Flat Cylindrical Punch Research Articles

Elastic Stress Field beneath a Sticking Circular Contact under Tangential Load

Based on a potential theoretical approach, the subsurface stress field is calculated for an elastic half-space which is subject to normal and uniaxial tangential surface tractions that—in the case of elastic decoupling—correspond to rigid normal and tangential translations of a circular surface domain. The stress fields are obtained explicitly and in closed form as the imaginary parts of compact complex-valued expressions. The stress state in the surface and on the central axis are considered in detail. As, within specific approximations that have been discussed at length in the literature, any tangential contact problem with friction can be understood as a certain incremental series of such rigid translations, the solutions presented here can serve as the basis of very fast superposition algorithms for the analysis of subsurface stress fields in general tangential contact problems with friction. This idea is demonstrated by means of the frictional tangential contact between an elastic half-space and a rigid cylindrical flat punch with rounded corners.

A General Approximate Solution for the Slightly Non-Axisymmetric Normal Contact Problem of Layered and Graded Elastic Materials

We present a general approximate analytical solution for the normal contact of layered and functionally graded elastic materials for almost axisymmetric contact profiles. The solution only requires knowledge of the corresponding contact solution for indentation using a rigid cylindrical flat punch. It is based on the generalizations of Barber’s maximum normal force principle and Fabrikant’s approximation for the pressure distribution under an arbitrary flat punch in an inhomogeneous case. Executing an asymptotic procedure suggested recently for almost axisymmetric contacts of homogeneous elastic media results in a simple approximate solution to the inhomogeneous problem. The contact of elliptical paraboloids and indentation using a rigid pyramid with a square planform are considered in detail. For these problems, we compare our results to rigorous numerical solutions for a general (bonded or unbonded) single elastic layer based on the boundary element method. All comparisons show the quality and applicability of the suggested approximate solution. Based on our results, any compact axisymmetric or almost axisymmetric contact problem of layered or functionally graded elastic materials can be reduced asymptotically to the problem of indenting the material using a rigid cylindrical flat punch. The procedure can be used for different problems in tribology, e.g., within the framework of indentation testing or as a tool for the analysis of local features on a rough surface.

A Simple Semi-Analytical Method for Solving Axisymmetric Contact Problems Involving Bonded and Unbonded Layers of Arbitrary Thickness

In the present work, a recently extended version of the method of dimensionality reduction (MDR) for layered elastic media is applied for the first time using a semi-analytical approach. It is based on a priori knowledge of the cylindrical flat punch solution which is determined numerically using the boundary element method (BEM). We consider arbitrary indenters of revolution producing a circular area of contact with bonded and unbonded layers of arbitrary thickness. The proposed method reduces the contact solution to the numerically efficient evaluation of simple one-dimensional integrals. We further show that the solution of JKR-adhesive contacts with layers and contacts with linear-viscoelastic layers is straightforward using the well-known MDR formalisms. A specific focus has been devoted to study the thickness effect in different application examples. Comparisons with the literature and finite element simulations show very good agreement with the proposed method.

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.

Analytical and numerical results for the elasticity and adhesion of elastic films with arbitrary Poisson’s ratio and confinement

ABSTRACT We present an approximate, analytical treatment for the linearly elastic response of a film with arbitrary Poisson's ratio , which is indented by a flat cylindrical punch while resting on a rigid foundation. Our approach is based on a simple scaling argument allowing the vast changes of the elastomer’s effective modulus with the ratio of film height and indenter radius to be described with a compact, analytical expression. This yields exact asymptotics for large and small reduced film heights , whereby it also reproduces the observation that has a pronounced minimum for at . Using Green’s function molecular dynamics (GFMD), we demonstrate that the predictions for are reasonably correct and generate accurate reference data for effective modulus and pull-off force. GFMD also reveals that the nature of surface instabilities occurring during stable crack growth as well as the crack initiation itself depend sensitively on the way how continuum mechanics is terminated at small scales, that is, on parameters beyond the two dimensionless numbers and defining the continuum problem.

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.

Indentation of an elastic half-space by the cylindrical flat punch with a rounded edge under non-monotonic loading

The paper presents a novel approach to solving the contact problem for interaction with friction between a rigid cylindrical flat punch with rounded corners and a linearly elastic half-space. Increasing and decreasing normal loads act on the punch sequentially. Coulomb’s law is used to account for friction. The contact problem is reduced to nonlinear operator equations that must be solved at each step of the discrete loading process. The numerical method is applied. This method includes regularization of the equation, discretization of the regularized equations and the usage of an iterative process to obtain the approximate solution. The calculations were performed for different values of the relative radius of the flat area of the punch base. Distributions of contact traction and configuration of the stick and slip zones are studied at each monotonic stage of the loading process.

