Indentation Contact Research Articles

Grasping spherical deformable objects using parallel gripper with planar or concave jaws

The goal is to demonstrate that spherical concave jaws of a parallel gripper induce smaller indentation displacements and smaller contact pressures to spherical deformable objects, compared to planar concave jaws. A Festo electric parallel gripper type HGPLE-14-60 is used here to grasp spherical deformable objects with gripping forces from 0 to 50 N. It is equipped with two types of parallel almost rigid jaws: planar jaws, versus spherical concave jaws with spherical concavities of radii 75 mm and 50 mm. The advantage of using spherical concave jaws rather than planar jaws is proved analytically for a purely Hertzian theoretical spherical object, and experimentally for two spherical objects with nonlinear viscoelasticity: a tennis ball and a small deformable water ball. So, the obtained results show clearly that indentation displacements and contact pressures are smaller when using the spherical concave jaws and quantify this reduction. Further publication will concern the experimental grasping of apples and oranges using spherical concave jaws versus planar jaws.

Indentation response characteristics of a piezoelectric semiconductor layer

The interaction of piezoelectricity with semiconducting property in piezoelectric semiconductors (PSCs) can be utilized to realize the amplification and gain of elastic waves and to tune the electronic property. This not only makes PSCs have enormous potential in multifunctional electronic devices, but also raises many multi-field coupled problems that need to be investigated. This paper considers the axisymmetric frictionless indentation responses of a PSC layer, which is perfectly bonded to a rigid substrate and acted on by a rigid spherical indenter. While both the indenter and the rigid substrate are assumed to be electrically insulating, the interaction of piezoelectricity and semiconducting property of a PSC layer is fully taken into consideration. By the Hankel integral transformation, the indentation problem is reduced to a Fredholm integral equation of the second kind, which is solved numerically. For the PSC ZnO layer, the numerical results for the indentation force, electric potential and contact radius are presented to systemically explore the effect of the layer thickness, indenter size and semiconducting property on the response of the PSC layer under indentation. It is found that the critical thickness, at which the thickness effect may be neglected, is dependent on the indentation depth. The influence range of semiconducting property on indentation response is related to the thickness of the PSC layer. Furthermore, the theoretical results based on the singular integral equation method are verified by the finite element simulation. This study is useful for a better understanding of the interaction between piezoelectricity and semiconducting property of PSC materials, which has potential value for developing indentation techniques to extract the coupling characteristics of PSC materials.

Graphene‐Induced Surface Softening and Nanostructure Evolution of Platinum Foils

While it has been previously accepted that graphene growth on metal films by chemical vapor deposition (CVD) protects the surfaces by stiffening and hardening, in this study, an unusual opposite effect is reported. Herein, we use nanoindentation to study the mechaniported. Herein, we use nanoindentation to study the mechanical behavior of graphene‐covered platinum foils. Two graphene growth recipes using undiluted and diluted methane flow are studied, aiming to achieve a bulk or a surface‐mediated graphene growth mechanism, respectively. Contrary to previous reports, a 17% decrease is observed in the elastic modulus of the Pt surfaces when covered by graphene compared to graphene‐free regions for both recipes, when using the real indentation contact area extracted via atomic force microscopy (AFM) for the estimation. By performing cross‐sectional transmission electron microscopy (TEM), subsurface multilayers responsible for the decrease in stiffness are revealed and these observations and the mechanism of layer formation are explained. Hence, in this study, it is highlighted that surface stiffening of metals by graphene CVD has exceptions, especially in the case of metals with high carbon solubility. Moreover, in this study, approaches for combining cross‐sectional TEM, topological scans from AFM, and raw load–displacement data from nanoindentation to provide a complete, multiscale elucidation of the mechanical behavior of a material surface are described.

