Flat-ended Cylindrical Punch Research Articles

Modulating adhesion strength in multi-ferroic composite materials: Insights from adhesive contact with arbitrary profile indenters

Adhesion control is a critical aspect of various applications, from industrial adhesion devices to the locomotion of insects on ceilings and walls. Multi-ferroic materials, which encompass mechanical, electrical, and magnetic properties, offer approaches for reversible adhesion control. This study presents a comprehensive theoretical framework for adhesive contact in multi-ferroic composite materials when subjected to axisymmetric rigid indenters with arbitrary profiles. We analytically derive the physical fields for various contact models, including Hertz contact, Johnson–Kendall–Roberts (JKR), and Maugis–Dugdale (MD) adhesive models. The obtained energy release rates indicate that the electric and magnetic potentials can modulate adhesion strength. The Griffith energy balance relation is employed to derive the indentation forces and penetration depths, which can be extended to a range of common indenters. Notably, the classical approximations fail when using small spherical indenters, but the study provides valid alternatives. The influence of amplitude and wavelength on contact behavior is explored, with greater effects observed for larger or smaller values. For cosine-shaped indenters, equivalence to flat-ended cylindrical punches is established under specific conditions. The study also reveals that the power indices for power-law-shaped indenters change the influence of electric and magnetic potentials on pull-off forces. These findings provide a theoretical fundament associated with the biomimetic and artificial adhesive systems and the modern testing techniques.

Rate-dependent JKR-type decohesion of a cylindrical punch from an elastic substrate

Recently published experimental data on non-quasistatic detachment of a flat-ended cylindrical punch from an adhesive rubber layer are analyzed in the framework of axisymmetric rate-dependent JKR-type model. The functional dependence of the work of adhesion on the velocity of the contour of contact area is assumed according to the known Gent–Schultz model. The evolution of the variable contact radius as a function of the punch displacement is described by a first-order ordinary differential equation, which possesses the localization property for its solutions, meaning that the detachment occurs at some nonzero contact radius. To facilitate the model fit to experimental force-displacement curve, a computationally efficient analytical approximate solution is suggested. A parametric analysis of the basic case (when the rubber layer is approximated by an elastic half-space) is presented.

An adhesive detachment paradox: Does the substrate thickness matter?

A normal adhesive contact between a flat-ended cylindrical punch with elliptical cross-section and the surface of an elastic substrate, which can be regarded as an elastic layer of finite thickness, is considered. The experimental evidence published elsewhere indicates that the initiation of detachment can occur at the ends of the minor axis of the elliptical contact area, which eventually comes into contradiction with the surface energy theory developed so far. This paradox of adhesive detachment is examined in the framework of the JKR-type model formulated in terms of the stress intensity factor (SIF) of the contact normal stress. Based on the asymptotic model for a relatively thick elastic layer, the contact SIFs at the ends of the minor axis are shown to grow with decreasing the relative layer thickness faster than those at the ends of the major axis of the initial contact area. A plausible explanation for the observed inconsistency between experiment and state-of-the-art theory is found in the effect of the nonuniform elastic deformations on the square root singularity of the contact pressure at the punch edge.

Indentation of a nanolayer on a substrate by a rigid cylinder in adhesive contact

Nanoindentation is employed to characterize the mechanical properties at the nanoscale. This paper considers the mechanical response of a nanoscale elastic layer on an elastic substrate that is indented by an adhesively bonded flat-ended rigid cylindrical punch. The complete Gurtin–Murdoch continuum model is employed to capture the size effects. The contact problem is analyzed by relating displacements of the contact region to contact stresses by a flexibility equation system, which is developed by discretizing the contact region into annular elements. The flexibility equation involves displacement influence functions corresponding to axisymmetric normal and radial surface ring loads applied on the layer-substrate system. The displacement influence functions are derived by using the Hankel integral transforms. Convergence and accuracy of the proposed solution scheme are verified by comparing with limiting cases such as the classical elasticity solution. Selected numerical results indicate that the substrate becomes stiffer and the elastic field is size-dependent due to the surface energy effects.

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.

