mg-RE alloy, particularly increasing the τ0 (critical resolved shear stress, CRSS) and τ1 values for basal <a> slip and {10-12} twinning. The ratios of CRSS for other deformation mechanisms to basal <a> slip are approximately as follows: CRSSTwin/CRSSBas = 2, CRSSPri/CRSSBas ≈ 2.7 and CRSSPyr/CRSSBas ≈ 3.3, while these ratios in traditional alloys are generally higher. The stress-strain curves and pole figures obtained from the modified VPSC model demonstrate excellent agreement with experimental results. According to the VPSC simulation results, the primary factor contributing to tensile anisotropy is the disparity in the activation levels of slip systems. The inclusion of rare-earth elements mitigates the tension-compression asymmetry by reducing the difference of CRSS between different deformation mechanisms.

High temperature uniaxial deformation characteristics in Al-Li alloy: Insights into the perspective of microstructure, microtexture and slip system activity

The present study investigates the uniaxial deformation response of Al-Li alloy at elevated temperatures (673 K and 773 K) and nominal strain rate of 0.0001 /s. The alloy exhibits significant softening following deformation at 673 K. On the contrary, a steady state followed by marginal softening is observed in the flow curve and the alloy experiences elongation close to superplastic regime during deformation at 773 K. The microstructure evolution in both the deformed specimens reveals the prevalence of dynamic recrystallization (DRX) via continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX) mechanisms which resulted in flow softening. The evolution of Copper {112}〈111〉 as well as S texture {123}〈634〉 components and weakening of Cube texture {001}〈100〉 are observed in both the deformed specimens. Visco-plastic self-consistent (VPSC) simulation reveals that the activation of non-octahedral (NOC) slip systems ({100}〈110〉 and {110}〈110〉) in conjunction with octahedral (OC) slip system ({111}〈110〉) predicts the microtexture evolution accurately for both the deformation conditions. The higher activation of NOC slip systems and the simultaneous occurrence of dislocation slip as well as grain boundary sliding accommodated by dislocation slip could be ascribed to the significant improvement in elongation close to superplastic regime at 773 K.

Excellent strength-ductility synergy in a novel medium manganese steel containing 2.4Al-2.9Mn-4.1Ni realized through limited thermo-mechanical processing steps

In this study, the effect of microstructural and micro-textural evolution on tensile properties in hot forged (HF) and hot rolled (HR) medium-Mn steel containing ∼4 wt% Ni is systematically investigated. The microstructures of HF and HR specimens comprise of martensite (α′), nanosized NiAl (B2) precipitates and retained austenite (RA). The excellent tensile properties in HF and HR specimens have been achieved through minimal thermomechanical processing routes. The HR specimen exhibits better strength (∼1868 ± 69 MPa), and ductility (∼16.5 ± 1%) as compared to the HF specimen (∼1765 ± 32 MPa, and ∼12 ± 2%). The prior austenite grain (PAG) size of HR specimen is lower than HF, leading to lower width of lath martensite which contributes to achieving higher strength in the former specimen. Apart from the lath width, the presence of twin martensite along with RA, higher fraction of high angle grain boundaries (HAGBs), and ∑3 boundaries improve the strength-ductility synergy in HR specimen as compared to HF condition. The development of higher intensity γ-fiber <111>//ND during hot rolling has resulted in better ductility in HR specimen, whereas the presence of high intensity Cube texture {001}<100> has deteriorated the tensile properties of HF specimen. Further, visco-plastic self-consistent (VPSC) simulation has been carried out to understand the influence of primary {110}<111> and secondary {112}<111> slip systems activation on strain hardening response of the specimens. It has been observed that the higher activation of primary slip system {110}<111> in HR specimen leads to better strain hardening response at stage IV as compared to HF specimen.

