Flat Punch Indentation Research Articles

Analysis of stress and deformation of an exponentially graded viscoelastic coated half plane under indentation by a rigid flat punch indenter tip

This paper solves the dynamic contact problem when a rigid flat punch indents into an exponentially graded (FG) viscoelastic coated homogeneous half-plane. A harmonic vertical force is applied to the FG coating, and the solution is obtained for the stress and displacement for both the FG viscoelastic coating and the half-plane using the Helmholtz functions and the Fourier integral transform technique. By applying specific boundary conditions, the contact mechanics problem is converted into a singular integral equation of the first kind. This equation is then solved numerically using the Gauss-Chebyshev integration formulas. The analysis provides detailed insights into how various parameters—such as external excitation frequency, loss factor ratio, Young’s modulus ratio, density ratio, Poisson’s ratio, indentation load, and punch length—affect the dynamic contact stress and dynamic in-plane stress.

Wear and Subsurface Stress Evolution in a Half-Space under Cyclic Flat-Punch Indentation

Wear is a tremendously important phenomenon, which takes place on the surfaces of two solids in contact under cyclic loads and constitutes one of the most-significant ways of failure for mechanical elements. However, it is not the only source of failure in contacting solids. The subsurface stresses should also be considered, due to the fatigue and crack initiation problems. Nevertheless, these stresses (i.e., their maximum values and distributions) evolve with the solids’ surface wear (i.e., with the load cycles) and also depend on the friction intensity. Therefore, their evolution should be properly computed to predict failures in mechanical elements under wear conditions. This work focused on the study of the evolution of the surface wear and the subsurface stress distributions generated—in an elastic half-space—by a cylindrical flat-ended punch, under cyclic indentation loading (i.e., radial fretting wear conditions). Based on a numerical scheme recently presented by the authors, this is the first time that, for this contact problem, the surface wear and subsurface stress distribution (i.e., maximum value and its location)—and its evolution—were simultaneously analyzed when orthotropic friction and fretting wear conditions were considered. The studies presented in this work were developed for purely elastic contact assumptions.

Strength determination for rough substrate-coating interfaces with three-dimensional defect structure

Quantitative information on the strength of interfaces between thin ceramic coatings and their substrates is crucial when aiming to understand their failure behavior. Many technically relevant substrate-coating interfaces are not ideally planar, but rather rough and contain stress concentrators forming three-dimensional defect structures. An example for such a realistic case, a polycrystalline diamond coating that partially penetrates voids and cavities in its Co binder-depleted WC-Co hard metal substrate, was investigated within the current work with respect to its unknown interface strength behavior. Special focus was laid on the influence of the applied load direction on the observed fracture behavior. Micromechanical specimens were produced via focused ion beam milling as geometry variants of a micro shear compression specimen with their loaded areas' relative inclination towards the substrate-coating interface varied from 0° to 88°. Specimen loading was performed until fracture with a flat punch indenter in a scanning electron microscope. The recorded fracture loads were associated with the spatial stress distributions at fracture via finite element-based analysis. A plateau of the determined maximum principal stress triggering fracture in the ceramic-ceramic interfaces was found for inclination angles ≥45°. This plateau value was identified as the interface strength by observation of the crack path at the substrate-coating interface via scanning electron microscopy and analysis of the effectively loaded interface area values. The presented novel material testing technique gives first and previously not accessible insight into the fracture behavior of rough substrate-coating interfaces with complex defect structure.

Nanoindentation in finite thickness viscoelastic materials

In this work, we present an analytical model to describe atomic force microscopy force curves of standard linear solid and power-law viscoelastic materials by taking indenter geometry and finite thickness effects into account. We show that conical/pyramidal cantilevers are less susceptible to finite thickness effects than other shapes, such as spherical and flat punch indenters. This is confirmed by finite element modeling of the stress field distribution within the sample. We also perform a systematic error analysis for the cases where finite thickness samples are analyzed with an infinite thickness force model. In particular, we show that for spherical indenters and indentation depth up to 20% of sample thickness, the mechanical response of viscoelastic materials will wrongly mimic a purely elastic behavior even within timescales where viscoelastic relaxation should appear.

