Large Indentation Depths Research Articles

Identifikasi Tegangan pada Permukaan Karet SBR-25 saat mengalami Kontak Abrasi: Investigasi Numerik

Keausan akibat abrasi pada komponen yang terbuat dari material karet seperti pada ban kendaraan atau seal sangat menentukan umur pakai dari komponen tersebut. Dalam material karet, ketika permukaan yang masih halus mengalami abrasi, maka akan terbentuk permukaan yang bergerigi secara paralel yang arahnya tegak lurus dengan arah gerak abrasi. Bentuk permukaan yang bergerigi ini akan terus menerus terbentuk selama proses kontak abrasi masih berjalan. Keausan abrasi terjadi akibat tegangan pada material karet melampaui tegangan patah material. Tetapi analisis keausan abrasi pada karet masih sangat sulit dilakukan secara analitik dikarenakan sifat karet yang non linier dan hyperelastic. Dengan menggunakan metoda numerik, tulisan ini membahas tegangan yang terjadi pada permukaan karet SBR-25 yang sudah terabrasi. Sebagai studi awal, analisis dilakukan dalam dua dimensi dengan menggunakan perangkat lunak komersial ABAQUS 6.14-5 dengan memodelkan karet yang kontak dengan indenter yang kaku. Simulasi dilakukan dengan variasi kedalaman indentasi, kekasaran permukaan dan dimensi gigi (chip). Secara umum hasil menunjukkan bahwa makin besar kedalaman indentasi dan kekasaran permukaaan akan meningkatkan nilai tegangan maksimum. Disisi lain, lokasi terjadinya tegangan maksimum (tegangan kritis) juga sangat dipengaruhi oleh kedalaman indentasi, kekasaran permukaan dan dimensi dari chip.

Strain rate sensitivity of a novel refractory high entropy alloy: Intrinsic versus extrinsic effects

In recent years, there is great interest in development of “reduced activity” refractory alloys for next generation nuclear applications for safe and efficient post-service recycling. Here, the strain rate sensitivity of a refractory high entropy alloy, namely HfTaTiVZr, was investigated consisting of all reduced activation elements. The intrinsic versus extrinsic effects in rate sensitivity were evaluated for fundamental understanding of the differences in loading condition. Uniaxial bulk and micro-pillar compression tests were performed along with multi-axial nano-indentation in a wide range of strain rates. The extrinsic strain rate sensitivity obtained from micro-pillar compression and bulk compression was higher than its intrinsic characteristic determined from nano-indentation. The low value of strain rate sensitivity obtained from nano-indentation was attributed to greater degree of dislocation entanglement in confined volume beneath the indenter. On the other hand, the high value of strain rate sensitivity in case of micro-pillar compression tests was attributed to the extrinsic effect of larger surface to volume ratio which helped in annihilation of dislocations through the free surface. A pronounced indentation size effect of strain rate sensitivity was also observed. At smaller depth, higher mobility and diffusion of dislocations near the free surface resulted in higher strain rate sensitivity compared to that at larger indentation depth.

A study of deformation behavior and phase transformation in 4H-SiC during nanoindentation process via molecular dynamics simulation

The deformation behavior and phase transformation of 4H silicon carbide (4H-SiC) during nanoindentation process is investigated with a cube corner diamond indenter through molecular dynamics simulation. It is found through the research that the basal dislocations are most likely to be generated in (0001) face and the indentation process contributes to the distortion of 4H-SiC lattice. In addition, phase transformation from 4H-SiC to 3C-SiC is firstly observed via MD simulations during indentation process. Cross-sectional observation in (12¯10) plain shows that 3C-SiC layers appear firstly during nanoindentation process, and the layers are observed at small indentation depth. 3C-SiC grain is generated based on 3C-SiC layers, and the transformation is more likely to appear at larger indentation depth. The phase transformation from 4H-SiC to 3C-SiC results from the shear stress induced by indenter during loading process. 3C-SiC grain and layers are both generated from the slip of 3C seeds under the influence of shear stress, and the condition of 3C-SiC grain formation is stricter. Moreover, the P-h curve is studied and the vertical deformation mode during indentation process on 4H-SiC can be reflected on P-h curve as small pop-in events. The findings are meaningful for the study of deformation mechanism of SiC and the application of SiC in precision machining.