Effects of temperature on critical resolved shear stresses of slip and twining in Mg single crystal via experimental and crystal plasticity modeling

Magnesium (Mg) single crystal specimens with three different orientations were prepared and tested from room temperature to 733 K in order to systematically evaluate effects of temperature on the critical resolved shear stress (CRSS) of slips and twinning in Mg single crystals. The duplex non-basal <a> slip took place in the temperature range from 613 to 733 K when the single crystal samples were stretched along the <01¯10> direction. In contrast, the single basal <a> slip and prismatic <a> slip were mainly activated in the temperature range from RT to 733 K when the tensile directions were inclined at an angle of 45° with the basal and the prismatic plane, respectively. Viscoplastic self-consistent (VPSC) crystal modeling simulations with genetic algorithm code (GA-code) were carried out to obtain the best fitted CRSSs of major deformation modes, such as basal <a> slip, prismatic <a> slip, pyramidal II <c+a>, {101¯2} tensile twinning and {101¯1} compressive twinning when duplex slips accommodated deformation. Additionally, CRSSs of the basal <a> and the prismatic <a> slip were derived using the Schmid factor (SF) criterion when the single slip mainly accommodated deformation. From the CRSSs of major deformation modes obtained by the VPSC simulations and the SF calculations, the CRSSs for basal <a> slip and {101¯2} tensile twinning were found to show a weak temperature dependence, whereas those for prismatic <a>, <c+a> slip and {101¯1} compressive twinning exhibited a strong temperature dependence. From the comparison of previous results, VPSC-GA modeling was proved to be an effective method to obtain the CRSSs of various deformation modes of Mg and its alloys.

Analysis of the dislocation activity of Mg-Zn-Y alloy using synchrotron radiation under tensile loading.

An understanding of deformation behavior and texture development is crucial for the formability improvement of Mg alloys. X-ray line profile analysis using the convolutional multiple whole profile (CMWP) fitting method allows the experimental determination of dislocation densities separately for different Burgers vectors up to a high deformation degree. A wider use of this technique still requires exploration and testing of various materials. In this regard, the reliability of the CMWP fitting method for Mg-Zn-Y alloys, in terms of the dislocation activity during tensile deformation, was verified in the present study by the combined analysis of electron backscatter diffraction (EBSD) investigation and visco-plastic self-consistent (VPSC) simulation. The predominant activity of non-basal 〈a〉 dislocation slip was revealed by CMWP analysis, and Schmid factor analysis from the EBSD results supported the higher potential of non-basal dislocation slip in comparison with basal 〈a〉 dislocation slip. Moreover, the relative slip activities obtained by the VPSC simulation also show a similar trend to those obtained from the CMWP evaluation.

Deformation-induced martensite transformation and variant selection in AISI 316L austenitic stainless steel during uniaxial tensile deformation

Present work has investigated the orientation dependence of deformation-induced martensite (DIM) transformation and contemporaneous variant selection in AISI 316L austenitic stainless steel during uniaxial tensile loading. The combined effect of slip and deformation-induced martensite transformation have been analysed comprehensively using experimental macrotexture analysis, visco-plastic self-consistent (VPSC) simulation and reconstruction of prior-austenite orientations from electron backscatter diffraction (EBSD) data. It has been shown that when the polycrystalline austenitic material is deformed, grains with orientations like Brass, Rot-Goss, Rot-Cu undergo plastic deformation by slip and rotate towards {110}<111> orientation. Grains of this orientation eventually undergo DIM transformation at sufficiently higher engineering strain (≥69%) levels. Variant selection during DIM transformation from {110}<111> component of austenite has been critically examined using a model developed based on the phenomenological theory of martensite crystallography (PTMC). It has been observed that in general, variants with higher interaction energies are preferred over the others. The results in turn indicate that Patel-Cohen theory, which is believed to be valid for stress-induced martensite (i.e. during elastic deformation), holds equally good for strain-induced martensite (i.e. during plastic deformation) as well.

