Indentation Depth Research Articles

Numerical and experimental study of influence function in magnetorheological finishing (MRF) of freeform surface

In the present work, a dynamic viscosity model is proposed based on the varying magnetic flux density of the neodymium permanent magnet along its width. The proposed viscosity model is helpful in analysing the influence function in a better way as compared to standard non-Newtonian fluid models. During the finishing process, the research of influence function aids in establishing the right range of process parameters. MR fluid flow on the freeform surface is examined numerically and experimentally to better understand the influence function. The flow behaviour of the MR fluid is investigated using the three-dimensional (3D) computational fluid dynamics (CFD) simulation, wall shear stress and dynamic pressure are estimated on the Oxygen-free high conductivity (OFHC) copper for various process parameters (working gap and rotational speed). On the convex and concave sections of a freeform surface, indentation depth is estimated for various process parameters using the results of dynamic pressure and empirical relation. Finishing tests are performed to investigate forces (tangential and normal) and indentation depth on the workpiece, and the results are evaluated.

Precise determination of Young’s modulus of amorphous CuZr/nanocrystalline Cu multilayer via nanoindentation

Extracting mechanical data of thin films on rigid substrates using nanoindentation is compromised by the mechanical properties of underlying substrates, which may falsify the obtained results. With ongoing miniaturization, the substrate influence becomes more pronounced. In this study we present an experimental approach to extract the true Young’s modulus of crystalline-amorphous multilayers by means of nanoindentation. We used 1 µm thick multilayers comprised of amorphous CuZr and nanocrystalline Cu. All films were deposited onto two rigid substrate types with Young’s moduli below and above the ones expected for the deposits (film-to-substrate hardness and elastic moduli ratios between 0.3 to 1.1 and 0.6 to 1.5, respectively). Linear extrapolation of indentation data to zero indentation depth allows to precisely determine the real film’s Young’s modulus. Same investigations were performed on monolithic Cu and CuZr films of same thickness. While the hardness values change with the variation of the bilayer thickness of the multilayer structures, the Young’s modulus is not affected by the interfaces.Graphical abstract

Nanoindentation study of δ-phase zirconium hydride using the crystal plasticity model

Zirconium hydride precipitation degrades the fracture toughness of nuclear reactor fuel cladding tube. Due to the difficulty of experiment, deep understanding on mechanical properties of zirconium hydride via numerical approaches is in a great need. To study the mechanical properties of zirconium hydride, the crystal plasticity finite element model considering geometrically necessary dislocations evolution is used to simulate the nanoindentation deformation behavior of single-crystal δ-hydride. The parameters in the crystal plasticity model are calibrated by Young's modulus along different crystallographic orientations and experimental stress-strain data at different strain rates. The predicted polycrystalline Young's modulus, Poisson's ratio, and nanoindentation hardness are in good agreement with the experimental results. The simulation results show that the nanoindentation hardness strongly depends on the indentation depth when it is smaller than 500 nm. Furthermore, the effects of crystallographic orientation and zirconium matrix on the indentation results are also studied. We find that the nanoindentation hardness of δ-hydride is slightly orientation dependent. For smaller hydride size or larger indentation depth, the surrounding zirconium matrix undergoes plastic deformation, which leads to a significant underestimate of the nanoindentation hardness of the hydride.

Nanoindentation‐induced evolution of atomic‐level properties in silicate glass: Insights from molecular dynamics simulations

AbstractIndentation has been widely used for investigating the mechanical behavior of glasses. However, how the various microscopic properties (such as atomic structure and mechanics) of glass evolve from the immediate contact with the indenter to the far‐field regions, and how these observables are correlated to each other remain largely unknown. Here, using large‐scale molecular dynamics simulations, we investigate the response of a prototypical sodium silicate glass under shape contact load up to an indentation depth of 25 nm. Both the short‐ and intermediate‐range structures are found to exhibit notable changes below the indent, indicating that indentation deformation induces a more disordered and heterogeneous network structure. In addition, we find that the indentation‐induced changes of local properties all exhibit an exponential decaying behavior with increasing distance from the indent. Comparison of the characteristic decay lengths of these local properties indicates that the structural origins of shear flow and densification are the changes of the network modifier's coordination environment and the inter‐tetrahedral connection, respectively. The decay of densification is considerably slower than that of shear strain, implying that the former might contribute more to the deformation at the far‐field regions. Our findings not only contribute to an atomistic understanding of the indentation response of silicate glasses but also pave the way toward rational design of damage‐resistant glassy materials.