Effect of pressure on pull-off of flat cylindrical punch adhered to circular membrane

ABSTRACT Pressure can sometimes be utilized to increase or decrease the strength of adhesion. This phenomenon is analyzed for pull-off of a flat, circular cylindrical punch from a circular membrane. The pressure is applied, and then the punch is pulled upward. Both force control and displacement control are considered, and the pressure may be positive (acting upward) or negative (acting downward) on the membrane. The membrane is assumed to be linearly elastic, and Föppl-von Kármán theory is used to allow moderate displacements. The JKR theory of adhesion is adopted. A transversality (debonding) condition is derived, and then the effects of the work of adhesion, Poisson’s ratio, residual stress, and the relative radius of the punch to that of the membrane are investigated. With an increase in pressure, the pull-off force decreases, the pull-off deflection of the punch relative to the initial flat membrane level increases, and the total pull-off punch deflection from the pressurized membrane may increase or decrease.

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.

Extrinsic and Intrinsic Mechanical Responses of Confined Indented Thin Films

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 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.

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.

Determination of power hardening elastoplastic constitutive relation of metals through indentation tests with plural indenters

The accurate acquisition of the elastoplastic mechanical parameters of metals through in situ indentation tests is an important topic, especially for the technological domains of micro-nano manufacturing. In view of existing uniqueness and effectiveness problems of the current indentation reverse analyses, a method for extracting the power hardening elastoplastic constitutive relation using plural indenters is proposed. Elastic modulus E and Poisson's ratio υ are obtained on the basis of the test result in cylindrical flat punch indenter, and the loading curves are corrected by eliminating the indentation size effects of two pyramid indenters with different equivalent semi-cone angles. The yielding stress σy and strain hardening exponent n can be uniquely determined by combining the representative stress σr under two pyramid indenters that are obtained from the numerical inversion analyses with corresponding representative plastic strain ɛr of certain pyramid indenters. Specific implementing procedures are carried out on Cu and Al. Results show the effectiveness and accuracy of this analytical method.

Surface normal deformation in elastic quarter-space

An efficient and explicit solution for the surface deformation of quarter-space under normal load is developed using the concept of flexibility matrix, which serves like springs in response to loads. Quarter-space is characterized by the unbounded side surface, such as in roller bearings and gears. The solution method is verified using a typical case. The edge effect on surface deformation under three load types namely, Hertzian point, flat cylindrical punch and Hertzian line, are evaluated. The effect can be considerable if the applied load is close to edge. The flexibility matrix is constant for a given case. Hence, the solution method is highly efficient, and particularly suitable for quarter-space problems which require iterative calculations, such as elasto-hydrodynamic lubrication analyses.

Reduction of friction by normal oscillations. I. Influence of contact stiffness

The present paper is devoted to a theoretical analysis of sliding friction under the influence of oscillations perpendicular to the sliding plane. In contrast to previous works we analyze the influence of the stiffness of the tribological contact in detail and also consider the case of large oscillation amplitudes at which the contact is lost during a part of the oscillation period, so that the sample starts to “jump”. It is shown that the macroscopic coefficient of friction is a function of only two dimensionless parameters—a dimensionless sliding velocity and dimensionless oscillation amplitude. This function in turn depends on the shape of the contacting bodies. In the present paper, analysis is carried out for two shapes: a flat cylindrical punch and a parabolic shape. Here we consider “stiff systems”, where the contact stiffness is small compared with the stiffness of the system. The role of the system stiffness will be studied in more detail in a separate paper.

THE JKR-ADHESIVE NORMAL CONTACT PROBLEM OF AXISYMMETRIC RIGID PUNCHES WITH A FLAT ANNULAR SHAPE OR CONCAVE PROFILES

The JKR-adhesive frictionless normal contact problem is solved for the flat annular and the conical or spherical concave rigid punch indenting an elastic half space. The adhesive solution can be derived analytically from the non-adhesive one, the latter one being calculated by the boundary element method. It is found that the annular flat punch will always start to detach at the outer boundary. The pull-off forces for both concave punch shapes almost do not depend on the pull-off boundary regime and can be significantly larger than the pull-off force for the cylindrical flat punch.

