Anisotropic Plastic Deformation Research Articles

Revealing the grain boundary effect on interfacial adhesion in polycrystal Fe/Ni interfaces by using a multi-scale CZM-CPFEM approach

In layered structure, interface plays a significant role in property improvement, whereas its multiple factors at various length scales restricted further understanding. Previous research found a novel grain boundary (GB)-interface interaction: crack initiation locally occurred at the junctions between pre-existing GBs and interface. This leads to decreased interfacial strength. To clarify the mechanisms of such GB-interface interaction, the present study proposed a multi-scale cohesive zone model-crystal plasticity finite element method (CZM-CPFEM) model to investigate the effect of pre-existing GB on intrinsic bonding strength at atomic scale and interfacial stress distribution at micro scale, respectively. At atomic scale, interfacial fracture criteria were modelled according to Molecular Dynamics (MD)-based traction-separation relationships. The accuracy of CZMs was improved by considering both isothermal holding and tilting configuration effects. At micro scale, a practical interfacial microstructure was used to construct CPFEM models. Tensile simulations showed that the local stress concentration occurred at junctions, attributed to the anisotropic plastic deformation behaviours across the GB. On the other hand, weak bonding adhesion at the junction only affects the local crack initiation strength, showing insignificant impacts on the overall interfacial fracture behaviour.

Enhanced mechanical properties of thermo-mechanically affected zone of friction-stir welded AZ61 magnesium alloy joint

Friction-stir welded (FSW) magnesium alloy joints frequently fracture at thermo-mechanically affected zone (TMAZ), and the joints exhibit unsatisfactory welding efficiency and ductility. The TMAZ is considered as the weakest region of the entire joint. Enhance the mechanical properties of TMAZ can improve the performance of the welded joint. In this work, subsequent aging treatment and pre-strain of 3% along the weld seam were conducted on the FSW AZ61 magnesium alloy joint. The microstructure of the TMAZ is characterized by abundant nanoscale second phase particles and {10–12} twins. The reduced basal texture intensity decreased the anisotropy of plastic deformation. The welded joint showed a good synergic of welding efficiency (96%) and ductility (20%). The enhanced strength is attributed to the blocking effect of nanoscale particles and grain/twin boundaries to dislocation movement. The increasing of twin boundaries is the main reason for the improvement of work hardening ability and ductility during tensile deformation. This work demonstrated that introducing {10–12} twins and nanoscale particles into TMAZ is an effective way to improve the balance of strength and ductility of the welded joint due to the synergistic effect of multiple strengthening and toughening mechanisms.

Anisotropic behavior of as-extruded 7003 aluminum alloy under quasi-static compression and high-speed impact

The anisotropic behavior of as-extruded 7003 aluminum alloy under quasi-static compression and high-speed impact was studied using samples with axes parallel to extrusion direction (ED) (0° sample), at an angle of 45° to ED (45° sample), and perpendicular to ED (90° sample). The experimental results show that the yield stress of the 0° sample is the highest, while the 45° sample is the lowest. Compared with other samples, the 90° sample is more sensitive to the applied strain rate, which experiences a rapid failure after reaching peak stress under high-speed impact. Under quasi-static compression and high-speed impact, the 0° sample exhibits nearly uniform deformation, while the 45° and 90° samples exhibit anisotropy behavior. Due to the occurrence of adiabatic shear, the plastic deformation anisotropy in 45° and 90° samples under high-speed impact is more significant compared to quasi-static compression. For the 45° and 90° samples, the r values, which characterize plastic deformation anisotropy, decrease from 0.77 to 0.82 under quasi-static compression to 0.46 and 0.40 under high-speed impact. In addition, adiabatic shear bands are observed in all deformed samples under high-speed impact, while only the 90° sample fractures. Due to the significant difference in Schmidt factors along ED and transverse direction (TD), plastic deformation of the 90° sample under high-speed impact is mainly concentrated in TD, while the deformation in ED is very small. The extremely uneven deformation leads to earlier nucleation and faster development of ASBs in TD, causing the 90° sample to fracture under high-speed impact.

