Plastic Lattice Research Articles

Thermally induced reorientation and plastic deformation of B19’ monoclinic martensite in nanocrystalline NiTi wires

Functional behavior of nanocrystalline NiTi shape memory wires having various austenitic microstructures was investigated by thermomechanical testing and TEM analysis of martensite microstructures in deformed wires. Three phenomena are reported and discussed in this work. First, it is observed that martensitic NiTi wire heated under low applied stresses elongates several percent before it shortens due to reverse martensitic transformation. This phenomenon is explained as being due to thermally induced martensite reorientation proceeding via motion of interfaces between (001) compound twin domains existing in the microstructure of selfaccommodated B19’ martensite. Second, it is shown that martensite stabilization by deformation (upward shift of the As temperature after deformation in martensite) is not caused by plastic deformation and lattice defects introduced by deformation, as frequently argued in the literature, but that it is due to change of martensite variant microstructures in polycrystal grains during the reorientation process. Finally, it is observed that generation of unrecovered plastic strains and dislocation defects accompanies all martensitic transformation/reorientation/detwinning/ processes in NiTi, though in different extents. It is found that: i) no plastic strains and lattice defects are generated by martensitic transformation proceeding in the absence of external stress, ii) plastic strains, which are generated by martensitic transformations proceeding under external stress, are significantly larger than plastic strains generated during reorientation or detwinning processes in martensite, iii) plastic strains generated while the wire shortens during reverse transformation upon heating are larger than plastic strains generated while it elongates upon forward transformation on cooling. It is proposed that plastic deformation proceeds in the oriented martensite phase via [100](001) dislocation slip. The coupled martensitic transformation and [100](001) dislocation slip in martensite constitutes a TWIP/TRIP like deformation mechanism enabling functional fatigue of NiTi taking place at low stresses below the yield stress for plastic deformation of martensite.

Magnetization loops and non-scaling behavior of flux pinning force of Fe1+y Te1−x Se x studied by numerical simulation

The magnetization of type-II superconductors has usually been described using the critical state models (CSMs). However, CSMs do not consider the time-dependent magnetic relaxation. In this work, to study the influence of magnetic relaxation on the magnetic hysteresis loops (MHLs), critical current density J c, and flux pinning force F p, a numerical method proposed by (Qin and Yao 1996 Phys. Rev. B 54 7536) was adopted and extended to the quasi-two-dimensional case. MHLs at different temperatures measured by using applied field with different sweeping rates can be well reproduced. The critical current density after relaxation J s, and F p can also fit the experimental results well. Based on the numerical simulation, the non-scaling behavior of field-dependent normalized pinning force has been proven to be due to the magnetic relaxation. By comparing the normalized pinning force with the Dew-Hughes model, the dominant pinning type in Fe1+y Te0.6Se0.4 has been confirmed to be the volume Δκ pinning. In addition, the second peak effect is found to be related to the flux lattice transition from elastic lattice to plastic lattice (E-P transition).

Development of a Computational Model of Lattice Structure

This paper deals with the description of the mechanical properties of the plastic lattice structure. These structures are nowadays used in the additive manufacturing. The final goal was to found a mathematical formula, which allowed the FEM simulation of the described lattice structures as the structure were a solid material. The formula stablishes relationship between the original material Young Modulus and weight ratio of the lattice cell. Validation of the formula was performed by the mechanical test. The basis of the study was real testing and measurement, analysis of simulation using the finite element method and the Gibson-Ashby model with some enhancements to get to results within 95% of reliability.

Practical strategies for SARS-CoV-2 RT-PCR testing in resource-constrained settings

Alternatives to nasopharyngeal sampling are needed to increase capacity for SARS-CoV-2 testing. Among 275 participants, we piloted the collection of nasal mid-turbinate swabs amenable to self-testing, including polyester flocked swabs as well as 3D-printed plastic lattice swabs, placed into viral transport media or an RNA stabilization agent. Flocked nasal swabs identified 104/121 individuals who were PCR-positive for SARS-CoV-2 by nasopharyngeal sampling (sensitivity 87%, 95% CI 79-92%), missing those with low viral load (<106 viral copies/mL). 3D-printed nasal swabs showed similar sensitivity. When nasal swabs were placed directly into RNA preservative, the mean 1.4 log decrease in viral copies/uL compared to nasopharyngeal samples was reduced to <1 log, even when samples were left at room temperature for up to 7 days. We also evaluated pooling strategies that involved pooling specimens in the lab versus pooling swabs at the point of collection, finding both successfully detected samples with >105 viral copies/mL.