Application of Artificial Intelligence Technology for Prompt Diagnosis of Cast Iron Mechanical Properties

Kinetic indentation is widely used to measure physical and mechanical properties of materials as one of the most universal methods for non-destructive testing. This paper uses the latest advances in artificial intelligence and capabilities of the Python programming language libraries allowing to carry out accurate measurements of cast iron hardness based on the data of the material’s micro-impact loading diagram. It has been shown that use of machine learning allows eliminating gross errors and reducing the error of indirect hardness evaluation in several times – down to 10 units according to Brinell HB. It has also been established that formation of additional features for training models (based on traditionally used characteristics: penetration depths, indenter movement speed and contact forces at certain points in time) has a positive effect on the accuracy of measurements, but amount of measurements should also be optimized. Feasibility of effective use of machine learning to evaluate hardness has been demonstrated by comparing of calculated hardness values with data obtained with standard testing methods. Advantage of the developed testing method is the fact that the developed algorithms can be used for prompt diagnostics of cast iron hardness using existing equipment. It is appropriate to extend the proposed approach for determination of other mechanical properties of cast iron: yield strength, strain hardening index, creep, relaxation, determined by indentation methods.

A modified PODI-RBF method to improve the accuracy of local solutions for real-time finite element simulations of indenter contact problems

In this paper, a novel method is proposed to improve the accuracy of local solutions of the PODI-RBF method for real-time finite element (FE) simulations of indenter contact problems. In the offline stage, proper orthogonal decomposition (POD) basis vectors and coefficients are extracted from solution snapshots collected from full-order FE simulations of indenter contact problems with training contact locations and indentation depths. In the online stage, RBF interpolation is used to estimate POD basis vectors and coefficients for a new contact loading. Although the POD with interpolation (PODI) method using RBFs is very useful for obtaining FE solutions of indenter contact problems in real time, local solutions near a new contact location are less accurate when a new contact location is not close to the training contact locations. To improve the accuracy of local solutions near a new contact location, the first POD basis vector is replaced by the shifted first POD basis vector for the closest training contact location to the new contact location. Numerical results show that the modified PODI-RBF method is efficient and effective to achieve real-time FE simulations of indenter contact problems while improving the accuracy of local solutions near contact locations.

Snap-through eversion of axisymmetric shells under contact indentation

In this paper, we systematically investigate the stability of an axisymmetric shell and the snap-through eversion induced by indentation through a discrete numerical approach. To capture the intricate interplay between the geometric and boundary nonlinearities during contact actuation, we employ the discrete axisymmetric shell model accompanied by the incremental potential formulation for our analysis. Our results reveal that the indentation response of a spherical shell can be classified into three groups, i.e. monotonous, monostable and bistable behaviours, whose boundaries can be characterized by a simple scaling law. We further discover that, for bistable shells, the snap-through eversion happens at a critical state where the configurations are universal, which is independent of the indenter size and can be captured by a simple geometric model. One interesting prediction of our model is that, with increasing indenter size, the contact state between the shell and indenter changes from conformal contact to partial separation, which is validated by a finite element method simulation. Our findings may provide explanations for some biophysical phenomena (e.g. cell fusion) and can also guide optimal designs of intelligent structures (e.g. soft actuators and soft robots).

Compressive failure of thermally strengthened glass spheres — Why are Prince Rupert's drops so strong?

This paper aims to elucidate the exceptional high strength of Prince Rupert's Drops (PRDs). PRDs are idealized as thermally strengthened Glass Spheres (SGSs), and their compressive failure mechanisms are investigated experimentally and numerically. The distributions of residual stress within SGS specimens are quantitatively characterized using an integrated photo-elastic method. Uniaxial compression tests conducted on these specimens reveal that the compressive residual stress present on the sphere's surface significantly enhances its strength. High-speed video images demonstrate that SGSs fail at the equatorial region, in contrast to annealed glass spheres (AGS) which typically fracture near the Hertzian contact zone. Numerical simulations suggest that the residual stress mitigates the maximum principal stress on the surface of SGSs, thereby impeding the development of flaws on the surface of the specimens. Ultimately, failure of SGS specimens under pressure occurs due to the “squeezing” effect, in contrast to AGSs which commonly fail due to contact indentation.