Shear-induced directional grain growth in Ag nanocrystalline films under nanoindentation

Nanocrystalline metallic materials exhibit different mechanical properties compared with coarse-grained counterparts. In essence, the high density of grain boundaries contributes to significant portion of plasticity, which is more pronounced in thin films. Due to intrinsic geometric limitation, the responses of nanocrystalline films under shear-dominant loading are seldom understood. Here, we take Ag film as an example, with a larger indentation depth than film thickness, the deformation beneath the pyramidal surfaces of the indenter is considered to be dominated by in-plane shear stress with gradient distribution. The shear-dominant loading leads to directional grain elongation within indentation region, accompanied with frequent formation of nanotwins across the grain boundaries. These findings enrich our understanding of stress induced grain growth under nanoindentation, and provide a novel way to study shear-dominated plastic deformation in metallic nanocrystalline films.

Research on Opening Performance of Metal Diaphragm in Double Pulse Solid Rocket Motor

In order to investigate the effect of different double-pulse solid rocket motor metal diaphragm configurations on opening performance, a compartment device is designed. A modified Johnson-Cook principal structure model and damage criterion are used to simulate the pressure-bearing forces of the compartment structure based on finite element software. In order to obtain the parameters of J-C model, Quasi-static tensile tests at the strain rates of 10−4~10−1s−1 and temperatures of 300K~450K were carried out on 2A12 aluminium alloy dumbbell-type specimens. By varying the depth and width of the indentations on the metal diaphragm, and the finite element numerical simulation of the operation of the compartment under the action of solid rocket motor I and II pulses is also carried out. The results show that when the indentation depth is large, the indentation depth is the main factor affecting the opening pressure of the diaphragm; when the indentation depth decreases, the influence of the indentation width on the opening pressure of the diaphragm is more obvious.

Computational modeling reveals a vital role for proximity-driven additive and synergistic cell-cell interactions in increasing cancer invasiveness.

Solid-tumor cell invasion typically occurs by collective migration of attached cell-cohorts, yet we show here that indirect cell-interactions through the substrate can also drive invasiveness. We have previously shown that well-spaced, invasive cancer cells push-into and indent gels to depths of 10 µm, while closely adjacent, non-contacting cancer cells may reach up to 18 µm, potentially relying on cell-cell interactions through the gel-substrate. To test that, we developed finite element models of indenting cells, using experimental gel mechanics, cell mechanostructure, and force magnitudes. We show that under 50-350 nN of combined traction and normal forces, a stiff nucleus-region is essential in facilitating 5-10 µm single-cell indentations, while uniformly soft cells attain 1.6-fold smaller indentations. We observe that indentation depths of cells in close proximity (0.5-50 µm distance) increase relative to well-spaced cells, due to additive, continuum mechanics-driven contributions. Specifically, 2-3 cells applying 220 nN normal forces gained up to 3% in depth, which interestingly increased to 7.8% when two cells, 10 µm apart, applied unequal force-magnitudes (i.e., 220 and 350 nN). Such additive, energy-free contributions can reduce cell mechanical energy -output required for invasiveness, yet the experimentally observed 10-18 µm depths likely necessitate synergistic, mechanobiological changes, which may be mechanically triggered. We note that nucleus stiffening or cytoplasm softening by 25-50% increased indentation depths by only 1-7%, while depths increase nearly linearly with force-magnitude even to two-fold levels. Hence, cell-proximity triggered, synergistic and additive cell-interactions through the substrate can drive collective cancer-cell invasiveness, even without direct cell-cell interactions. STATEMENT OF SIGNIFICANCE: Metastatic cancer invasion typically occurs collectively in attached cell-cohorts. We have previously shown increased invasiveness in closely adjacent cancer cells that are able to push-into and indent soft-gels more deeply than single, well-spaced cells. Using finite element models, we reveal mechanisms of cell-proximity driven invasiveness, demonstrating an important role for the stiff nucleus. Cell-proximity can additively induce small increase in indentation depth via continuum mechanics contributions, especially when adjacent cells apply unequal forces, and without requiring increased cell-mechanical-energy-output. Concurrently, proximity-triggered synergistic interactions that produce changes in cell mechanics or capacity for increased force-levels can facilitate deep invasive-indentations. Thus, we reveal concurrent additive and synergistic mechanisms to drive collective cancer-cell invasiveness even without direct cell-cell interactions.