Impression creep characterization of cast Al–7Si–0.3Mg alloy

The creep behavior of the as cast A356 (Al–7Si–0.3Mg) alloy is investigated by the impression creep test with a flat-ended cylindrical punch over a wide range of stress between 280 and 630 MPa and at the temperature range of 493 to 553 K. The tilt casting method is used to fabricate the cast A356 alloy. The microstructure of the alloy is characterized by the dendritic primary α-Al, the eutectic Si phase and the iron-rich intermetallics (α-AlFeSi and β-AlFeSi). The stress exponent is found to be in the range of 6.1 to 7.6 and the activation energy is determined in the range of 134 to 152 kJ mol−1. It is found that the self-diffusion climb controlled creep is the operative creep mechanism. No evidence of the threshold stress is observed for the present alloy.

A STUDY ON GROSS SLIP AND FRETTING WEAR OF CONTACTS INVOLVING A POWER-LAW GRADED ELASTIC HALF-SPACE

For the steady wear state of two contact problems involving power-law graded materials, closed-form solutions are derived in terms of pressure distribution and limiting shapes of profile. Both gross slip of an initially flat-ended cylindrical punch on a power-law graded half-space and the load-controlled fretting wear under partial slip of an initially parabolic indenter are studied. In the case of gross slip at fixed penetration depth there exists a certain exponent of elastic inhomogeneity, for which the effective volume change takes its maximum value. To minimize wear due to fretting under partial slip, an amplitude dependent design of the material gradient is necessary. For large amplitudes of the tangential force a gradient ranged from a soft surface to a hard ground is beneficial, small amplitudes require a reverse gradient characterized by a hard surface and a soft ground. However, the choice of the material gradient also has a decisive influence on the strength of stress singularities at the contact edge and thus the initiation of fretting fatigue cracks, which is why it is discussed in more detail.

Elastic layer under axisymmetric indentation and surface energy effects

In this paper, a continuum-based approach is adopted to investigate the contact problem of an elastic layer with finite thickness and rigid base subjected to axisymmetric indentation with the consideration of surface energy effects. A complete Gurtin–Murdoch surface elasticity is employed to consider the influence of surface stresses. The indentation problem of a rigid frictionless punch with arbitrary axisymmetric profiles is formulated by employing the displacement Green’s functions, derived with the aid of Hankel integral transform technique. The problem is solved by assuming the contact pressure distribution in terms of a linear combination of admissible functions and undetermined coefficients. Those coefficients are then obtained by employing a collocation technique and an efficient numerical quadrature scheme. The accuracy of proposed solution technique is verified by comparing with existing solutions for rigid indentation on an elastic half-space. Selected numerical results for the indenters with flat-ended cylindrical and paraboloidal punch profiles are presented to portray the influence of surface energy effects on elastic fields of the finite layer. It is found that the presence of surface stresses renders the layer stiffer, and the size-dependent behavior of elastic fields is observed in the present solutions. In addition, the surface energy effects become more pronounced with smaller contact area; thus, the influence of surface energy cannot be ignored in the analysis of indentation problem especially when the indenter size is very small such as in the case of nanoindentation.

Use of loading-unloading compression curves in medical device design

The paper presents a method and experimental results regarding mechanical testing of soft materials. In order to characterize the mechanical behaviour of technological materials used in prosthesis, a large number of material constants are required, as well as the comparison to the original. The present paper proposes as methodology the comparison between compression loading-unloading curves corresponding to a soft biological tissue and to a synthetic material. To this purpose, a device was designed based on the principle of the dynamic harness test. A moving load is considered and the force upon the indenter is controlled for loading-unloading phases. The load and specimen deformation are simultaneously recorded. A significant contribution of this paper is the interpolation of experimental data by power law functions, a difficult task because of the instability of the system of equations to be optimized. Finding the interpolation function was simplified, from solving a system of transcendental equations to solving a unique equation. The characteristic parameters of the experimentally curves must be compared to the ones corresponding to actual tissue. The tests were performed for two cases: first, using a spherical punch, and second, for a flat-ended cylindrical punch.