Characterization of power-law constitutive relationship of nickel-based single crystal superalloys under different loading rates by nanoindentation with different types of indenters

This work attempts to explore a method to characterize the effect of loading rate on the power-law constitutive parameters of nickel-based single crystal superalloys (NBSX) by nanoindentation, which avoids the influence of indentation sinking-in or piling-up and indentation size effects. Specifically, combing the reduced modulus obtained from a cylindrical flat punch indentation test with the indentation contact stiffness obtained from two pyramidal indentation tests with different equivalent half cone angles, the actual indentation projected contact area of two pyramidal indenters can be acquired. Based on the actual projected contact area and the intrinsic hardness results calculated by Nix-Gao model, the corrected indentation load-depth curves from two pyramidal indenters are constructed. The elastic modulus can be known from the reduced modulus in advance, and then according to the equivalent half cone angle of the pyramidal indenters and the corrected indentation load-depth curves, the representative strain and stress of two pyramidal indenters are obtained, respectively. The power-law constitutive parameters of NBSX along [001] orientation under different loading rates are accomplished by inverse analyses of the representative stress and strain of two pyramidal indenters, and verified by the test results of a pyramidal indenter with another equivalent half cone angle. Results demonstrate the effectiveness of the explored method.

Nanoindentation of softening modern oil paints

A methodology was developed to address challenges associated with the use of nanoindentation to characterize small volumes of soft-matter thin films, encountered in many research fields including heritage conservation. The methodology is based on the use of a flat-punch indenter, whose radius is so dimensioned to be able to predict the effect of substrate rigidity using an existing solution independently of the film’s Poisson’s ratio and frictional characteristic. The film’s mechanical response is analyzed in a minimally strained condition at the onset of full contact to fulfill the solution’s assumption of linear viscoelasticity. The indentation response prior to full contact is corrected for the substrate effect using a model of structural compliance coupled with the solution. Homogeneity of the film material, further assumed by the solution, can thus be established based on its constant loss tangent response while deforming linear viscoelastically prior to full contact. This methodology was applied to minute volumes of bone black oil paints sampled from modern paintings by Karel Appel and Asger Jorn, across a range of relative humidities. The methodology not only differentiated between viscoelastic behaviors of these paints from the same period, but also facilitated the discovery that they possess softening points below the target humidity range of museums. The latter finding convincingly explains why these paints exhibit conservation problems even in a standard climate-controlled museum environment. The methodology can be applied to polymer coatings and thin biological tissues, whose Poisson’s ratios and frictional characteristics are not exactly known.

Finite Element Analysis of Nanoindentation Responses in Bi2Se3 Thin Films

In this study, the nanoindentation responses of Bi2Se3 thin film were quantitatively analyzed and simulated by using the finite element method (FEM). The hardness and Young’s modulus of Bi2Se3 thin films were experimentally determined using the continuous contact stiffness measurements option built into a Berkovich nanoindenter. Concurrently, FEM was conducted to establish a model describing the contact mechanics at the film/substrate interface, which was then used to reproduce the nanoindentation load-depth and hardness-depth curves. As such, the appropriate material parameters were obtained by correlating the FEM results with the corresponding experimental load-displacement curves. Moreover, the detailed nanoindentation-induced stress distribution in the vicinity around the interface of Bi2Se3 thin film and c-plane sapphires was mapped by FEM simulation for three different indenters, namely, the Berkovich, spherical and flat punch indenters. The results indicated that the nanoindentation-induced stress distribution at the film/substrate interface is indeed strongly dependent on the indenter’s geometric shape.

Modeling and inverse identification method for the characterization of elastic–plastic contact behavior during flat punch indentation

In this work, an inverse identification method is developed for the experimental characterization of the elastic–plastic contact in indentation problem. The method consists of a modeling procedure and an identification procedure. In the modeling, a discrete interfacial stress model is developed and the 2D frictional flat but round punch condition (of which frictionless, sharp corner contact is a special case) is formulated. Only the tendencies of stress distributions are required to be constrained in the model which can highly increase the scope of application. In the identification, an alternative optimization scheme is proposed in which the contact parameters can be inversed by matching the modeled displacement to the experimental data. A displacement-based yield criterion is developed so the plastic domain can be recognized without solving the stress or strain. The proposed method can characterize all of the contact parameters only by using the easy-acquired displacements. Simulation and experiments show that the proposed method can accurately characterize the contact from noisy measurements.

Multiregional viscoelastic properties of the porcine brain in the horizontal plane.

Comparison between the corpus callosum and different regions of corona radiata in the horizontal plane was tested in the article. A series of flat-punch indentation experiments were conducted on the corpus callosum and different regions of corona radiata with different loading rates on the porcine brain. A linear viscoelastic model with prony series approximation was fitted to the force-time data of all regions. The experiment data from different loading rates demonstrated that both the corona radiata and corpus callosum increased in stiffness with the increasing loading rates. The corona radiata seems to be stiffer than the corpus callosum in the horizontal plane. During the period of relaxation, statistical comparisons among the different regions showed that the posterior region of the corona radiata seems to be stiffer than the anterior and superior.