The Truncated Cone Effect in AFM Nanoindentation on Soft Materials

Background: Atomic Force Microscopy (AFM) nanoindentation is the principal method for the characterization of soft materials at the nanoscale. In most cases, pyramidal tips are used and approximated to perfect cones. However, the extended use of the AFM tip may alter its sharpness. Objective: In many cases, a truncated cone shape is appropriate for tip modeling. In this technical note, the equation that relates the force with the indentation depth when indenting an elastic halfspace using a truncated cone is derived. Methods: The nanoindentation equation for a truncated cone tip is derived using the fundamental differential equation that relates the sample’s contact stiffness with Young’s modulus. Results: When fitting Sneddon’s equation (which is valid for a perfect cone) on data obtained using a truncated cone-shaped AFM tip, the results show a ‘pseudo-softening’ behavior. Conclusion: The AFM tip's sharpness in nanoindentation experiments is a crucial parameter for obtaining the correct mechanical patterns of unknown samples.

Finite element based indentation contact analysis of SWCNT nano-composite

The focus of the present study is to simulate the indentation type contact behaviour of single walled carbon nanotube (SWCNT) based nanocomposite. The contact system consists of a deformable Aluminium matrix, reinforced with a group of SWCNTs, and a conical indenter which is assumed as rigid. Downward and upward displacement is imparted on the conical indenter in order to simulate the loading and unloading phases of the contact. The model has been developed using APDL code on the ANSYS platform. Adequacy and validity of the model has been established by comparison with results from already published papers available in literature and the matching between the two sets of results is found to be excellent. In terms of results, contact forces, contact area, contact pressure and deformation behaviour are extracted from the analysis with varying wall thickness of CNTs. Detailed analysis of the obtained results has been carried out and it is found that sink in and pile up (in one particular scenario) behaviour is exhibited. It is also found that due to high deformation of the tubes at high indentation depth, there is material flow towards the axis of symmetry and creation of small elastic zones in the matrix material.

Dynamic responses of metal foam sandwich beam under repeated impacts considering impact location and face thickness distribution

Owing to the excellent mechanical performance, the metal foam sandwich structures have potential applications in the design of protective equipment, which can improve the impact resistance of engineering structures. In this paper, the nonlinear finite element model is employed to investigate the dynamic behaviors of metal foam sandwich beam (MFSB), and the accuracy of the finite element method is verified by repeated impact tests. In addition, the effects of impact location and face thickness on the dynamic behavior of the MFSB are examined. Results show that, as the distance from the impact position to the middle span of the beam increases, the deflections of face sheets decrease gradually, and the loading and unloading stiffness increases. The thickness of front face sheet affects the depth of indentation, while the total thickness of the front and back face sheets decides the overall deformation, loading and unloading stiffness. Overall, as the impact number increases, the influences of impact location and face thickness on the dynamic behavior of MFSB enhances gradually.

Simulation and modeling of magnetorheological shear thickening polishing processes for slender tube

Slender tubes have widespread applications in the fields of medical industries, aerospace, and chemical industries. In present study, a magnetorheological shear thickening polishing (MSTP) method was proposed to improve the surface quality of slender tube. The magnetic field generator integrated with four-pair electromagnetic coils and permanents is designed, in which the rheological properties of the polishing media and the polishing forces are regulated precisely. The magnetic flux density is explored based on finite element analysis (FEA). A mathematical model of magnetic force is established on single abrasive particle. Computational fluid dynamics (CFD) simulations of the polishing media with six cases were performed to investigate the shear stress. The effects of various processing conditions, including the magnetic flux density, the inlet pressure and the rotational speed, on rheological properties (shear rate, shear stress, and profile velocity) are investigated using the optical polishing media (Case 5). A material removal rate model was established based on calculations of the indentation depth and indentation diameter formed by abrasive particles. The results show that the indentation depth of t=7.1×10−14 m and surface roughness peaks change of 6.78×10−8 m is obtained under the shear stress of 10206 Pa. The feasibility of the MSTP method was demonstrated by predicting the initial and machined surfaces using Gaussian filtering.