Indentation Strain Rate Sensitivity of CoCrFeNiAl0.3 High‐Entropy Alloy

In this paper, the mechanical properties of CoCrFeNiAl0.3 high‐entropy alloy (HEA) under different strain rates are investigated using nanoindentation at room temperature. Experimental results show that the contact stiffness increases almost linearly with indentation depth and the elastic modulus is invariable under different indentation strain rates, while the indentation hardness under higher strain rate is relatively larger, and the hardness under large indentation depth is relatively smaller for each indentation strain rate. The indentation size effect of hardness and strain rate sensitivity exponent m under different indentation strain rates are analyzed, then the hardness and m free from the effect of indentation depth are obtained. Finally, this investigation reveals the size effects of the hardness of HEA in light of the strain rate sensitivity and activation volume of the dislocation nucleation.

Determination of elastic properties of urea-formaldehyde microcapsules through nanoindentation based on the contact model and the shell deformation theory

Characterization of the mechanical properties of urea-formaldehyde microcapsules filled with epoxy resin is of importance for achieving self-healing of cementitious composites. In this study, the morphology of microcapsules, including diameter and thickness, was characterized using scanning electron microscopy. The mechanical properties of single microcapsules, including Young's modulus and hardness, were determined through a nanoindentation technology based on the elastic contact theory using a Berkovich indenter. Moreover, to investigate the structural effects of microcapsules, a diamond plate indenter was used, and the Young's modulus of the microcapsule wall was calculated through the ordinary least square optimization method according to three analytical solutions on the basis of thin shell theory, namely Reissner, Pogorelov, and Lukasiewicz methods. It is shown that the results of the contact and thin shell theory were similar, in which the similarity occurs only in the case of a small deformation. When the deformation was large (indentation depth >900 nm), the structural effect became significant. In addition, the finite element method was applied to simulate the mechanical response of the microcapsules using the results obtained. The validity of the approach was approved.

Determination of the proof strength and flow properties of materials from spherical indentation tests: An analytical approach based on the expanding cavity model

An analytical method based on the extended expanding cavity model was proposed in this study to determine the proof strength Rp0.2 and flow properties of materials that obey the Johnson–Cook constitutive model from spherical indentation tests. The introduction of the Johnson–Cook model made the proposed method suitable for the tensile property evaluation of materials not only at room temperature but also at elevated temperatures. The validity of the expanding cavity model was verified through comparisons of von Mises equivalent strain distributions obtained from finite element analyses with the corresponding results from theoretical analysis. From the parameter analysis, it was found that the indentation governing parameter ψempirical in the empirical method was actually determined by the tangential modulus Ep and the hardening exponent n and thus should not be considered as a constant. We also analyzed the unreliability of previous plastic zone radius rp calculation method at large indentation depths (with obvious pileup phenomenon) and put forward a new calculation method of rp based on the force balance. Finite element calculations of spherical indentation tests with tensile properties of Ti6Al4V and AISI 4340 were conducted in this study as substitutes for spherical indentation tests. The load–depth data and rp from finite element calculations were employed in the reverse analysis, the results of which showed that spherical indentation tests can provide the same reliable Rp0.2 as tensile tests and even the whole stress–strain curves. Furthermore, the influence of friction and the measuring system strain threshold in the measurement of rp, which may be inevitable in experiments, were also thoroughly discussed in this study, which also helped to verify the robustness of this study.

Nonlinear compliance of elastic layers to indentation.