Microstructure evolution accounting for crystal plasticity in the context of the multiphase-field method

AbstractThe role of grain boundaries (GBs) and especially the migration of GBs is of utmost importance in regard of the overall mechanical behavior of polycrystals. By implementing a crystal plasticity (CP) theory in a multiphase-field method, where GBs are considered as diffuse interfaces of finite thickness, numerically costly tracking of migrating GBs, present during phase transformation processes, can be avoided. In this work, the implementation of the constitutive material behavior within the diffuse interface region, considers phase-specific plastic fields and the jump condition approach accounting for CP. Moreover, a coupling is considered in which the phase-field evolution and the balance of linear momentum are solved in each time step. The application of the model is extended to evolving phases and moving interfaces and approaches to strain inheritance are proposed. The impact of driving forces on the phase-field evolution arising from plastic deformation is discussed. To this end, the shape evolution of an inclusion is investigated. The resulting equilibrium shapes depend on the anisotropic plastic deformation and are illustrated and examined. Subsequently, evolving phases are studied in the context of static recrystallization (SRX). The GB migration involved in the growth of nuclei, which are placed in a previously deformed grain structure, is investigated. For this purpose, three approaches to strain inheritance are compared and, subsequently, different grain structures and distributions of nuclei are considered. It is shown, how the revisited method contributes to a simulation of SRX.

Fracture Prediction of Aluminum Alloy Sheet AA2024-T3 Using Analytical Stress and Experimental Strain Based Failure Criteria

In this work, the fracture prediction of aluminium alloy sheet, grade AA2024-T3 was investigated using the Fracture Forming Limit Curve (FFLC) and Analytical Fracture Forming Limit Stress Curve (FFLSC) as failure criteria. Initially, the FFLC was experimentally achieved by means of the Nakajima Stretch forming test coupled with GOM strain measurement system, providing the Digital Image Correlation (DIC) technique. Subsequently, the analytical FFLSC was plastically computed using experimental FFLC data combination with Swift hardening model and anisotropic Hill’48 yield model for representing anisotropic plastic deformation behaviour on examined sheet. Finally, Fukui stretch drawing and Three point bending tests were conducted both experiment and numerical simulation to evaluate the fracture state and verifying an applicability of obtained FFLC and FFLSC. In the simulation, the ABAQUS 2017 element deletion function was employed for directly implementing the fracture criteria regarding the FFLC and FFLSC. It was concluded that the analytical FFLSC could more realistically predict fracture behaviour better than the FFLC based on strain. In term of percentage error, the analytical FFLSC generated an error less than the FFLC.

Deformational response of a marine silty-clay with varying organic content in the triaxial compression space

This study characterises the effects of naturally varying organic content on the compression and shear behaviour of a marine silty-clay from the Netherlands. Index properties and mechanical properties are determined through laboratory tests, including oedometer and multistage loading-unloading triaxial stress paths. The results indicate a significant impact of the organic content on the compression response, with both the loading and reloading indexes increasing as the loss on ignition increases from 3% to 7%. Additionally, the study suggests a directional response of the compression behaviour, with the loading index increasing with the stress ratio. The influence of the organic content on shear strength appears to be less significant. No brittle response is observed during shearing, and a similar ultimate stress ratio is attained by all samples. However, a unique critical state line can only be identified for samples with similar organic content, as its intercept and slope are found to increase with increasing organic content. The experimental results from stress paths at constant stress ratio reveal an anisotropic pre-failure plastic deformation mode, which depends on the previous stress history and loading direction. This suggests that the stress–dilatancy relationship cannot be formulated as a unique function of the stress ratio. The high-quality experimental data presented in the study enlarge the database on soft organic soils in view of the development of advanced constitutive models.

Constitutive modeling of clay shales in undrained conditions and its experimental verification for Opalinus Clay

Clay shales are low-permeable sedimentary rocks that exhibit inherent cross-anisotropic stiffness, strength, and permeability. Accurate design of tunnels excavated in clay shales requires appropriate constitutive models that account for the anisotropic properties of the host rock, especially under undrained conditions. This paper presents a transversely isotropic elastoplastic-damage model for fully-saturated clay shales in undrained conditions. The model describes four deformation regimes observed during consolidated undrained experiments, i.e. (1) transversely isotropic elastic deformation, (2) anisotropic plastic deformation with cross-anisotropic peak strength, (3) semi-brittle post-peak softening due to both strength and stiffness degradation, and (4) residual strength state. The performance of the model was evaluated using available laboratory tests for Opalinus Clay, the selected host rock for underground disposal of radioactive waste in Switzerland. A large experimental data set, consisting of 18 undrained triaxial compression tests, was used to back-calculate the required model parameters. The adopted experimental data include the effective stress path and the stress–strain curves of specimens with bedding orientations between 0° and 90° with respect to the loading and effective consolidation stresses between 0.76 and 16 MPa. It is shown that the proposed model adequately captures the key material features of Opalinus Clay observed in the undrained experiments.