Novel Process Modeling of Magnetic-Field Assisted Finishing (MAF) with Rheological Properties

The performance of a magnetic-field-assisted finishing (MAF) process, an advanced surface finishing process, is severely affected by the rheological properties of an MAF brush. The yield stress and viscosity of the MAF brush, comprising iron particles and abrasives mixed in a liquid carrier medium, change depending on the brush’s constituents and the applied magnetic field, which in turn affect the material removal mechanism and the corresponding final surface roughness after the MAF. A series of experiments was conducted to delineate the effect of MAF processing conditions on the yield stress of the MAF brush. The experimental data were fitted into commonly used rheology models. The Herschel–Bulkley (HB) model was found to be the most suitable fit (lowest sum of square errors (SSE)) for the shear stress–shear rate data obtained from the rheology tests and used to calculate the yield stress of the MAF brush. Processing parameters, such as magnetic flux density, weight ratio of iron and abrasives, and abrasive (black ceramic in this study) size, with p-values of 0.031, 0.001 and 0.037, respectively, (each of them lower than the significance level of 0.05), were all found to be statistically significant parameters that affected the yield stress of the MAF brush. Yield stress increased with magnetic flux density and the weight ratio of iron to abrasives in MAF brush and decreased with abrasive size. A new process model, a rheology-integrated model (RM), was formulated using the yield stress data from HB model to determine the indentation depth of individual abrasives in the workpiece during the MAF process. The calculated indentation depth enabled us to predict the material removal rate (MRR) and the instantaneous surface roughness. The predicted MRR and surface roughness from the RM model were found to be a better fit with the experimental data than the pre-existing contact mechanics model (CMM) and wear model (WM) with a R2 of 0.91 for RM as compared to 0.76 and 0.78 for CMM and WM. Finally, the RM, under parametric variations, showed that MRR increases and roughness decreases as magnetic flux density, rotational speed, weight ratio of iron to abrasive particles in MAF brush, and initial roughness increase, and abrasive size decreases.

Small-depth nanoindentation studies of an additively manufactured titanium alloy: Anisotropic nanomechanical properties and correlation with microscopic mechanical behaviour

Nanoindentation has been widely used to measure local mechanical properties of heterogeneous materials. The nanohardness (H), typically measured at indentation depths more than 200 nm, cannot be well correlated with the global mechanical behaviour of tested materials. Here, we study the H of the α phase in an additively manufactured titanium alloy using a nanoindentation mapping method with small indentation depths (< 200 nm). The results show that the α grains with various crystal orientations exhibit two groups of H values, different from a wide range of H values measured by conventional large-depth nanoindentation. The two groups of H values are attributed to a contribution of elasticity in the measurement of the H values using the small-depth nanoindentation. Furthermore, we correlate the H with the microscopic mechanical behaviour of α grains: With respect to the tensile direction, hard α grains are plastically deformed by shear banding and soft α grains are deformed by dislocation slip.

Friction in Adhesive Contacts: Experiment and Simulation

An experimental study of the process of friction between a steel spherical indenter and a soft elastic elastomer, with a strongly pronounced adhesive interaction between the surfaces of the contacting bodies, is presented. We consider sliding of the indenter at low speed (quasi-static contact) for different indentation depths. The forces, displacements and contact configuration as functions of time were recorded. The most important finding is that under conditions of uni-lateral continuous sliding, the tangential stress in the contact area remains constant and independent on the indentation depth and details of loading. We suggest a simple numerical model in which the elastic substrate is considered as a simple elastic layer (thus reminding a two-dimensional elastic foundation), although with in-plane elastic interactions. It is found that this model leads to the dynamic scenarios which qualitatively resemble the experimentally observed behavior of the considered system.

Research on Determining Elastic-Plastic Constitutive Parameters of Materials from Load Depth Curves Based on Nanoindentation Technology.