The in-plane elastic-plastic response of an incompressible, filled hexagonal honeycomb

Exact solutions are derived for the small-strain, in-plane, elasto-plastic response of a hexagonal honeycomb using slender beam theory; incompressibility of the honeycomb is enforced by filling its voids with an incompressible, inviscid fluid. The honeycomb has sides of equal length, but its inclined struts subtend an angle that can deviate from 120° with respect to the vertical side walls. The relative density is sufficiently small that the struts are slender and can be treated as Euler-Bernoulli beams. Exact solutions are obtained for the elastic moduli and macroscopic yield surface of the rigid, ideally plastic lattice under general in-plane loading: the solutions satisfy equilibrium, compatibility and the constitutive response of each elastic, ideally plastic beam. Prior to conducting an elastic analysis, and a rigid, ideally plastic analysis, initial insight is gained by exploring the vector space of inextensional collapse mechanisms of the pin-jointed, compressible version of the hexagonal truss. Two inextensional collapse mechanisms of the compressible honeycomb are identified from the null space of the kinematic matrix. The presence of an incompressible, inviscid fluid in the voids of the honeycomb locks-up one mechanism but the other mechanism survives and generates macroscopic shear strain. Consequently, the incompressible hexagonal honeycomb with rigid joints has a high shear compliance and a low shear strength, with values equal to that of the unfilled, compressible honeycomb. In contrast, macroscopic tensile straining of the incompressible honeycomb requires the stretching of bars in addition to bar-bending, and the tensile modulus and strength of the incompressible honeycomb are thereby elevated. Explicit analytical formulae are derived for the macroscopic tensile modulus and strength of the incompressible honeycomb.

Cold Gas-Dynamic Spray for Catalyzation of Plastically Deformed Mg-Strips with Ni Powder.

Magnesium hydride (MgH2) has received significant attention due to its potential applications as solid-state hydrogen storage media for useful fuel cell applications. Even though MgH2 possesses several attractive hydrogen storage properties, it cannot be utilized in fuel cell applications due to its high thermal stability and poor hydrogen uptake/release kinetics. High-energy ball milling, and mechanically-induced cold-rolling processes are the most common techniques to introduce severe plastic deformation and lattice imperfection in the Mg/MgH2. Furthermore, using one or more catalytic agents is considered a practical solution to improve both the de-/rehydrogenation process of MgH2.These treatments are usually dedicated to enhance its hydrogen storage properties and deduce its thermal stability. However, catalyzation of Mg/MgH2 powders with a desired catalytic agent using ball milling process has shown some disadvantages due to the uncontrolled distribution of the agent particles in the MgH2 powder matrix. The present study has been undertaken to employ a cold gas-dynamic spray process for catalyzing the fresh surfaces of mechanically-induced cold-rolled Mg ribbons with Ni powder particles. The starting Mg-rods were firstly heat treated and forged 200 times before cold rolling for 300 passes. The as-treated ribbons were then catalyzed by Ni particles, using cold gas-dynamic spray process. In this catalyzation approach, the Ni particles were carried by a stream of Ar gas via a high-velocity jet at a supersonic velocity. Accordingly, the pelted Ni particles penetrated the Mg-substrate ribbons, and hence created numerous micropores into the Mg, allowed the Ni particles to form a homogeneous network of catalytic active sites in Mg substrate. As the number of coating time increased to three times, the Ni concentration increased (5.28 wt.%), and this led to significant enhancement of the Mg-hydrogen storage capacity, as well as improving the de-/rehydrogenation kinetics. This is evidenced by the high value of hydrogen storage capacity (6.1 wt.% hydrogen) and the fast gas uptake kinetics (5.1 min) under moderate pressure (10 bar) and temperature (200 °C). The fabricated nanocomposite MgH2/5.28 wt.% Ni strips have shown good dehydrogenation behavior, indicated by their capability to desorb 6.1 wt.% of hydrogen gas within 11 min at 200 °C under 200 mbar of hydrogen pressure. Moreover, this system possessed long cycle-life-time, which extended to 350 h with a minimal degradation in the storage and kinetics behavior.