Thin samples adherent to a rigid substrate are considerably less compliant to indentation when compared to specimens that are not geometrically confined. Analytical corrections to this so-called substrate effect exist for various types of indenters but are not applicable when large deformations are possible, as is the case in biological materials. To overcome this limitation, we construct a nonlinear scaling model characterized by one single exponent, which we explore employing a parametric finite element analysis. The model is based on asymptotes of two length scales in relation to the sample thickness, i.e., indentation depth and radius of the contact area. For small indentation depth, we require agreement with analytical, linear models, whereas for large indentation depth and extensive contact area, we recognize similarity to uniaxial deformation, indicating a divergent force required to indent nonlinear materials. In contrast, we find linear materials not to be influenced by the substrate effect beyond first order, implying that nonlinear effects originating from either the material or geometric confinement are clearly separated only in thin samples. Furthermore, in this regime the scaling model can be derived by following a heuristic argument extending a linear model to large indentation depths. Lastly, in a large indentation setting where the contact is small in comparison with sample thickness, we observe nonlinear effects independent of material type that we attribute to a higher-order influence of geometrical confinement. In this regime, we define a scalar as the ratio of strains along principal axes as obtained by comparison with the case of a point force on a half-space. We find this scalar to be in quantitative agreement with the scaling exponent, indicating an approach to distinguish between nonlinear effects in the scaling model. While we conjecture our findings to be applicable to other flat-ended indenters, we focus on the case of a flat-ended cylinder in normal contact with a thin layer. The analytical solution for small indentation associated with this problem has been given by Hayes et al. (J Biomech 5:541-551, 1972), for which we provide a convenient numerical implementation.

Dynamical approach to displacement jumps in nanoindentation experiments

The load-controlled mode is routinely used in nanoindentation experiments. Yet there are no simulations or models that predict the generic features of force-displacement F-z curves, in particular, the existence of several displacement jumps of decreasing magnitude. Here, we show that the recently developed dislocation dynamical model predicts all the generic features when the model is appropriately coupled to an equation defining the load rate. Since jumps in the indentation depth result from the plastic deformation occurring inside the sample, we devise a method for calculating this contribution by setting up a system of coupled nonlinear time evolution equations for the mobile and forest dislocation densities. The equations are then coupled to the force rate equation. We include nucleation, multiplication, and propagation threshold mechanisms for the mobile dislocations apart from other well known dislocation transformation mechanisms between the mobile and forest dislocations. The commonly used Berkovitch indenter is considered. The ability of the approach is illustrated by adopting experimental parameters such as the indentation rate, the geometrical quantities defining the Berkovitch indenter including the nominal tip radius, and other parameters. We identify specific dislocation mechanisms contributing to different regions of the F-z curve as a first step for obtaining a good fit to a given experimental F-z curve. This is done by studying the influence of the parameters on the model F-z curves. In addition, the study demonstrates that the model predicts all the generic features of nanoindentation such as the existence of an initial elastic branch followed by several displacement jumps of decreasing magnitude, and residual plasticity after unloading for a range of model parameter values. Further, an optimized set of parameter values can be easily determined that gives a good fit to the experimental force-displacement curve for Al single crystals of (110) orientation. The stress corresponding to the maximum force on the elastic branch is close to the theoretical yield stress. We also elucidate the ambiguity in defining the hardness at nanometer scales where the displacement jumps dominate. For larger indentation depths where displacement jumps disappear, the indentation size effect is predicted. The approach also provides insights into several open questions.

3D Dislocation structure evolution in strontium titanate: Spherical indentation experiments and MD simulations

AbstractIn the present work, the dislocation structure evolution around and underneath the spherical indentations in (001) oriented single crystalline strontium titanate (STO) was revealed by using an etch‐pit technique and molecular dynamics (MD) simulations. The 3D defect structure at various length scales and subsurface depths was resolved with the help of a sequential polishing, etching, and imaging technique. This analysis, combined with load‐displacement data, shows that the incipient plasticity (manifested as sudden indenter displacement bursts) is strongly influenced by preexisting dislocations. In the early stage of plastic deformation, the dislocation pile‐ups are all aligned in 〈100〉 directions, lying on {110}45 planes, inclined at 45° to the (001) surface. At higher mean contact pressure and larger indentation depth, however, dislocation pile‐ups along 〈110〉 directions appear, lying on {110}90 planes, perpendicular to the (100) surface. MD simulations confirm the glide plane nature and provide further insights into the dislocation formation mechanisms by tracing the evolution of the complete dislocation line network as function of indentation depth.