It is of great significance for structural design and engineering evaluation to obtain the elastic-plastic parameters of materials. The inverse estimation of elastic-plastic parameters of materials based on nanoindentation technology has been applied in many pieces of research, but it has proved to be difficult to determine the elastic-plastic properties of materials by only using a single indentation curve. A new optimal inversion strategy based on a spherical indentation curve was proposed to obtain the elastoplastic parameters (the Young's modulus E, yield strength σy, and hardening exponent n) of materials in this study. A high-precision finite element model of indentation with a spherical indenter (radius R = 20 µm) was established, and the relationship between the three parameters and indentation response was analyzed using the design of experiment (DOE) method. The well-posed problem of inverse estimation under different maximum indentation depths (hmax1 = 0.06 R, hmax2 = 0.1 R, hmax3 = 0.2 R, hmax4 = 0.3 R) was explored based on numerical simulations. The results show that the unique solution with high accuracy can be obtained under different maximum press-in depths (the minimum error was within 0.2% and the maximum error was up to 1.5%). Next, the load-depth curves of Q355 were obtained by a cyclic loading nanoindentation experiment, and the elastic-plastic parameters of Q355 were determined by the proposed inverse-estimation strategy based on the average indentation load-depth curve. The results showed that the optimized load-depth curve was in good agreement with the experimental curve, and the optimized stress-strain curve was slightly different from the tensile test, and the obtained parameters were basically consistent with the existing research.

Interactions of CO2–H2O-coal and its impact on micro mechanical strength of coal

High temperature flue gas enhanced coalbed methane (CBM) recovery is a potential technique for improving CBM recovery efficiency and carbon sequestration, and it is of significance to carbon emission reduction in coal mine area. Previous research has demonstrated that the injection of CO2 could markedly alter the mechanical properties of coal seam, which further changes the gas flow and long-term safety of CO2 storage. Aiming at this issue, we studied the coupling effect of CO2–H2O on micro mechanical properties of coal with nanoindentation method. And the pore-fracture structure and minerals of the target sample was systematically characterized with LF-NMR and SEM to explore the influence mechanism of CO2–H2O on coal. The results show that (1) the micro strength of coal is obviously weakened after the treatment of CO2–H2O, and with an increase of the time, both the hardness and reduced modulus decreases, while the indentation depth shows an opposite trend. (2) Compared with the control group, the volumes of micropore, minipore, mesopore and macropore/microfracture in coal treated by CO2–H2O all increase in varying degrees. The increase of micropore volume is generally less than 20%. While the increases of the volumes of mesopore and macropore/microfractures are significant, with the maximum increase of 44.13% for the mesopore, and 299.58% for the macropore/microfracture. (3) Ulan coal contains a large number of calcareous minerals, which undergo chemical reaction after encountering the acid solution formed by CO2–H2O, resulting in dissolution of part of the minerals, which can be evidenced by the corrosion pits observed on the coal surface. (4) The injection of CO2 results in nonuniform swelling of the coal, which further leads to the formation of new cracks and the resultant coal strength deterioration. In addition, the acid solution formed by CO2–H2O reacts with the minerals in coal, resulting in dissolution of carbonate and other minerals in the coal, thus weakening the coal strength. The research results in this work provide basic support for the evaluation of the effectiveness of high temperature flue gas enhanced CBM and the safety of long-term CO2 storage.

Pattern characterization using topological data analysis: Application to piezo vibration striking treatment

Quantifying patterns in visual or tactile textures provides important information about the process or phenomena that generated these patterns. In manufacturing, these patterns can be intentionally introduced as a design feature, or they can be a byproduct of a specific process. Since surface texture has significant impact on the mechanical properties and the longevity of the workpiece, it is important to develop tools for quantifying surface patterns and, when applicable, comparing them to their nominal counterparts. While existing tools may be able to indicate the existence of a pattern, they typically do not provide more information about the pattern structure, or how much it deviates from a nominal pattern. Further, prior works do not provide automatic or algorithmic approaches for quantifying other pattern characteristics such as depths’ consistency, and variations in the pattern motifs at different level sets. This paper leverages persistent homology from Topological Data Analysis (TDA) to derive noise-robust scores for quantifying motifs’ depth and roundness in a pattern. Specifically, sublevel persistence is used to derive scores that quantify the consistency of indentation depths at any level set in Piezo Vibration Striking Treatment (PVST) surfaces. Moreover, we combine sublevel persistence with the distance transform to quantify the consistency of the indentation radii, and to compare them with the nominal ones. Although the tool in our PVST experiments had a semi-spherical profile, we present a generalization of our approach to tools/motifs of arbitrary shapes thus making our method applicable to other pattern-generating manufacturing processes.