An Inverse Identification Method for the Characterization of Elastic Conforming Contact Behavior During Flat Punch Indentation

An Inverse Identification Method for the Characterization of Elastic Conforming Contact Behavior During Flat Punch Indentation

Non-fouling polymer films on hard-anodized aluminum substrates: Nanomechanical properties and modelling

In this paper, hard-anodized aluminum is used as a substrate to support a polymeric anti-biofouling coating based on a non-toxic, environmentally benign zwitterionic polymer (sulfobetaine methacrylate (pSBMA)). The coating is processed from an aqueous solution of the monomer via a photografting technique. Nanostructured coatings are obtained with a morphology that suggests tethered, cross-linked brushes akin to nanoropes. The antifouling properties are demonstrated using protein and bacteria adsorption on structured surfaces. Using the nanoindentation technology with a variety of testing methods, in wet and dry coating conditions, the elastic modulus and hardness of the polymer film and the substrate are obtained. The static elastic modulus and hardness are in the range of 2.0 GPa and of 220 MPa, respectively, with little effects of whether the films are tested in wet or dry condition. Moreover, the apparent modulus of the polymer coating is measured with different testing frequencies and loading rates using a cylindrical flat-punch and spherical indenters. The values obtained are in broad agreement with those obtained with the Berkovich indenter, but reflect the visco-elastic nature of the film, depending on the testing frequency and loading rate. The resistance of the coating to scratching is studied by applying fixed loads on the top surface, where the load and scratch profiles during the scratch are recorded and analyzed. Finite element models of the nanoindentation and scratch process are proposed and compared to the experimental results. The numerically obtained indentation depth-load curves and scratch profiles show a strong agreement with the experimentally obtained ones. Furthermore, stress and strain distributions on the coating surface are analyzed and the coefficient of friction is calculated for two different loads.

A Bacteria and Cell Repellent Zwitterionic Polymer Coating on Titanium Base Substrates towards Smart Implant Devices.

Biofouling and biofilm formation on implant surfaces are serious issues that more than often lead to inflammatory reactions and the necessity of lengthy post-operation treatments or the removal of the implant, thus entailing a protracted healing process. This issue may be tackled with a biocompatible polymeric coating that at the same time prevents biofouling. In this work, oxygen plasma-activated silanized titanium substrates are coated with poly(sulfobetaine methacrylate), a zwitterionic antibiofouling polymer, using photopolymerization. The characterization of polymer films includes FT-IR, AFM, and adhesion strength measurements, where adhesion strength is analyzed using a cylindrical flat punch indenter and water contact angle (WCA) measurements. Both cytotoxicity analysis with primary human fibroblasts and fluorescence microscopy with fibroblasts and plaque bacteria are also performed is this work, with each procedure including seeding on coated and control surfaces. The film morphology obtained by the AFM shows a fine structure akin to nanoropes. The coatings can resist ultrasonic and sterilization treatments. The adhesion strength properties substantially increase when the films are soaked in 0.51 M of NaCl prior to testing when compared to deionized water. The coatings are superhydrophilic with a WCA of 10° that increases to 15° after dry aging. The viability of fibroblasts in the presence of coated substrates is comparable to that of bare titanium. When in direct contact with fibroblasts or bacteria, marginal adhesion for both species occurs on coating imperfections. Because photopolymerization can easily be adapted to surface patterning, smart devices that promote both osseointegration (in non-coated areas) and prevent cell overgrowth and biofilm formation (in coated areas) demonstrate practical potential.

Extrinsic plastic hardening of polymer thin films in flat punch indentation

ABSTRACT Confined geometries offer useful and experimentally amenable mechanical testing arrangements in which to study the molecular and micro-structural processes which govern plastic yield in stress environments dominated by hydrostatic pressure over shear. However, the changes to macroscopic stress – strain behaviour that result from switching from an unconfined mode such as uniaxial compression to a confined one are often overlooked and display a surprising level of complexity, even for simple elastic – plastic constitutive models. Here we report a confinement induced strain hardening effect in polystyrene thin films achieved through repeated plastic loading with a cylindrical flat punch whose diameter is many times the initial film thickness. This high aspect ratio combines with constraint provided by film material surrounding the contact to generate a state of confined uniaxial strain in the indented region, rendering the deformation one dimensional. By repeated loading past the yield point into the plastic domain, we achieve a 66% increase in the confined yield stress, from 0.3 GPa to 0.5 GPa. Through finite element simulation and analytic modelling of the principal stresses and strains, we show that this effect arises not from intrinsic changes to the structure of the material, but rather residual stresses imparted during plastic loading. We contrast this effect with intrinsic changes to glassy thin films such as physical ageing and thermal cross-linking.