Response of thin-skinned sandwich panels to contact loading with flat-ended cylindrical punches: Experiments, numerical simulations and neutron diffraction measurements

The response of aluminium foam-cored sandwich panels to localised contact loading was investigated experimentally and numerically using flat-ended cylindrical punch of four varying sizes. ALPORAS and ALULIGHT closed-cell foams of 15 mm thickness with 0.3 mm thick aluminium face sheets (of 236 MPa yield strength) were used to manufacture the sandwich panels. Face sheet fracturing at the perimeter of the indenter, in addition to foam cells collapse beneath the indenter and tearing of the cell walls at the perimeter of the indenter were the major failure mechanisms of the sandwich panels, irrespective of the strength and density of the underlying foam core. The authors employed a 3D model in ABAQUS/Explicit to evaluate the indentation event, the skin failure of the face sheets and carry out a sensitivity study of the panel's response. Using the foam model of Deshpande and Fleck combined with the forming limit diagram (FLD) of the aluminium face sheet, good quantitative and qualitative correlations between experiments and simulations were achieved. The higher plastic compliance of the ALPORAS led to increased bending of the sheet metal and delayed the onset of sheet necking and failure. ALULIGHT-cored panels exhibited higher load bearing and energy absorption capacity, compared with ALPORAS cores, due to their higher foam and cell densities and higher yield strength of the cell walls. Additionally, they exhibited greater propensity for strain hardening as evidenced by mechanical testing and the neutron diffraction measurements, which demonstrated the development of macroscopically measurable stresses at higher strains. At these conditions the ALULIGHT response upon compaction becomes akin to the response of bulk material with measurable elastic modulus and evident Poisson effect.

Determination of Elastic Modulus of Gelatin Gels by Indentation Experiments

Mechanical characterization of hydrogels is a challenging task because they are much softer than metals, ceramics or polymers. The elastic modulus of hydrogels is within 100-102kPa range. Because they easily break and slump under their own weight, tensile and bending tests are not suitable configurations to assess elastic modulus. This work reports on the determination of elastic modulus of a gelatin gel by indentation experiments. Indentation is very simple configuration, it is of technological importance and it can be applied at different length scales with high accuracy. The gelatin hydrogel behavior is first calibrated by uniaxial compression and low strain rheological measurements. It behaves as a hyperelastic solid with strain hardening capability at large strains and shows no dependence with frequency in the linear viscoelastic range. It can be properly characterized by the First order Ogden material model. Indentation experiments are carried out at macro and nanoscales using spherical and flat-ended cylindrical punches. Elastic contact solutions and inverse analysis accounting for hyperelasticity are used to extract the elastic modulus from experimental force-depth curves. Adhesion between punch and hydrogel influences the indentation response and affects the accuracy of elastic modulus determination in a larger extent than the assumption of linear elasticity. Adhesion leads to overestimation of elastic modulus values. The influence of adhesive forces increases with decreasing the length scale. A markedly decay of elastic modulus with increasing maximum load is observed at nanoscale. A hybrid model based on Hertz elastic contact solution and Johnson-Kendal-Roberts model for adhesion is used to determine elastic modulus. This model yields an elastic modulus in good agreement with that obtained from uniaxial compression test.

Strain gradient solutions of half-space and half-plane contact problems

General solutions for the problems of an elastic half-space and an elastic half-plane, respectively, subjected to a symmetrically distributed normal force of arbitrary profile are analytically derived using a simplified strain gradient elasticity theory (SSGET) that contains one material length scale parameter. Mindlin’s potential function method and Fourier transforms are employed in the formulation, and the half-space and half-plane contact problems are solved in a unified manner. The specific solutions for the problems of a half-space/plane subjected to a concentrated normal force or a uniformly distributed normal force are obtained by directly applying the general solutions, which recover the existing classical elasticity-based solutions of the Flamant and Boussinesq problems as special cases. In addition, the indentation problems of an elastic half-space indented by a flat-ended cylindrical punch, a spherical punch, and a conical punch, respectively, are solved using the general solutions, leading to hardness formulas that are indentation size- and material microstructure-dependent. Numerical results reveal that the displacement and stress fields in a half-space/plane given by the current SSGET-based solutions are smoother than those predicted by the classical elasticity-based solutions and do not exhibit the discontinuity and/or singularity displayed by the latter. Also, the indentation hardness values based on the newly obtained half-space solution are found to increase with decreasing indentation radius and increasing material length scale parameter, thereby explaining the microstructure-dependent indentation size effect.