A Molecular Dynamics Study on the Dislocation-Precipitate Interaction in a Nickel Based Superalloy during the Tensile Deformation.

In the present paper, the dislocation-precipitate interaction in the Inconel 718 superalloy is studied by means of molecular dynamics simulation. The atomistic model composed of the ellipsoidal Ni3Nb precipitate (γ″ phase) and the Ni matrix is constructed, and tensile tests on the composite Ni3Nb@Ni system along different loading directions are simulated. The dislocation propagation behaviors in the precipitate interior and at the surface of the precipitate are characterized. The results indicate that the dislocation shearing and bypassing simultaneously occur during plastic deformation. The contact position of the dislocation on the surface of the precipitate could affect the penetration depth of the dislocation. The maximum obstacle size, allowing for the dislocation shearing on the slip planes, is found to be close to 20 nm. The investigation of anisotropic plastic deformation behavior shows that the composite system under the loading direction along the major axis of the precipitate experiences stronger shear strain localizations than that with the loading direction along the minor axis of the precipitate. The precipitate size effect is quantified, indicating that the larger the precipitate, the lower the elastic limit of the flow stress of the composite system. The dislocation accumulations in the precipitate are also examined with the dislocation densities given on specific slip systems. These findings provide atomistic insights into the mechanical behavior of nickel-based superalloys with nano-precipitates.

Formability prediction of high‐strength steel sheet using experimental, analytical and theoretical analysis based on strain and stress forming limit curves and its application to automotive forming parts

AbstractIn this work, the high‐strength steel (HSS) sheet dual‐phase 440 (DP440) were conducted to establish the forming limit curve (FLC) and analytical forming limit stress curve (FLSC) obtained from experimental forming limit curve. First, the Nakajima stretch forming examination was carried out to obtain forming limit curve of investigated sheet. Afterwards, the theoretical Marciniak–Kuczinsky (M–K) model was developed and calculated to evaluate localized necking limits both in strain and stress spaces combination with anisotropic yield criteria. Then, the analytical forming limit stress curves were plastically calculated by using experimental forming limit curve data combination with Swift hardening model and anisotropic yield criteria namely, Hill’48 and Yld2000‐2d for representing anisotropic plastic deformation behavior on examined steel sheet. Finally, automotive stamping parts were performed in order to verify an applicability of all developed curves. It was observed that the analytical forming limit stress curves could more precisely predict the formability of automotive parts better than the forming limit curve based on strain. Particularly, the one based on Yld2000‐2d predict better than the one based on Hill’48. Simultaneously, the experimental forming limit curve and analytical forming limit stress curve were also evaluated comparing with the theoretical calculated forming limit curve and forming limit stress curve using the Marciniak–Kuczinsky model. It should be noted again that the experimental forming limit curve and analytical forming limit stress curve are the best one. Therefore, the Yld2000‐2d yield function better represented the anisotropic behavior of the high‐strength steel sheet dual‐phase 440 than Hill′ 48 yield function, and can suitable be used for the analysis prediction and design of bumper automotive parts under forming processes.

Anisotropic deformation mechanisms of rolling-textured Zircaloy-4 alloy by a crystal plasticity model

This study focuses on investigating the anisotropic deformation behavior of rolling-textured Zircaloy-4 alloy under uniaxial tension along the rolling direction (RD) and transverse direction (TD). A dislocation density-based crystal plasticity finite element method is used to study the associated mechanisms. The simulation accurately reproduces the experimental results on stress–strain curves and strain hardening rate. The relationship between relative activities in different slip systems and anisotropic plastic deformation is established. It is revealed that in the tensile deformation, prismatic slip dominates plastic deformation in the RD, while both prismatic slip and basal slip dominate plastic deformation in the TD. The difference in the dominant slip modes leads to a lower yield stress and a higher strain hardening rate in the RD. Furthermore, the stress and strain distributions in the tensile direction are also statistically analyzed. It is found that a certain proportion of hard grains results in more severe stress concentration and lower uniform elongation in the TD specimen compared with the RD specimen. In addition, the strain rate sensitivity of the yield stress is investigated. It is shown that Zircaloy-4 alloy has almost the same yield anisotropy (TD > RD in terms of the yield stress) at different strain rates in the RD and TD.