Ladybug-inspired hierarchical composite adhesives for enhanced surface adaptability

Abstract Enhanced adhesion on rough surfaces is highly desired for a wide range of applications. On the other hand, surface roughness compatibility and structure stability are two critical but competing factors for biologically-inspired dry adhesives in the real world. Inspired by ladybug, a hierarchical structural composite dry adhesive (denoted as PP-M) with enhanced robustness on surface roughness is developed, which is composed of a thin compliant contact layer (a thin soft polydimethylsiloxane (PDMS) film supported discretely by PDMS micropillars) and a rigid bottom layer magnetorheological elastomers (MREs). The PP-M shows a high pull-off strength of 8.2 N cm−2 on a smooth surface and nano-scale rough surface at a mild preload (2 N cm−2). For micro-scale rough surfaces, the PP-M exhibits better surface adaptability compared to the double-layered adhesive (PDMS on MRE) without micropillar support. The increased compliance of the contact layer also leads to a 2.11 fold superior pull-off strength at a wider range of roughness (Sq > 2.23 μm). Element analysis confirms PP-M’s enhanced adaptability, attributed to deeper indentation and lower contact stress. This hierarchical composite structure in PP-M, characterized by a ‘soft on top and hard on bottom’ stiffness distribution, synergizes the flexible contact layer with the stiff MRE bottom layer, leading to superior adhesive properties. The results provide a new reference for achieving enhanced adhesion on rough surfaces.

Investigation of the effects of graphene on Al0.3CoCrFeNi high entropy alloy/3graphene composite materials based on different crystal structures

The influence of graphene layers and crystal structure types on the nanoindentation reinforcement mechanism of Al0.3CoCrFeNi high-entropy alloy/graphene (HEA/Gp) composite materials was studied using molecular dynamics (MD) simulations. The results indicate that the influence of graphene layers on composite materials is related to the position of the indenter. Before the indenter contacts the graphene layer, some dislocations are absorbed by the graphene, unable to form dislocation cells and dislocation locks to hinder the deformation of the matrix, resulting in the hardness of the composite material being lower than that of the HEA matrix. After the indentation contacts the graphene layer, dislocations can penetrate the graphene to form a high-density dislocation cell. Due to graphene's excellent deformation resistance, the composite material's load-bearing capacity is much greater than that of the HEA matrix. In addition, stress propagates along the grain boundaries in polycrystalline and twinned polycrystalline structures. Grain boundaries decrease the material strength, while twinned boundaries can refine grain size and enhance grain stability. Additionally, composite materials' elastic recovery increases first and then decreases with the increase in graphene layers and twinning. The hardness of the material shows an anomalous phenomenon about grain size following a Hall-Petch relationship. When the angle between graphene layers is 0, the stress distribution inside the material is most uniform.

Surface effect on the partial-slip contact of a nano-sized flat indenter

The partial-slip contact at nano-scale is always influenced by a surface effect. A new model based on the Gurtin-Murdoch (G-M) surface elasticity theory is proposed in this paper to study the partial-slip contact behavior of a rigid flat nano-indenter on an elastic half-space. The surface effect in the partial-slip contact is characterized via a non-classical boundary condition involving a surface-induced normal traction related to the residual surface stress and a surface-induced tangential traction related to the surface elasticity, the influences of which on stress and displacement fields and the stick-slip state at the contact surface are investigated. It is found that, with the increase of residual surface stress, both the normal pressure and vertical and horizontal displacements in the contact zone decrease, the relative slip between indenter and substrate reduces and the stick region is enlarged. Such effects are basically attributed to the action of the surface-induced normal traction opposite to the externally applied compression. However, the increase of surface elastic constants is conductive to the relative slip and results in a shrinkage of the stick region, which is attributed to the action of the surface-induced tangential traction opposite to the frictional stress. An interesting phenomenon is further unveiled that, when the frictional coefficient increases, the dominant role in affecting the stick-slip state changes from the surface-induced tangential traction to the normal one, thus inspiring a feasible route to manipulate the surface effect by tuning the frictional coefficient of substrate. The present research enables one to better understand the partial-slip contact behavior of nano-indenters, which is of guiding value for anti-wear designs in nano-mechanical devices.