A finite element coupled visco-plastic self-consistent simulation to predict micro-texture and anisotropy evolution during single point incremental forming in Al-Li alloy

A finite element coupled visco-plastic self-consistent simulation to predict micro-texture and anisotropy evolution during single point incremental forming in Al-Li alloy

Reconstructing orientation data from the images of IPF maps and ODF sections extracted from the literature: A data-collection method for machine learning

Crystallographic orientation data are used as a precursor to various microstructural and textural analyses as well as to perform simulations such as crystal plasticity. In the current study, a novel method is developed to reconstruct orientation data from the images of inverse pole figure (IPF) maps and sections of orientation distribution functions (ODFs) extracted from published articles. Crystallographic orientation can be expressed by Miller indices {hkl}〈uvw〉 where the {hkl} plane normal is parallel to the normal direction (ND) and the 〈uvw〉 direction is parallel to the rolling direction (RD) of the specimen. The {hkl} values of the orientations were obtained by the image processing of ND-IPF maps while the corresponding 〈uvw〉values were obtained by optimization of the ODF sections via the use of a genetic algorithm (GA). The MTEX software was used to generate ODF sections with optimized data, and these were then compared with real ODF sections to evaluate the error function of the GA. The quality of the reconstruction of orientation data was evaluated by performing the proposed method on images from the ND-IPF map and ODF sections produced through previously available experimental data. The results of both reconstructed and actual data were compared in terms of grain-size distribution, misorientation-angle distribution, texture component fractions, and the overall {hkl} and 〈uvw〉 axis distributions. Furthermore, a visco-plastic self-consistent (VPSC) simulation equipped with a Marciniak-Kuczyński (M-K) model along with visco-plastic fast Fourier transform (VPFFT) simulation was applied to reconstructed orientation data in order to obtain the plastic strain ratio (r-value), the forming limit curves (FLCs), and the strain localization distribution, respectively.

Investigations on the interface-dominated deformation mechanisms of two-dimensional MAX-phase Ti3Al(Cu)C2 nanoflakes reinforced copper matrix composites

Two-dimensional (2D) materials showing the giant advantage over their bulk counterparts are believed to be the ideal reinforcement for metal matrix composites, whereas the deformation mechanism of which is currently unknown. Herein, we investigated the interface effect of 2D MAX phase Ti3Al(Cu)C2 nanoflakes (MAX NFs) obtained by a Cu-atoms-diffusion assisted exfoliation method on the plastic deformation process of Cu matrix. Tensile tests demonstrated a simultaneous enhancement in strength and fracture elongation with the increase of MAX NFs content. The composites exhibited a four-stage deformation process involving an extended “yield plateau” before obvious strain hardening stage. Microstructural examination revealed that the 2D nature of MAX NFs and the coherent interface structure facilitated the nucleation of partial dislocations, which coordinated the initial plastic deformation by gliding and interacting to form Lommer-Cottrel (LC) locks. At high strain levels, both LC locks and MAX NFs served as obstacles for dislocation cross-slip and thus achieved significant forest hardening (or latent hardening) effect, validated by EBSD texture from the in-situ tensile tests and visco-plastic self-consistent simulation. This sort of interface-induced microstructure evolution promoted tortuous micro-cracks along discontinuous slip bands and significant crack bridging and deflection extrinsic toughening mechanisms. The current findings provide a possible strategy of simultaneously enhancing strength and ductility through tailoring 2D geometric shape of reinforcements and their interface with the metal matrix.

Effect of microalloyed Al and Ca on mechanical properties and corrosion resistance of high-speed extruded Mg-2Zn-1Mn (mass%) alloy

Mechanical properties and corrosion resistance of high-speed extruded Mg-2Zn-1Mn (mass%) alloys microalloyed with Al and/or Ca were evaluated. The microalloying of Al improved the tensile yield strength, while the compressive yield strength remained unchanged, which deteriorated the yield anisotropy. The Al addition also deteriorated the corrosion resistance owing to the formation of coarse βMn phases that promoted the galvanic corrosion. By the single addition of Ca, both tensile and compressive yield strengths increased, which led to a slight improvement of the yield anisotropy. A texture weakening, which was attributed to the single Ca addition, also improved the ductility slightly. Such property improvements were achieved without the loss of corrosion resistance. A ViscoPlastic Self-Consistent simulation revealed that the single Ca addition was effective for the hardening of both basal and prismatic slips, which improved the yield strength in both tension and compression. • Microalloyed ZM21 alloys were extrudable at a high speed of 60 m/min. • Single Ca addition was effective in improving tensile and compressive properties. • Al addition increased yield anisotropy in tension and compression. • Al addition promoted micro galvanic corrosion.