SrTiO3 surface micro-structuring with swift heavy ions in grazing incidence geometry

In this work, we present first experimental results on the micro-structuration of monocrystalline strontium titanate (100)-SrTiO3. A self-organized structure appears on its surface due to irradiation with 0.71 MeV/u 129Xe23+ and 0.55 MeV/u 136Xe19+ swift heavy ions at room temperature and under grazing incidence. The resulting wave-like structure appears normal to the direction of the ion beam. X-ray diffraction (XRD) and transmission electron microscopy (TEM) analyses were undertaken to probe microstructural properties below the surface, revealing in particular surface amorphization at high fluences. Such amorphous surface layers, further irradiated at high fluences, may lead to an anisotropic plastic deformation (hammering) effect, inducing the observed self-organized structure due to the grazing angle configuration. This surface morphology was characterized by atomic force microscopy (AFM). A dependency of the periodicity as well as the width of the undulations on the irradiation angle was found as they evolve in the same way. As the ripple formation depends on the irradiation parameters, the characteristics of these patterns can be controlled and thus opens the possibilities for custom surface structuration.

Multilayer Laminated Copper Electrodeposits and Their Mechanical Properties

Copper (Cu) foils are used as anode current collectors in secondary batteries and to increase their capacity thin foils 8 μm thick, or less, have been commercialized. The change of mechanical properties according to the thickness of the foils was investigated from the viewpoint of the crystallographic microstructure. The elongation tends to decrease with decreasing thickness of the Cu foils but is limited by an increase in the ratio (D/t) of the grain size (D) to the thickness (t), which can lead to anisotropic plastic deformation. Two electroplating methods are proposed based on the concentration of the additive in the plating solution and by modulating the current density to develop multilayer laminate structures with alternating layers exhibiting different recrystallization behaviors to enhance the mechanical properties of Cu foils. Cycling between two electroplating solutions with different additive concentrations enables the control of the recrystallization behavior, although it likely presents challenges at the production scale. Alternatively, the periodic variation of the current density is used to alter the microstructure and recrystallization behaviors, enabling the formation of locally irregular grain extrusions between the layers. Mechanical measurements reveal a Hall-Petch relationship between the grain size and yield strength in the multilayer laminated foils.

Strain-Rate Effect on Anisotropic Deformation Characterization and Material Modeling of High-Strength Aluminum Alloy Sheet

Aluminum alloy sheets are widely applied as structure components in automotive, aircraft and other industries to realize lightweight. Nowadays, many high strain rate forming techniques have been developed to improve their formability and widen their application. To ensure the reliability of the aluminum alloy structure components under high strain rate conditions, it is imperative to develop a thorough understanding of the alloy’s mechanical properties. In this paper, taking high-strength 6XXX aluminum alloy sheet as an example, the anisotropic deformation characterization and corresponding material models at various strain-rate conditions are investigated systematically. The material hardening curves and anisotropic plastic yielding stresses were achieved based on the quasi-static uniaxial tensile test and the split Hopkinson tensile bar tests. In this study, the Johnson–Cook hardening model and two anisotropic yield functions are applied to well describe the strain-rate-dependent anisotropic plastic deformation behavior. In addition, the fractographic characterization of the fractured samples at various strain-rate conditions are measured and compared. The study systematically investigates the influence of strain rate on the anisotropic deformation behavior of the high-strength aluminum alloy sheets and gives the basic experimental data for their application in engineering fields in the future.