A statistical study of the relationship between plastic strain and lattice misorientation on the surface of a deformed Ni-based superalloy

Misorientation data from Electron Backscatter Diffraction (EBSD) is often used to identify strain localisation and quantify plastic strain at the microstructural scale. However, the exact relationship between local plastic strain and misorientation and how it changes at the grain and sub-grain level has not been studied in detail. We have used high resolution digital image correlation (HRDIC) to measure plastic strain at the sub-micron scale on the surface of a nickel superalloy strained to 2%. The strain values have been correlated to different misorientation measures at the grain and subgrain scale, over several hundreds of grains. We show that although the grain mean plastic strain is positively correlated to the lattice misorientation, there is a large scatter in the correlation, which depends on the misorientation measure used. There is also essentially no correlation between the magnitude of grain strain and grain orientation derived parameters like the Schmid factor and the Taylor factor, largely due to deformation bands at the mesoscale that are not crystallographic. At these strain levels, the relationship between misorientation and plastic strain is affected by the differences in how slip (discontinuous) and lattice rotation (continuous) develop, by local grain interactions and the development of transgranular strain localisation. It is therefore effectively not possible to quantify plastic strain within individual grains using EBSD derived misorientation values alone, although some measures of misorientation are more appropriate than others if there is an understanding of the underlying local plastic phenomena. Whereas slip is localised in slip bands, the misorientation varies smoothly in a manner that is only weakly spatially correlated to the slip. These findings have implications for the modelling of the deformed state of polycrystalline metals at the microstructural scale using continuum mechanics.

Tunable surface acoustic waves on strain-engineered relaxor K0.7Na0.3NbO3 thin films

In this work, we demonstrate the electronic tunability of surface acoustic waves (SAWs) in epitaxially strained relaxor-type ferroelectric thin films. Epitaxial K0.7Na0.3NbO3 thin films of typically 30 nm in thickness are grown via pulsed laser deposition on (110)-oriented TbScO3. A partial plastic lattice relaxation of the epitaxial strain in these samples leads to a relaxor-type ferroelectricity of these films, which strongly affects the SAW properties. Without electronic bias, only tiny SAW signals of ∼0.2 dB can be detected at room temperature, which can be boosted up to ∼4 dB by a static voltage bias added to the high frequency driving current of the SAW transducers. Upon field cooling below the freezing temperature of polar nanoregions (PNRs), this strong SAW signal can be preserved and is even enhanced due to a release of the electronically fixed PNRs if the bias is removed. In contrast, at elevated temperatures, a reversible switching of the SAW signal is possible. The switching shows relaxation dynamics that are typical for relaxor ferroelectrics. The relaxation time τ decreases exponentially from several hours at freezing temperature to a few seconds (&amp;lt;5 s) at room temperature.

Fault-tolerant elastic-plastic lattice material.

The paper describes a fault-tolerant design of a special two-dimensional beam lattice. The morphology of such lattices was suggested in the theoretical papers (Cherkaev and Ryvkin 2019 Arch. Appl. Mech. 89, 485-501; Cherkaev and Ryvkin 2019 Arch. Appl. Mech. 89, 503-519), where its superior properties were found numerically. The proposed design consists of beam elements with two different thicknesses; the lattice is macro-isotropic and stretch dominated. Here, we experimentally verify the fault-tolerant properties of these lattices. The specimens were three-dimensional-printed from the VeroWhite elastoplastic material. The lattice is subjected to uniaxial tensile loading. Due to its morphology, the failed beams are evenly distributed in the lattice at the initial stage of damage; at this stage, the material remains intact, preserves its bearing ability, and supports relatively high strains before the final failure. At the initial phase of damage, the thinner beams buckle; then another group of separated thin beams plastically yield and rupture. The fatal macro-crack propagates after the distributed damage reaches a critical level. This initial distributed damage stage allows for a better energy absorption rate before the catastrophic failure of the structure. The experimental results are supported by simulations which confirm that the proposed fault-tolerant material possesses excellent energy absorption properties thanks to the distributed damage stage phenomenon. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.