Atomic-scale analysis of nanoindentation behavior of high-entropy alloy

Using molecular dynamics simulations, we study the elastic and plastic deformations of indentation in FeCrCuAlNi high-entropy alloy (HEA). The indentation tests are carried out using spherical rigid indenter to investigate the effects of high-entropy and severe lattice distortion in terms of shear strain, indentation force, surface morphology, defect structure, dislocation evolution and radial distribution function on the deformation processes. It can be found that when the indentation depth increases, the shear stress requires for the occurrence of the contact area between the indenter and the substrate increased, which is attributable to a higher probability to observe the dislocation evolution under a large indentation depth. The indentation test also shows that the equal element addition can significantly improve the mechanical properties of HEA compared with the conventional alloy. Based on the Hertzian fitting, the FeCrCuAlNi HEA has the Young’s modulus of 161[Formula: see text]GPa and hardness of 15.4[Formula: see text]GPa, respectively. These values are higher than that of traditional metal materials, due to the low stacking fault energy and the dense atomic arrangement in the slip plane of HEA. In the plastic region, the Fe element causes the more stable crystal structure, much stronger than the Cu element, presumably resulted from a variety of crystal structures for Fe in the multicomponent FeCrCuAlNi alloy. Further, this effective strategy is used to accelerate the discovery of excellent mechanical properties of HEAs.

Failure by fracture in sheet–bulk metal forming

This article investigates the possibility of failure by crack-opening mode III (out-of-plane shearing) in sheet–bulk metal forming processes. The investigation makes use of experimentally and theoretically determined fracture-forming limits of aluminium AA1050-H111 sheets with 1 mm thickness, experimental tests in incremental ploughing with a roll-tipped tool and numerical simulation using a commercial finite element programme. Results show that incremental ploughing of thin sheets with a roll-tipped tool under large indentation depths gives rise to transverse cracks that are triggered at the upper groove surface and propagate downward across thickness along an inclined direction to the sheet surface. In contrast to sheet–metal forming processes that only fail by fracture in crack-opening modes I and II, sheet–bulk metal forming processes present the unique ability of failing in all three possible crack-opening modes, namely, in mode III that is typical of bulk metal–forming processes.

The shallow shell approach to Pogorelov's problem and the breakdown of 'mirror buckling'.

We present a detailed asymptotic analysis of the point indentation of an unpressurized, spherical elastic shell. Previous analyses of this classic problem have assumed that for sufficiently large indentation depths, such a shell deforms by 'mirror buckling'-a portion of the shell inverts to become a spherical cap with equal but opposite curvature to the undeformed shell. The energy of deformation is then localized in a ridge in which the deformed and undeformed portions of the shell join together, commonly referred to as Pogorelov's ridge. Rather than using an energy formulation, we revisit this problem from the point of view of the shallow shell equations and perform an asymptotic analysis that exploits the largeness of the indentation depth. This reveals first that the stress profile associated with mirror buckling is singular as the indenter is approached. This consequence of point indentation means that mirror buckling must be modified to incorporate the shell's bending stiffness close to the indenter and gives rise to an intricate asymptotic structure with seven different spatial regions. This is in contrast with the three regions (mirror-buckled, ridge and undeformed) that are usually assumed and yields new insight into the large compressive hoop stress that ultimately causes the secondary buckling of the shell.

Mechanically, the Shoot Apical Meristem of Arabidopsis Behaves like a Shell Inflated by a Pressure of About 1 MPa.

In plants, the shoot apical meristem contains the stem cells and is responsible for the generation of all aerial organs. Mechanistically, organogenesis is associated with an auxin-dependent local softening of the epidermis. This has been proposed to be sufficient to trigger outgrowth, because the epidermis is thought to be under tension and stiffer than internal tissues in all the aerial part of the plant. However, this has not been directly demonstrated in the shoot apical meristem. Here we tested this hypothesis in Arabidopsis using indentation methods and modeling. We considered two possible scenarios: either the epidermis does not have unique properties and the meristem behaves as a homogeneous linearly-elastic tissue, or the epidermis is under tension and the meristem exhibits the response of a shell under pressure. Large indentation depths measurements with a large tip (~size of the meristem) were consistent with a shell-like behavior. This also allowed us to deduce a value of turgor pressure, estimated at 0.82±0.16 MPa. Indentation with atomic force microscopy provided local measurements of pressure in the epidermis, further confirming the range of values obtained from large deformations. Altogether, our data demonstrate that the Arabidopsis shoot apical meristem behaves like a shell under a MPa range pressure and support a key role for the epidermis in shaping the shoot apex.