A theoretical model for elastic-perfectly plastic flat cylindrical punch indentation

Instrumented indentation is widely used to evaluate the hardness and other mechanical properties of materials. This requires a theoretical model for the indentation curve (load vs. penetration) based on the Young's modulus, Poisson's coefficient, yield stress, hardening exponent, friction, and shape of the indenter. Several papers have been devoted to modeling spherical, conical, or pyramidal indentation in cases of both elastic and plastic deformation; in contrast, there are relatively few theoretical studies on flat cylindrical punch in the elastic–plastic regime. Indeed the singularity in the stress field at the edge of the contact is difficult to solve even if the aim is only to obtain an approximate solution. In this paper, after reviewing the theoretical basis of flat cylindrical indentation for elastic and rigid-plastic materials three different steps have been used to describe the entire progress of penetration: pseudo-elastic, elastic–plastic and full plastic. This final condition begins when the entire contact area undergoes plastic deformation. Using this classification as the starting point, a new simplified equation represents the stiffness of the specimen under flat cylindrical indentation, taking into account the elastic–perfectly plastic behavior. Integrating this equation gives the curve of indentation for an elastic–perfectly plastic material. As the characteristic parameters of this equation are unknown, in this paper the results of an extended numerical investigation using finite-element models of many different materials facilitates their calculation and validates the model. Using this new model, the direct and the inverse problems of flat indentation can be solved with good accuracy as shown through several FEM analyses. Finally, considering that the new model does not take the hardening effect into account, experimental data from the literature facilitate the verification of the relevance of this approximation. This final check successfully assesses the accuracy and the usefulness of the new method.

Effect of primary creep on the relationship between indentation and uniaxial creep: A theoretical model

In this work, a theoretical model is developed to address the effect of primary creep on the relationship between indentation and uniaxial creep tests. By considering the expansion of a spherical cavity in the materials following the primary creeping law, a general expression of the conversion factor is deduced during the primary creep stage. For creep tests with spherical and flat punch indenters, a closed-form formula is specified for the conversion factor that is determined by the stress exponent and hardening exponent. By further considering the difference of the critical time at the onset of steady-state creep deformation between uniaxial and indentation creep tests, it becomes available to convert the indentation creep data into uniaxial creep results during the steady-state creep stage. The rationality and accuracy of the proposed model are verified by comparing with the experimental data of Sn37Pb solder, AZ31 Mg alloy and Succinonitrile. Furthermore, the comparison with previous theoretical models indicates that the ignoring of primary creep effect could lead to the deviation of converted indentation creep data from uniaxial creep results.

Creep behaviour of elastomeric nanocomposites by flat punch indentation: Influence of graphene modification and content

Creep can be understood as the resistance of a material to a continuous stress and represents an important property for engineering design. The creep behaviour of a series of nanocomposites with electromechanical applications based on a thermoplastic elastomer, poly(styrene-b-ethylene-co-butylene-b-styrene) (SEBS), and small amounts of graphene has been explored using cylindrical flat punch depth-sensing indentation. Special attention is paid to the influence of the nature of the polymer brushes (polyethylene or polystyrene) attached to the graphene surface. Common methodologies for indentation creep analysis are critically examined and brought together to provide a comprehensive picture of creep deformation. It is found that graphene significantly reduces the creep rate and this is most significant under viscoplastic deformation than in the linear viscoelastic regime. Most interesting, polyethylene branches reduce visco-elastic-plastic flow in a more effective manner and this is attributed to the selective interaction of the filler with the matrix chains.