Effective characterization for the dynamic indentation and plastic parameters acquisition of metals

As a fundamental test technique for the mechanical properties of materials, indentation shows broad application prospects. Compared to the well-studied quasi-static indentation, relatively few and incomplete studies on the dynamic indentation test and characterization have been performed. In this work, a dynamic indentation test technique based on the split Hopkinson pressure bar system is developed, and the corresponding “three-wave method” is proposed to effectively acquire the time-resolved dynamic indentation load and depth. Systematic indentation tests under different loading rates and indenter cone angles are conducted on typical metal materials such as Cu, α-Fe, and α-Ti. Based on the dynamic indentation contact stiffness analysis and indentation theory the indentation hardness under different loading conditions are determined. A procedure for plastic parameter inversion of metal materials, including strain hardening and strain rate strengthening terms based on dynamic indentation, is provided. The effectiveness is verified by the traditional compression test results, providing a new method for characterizing the dynamic mechanical properties of metal materials.

Collagen Networks under Indentation and Compression Behave Like Cellular Solids.

Simple synthetic and natural hydrogels can be formulated to have elastic moduli that match biological tissues, leading to their widespread application as model systems for tissue engineering, medical device development, and drug delivery vehicles. However, two different hydrogels having the same elastic modulus but differing in microstructure or nanostructure can exhibit drastically different mechanical responses, including their poroelasticity, lubricity, and load bearing capabilities. Here, we investigate the mechanical response of collagen-1 networks to local and bulk compressive loads. We compare these results to the behavior of polyacrylamide, a fundamentally different class of hydrogel network consisting of flexible polymer chains. We find that the high bending rigidity of collagen fibers, which suppresses entropic bending fluctuations and osmotic pressure, facilitates the bulk compression of collagen networks under infinitesimal applied stress. These results are fundamentally different from the behavior of flexible polymer networks in which the entropic thermal fluctuations of the polymer chains result in an osmotic pressure that must first be overcome before bulk compression can occur. Furthermore, we observe minimal transverse strain during the axial loading of collagen networks, a behavior reminiscent of open-celled cellular solids. Inspired by these results, we applied mechanical models of cellular solids to predict the elastic moduli of the collagen networks and found agreement with the moduli values measured through contact indentation. Collectively, these results suggest that unlike flexible polymer networks that are often considered incompressible, collagen hydrogels behave like rigid porous solids that volumetrically compress and expel water rather than spreading laterally under applied normal loads.

Accurate vertical nanoelectromechanical measurements

Piezoresponse Force Microscopy (PFM) is capable of detecting strains in piezoelectric materials down to the picometer range. Driven by diverse application areas, numerous weaker electromechanical materials have emerged. The smaller signals associated with them have uncovered ubiquitous crosstalk challenges that limit the accuracy of measurements and that can even mask them entirely. Previously, using an interferometric displacement sensor (IDS), we demonstrated the existence of a special spot position immediately above the tip of the cantilever, where the signal due to body-electrostatic (BES) forces is nullified. Placing the IDS detection spot at this location allows sensitive and BES artifact-free electromechanical measurements. We denote this position as xIDS/L=1, where xIDS is the spot position along the cantilever and L is the distance between the base and tip. Recently, a similar approach has been proposed for BES nullification for the more commonly used optical beam deflection (OBD) technique, with a different null position at xOBD/L≈0.6. In the present study, a large number of automated, sub-resonance spot position dependent measurements were conducted on periodically poled lithium niobate. In this work, both IDS and OBD responses were measured simultaneously, allowing direct comparisons of the two approaches. In these extensive measurements, for the IDS, we routinely observed xIDS/L≈1. In contrast, the OBD null position ranged over a significant fraction of the cantilever length. Worryingly, the magnitudes of the amplitudes measured at the respective null positions were typically different, often by as much as 100%. Theoretically, we explain these results by invoking the presence of both BES and in-plane forces electromechanical forces acting on the tip using an Euler–Bernoulli cantilever beam model. Notably, the IDS measurements support the electromechanical response of lithium niobate predicted with a rigorous electro-elastic model of a sharp PFM tip in the strong indentation contact limit [deff≈12pm/V, Kalinin et al., Phys. Rev. B 70, 184101 (2004)].