Elastic and plastic deformations in a high entropy alloy investigated using a nanoindentation method

We employed instrumented indentation technique to study the elastic and plastic deformations in a face-centered cubic (fcc) high-entropy alloy NiFeCoCrMn. Single-crystal Ni was also examined for direct comparison. Tests were carried out using indenters with different tip radii to investigate the effect of indented volume on deformation processes. It was found that when the tip radius increased, the shear stress required for the occurrence of indentation pop-in decreased, which was attributable to a higher probability to find dislocations under a larger tip radius. We proposed a statistical model to describe the results quantitatively. In the plastic region, NiFeCoCrMn was much stronger than Ni, presumably resulted from a large lattice distortion in the multicomponent NiFeCoCrMn alloy. We found that the response of both materials at large indentation depth could be described by the classical Nix-Gao model, but when the indentation depth was shallow, the indenter tip must be treated as a sphere and Swadener's model offered a better description. In any event, it was necessary to introduce a scaling factor f to describe the effective stressed volume underneath the indenter tip to compensate for the overestimated hardness values. A map of indentation pressure against dislocation density was also summarized in this study.

Nanoindentation of Functionally Graded Polymer Nanocomposites: Assessment of the Strengthening Parameters through Experiments and Modeling

NNanoindentation tests were carried out on the surface of polymer nanocomposites exhibiting either graded or homogeneous distributions of Fe3O4@silica core-shell nanoparticles in a photocurable polymeric matrix. The results reveal a complex interplay between graded morphology, indentation depth and calculated modulus and hardness values, which was elucidated through numerical simulations. First, it was experimentally shown how for small (1 µm) indentations, large increases in modulus (up to +40%) and hardness (up to +93%) were obtained for graded composites with respect to their homogeneous counterparts, whereas at a larger indentation depth (20 µm) the modulus and hardness of the graded and homogeneous composites did not substantially differ from each other and from those of the pure polymer. Then, through a Material Point Method approach, experimental nanoindentation tests were successfully simulated, confirming the importance of the indentation depth and of the associated plastic zone as key factors for a more accurate design of graded polymer nanocomposites whose mechanical properties are able to fulfill the requirements encountered during operational life.

Investigating the Influence of Anti-Cancer Drugs on the Mechanics of Cells Using AFM

The cytoskeleton comprises microtubules, actin microfilaments, and intermediate filaments. The cytoskeleton plays a role in the mechanical function of cell adhesion, motility, and migration. Currently, cancer cell mechanics is an important topic of understanding cancer progression. Atomic force microscopy (AFM) is one of the techniques used to determine the mechanical properties of cells. In this study, AFM was used to measure the force curves of U937 cancer cells treated with two types of anticancer drugs (colchicine and taxol), and alterations in the Young’s modulus were subsequently investigated. The study results indicate that the force curve trend was dissimilar among the three types of cells (cells in the control group and in two types of anticancer drugs). In addition, when using the AFM to analyze the influence of drugs on the mechanical properties of cells, applying a small loading force from the AFM tip (small cell indentation depth) produced more accurate results. At a small cell indentation depth, the Young’s modulus order was Ecolchicine < Econtrol < Etaxol because colchicine caused the cell microtubules to disassemble, thereby reducing cell strength, whereas taxol caused the microtubules to assemble, which increased cell strength. At a large cell indentation depth, the Ecolchicine value was the largest because colchicine reduced the strength and height of the cells and the effect of the underlying substrate was reflected in and influenced the force curve.