CLINICAL ASSESSMENT OF THE EFFICIENCY OF THE APPLICATION OF THE IMPROVED TECHNIQUE OF MANUFACTURING PLASTIC BASES OF REMOVABLE DENTURES

Complete removable dentures remain one of the most popular types of prosthetics in Ukraine. Despite this, their effectiveness remains insufficient, due to the poor influence of plate bases made of acrylic plastics.&#x0D; It is proposed to improve the technology of making bases of removable dentures from acrylic plastics in two directions: firstly, by modernizing the method of pressing acrylic plastics, and secondly, by applying coating on the inner surface.&#x0D; The purpose of the research is to develop a clinical examination of the advanced technique for the manufacture of plate bases of removable dentures in edentulous patients.&#x0D; Materials and methods of the research. Clinical testing was carried out among 30 patients of middle and elderly age (60-82 years old), equal to men and women, with complete absence of teeth, who were made of two sets of removable dentures on both jaws (one by traditional method, another - by own one). The originality of the technique consisted of the application of a self-made construction of bugel, and applying a solution of polyvinyl alcohol for covering of inner surface of dentures.&#x0D; To evaluate clinical effectiveness, it was used the results of a clinical examination, in particular study of the mucous membrane of the prosthetic bed, and the evaluation of the functional efficacy of the prosthesis after 1 and 6 months after the delivery of the prosthesis.&#x0D; Results of the research and their discussion. With the use of a bugel of the original design, the thickness of the plastic lattice was 0.15 ± 0.05 mm, while it was 0.75 ± 0.20 mm when using the traditional method of pressing (p˂0.05).&#x0D; The application of the improved technique allowed reducing the number of cases of mucosal damage after 1 month of use of dentures to 20.0 ± 7.3% versus 30.0 ± 8.4% with traditional technology (р˂0.05). However, after 6 months, no reliable differences between the state of the mucous membrane for dentures manufactured according to different technologies were been established (p&gt; 0,05).&#x0D; After 1 month of use of dentures made according to the traditional technology, the first level of stability (good fixation, characterized by the displacement of the complete removable prosthesis within the softness of soft tissues with the preservation of the closing valve) was recorded in 90.0 ± 5.5% of observations, and for improved – in 93.3 ± 4.6% (p&gt; 0.05).&#x0D; The number of corrections was 3.5 ± 0.5 visits when applying traditional technology of the plastic bases, and for the improved one it was 2.1 ± 0.2 (p &lt;0.05).&#x0D; Also, greater chewing efficiency is established for dentures, the bases of which were made according to the advanced technology, was 51.2 ± 1.6% against 46.8 ± 1.5% in 1 month and 60.5 ± 1.8% against 55.3 ± 1.6% after 6 months (p˂0.05). The difference between time of chewing for two series of dentures was not reliable (p &lt;0.05).&#x0D; Conclusions. The use of the advanced technique for the manufacture of plate bases of complete removable dentures allows achieving a better state of the mucous membrane of the oral cavity after 1 month of using dentures, which is associated with a decrease in the toxic effects of the residual monomer. The best parameters of the functional efficacy of the prostheses can be explained by a more pronounced balance due to the lack of the lattice and, consequently, greater precision of the occlusal contacts of the dentures, which ensures better fixation and stabilization, and therefore creates optimal conditions for functioning.&#x0D; Prospects for further research. The obtained results give an opportunity to recommend the application of the advanced method for the prosthetics of defects in dentitions with removable dentures with bases made of acrylic plastics.

Direct Crystal Elastoviscoplasticity Model: An Application to the Study of Single Crystal Deformation

This paper models the uniaxial compression of a single crystal of commercial purity aluminum, and compares the modeling results with experimental data. The problem is solved using a first-type direct model based on the finite element method. The material behavior is described by a crystal elastoviscoplasticity model that explicitly accounts for shearing on crystallographic planes. The main feature of this study is a physically sound description of the geometric nonlinearity associated with crystal lattice rotation. The modeling results show that the original homogeneous single crystal is divided into volumes with different plastic shear rate intensity and lattice orientation, which is in satisfactory agreement with experimental data.

Intragranular localization induced by softening crystal plasticity: Analysis of slip and kink bands localization modes from high resolution FFT-simulations results

We investigate the ability of local continuum crystal plasticity theory to simulate intense slip localization at incipient plasticity observed experimentally in metals exhibiting softening mechanisms. A generic strain softening model is implemented within a massively parallel FFT solver framework to study intragranular strain localization throughout high resolution polycrystalline simulations. It is coupled to a systematic analysis strain localization modes: Equivalent plastic strain and lattice rotation fields are processed to create binary maps of slip and kink bands populations, estimate their volume fraction and mean strain level. High resolution simulations show the formation of an intragranular localization band network. The associated localization maps are used to identify accurately slip and kink bands populations and highlight the distinct evolution of kink bands, influenced by lattice rotation. Results highlight that the analysis of the nature of localization bands in numerical studies is fundamental to asses the validity of polycrystalline simulations. Indeed, it is evidenced that selection between slip or kink localization modes is only due to grain to grain incompatibilities as these two localization modes are equivalent in classical crystal plasticity models. As a result they predict the formation of a large amount of kink bands in contradiction with experimental observations of softening metals. We show that this holds for complex physics based models too. Hence, the use of classical crystal plasticity for strain localization simulation should be reconsidered in order to predict realistic localization modes.