Simultaneous improvements in strength and ductility of as-extruded Mg-1.0Sn-0.5Zn alloy via Ce addition in combination with pre-twining deformation

In the present study, the comprehensive effects of Ce addition and pre-twining deformation on the microstructure evolution and mechanical properties of Mg-1.0Sn-0.5Zn alloys were systematically investigated. After Ce addition, two phases (CeMgSn and CeMgZn2) were newly emerged, which eventually hampered grain growth and postponed {10−12} tensile twin extinction during annealing subsequent to pre-compression. Besides, due to prominent grain refinement, the addition of Ce into as-extruded Mg-Sn-Zn alloy gave rise to a noticeable improvement in strength. As for the application of pre-twining deformation, it could induce a significant increase in the tensile ductility via texture tailoring, and the relative Visco-Plastic Self-Consistent (VPSC) simulation confirmed that the main reason was attributed to the vigorous activation of {10−12} tensile twins. As a result, both the strength and ductility of the as-extruded Mg-Sn-Zn alloy were substantially improved via the combination of Ce addition (obvious grain refinement) and pre-twining deformation (effective texture regulation).

Crystallographic texture evolutions of Ti-6Al-4V chip foils in relation to strain path and high strain rate arising from large strain extrusion machining process

Large strain extrusion machining (LSEM) is a promising process to create chip foils with ultrafine grains and a certain type of crystallographic texture. Disclosing the interconnection between the deformation histories and the crystallographic texture variations resulting from the LSEM process is vital for the texture generation and control of Ti-6Al-4V chip foils. Electron-backscattered diffraction and viscoplastic self-consistent (VPSC) simulation were combined based on numerical simulation to study evolutions of crystallographic textures for chip foils during LSEM of Ti-6Al-4V. The deformation histories during LSEM process were also analyzed by coupling theoretical analysis with digital image correlation technique. The role of individual type of slip system on the texture variation of Ti-6Al-4V chip foils was identified by modifying the Voce hardening parameters in VPSC model. It is seen that strain path controlled by the chip thickness ratio changes the inclination of generated textures in chip foils. Basal and 1-st order pyramidal <c+a> slip systems are the main deformation modes in high strain rate deformation condition of LSEM process. Similar textures are formed under large strain and high strain rate deformation in LSEM comparing with that in free machining process. The conclusions are useful to control the crystallographic texture generation in LSEM of Ti-6Al-4V by optimizing cutting speeds and chip thickness ratios.

Prediction and control of bending quality of double-layered gap tube

Thin-walled double-layered gap tube (DLGT) has a promising potential to be widely used in making aerospace pipeline systems and the complicated structures in many industrial clusters. However, it presents a challenge to achieve precisely forming of the needed tube structure. During the rotary draw bending (RDB) of DLGT, the diversities of materials and geometries to be made lead to the difficulties in accurate prediction and efficient control of the forming quality. For an accurate prediction, the anisotropic characterization of the thin-walled tube was realized by designing a novel ring hoop specimen and the viscoplastic self-consistent model simulation. Three yield criteria were employed, and it is found that Yld2000-2D criterion has the best prediction accuracy. For efficient control, the rigid constraints of forming dies and flexible constraints of filling medium were employed. For rigid constraints, it is proven that the traction force provided by the inner clamp die is decisive in preventing the wrinkling and slip of tube and the fully constrained die structure has the best controllability of forming quality. For flexible constraints, the solid structure of filling medium provides more uniform constraints to tubes and is the most ideal structure. When a special channel structure is required, the outer channel structure plays a more significant role in the deformation of the inner tube, resulting in a better controllability of forming quality than the inner channel structure.

Numerical and experimental analysis of deformation behaviors and microstructure evolution in the thread rolling process

The thread rolling process is an advanced bulk forming process to produce thread parts. The superior performance of the formed thread parts as compared to those manufactured by the cutting process closely relates to the microstructure of the formed thread parts. In this study, a finite element model (FEM) was established to analyze the deformation characteristics in the thread rolling process. The viscoplastic self-consistent (VPSC) simulation was coupled with FEM to investigate the texture evolution and distribution. Besides, the thread rolling experiments were carried out, and the microstructure on different positions of formed thread parts was observed to analyze the characteristics of the microstructure and verify the simulation. Simulation and experimental results showed that the materials were mainly stretched on the bottom and top of formed thread parts, while on the flank they were obviously rotated. On the bottom and the flank of the formed thread parts, the grains were severely refined, and an obvious γ fiber texture was formed. On the top of the formed thread part, {001} <110> texture was observed.