Finite Element Analysis of Plastic Deformation During Impression Creep

Finite element (FE) analysis of plastic deformation associated with impression creep deformation of 316LN stainless steel was carried out. An axisymmetric FE model of 10 × 10 × 10 mm specimen with 1-mm-diameter rigid cylindrical flat punch was developed. FE simulation of impression creep deformation was performed by assuming elastic-plastic-power-law creep deformation behavior. Evolution of the stress with time under the punch during elastic, plastic, and creep processes was analyzed. The onset of plastic deformation was found to occur at a nominal stress about 1.12 times the yield stress of the material. The size of the developed plastic zone was predicted to be about three times the radius of the punch. The material flow behavior and the pile-up on specimen surface have been modeled.

Obtaining full contact for measuring polydimethylsiloxane mechanical properties with flat punch nanoindentation

Procedure to establish full contact between the sample and the 1mm diameter cylindrical flat punch tip to measure polydimethylsiloxane (PDMS) mechanical properties using the Hysitron TriboIndenter is described. This procedure differs from the standard automated indentation because each indent has to be performed manually after establishing full contact with the sample surface. Incomplete contact happens because of the sample tilt with respect to the flat punch surface and results in incorrect elastic modulus values.•Automated indentation results in incorrect values of the elastic modulus due to initial incomplete contact between the flat punch and the PDMS sample surface, caused by the tilt, and using the unloading slope, which is affected by viscoelastic soft polymer deformation.•Correct procedure requires establishing the full contact between the tip and the sample. This is achieved by moving the tip into the sample in 1–2μm increments, up to 40–80μm maximum combined displacement, until the loading stiffness no longer increases.•The elastic modulus is calculated from the loading stiffness and the diameter of the flat punch, instead of the unloading stiffness, which is larger due to viscoelastic unloading. After establishing the full contact, other mechanical testing can be conducted.

Evaluation of creep deformation behaviour of different microstuctural zones of 316LN SS weld joint using impression creep testing technique

Impression creep technique, which uses flat ended cylindrical indenter, is an attractive material non-invasive technique for evaluating creep properties as it enables probing small volume of material and requires short time for testing. The present investigation discusses the application of impression creep technique for characterising the creep behaviour of different microstructural regions in a high nitrogen grade of 316LN SS weld joint. Impression creep tests were carried out at 923 K on the weld metal, the base metal and the heat-affected zone in 316LN SS weld joint. The impression creep curves exhibited the first two characteristic stages of the creep processes, namely, a primary creep stage and a secondary creep stage. The rate at which the cylindrical flat punch penetrated into the test specimen was controlled by the time dependence of the movement of the material underneath the punch. The weld metal, the base metal and the heat affected zone exhibited distinct creep behaviour. The difference in creep behaviour of each zone was correlated with the difference in microstructure and morphology of the weld joint. A comparison was made between the data obtained from impression creep tests and from independent uniaxial creep tests on the weld metal and the base metal. A good correlation was established between impression creep and uniaxial creep results.

Flat punch adhesion: transition from fracture-based to strength-limited pull-off

The adhesion of a cylindrical flat punch to a surface due to interatomic forces is a well-known problem that is important in many applications, including indentation experiments and the adhesion of fibrillar structures. Traditionally, the pull-off force has been related to the work of adhesion and punch geometry via the Kendall solution that uses a Griffith energy balance to assess crack propagation and pull-off. More recently, it has been shown that under certain conditions, notably at small punch diameters, the contact can behave in a ‘strength-limited’ fashion in which the interface separates uniformly rather than via crack propagation. Here, a Maugis-Dugdale-type analysis of power-law-shaped bodies in contact is used to examine the change in behaviour from the fracture-based Kendall solution to strength-limited pull-off for cylindrical flat punches. The transition from fracture-based to strength-limited behaviour is described in terms of a non-dimensional parameter that is similar to previous quantities used to describe the transition and is a function of the punch size, the elasticity of the contact, and the adhesion properties. The results of this relatively simple analysis compare favourably with results from more complex computational simulations. In addition, the results are used to develop a function that quantifies the transition between the Kendall solution and the strength-limited solution in order to facilitate interpretation of adhesion measurements in the transition regime between the two limits. Finally, the power-law analysis is used to assess the sensitivity of the transition to the exact shape of the punch.