Anisotropic Plastic Deformation Research Articles

Anisotropic Plastic Deformation Mechanism and Indentation Size Effect During Berkovich Nanoindentation Process of ZnSe Crystals in Micro-nanoscale

Anisotropic Plastic Deformation Mechanism and Indentation Size Effect During Berkovich Nanoindentation Process of ZnSe Crystals in Micro-nanoscale

Tailoring nanotwinned Cu interlayers for localizing anisotropic plastic deformation during low energy input ultrasonic welding of robust Cu-Cu joints

Tailoring nanotwinned Cu interlayers for localizing anisotropic plastic deformation during low energy input ultrasonic welding of robust Cu-Cu joints

A study on anisotropic hardening of 7075 aluminum alloy based on non-associated flow rules

The accurate description of anisotropic plastic deformation is key to accurately predicting the stamping forming of metal sheets. The anisotropic yield criterion, when based on the assumption of isotropic hardening, often leads to significant inaccuracies. To address this issue, this paper observes the anisotropic hardening phenomenon through non-associated flow rules and evaluates the anisotropy of 7075-O aluminum alloy. Through a series of tensile tests, we determined the mechanical properties of 7075-O aluminum alloy in three distinct orientations. To describe the metal hardening behavior, we employed the Swift-Voce hardening criterion. From the hardening curves in three different directions, it was found that AA7075-O exhibits plastic anisotropy. Based on the VUMAT subroutine, finite element simulation of AA7075-O tensile tests was conducted through Abaqus. Compared with the Hill48 model, it was found that the simulated values of the S–Y2009 anisotropic hardening model have a higher degree of agreement with the experimental curves. The S–Y2009 anisotropic hardening model was adopted to predict the earing behavior of AA7075-O during circular cup deep drawing. The root mean square error between the predicted values of the S–Y2009 model and the experimental values was only 0.1795, which is far smaller than that of the Hill48 yield model. Therefore, the SY2009 model has important guiding significance for the stamping forming of metal sheets.

Characterization of the strain rate sensitivity of basal, prismatic and pyramidal slip in Zircaloy-4 using micropillar compression

The slip strength of individual slip systems at different strain rates will control the mechanical response and strongly influence the anisotropy of plastic deformation. In this work, the slip activity and strain rate sensitivity of the <a> basal, <a> prismatic, and <c+a> pyramidal slip systems are explored by testing at variable strain rates (from 10−4 s−1 to 125 s−1) using single crystal micropillar compression tests. These systematic experiments enable the direct fitting of the strain rate sensitivities of the different slips using a simple analytical model and this model reveals that deformation in polycrystals will be accommodated using different slip systems depending on the strain rate of deformation in addition to the stress state (i.e. Schmid's law). It was found that the engineering yield stress increases with strain rate, and this varied by slip systems. Activation of the prismatic slip system results in a high density of parallel, clearly discrete slip planes, while the activation of the <c+a> pyramidal slip leads to the plastic collapse of the pillar, leading to a ‘mushroom’ morphology of the deformed pillar. This characterization and model provide insight that helps inform metal forming and understanding of the mechanical performance of these engineering alloys in the extremes of service conditions.

Modeling the heterogeneous and anisotropic plastic deformation of lath martensite

The plastic behavior of microscale lath martensite samples is highly anisotropic. Depending on the orientation, the deformation of such samples may be heterogeneous, with only a few localized slip traces, while the remainder of the sample remains largely elastic. Although several continuum plasticity models that account for the anisotropy exist, they cannot reproduce the heterogeneous response observed in experiments. In this study, a model for lath martensite at the microscale is proposed which captures the orientation-dependent heterogeneous behavior observed in experiments. Before formulating the model we first study in detail two idealized cases, in which two different deformation mechanisms are activated. In both cases, the lath martensite is modeled using a discrete slip plane model. In the model, the activation stress of the individual slip systems varies randomly in space according to a distribution based on the underlying dislocation motion. The two configurations differ only in the orientation of the applied tensile load relative to that of the laths — either perpendicular or at 45°. In the latter case, slip along the so-called habit plane results in localized plastic deformation, while the former results in a more diffuse activation of plasticity. Insights obtained based on the idealized cases are used to formulate a three-dimensional constitutive model which captures both deformation mechanisms. The model is applied to microtensile tests of single-packet lath martensite samples. It is shown that the orientation-dependent heterogeneity is accurately captured by the two deformation mechanisms accounted for by the model.

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.

Slip system level strengthening in nano-indentation of single crystalline copper: Numerical study via a non-local CPFEM model

A three-dimensional non-local crystal plasticity finite element model (CPFEM) integrating the evolution of geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs) was developed to simulate the nano-indentation of single crystal copper. The simulation accurately reproduced published experimental results when considering force-depth curves, indentation size effect (ISE), anisotropic plastic deformation and sink-in phenomenon. The accumulated slip, i.e., shear strain in individual slip systems, was quantitively investigated. It is anticipated that the developed non-local CPFEM model can support future sub-micro and nanoscale manufacturing research as it enables the rapid exploration of slip system level mechanical response of a diverse range of crystalline alloys.

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

The 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.