Anisotropic mechanical behavior prediction of aluminum alloy sheet based on an anisotropic GTN model: Modeling, simulation and experimental investigation

The rolled aluminum alloy sheets usually have anisotropic properties that affect its ductile fracture behavior. In order to study the plastic anisotropy and ductile fracture behavior of aluminum alloy 6016 sheet, the Hill48 anisotropic yield criterion is introduced into the Gurson–Tvergaard–Needleman (GTN) model forming an anisotropic GTN model. In this model, two groups of Hill48 anisotropic yield constants, which are respectively calculated by Lankford's coefficient in different directions and the combination of the Lankford's coefficient and yield stress in different directions, are separately used to describe anisotropic mechanical behaviors. The failure void volume fraction is identified through microstructure analysis and the other damage parameters are calibrated through a finite element (FE) inverse calibration method. The abilities of these two groups of Hill48 anisotropic yield constants in predicting anisotropic mechanical behaviors of aluminum alloy 6016 sheet are examined by performing FE simulations of 0°, 45°, and 90° plate tensile tests, deep-drawing tests and Erichsen cupping tests. Results show that the Hill48 anisotropic yield constants calculated by the Lankford's coefficient in different directions have a better ability to predict local anisotropic plastic deformation especially the earing effect in the deep-drawing test, but the Hill48 anisotropic yield constants calculated by the combination of the Lankford's coefficient and yield stress in different directions have a better prediction ability in predicting global anisotropic mechanical behaviors of the aluminum alloy 6016 sheet.

Anisotropic mechanical responses and plastic deformation mechanisms of cadmium telluride under indentations

Anisotropic mechanical responses and plastic deformation mechanisms of cadmium telluride under indentations

Elastic and plastic anisotropy in a refractory high entropy alloy utilizing combinatorial instrumented indentation and electron backscatter diffraction

A comprehensive study was carried out to predict the elastic and plastic anisotropy of the non-equiatomic Mo15Nb35Ta35V5W10 Refractory High Entropy alloy (RHEA) using a high throughput combinatorial approach employing instrumented micro-indentation with electron backscatter diffraction (EBSD). The Levenberg–Marquardt optimization algorithm was utilized to determine elastic stiffness constant (C11= 267, C12= 115 and C44= 52 GPa) for accessing elastic anisotropy. The anisotropy in plastic deformation of<001>,<011> and<111> orientated grains can be attributed to the activation of the different {112}<111> slip system along with cross slip and the conservative movement of jogs on the screw dislocation. The spatial distribution of misorientation on <001>, <011> and <111> orientated grains as well as slip plane trace analysis, indicates that symmetry in misorientation pattern results from the flow of material along <111> slip direction on the indented surface. The results of the present investigation clearly indicate that the anisotropy in the elastoplastic behavior of novel RHEA is distinct from its constituent elements and that simple rule of mixtures is not sufficient to determine elastic modulus and lattice friction stress of RHEAs. Thus, high throughput experimental techniques are necessary to establish the structure-property linkages in novel multicomponent multi-principal RHEA compositions.

An exceptional ductility of AZ31 magnesium alloy sheet achieved by consecutive multi-pass cooperative lowered-temperature rolling

In this study, a novel technique of consecutive multi-pass cooperative lowered-temperature rolling (CMCLR) was proposed for the first time, with the purpose of preparing high performance wrought magnesium alloys. Based on this, a highly ductile magnesium alloy sheet could be effectively produced from ingot. The corresponding microstructure could directly evolve from coarse dendrites to equiaxed grains with an average size of ∼5 μm, which was attributed to the intense dynamic recrystallization (DRX) during isothermal deformation. The equivalent strain gradually decreased from the surface to the interior and edge of the rolled sheet due to the anisotropic plastic deformation. Instead, the temperature of the core of the sheet was slightly higher than that of the surface due to the deformation heat effect. The basal texture in the RD-TD plane generally weakened in the form of the splitting of basal texture toward the RD and the broadening of basal plane away from the pole center due to texture randomization dominated by DRXed grains. The exceptional ductility of more than 28.7% together with acceptable ultimate tensile strength of not less than 267 MPa was ascribed to the progressive work hardening as a result of seamless switching of multiple deformation modes, i.e., basal dislocation-slip-mediated deformation was preferentially operated and then was substituted by twinning-controlled deformation and non-basal dislocation-slip-dominated deformation. The selection of {101‾2} twin variants agreed well with geometrical compatibility factor (m’) criterion instead of Schmid’s law. The activated twin variants nearly engulfed the whole parent grains for the sake of preserving compatible deformation continuity at ambient temperature, giving rise to the formation of TD-split texture. Comparatively, the {101‾2} twinning could randomize the basal texture via reorienting grain orientations which in turn facilitated the reactivation of dislocation slip systems in the case of high temperature deformation.