Correction of substrate-induced thin-film modulus deviations in nanoindentation measurements

The influence of substrate effects on the accurate measurement of mechanical properties of thin films remains to be clarified. Therefore, in this study, (AlCrNbSiTi)N thin films were deposited on four substrates—Si, SiO2, sapphire (Al2O3), and Ni—with varying thicknesses. Nanoindentation testing was conducted to measure the mechanical properties, revealing variations in the modulus of the thin film depending on the substrate and film thickness. To address these variations, we introduced the concept of two springs connected in series, following Hooke's law, to determine the elastic deformations of the thin film and its underlying substrate. By applying linear regression to four datasets corresponding to equivalent film thicknesses but different substrates, substrate-induced measurement errors were effectively mitigated, and the true modulus of the thin film was determined. Furthermore, we introduced a k value to represent the ratio of the actual force on the substrate to the force exerted by the indenter. Our findings indicate that even when the indenter contact depth is less than 1% of the film thickness, the substrate is still subjected to 7.6% of the applied force. This underscores the non-negligible nature of substrate elastic deformation during the measurement process and importance of correcting for substrate-induced variations in thin-film moduli. The findings can contribute to advancing the understanding of mechanical properties in ceramics and related materials.

Contact Analysis of CNT-FGM Nanocomposite Using Indentation Contact Model

In the present paper, carbon nanotube (CNT) reinforced functionally graded (FG) material matrix nanocomposite (CNT-FGM) is indented with a rigid conical indenter and the contact behaviour of the CNT-FGM nanocomposite is analyzed in the context of variation in gradation parameter and wall thickness of the CNTs. The study is conducted on the basis of finite element model, which is developed utilizing Ansys Parametric Design Language (APDL) codes in commercial finite element modelling platform, ANSYS. The material model is developed considering the CNTs are uniformly distributed in the graded matrix, whose elastic properties vary along the direction of indentation. The gradation model, corresponding to the matrix material, adopted for the present study is a power law function. In this study, elastically graded material (EGM)matrix CNT reinforced CNT-FGM nanocomposite has been examined, varying the elastic gradation parameter (+2, 0 and -2) of the matrix material. Additionally, effect of the variations in CNT wall thickness are explored, while maintaining other parameter constant in the nanocomposite. A frictionless contact between the CNT-FGM substrate and rigid indenter is simulated for both loading and unloading process. Prior to extracting pertinent results, the current model undergoes validation by comparing its outcomes with those published in the literature. It is observed that the contact force-displacement plots align satisfactorily for both sets of data. Various contact parameters, such as contact force, contact area, contact pressure distribution, stress distribution, and deformation behavior during the indentation contact, are then extracted from the analysis. The observation indicates that positive gradation parameter result in superior contact properties compared to negative gradation parameters as well as without gradation.

Investigation of the Material Elasto-Plastic Response under Contact Indentation: The Effect of Indenter Material

When dealing with joints and bearings, high pressures localised at the contact interface lead to residual plastic strain. The present paper combines numerical simulations and experimental tests to investigate the role of the material constitutive law in the indentation process. Numerical indentation tests between similar materials showed a good agreement with the experiments when classical material laws recovered from tensile-compressive tests on bulk samples were accounted for. On the other hand, when simulating indentation between different materials in contact, the comparison between the numerical and experimental results highlighted the limits of using classical material laws. Bilinear material laws were then derived for different steel materials (ASP 2060 PM, 100Cr6, 440C, Marval X12, and Z15 CN17-03) in contact with a ceramic indenter, leading to the correct simulation of the residual indentation profiles (error less than 5%). The proposed approach to determine suitable material laws for indentation between dissimilar materials can be further applied when dealing with applications involving contacts undergoing local plastic deformation.