Microscopic heterogeneity of plastic strain and lattice rotation in partially recrystallized copper polycrystals

Partial recrystallization of highly deformed polycrystalline aggregates creates a bimodal grain size distribution, which improves ductility while maintaining relatively high strength. In this work, the microstructure evolution during isothermal annealing of cold rolled copper samples was investigated using electron backscattered diffraction (EBSD) and the macroscopic mechanical strength of partially recrystallized samples was measured under uniaxial tension. Different models were tested in order to reproduce both the macroscopic mechanical response and the microscopic strain field inside a sample with 41% recrystallized grains loaded inside a scanning electron microscope to allow in-situ EBSD mapping. Crystal plasticity based finite element modeling (CPFEM) performed on a 2D mesh conforming to the experimental microstructure was compared to 3D predictions on an idealized model microstructure.

Environmentally friendly nanocrystalline magnesium hydride decorated with metallic glassy-zirconium palladium nanopowders for fuel cell applications.

A new solid-state hydrogen storage system of magnesium hydride (MgH2) doped with 5 wt% of metallic glassy (MG) zirconium palladium (Zr2Pd) nanopowder was fabricated using a high-energy ball milling technique. The end-product obtained after 50 h of milling was consolidated into bulk buttons, using a hot-pressing technique at 350 °C. The results have shown that this consolidation step, followed by the repetitive pressing at ambient temperature did not affect the nanocrystalline characteristics of pressed powders. Recycling pressing demonstrated beneficial effects of plastic deformation and lattice imperfections on Mg, leading to its enhanced hydrogenation/dehydrogenation kinetics and cycle-life-time performance compared with untreated samples. The results elucidated that spherical, hard, nanopowder of MG-Zr2Pd were forced to penetrate the Mg/MgH2 matrix to create micro/nanopore structures upon pressing for 50 cycles. These ultrafine spherical metallic glassy particles (∼400 nm in diameter) acted as a micro-milling media for reducing the particle size of MgH2 powders into submicron particles. In addition, they played a vital role as grain growth inhibitors to prevent the undesired growth of Mg grains upon the application of a moderate temperature in the range of 50 °C to 350 °C. The apparent activation energy for the decomposition of this new consolidated nanocomposite material was measured to be 92.2 kJ mol−1, which is far below than the measured value of pure nanocrystalline MgH2 powders (151.2 kJ mol−1) prepared in the present study. This new binary system possessed superior hydrogenation kinetics, indicated by the rather low temperature (200 °C) required to uptake 6.08 wt% H2 within 7.5 min. More importantly, the system revealed excellent dehydrogenation kinetics at 225 °C as implied by the limited time needed to release 6.1 wt% H2 in 10 min. The MgH2/5 wt% MG-Zr2Pd system showed a high performance for cyclability, implied by the achievement of continuous cycles (338 cycles) at 225 °C without degradation over 227 h.

Multiscale Deformation of Commercial Titanium and Ti一6Al-4V Alloy Subjected to Electron Beam Surface Treatment

The paper studies the effect of electron beam irradiation on the surface morphology, microstructure, and phase transformations in the surface layers of commercial titanium and titanium alloy Ti-6Nl-4V. It has been found that the plastic deformation of the modified surface layers under uniaxial tension of the studied specimens occurs at several scale levels. The main plastic deformation mechanism of the modified surface layers is shear induced by the maximum tangential stresses. The dislocation deformation mechanisms effectively accommodate the material rotation caused by the displacement of one part of the crystal relative to the other. Noncrystallographic shear banding in the surface layer with a nonequilibrium martensitic structure is associated with plastic lattice distortion and with reversible structural phase transformations.