Tailoring the microstructure and texture of a dual-phase Mg–8Li alloy by varying the rolling path

Dual-phase Mg–Li alloys exhibit better formability than conventional Mg alloys. However, conventional processing methods, such as rolling and extrusion, usually result in a lamellar structure, which will generate a strong planar anisotropy. In the present study, an as-extruded dual-phase Mg-8Li plate was rolled along two different directions, extrusion direction (ED-rolling) and transverse direction (TD-rolling), with the aim to investigate the effect of rolling path on the microstructure, texture and in-plane mechanical anisotropy. The results show that the lamellar α+β structures in the initial plate well remained after 20% or 50% ED-rolling and subsequent annealing at 250 °C for 4 h. In contrast, this lamellar structure completely disappears after TD-rolling and subsequent annealing. The basal poles of grains close to the TD in α phase in the initial plate slightly rotate from TD towards the normal direction (ND) during ED-rolling, while are largely parallel to the ND after TD-rolling. The variation of rolling path hardly alters the texture of β phase. For both α and β phases, annealing does not change the type of texture, only reduce the maximum intensity of texture. The mechanisms for texture evolution during rolling were studied using visco-plastic self-consistent (VPSC) simulations. It is shown that the main texture features of rolled plates are determined by the activated deformation modes in each phase, while α/β phase boundaries will retard the texture evolution. After ED-rolling, there is an obvious anisotropy in work hardening behavior and elongation for tension along the TD and RD, while this mechanical anisotropy disappears after TD-rolling. The corresponding mechanism were discussed.

Slip system activity and lattice rotation in polycrystalline copper during uniaxial tension

The heterogeneous evolution of intragranular strain within polycrystalline copper grains is evaluated by in-situ electron back-scattering diffraction during uniaxial tension. Deformation heterogeneity between grains causes a proliferation of slip bands within grains and leads to lattice rotation within grains. The magnitude of intragranular orientation gradient development caused by lattice rotation is dependent on the initial grain orientation as well as grain interactions with its local neighbourhood. Uniaxial tensile deformation is accommodated by the activation of coplanar and non-coplanar slip systems with the highest and second highest Schmid factor values. Non-coplanar slip is predominantly observed in unstable 011 and “Other” (i.e.- those that do not belong to the 111, 001, and 011 fibres) grains. Viscoplastic self-consistent simulations revealed that the interactions with the homologous effective mediums provide additional rotation pathways for unstable 011 and “Other” grains to rotate towards more stable 111 and 001 orientations.

Simulation-aided analysis on mechanical properties of dilute Mg-Zn-Ca alloy sheets

The relationship between Zn content and room temperature (RT) mechanical properties of dilute Mg-xZn-0.1Ca (x = 0.1, 0.2,0.3, 0.5, 1.5, 2.5 in wt%) alloy sheets was investigated. The index Erichsen (IE) value, an indicator of stretch formability, was found to increase significantly from 6.6 mm to 8.4 mm by increasing the Zn content from 0.2 wt% to 0.3 wt%. Visco-Plastic Self-Consistent (VPSC) simulation revealed there was no apparent difference in the relative activity of deformation modes in Mg-0.2Zn-0.1Ca and Mg-0.3Zn-0.1Ca alloys. On the other hand, electron back-scattered diffraction observation showed that a component having basal poles tilted towards the transverse direction (TD) began to appear when 0.3 wt% of Zn was added, and the typical TD-split texture was developed when the Zn content was increased to more than 1.5 wt%. Therefore, the rapid improvement of RT formability observed in this study can be attributed to the formation of TD-split texture. In addition to this, the efficient scheme for parameter fitting required to use VPSC simulation was also proposed in this study.