Study of viscoelastic damage and micromechanism of polyurethane in freeze-thaw cycle environment

To investigate the viscoelastic properties of polyurethane under the action of freeze-thaw cycles. Polyurethane specimens excessed examined using atomic force microscopy, nanoindentation tests, and differential scanning calorimetry (DSC) after 0, 3, 5, and 7 freeze-thaw cycles. The molecular structure and property damage process was also investigated using molecular dynamics. The findings of molecular simulations revealed that the freeze-thaw cycle causes the aggregated system to disperse within the polyurethane molecule, resulting in an increase in its modulus. The testing findings revealed that the roughness of the polyurethane surface steadily decreased as the number of freeze-thaw cycles increased, as did the adhesion to various substrates. In the test results of nanoindentation, the elastic modulus showed an increasing trend, and the contact indentation depth gradually decreased. This suggests that freeze-thaw cycles impair polyurethane's elastic and flexible characteristics. The freeze-thaw cycle raised the melting temperature of polyurethane in the differential scanning calorimetry experiment findings. This confirms the experimental findings of increased elastic modulus and hardness in nanoindentation. In conclusion, further study may be undertaken to change polyurethanes by adding water-repellent compounds to them, which can be accomplished by modifying the molecular structure inside the polyurethanes to withstand environmental harm. The findings of this research lay a theoretical foundation for the resilience of polyurethane materials to environmental deterioration in a variety of industries, such as construction, where freeze-thaw cycles exist.

Softening of the Hertz indentation contact in nematic elastomers

Polydomain liquid crystalline (nematic) elastomers have highly unusual mechanical properties, dominated by the dramatically nonlinear stress–strain response that reflects stress-induced evolution of domain patterns. Here, we study the classical Hertz indentation problem in such a material. Experimentally, we find that polydomain nematic elastomers display a smaller exponent than the classical 3/2 in the load vs. indentation depth response. This is puzzling: asymptotically a softer stress–strain response requires a larger exponent at small loads. We resolve this by theory where three regimes are identified — an initial elastic regime for shallow indentation that is obscured in experiment, an intermediate regime where local domain pattern evolution leads to a smaller scaling in agreement with experiments, and a final stiffening regime where the completion of local domain evolution returns the response to elastic. This three-regime structure is universal, but the intermediate exponent is not. We discuss how our work supports a new mechanism of enhanced adhesion for pressure-sensitive adhesion of nematic elastomers.

Solitary wave-based site-specific bone quality assessment: A numerical study of the proximal femur

We examine numerically the feasibility of using a relatively new solitary wave-based non-destructive test (NDT) method for site-specific bone quality assessment. Towards this end, we present numerical predictions of the effective elastic modulus of trabecular bone in the proximal femur using highly nonlinear solitary waves (HNSWs) propagating in a one-dimensional chain of spherical steel particles. A computational bone reconstruction technique, enabled through topology optimization, is developed to generate high-resolution finite-element models representing the complex architecture of the trabecular network in the femoral neck region of the proximal femur. The reconstructed bone microstructure models are then used as the inspection medium in a virtual NDT setup in the form of a hybrid discrete-element/finite-element (DE/FE) model, capable of simulating the propagation of HNSWs in the granular chain and their interaction with the bone microstructures. By inserting a face sheet between the granular chain and the porous trabecular bone model, our calculations evince that dynamic loading by the incident solitary wave results in nearly uniaxial deformation of the bone microstructure (rather than localized contact indentations), and this is shown to enhance the accuracy and reliability of the solitary wave-based prediction of the bone’s effective elastic modulus. Using the delay of the primary reflected solitary wave in the estimation of the elastic modulus of bone, we are able to estimate the effective elastic moduli of the porous bone models with adequate accuracy. Based on these numerical findings, we believe that solitary wave-based non-destructive evaluation of computationally reconstructed artificial bone models could form the baseline for advanced bone quality assessment tools.

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.