Tribology behavior during indentation and scratch of thin films on substrates: effects of plastic friction

When friction stress on a contact surface reaches material yield strength in shear, contact slippage can occur even if the slipping condition for Coulomb friction is not satisfied. In this paper, a three-dimensional (3-D) scratch model is proposed, which considers combined Coulomb and plastic friction. Influences of plastic friction are discussed for two continuous displacement loading steps: indentation and scratch. For indentation, initially the sliding on the contact surface can not take place and the complete cohesion condition should be employed; then as the indenter is further compressed down to the coating surface, plastic friction instead of Coulomb friction prevails in most of the contact region. For scratch, the previous complete cohesion at the initial indentation is substituted by plastic or Coulomb slipping, and the slippage becomes plastic-sliding governed for a slightly large indentation depth. The effects of the indentation depth and the Coulomb friction coefficient on the scratch friction coefficient are discussed in detail. Several experimental phenomena are interpreted, which include that with an increase of the normal loading, the scratch friction coefficient reduces for the soft coating but grows for the hard coating; and with the growth of hardness after heat treatment, the scratch friction coefficient increases due to weak plastic slippage. Obtained results help to elucidate tribological behaviors during scratch and are helpful for the interpretation of experimental phenomena and the improvement of numerical simulations for the scratch process.

On the rate dependence of mechanical properties of aligned carbon nanotube arrays

Aligned carbon nanotube arrays are a new form of carbon nanomaterials that have received great interest due to their superior structure and properties. The present work comprehensively examines the rate-dependent mechanical deformation of the vertically aligned carbon nanotube arrays (VA-CNTs) by the use of indentation tests. The small-displacement, elastic property of the VA-CNTs was measured by a spherical indenter. The effective indentation strain rate was varied by adjusting the indenter unloading rate. The instantaneous modulus of the VA-CNTs has been calculated and is found to increase linearly with indentation strain rate. The large-displacement, plastic property of the VA-CNTs was measured by a cylindrical, flat-ended indenter. At large indentation depths, the stress–strain curve of the VA-CNTs reveals distinct plastic deformation. The indentation strain rate was varied by directly changing the indenter velocity. The yield strength (σ y) of the VA-CNTs also increases linearly with respect to indentation strain rate.

Dislocation dynamical approach to force fluctuations in nanoindentation experiments

We develop an approach that combines the power of nonlinear dynamics with the evolution equations for the mobile and immobile dislocation densities and force to explain force fluctuations in nanoindentation experiments. The model includes nucleation, multiplication, and propagation thresholds for mobile dislocations, and other well known dislocation transformation mechanisms. The model predicts all the generic features of nanoindentation such as the Hertzian elastic branch followed by several force drops of decreasing magnitudes, and residual plasticity after unloading. The stress corresponding to the elastic force maximum is close to the yield stress of an ideal solid. The predicted values for all the quantities are close to those reported by experiments. Our model allows us to address the indentation-size effect including the ambiguity in defining the hardness in the force drop dominated regime. At large indentation depths, the hardness remains nearly constant with a marginal decreasing trend.

Finite element study for conical indentation of elastoplastic micropolar material

Numerous experiments have repetitively shown that the material behavior presents effective size dependent mechanical properties at scales of microns or submicrons. In this paper, the size dependent behavior of micropolar theory under conical indentation is studied for different indentation depths and micropolar material parameters. To illustrate the effectiveness of the micropolar theory in predicting the indentation size effect (ISE), an axisymmetric finite element model has been developed for elastoplastic contact analysis of the micropolar materials based on the parametric virtual principle. It is shown that the micropolar parameters contribute to describe the characteristic of ISE at different scales, where the material length scale regulates the rate of hardness change at large indentation depth and the value of micropolar shear module restrains the upper limit of hardness at low indentation depth. The simulation results showed that the indentation loads increase as the result of increased material length scale at any indentation depth, however, the rate of increase is higher for lower indentation depth, relative to conventional continuum. The numerical results are presented for perfectly sharp and rounded tip conical indentations of magnesium oxide and compared with the experimental data for hardness coming from the open literature. It is shown that the satisfactory agreement between the experimental data and the numerical results is obtained, and the better correlation is achieved for the rounded tip indentation compared to the sharp indentation.