Predictive investigation on earring profiles of aluminum alloy sheet with a cylindrical-cup drawing test

In this work, two anisotropic yield models, namely, Hill’48 and Yld2004-18p, in combination with the Swift hardening law are proposed to predict anisotropic plastic deformation of sheet metals. Cup earring, widely known to occur in sheet material with great anisotropy, is employed as a model performance checker. As a result, cylindrical-cup drawing tests are carried out in this investigation. Meanwhile, highly-anisotropic aluminium alloys like AA2090-T3 and AA5052-H32 are introduced here to verify the model. The proposed models are implemented through a Fortran-based UMAT subroutine, run in the commercial finite element platform ABAQUS/IMPLICIT, on which all process simulations of cylindrical-cup drawing are executed. Two additional analytical models, one based on the anisotropy coefficients (R-values) and the other on the uniaxial yield stresses, are also included in this research to determine cup earring profiles for comparative study. Eventually, all computational results are experimentally validated. Among all calculation results, the Yld2004 18p-based simulation results agree the most with those from the experiments in terms of cup height and earring profiles especially for AA2090-T3. The other three models, in the meantime, return challenging results. In summary, the Yld2004 18p yield model in cooperation with the Swift hardening law is to a certain extent reliable for plasticity calculation of vastly-anisotropic sheet metal like AA2090-T3 but less dependable for AA5052-H32.

Effect of the Melt Pool Boundary Network on the Anisotropic Mechanical Properties of Selective Laser Melted 304L

Anisotropic mechanical properties are a well-known issue in selective laser melted parts. The microstructure produced by selective laser melting (SLM) is directional, including the solidified melt pool structures and grains. This work investigates the melt pool boundary’s effects on 304L stainless steel’s compressive properties. 304L stainless steel solid cylinders were built using a pulse laser SLM machine in four directions using three hatch angle rotations: 0°, 67°, and 105°. The twelve samples were compression tested, and the results were analyzed. Numerical models were also created with the different hatch angles and directions. The melt pool boundary network (MPBN) in each build was tracked using the model across multiple planes. Results showed that both the hatch angle and build orientation influenced the concentration of melt pool boundaries present in the manufactured samples. A weak negative correlation of compressive strength to the melt pool boundaries’ concentration was also observed, indicating that the melt pool boundary concentration negatively affected the material’s strength. Local anisotropic plastic deformation was also observed in some of the compressed samples. In those samples, it was observed that directions that plastically deformed more also contained higher concentration of the melt pool boundaries.

Effect of twins and plastic-deformation anisotropy of extruded magnesium alloy on fatigue crack growth and crack closure behavior

To study the effect of twins and plastic deformation anisotropy on the fatigue crack growth (FCG) behavior and crack closure behavior of extruded AZ31B magnesium alloys, two types of single-edge notched tensile specimens were prepared, with loading directions parallel (specimen E) and perpendicular (specimen T) to the extrusion direction (ED). FCG experiments using these specimens were performed at stress ratios R = 0.1 and −1, and cyclic speed of 10 Hz.In extruded magnesium alloy materials, the c-axis of the crystal is radially oriented on a plane perpendicular to the ED, indicating the generation of a strong texture.In the FCG experiment at R = −1 for specimen E, elongation in the c-axis direction occurred under compressive load, which generated {101‾2} <101‾1> tensile twins. The tensile twins increased the material deformation and fatigue crack opening distance. As a result, the effective stress intensity factor range ΔKeff increased, leading to the acceleration of the FCG velocity. At R = 0.1, tensile twins were not generated because the load waveform had no compressive load component; there was no change in ΔKeff and no acceleration of FCG.For specimen T at R = 0.1 and −1, tensile twin generation was expected because elongation in the c-axis direction occurred under tensile load. However, tensile twins did not occur, which is attributed to the effect of plastic deformation anisotropy. Therefore, for specimen T, the increase in ΔKeff and FCG acceleration did not occur, and no difference due to the R value was observed.