Effect of cross-linking and hydration on microscale flat punch indentation contact to collagen-hyaluronic acid films in the viscoelastic limit

The properties of the extracellular matrix (ECM) have profound impact upon cell behaviour. As an abundant protein in mammals, collagen is a desirable base material to engineer an ECM tissue scaffold, but its structural weakness generally requires molecular crosslinking or incorporation of additional ECM-based macromolecules such as glycosaminoglycans. We have performed microscopic indentation to test collagen films under dry and aqueous conditions prepared with different levels of physical and chemical crosslinking. Our technique isolates intrinsic properties of the poro-viscoelastic matrix in a regime minimizing the influence of drainage hydrodynamics and allows direct measurement of the effect of hydrating a specific sample. A doubling of the effective stress-strain stiffness under crosslinking could be directly correlated to structural changes in X-ray diffraction spectra, while electron microscopy revealed possible fibril bridging mechanisms explaining observed toughness. Overall, an intrinsic viscoelastic stress-strain response of collagen under various conditions of cross-linking was observed for both dry and wet conditions, with the latter most affected by indentation rate. Under creep testing, a three order of magnitude increase in dynamic compliance and factor three reduction in relaxation time was found going from the dry to hydrated state. When fitted to a simple viscoelastic model, crosslinking showed a tendency to decrease relaxation time in both states, but reduced dynamic compliance only in the hydrated case. This suggests a reduced role of virtual crosslinks under hydration. This is the first study reporting consistent mechanical testing of dry and hydrated ECM-derived biomaterials, accessing the intrinsic material mechanics under in vivo-like conditions. Statement of SignificanceThis manuscript presents new insights into the effect of crosslinking on mechanical properties of dry and hydrated collagen intended for tissue scaffolding applications. A novel microscopic indentation technique allowed testing of the poro-viscoelastic matrix isolated in a regime minimizing the influence of drainage hydrodynamics, so direct comparison of the effect of hydration on the intrinsic material behaviour to could be made. A variety of experimental techniques including X-ray diffraction, infrared spectroscopy, and scanning electron and atomic force microscopy were used to augment the mechanical testing. The results of creep testing were numerically analysed using a four-component viscoelastic model. This is the first mechanical testing of dry and hydrated ECM-derived biomaterials, accessing the intrinsic material mechanics under in vivo-like conditions.

Enhancement of mechanical properties of vertically aligned carbon nanotube arrays due to N+ ion irradiation

In this work we apply N+ ion irradiation on vertically aligned carbon nanotube (VACNT) arrays in order to increase the number of connections and joints in the CNT network. The ions energy was 50 keV and fluence 5 × 1017 ions cm−2. The film was 160 μm thick. SEM images revealed the ion irradiation altered the carbon bonding and created a sponge-like, brittle structure at the surface of the film, with the ion irradiation damage region extending ∼4 μm in depth. TEM images showed the brittle structure consists of amorphous carbon forming between nanotubes. The significant enhancement of mechanical properties of the irradiated sample studied by the cyclic nanoindentation with a flat punch indenter was observed. Irradiation on the VACNT film made the structure stiffer, resulted in a higher percentage recovery, and reduced the energy dissipation under compression. The results are encouraging for further studies which will lead to create a class of materials—ion-irradiated VACNT films—which after further research may find application in storage or harvesting energy at the micro/nanoscale.

The Boussinesq flat-punch indentation problem within the context of linearized viscoelasticity

The Boussinesq problem, namely the indentation of a flat-ended cylindrical punch into a viscoelastic half-space is studied. We assume a linear viscoelastic model wherein the linearized strain is expressed as a function of the stress. However, this expression is not invertible, which makes the problem very interesting. Based on the Papkovich–Neuber representation in potential theory and using the Fourier–Bessel transform for axisymmetric bodies, an analytical solution of the resulting time-dependent integral equation is constructed. Consequently, distribution of the displacement and the stress fields in the half space with respect to time is obtained in the closed form.

Structure and mechanical properties of electroplated mossy lithium: Effects of current density and electrolyte

Mechanical suppression, e.g., by applying stack pressures and using functionalized coatings, has been considered a promising approach to inhibit the formation of lithium (Li) dendrites and improve the cycling stability of the Li metal electrode. However, a lack of understanding of the mechanical behavior of electroplated mossy Li, consisting of loosely packed Li dendrites that are covered by solid electrolyte interphase, hinders the development of mechanical suppression strategies and limits the understanding of the electromechanical behavior of mossy Li. In this study, we investigated, using flat punch indentation in an argon-filled glovebox, the room temperature mechanical behavior and its relationship with the microstructure of mossy Li electroplated using different current densities (between 0.25 and 10 ​mA/cm2) in several electrolytes. The dendrite size decreases and the porosity of mossy Li increases with increasing current density. Mossy Li has lower Young’s modulus (E) but significantly higher creep resistance than bulk Li. A scaling relationship between E and porosity is established for mossy Li. The creep behavior of mossy Li exhibits a strong size effect, i.e., the steady-state impression velocity decreases with decreasing dendrite size. These findings provide a comprehensive understanding of the relationship between the microstructure and mechanical behavior of mossy Li.