A new diffraction line profile breadth analysis approach for evaluating plastic lattice strain anisotropy in cold-worked nickel under various strain paths

Plastic lattice strain anisotropy in polycrystalline aggregates involves complicated integration of single crystal elastic anisotropy, grain-grain interactions and orientation-dependent slip activations. It is essential to experimentally determine plastic lattice strain anisotropy for in-depth understanding elasto-plastic deformation mechanisms and rationalizing advanced models. Unlike the widely applied method for quantifying elastic lattice strain anisotropy utilizing diffraction peak shift, accurately evaluating plastic lattice strain anisotropy is still enormously challenging over the decades. In this work, we developed a new diffraction line profile breadth analysis approach to reliably assessing plastic lattice strain anisotropy based on the simple linear dependence in quasi elasto-plastic model. The approach is confirmed to be effective and adaptive in practical application by linearization of the experimental dependences for line profile broadening in nickel under various cold-working strain paths. Then the orientation-dependent plastic lattice strain values could be reliably estimated up to high strain levels, which were identical to the magnitude of published elastic lattice strain. The strain levels and strain paths dependent plastic anisotropy magnitude was also inferred and further compared with the results from classical elastic models, i.e., Reuss, Voigt, Reuss-Voigt average and Eshelby-Kröner models. Simultaneously, by further carrying out microstructural characterization and dislocation model based line profile analysis, correlative texture and dislocation (arrangement and edge/screw constituent) developments were found to be strongly depended on strain paths, as well as verified to be the primary contributions to strain anisotropy. In addition to the proposed explanations in two-phase composite model, the strain hardening was demonstrated to be impacted by strain anisotropy behaviors as well. The fundamental mechanisms and significance of above interrelated effects under various strain paths were also well discussed.

Определение деформаций сетчатой конструкции из углепластика с использованием оптоволоконных датчиков

Определение деформаций сетчатой конструкции из углепластика с использованием оптоволоконных датчиков

Hierarchy and scaling behavior of multi-rank domain patterns in ferroelectric K0.9Na0.1NbO3 strained films

The formation process of a ferroelectric multi-rank domain pattern in the thickness range of 7–52 nm is investigated for monoclinic K0.9Na0.1NbO3 strained epitaxial films on (110) NdScO3 substrates. Although the elastic strain energy density is degenerated for two pseudocubic orientations, a distinctive hierarchy of domain evolution is observed with exclusive in-plane a1a2 domains for very thin films and the retarded onset of a ferroelectric MC phase at larger film thickness. This is accompanied by a thickness dependent transformation from stripe domains to a herringbone pattern and, eventually, for the thickest film, to a checkerboard-like structure. These transformations in the domain arrangement and width are correlated to energetic aspects as depolarization field and anisotropic strain relaxation in the film. While for the MC domains plastic strain relaxation is throughout observed, the a1a2 domains show a two-step strain relaxation mechanism starting with an in-plane elastic shearing, which is followed by plastic lattice relaxation. Our results highlight a pathway for engineering and patterning of periodic ferroelectric domain structures.

Finite element analysis and experimental study of plastic lattice structures manufactured by selective laser sintering

The availability of additive manufacturing technologies in particular the selective laser sintering process has enabled the fabrication of high strength, lightweight and complex cellular lattice structures. In this study, the effective mechanical properties of selective laser sintering produced periodic lattice structures were investigated. Three different types of lattice structures were designed by repeating three types of open-form unit cells consisting of triangular prism, square prism and hexagonal prism. A novel approach of creating the complex and conformable lattice structures using traditional modelling software such as Creo® proposed by the authors was used. Based on the predesigned lattice structures, finite element analysis was carried out to evaluate the mechanical properties of these structures. For the experimental study, nylon samples were printed using a plastic selective laser sintering system and tested using a universal testing machine. Finite element analysis results show that lattice structures with triangular prism perform better than the other two prisms in terms of Young’s modulus to relative density ratio. Tensile tests results show good conformance with the results obtained from finite element analysis.

Investigation of the Anisotropic Mechanical Behaviors of Copper Single Crystals Through Nanoindentation Modeling

A crystal plasticity finite element method constitutive model was developed to investigate the anisotropic mechanical behaviors of (001), (011), and (111) initially orientated copper (Cu) single crystals during nanoindentation deformation. The numerical load-indentation depth curve and hardness-indentation depth curve were compared with experimental observations to validate the established three-dimensional (3D) CPFEM model. The difference of indentation loads between (111) crystal and (001) crystal is ~10.68 pct, and the difference of indentation modulus between (111) surface and (001) surface is ~10.80 pct. The numerical results show the noticeable indentation size effect for three crystals, and slightly different hardness values on different crystallographic planes. The equivalent plastic strain and lattice rotation angles were also analyzed on three through-thickness cross sections to study the plastic deformation-induced texture anisotropy.