Microindentation analysis of mechanical properties evolution during an artificial hydrocarbon generation process

The last decade witnessed rapid growth of shale oil and gas production. Increasing numbers of shale reservoirs have been explored and developed. Since hydrocarbon generation is an important process in forming a shale reservoir, it has attracted great attention from researchers. However, previous works mainly focus on geochemical changes during the hydrocarbon generation process, and investigations of the change of other parameters are insufficient. In this study, we intend to fill this gap in the literature by examining the mechanical properties evolution of organic-rich shales during an artificial hydrocarbon generation experiment. Continuous stiffness measurement (CSM) and microindentation test are used to measure the mechanical properties of rocks. The result of CSM shows the influence of indentation depth on Young's modulus. Three stages are identified, and a displacement of 4000 nm–6000 nm is determined to be appropriate for measuring bulk mechanical properties. Microindentation results of shales at different hydrocarbon generation stages exhibit a hill-like trend. The Young's modulus with an initial value of 42.15 GPa increases as the hydrocarbon generation proceeds, reaches a maximum value of 46.49 GPa, and then begins to decrease and reaches the lowest value of 37.41 GPa. Indentation hardness and estimated fracture toughness by an energy-based method show similar trends to Young's modulus. Scanning electron microscope observation of post-hydrocarbon-generation samples may provide an explanation of the hill-like trend.

Anisotropy of nanoindentation in copper single crystals under different orientations

The anisotropy of nanoindentation in copper single crystals is studied through experiments and simulations. Nanoindentation tests with different orientations were carried out, and the depth was 20nm-500nm. Simulations were carried out using crystal plasticity finite element method. The results show that sample with different orientations present anisotropic with increase of indentation depth. The accumulated plastic strains of the samples with different orientations are different due to the different angle between the loading direct and the normal to the slip surface. The cumulative plastic strain of oriented samples is the smallest, and orientation is the largest. The amount of slip coefficients initiated simultaneously for samples with different orientations is responsible for the differences in nanoindentation properties.

Influence of cantilever tip geometry and contact model on AFM elasticity measurement of cells.

We have measured the elastic properties of live cells by Atomic Force Microscope (AFM) using different tip geometries commonly used in AFM studies. Soft 4-sided pyramidal probes (spring constant = 12 mN/m and 30 mN/m, radius 20 nm), 3-sided pyramidal probes (spring constant = 100 mN/m, radius of curvature 65-75 nm), flat (circular) probes (spring constant = 63 mN/m, radius 290 nm) and spherical probes (spring constant = 43 mN/m, radius 5 μm) have been used. Cells (3T3 fibroblasts) having elastic moduli around 0.5 kPa were investigated. We found that cell measured stiffness shows a systematic dependence on tip geometry: the sharper the tip, the higher the average modulus values. We hypothesize that the blunter the tip, the larger the contact area over which the mechanical response is measured or averaged. If there are small-scale stiffer areas (like actin bundles) they will be easier to pick up by a sharp probe. This effect can be seen in the wider distribution of the histograms of the measured elastic moduli on cells. Furthermore, non-linear responses of cells may be present due to the high average pressures applied by sharp probes, which would lead to an overestimation of the Young's modulus. Pressure versus contact radius simulations for the different tip geometries for a 0.5 kPa sample suggested similar average pressure for Bio-MLCTs, PFQNM and cut tips, except spherical tips that showed much lower average pressure at the same 400 nm indentation. However, real data of the cells suggested different results. Using the same indentation depth (400 nm) PFQNM and Bio-MLCTs showed similar average pressure and it decreased for cut and spherical tips. The calculated contact area at 400 nm cell indentation, using the obtained apparent Young's modulus for each tip geometry, showed the following distribution: Bio-MLCTs < PFQNM < cut << spherical. In summary, tip geometry as well as average pressure and tip-sample contact area are important parameters to take into account when measuring mechanical properties of soft samples. The larger the tip radius, the larger the contact area that will lead to a more evenly distribution of the applied pressure.