A unified treatment of axisymmetric adhesive contact problems using the harmonic potential function method

A unified treatment of axisymmetric adhesive contact problems is provided using the harmonic potential function method for axisymmetric elasticity problems advanced by Green, Keer, Barber and others. The harmonic function adopted in the current analysis is the one that was introduced by Jin et al. (2008) to solve an external crack problem. It is demonstrated that the harmonic potential function method offers a simpler and more consistent way to treat non-adhesive and adhesive contact problems. By using this method and the principle of superposition, a general solution is derived for the adhesive contact problem involving an axisymmetric rigid punch of arbitrary shape and an adhesive interaction force distribution of any profile. This solution provides analytical expressions for all non-zero displacement and stress components on the contact surface, unlike existing ones. In addition, the newly derived solution is able to link existing solutions/models for axisymmetric non-adhesive and adhesive contact problems and to reveal the connections and differences among these solutions/models individually obtained using different methods at various times. Specifically, it is shown that Sneddon’s solution for the axisymmetric punch problem, Boussinesq’s solution for the flat-ended cylindrical punch problem, the Hertz solution for the spherical punch problem, the JKR model, the DMT model, the M-D model, and the M-D- n model can all be explicitly recovered by the current general solution.

Flat-ended circular cylindrical punch for initially stressed Neo-Hookean solids

The present paper reports the indentation of integral transform technique for a semi-infinite initially stressed elastic medium under the action of an axi-symmetric flat-ended circular cylindrical punch pressing the medium normally. The incremental deformation theory is used to solve the problems for Neo-Hookean solid. The distribution of incremental stress and strain is obtained by using the Hankel’s transformation. The effects of the punch have been studied numerically and presented in various forms of curves. The plane punch indentation has its broad applications in the field of Engineering Mechanics. There are so many firing and launching pads, which use the Neo-Hookean solid as buffer and bear the punch during the action of machines. Thus the present problem has a lot of applications to find the effect of punch on machines.

Self-Assembly and Adhesion of DOPA-Modified Methacrylic Triblock Hydrogels

Marine mussels anchor to a variety of surfaces by secreting liquid proteins that harden and form water-resistant bonds to a variety of surfaces. Studies have revealed that these mussel adhesive proteins contain an unusual amino acid, 3,4-dihydroxy-L-phenylalanine (DOPA), which is believed to be responsible for the cohesive and adhesive properties of these proteins. To separate the cohesive and adhesive roles of DOPA, we incorporated DOPA into the midblock of poly(methyl methacrylate)-poly(methacrylic acid)-poly(methyl methacrylate) (PMMA-PMAA-PMMA) triblock copolymers. Self-assembled hydrogels were obtained by exposing triblock copolymer solutions in dimethyl sulfoxide to water vapor. As water diffused into the solution, the hydrophobic end blocks formed aggregates that were bridged by the water-soluble midblocks. Strong hydrogels were formed with polymer weight fractions between 0.01 and 0.4 and with shear moduli between 1 and 5 kPa. The adhesive properties of the hydrogels on TiO2 surfaces were investigated by indentation with a flat-ended cylindrical punch. At pH values of 6 and 7.4, the fully protonated DOPA groups were highly adhesive to the TiO2 surfaces, giving values of approximately equal to 2 J/m2 for the interfacial fracture energy, which we believe corresponds to the cohesive fracture energy of the hydrogel. At these pH values, the DOPA groups are hydrophobic and have a tendency to aggregate, so contact times of 10 or 20 min are required for these high values of the interfacial strength to be observed. At a pH of 10, the DOPA groups were hydrophilic and highly swellable, but less adhesive gels were formed. Oxidation of DOPA groups, a process that is greatly accelerated at a pH of 10, decreased the adhesive performance of the hydrogels even further.

Indentation of a square elastomeric thin film by a flat-ended cylindrical punch in the presence of long-range intersurface forces

This paper reports an experimental study of the elastic deformation of a 200μm thick microfabricated square membrane with sides ranging from 8.5mmto15mm as indented by a fine cylindrical, flat-ended punch with diameter 500μm in the presence of long-range intersurface forces. An apparatus was constructed to allow simultaneously measurements of the indenter displacement and the applied force. A number of interesting phenomena such as the “jump-into-contact” and the “pull-off” between the membrane and the moving cylinder were observed. A simple theoretical analysis using linear elasticity was adopted to fit the load-displacement curve (compliance) and thus estimated the Young’s modulus of the membrane. The measured parameters are consistent with data reported in literature.

Axi-symmetric contact of a punch on an elastic half-space in the presence of tangential tractions

A solution of the axi-symmetric contact problem when an elastic half-space is loaded by both normal and tangential tractions over a circular region is presented. It is assumed that the indenter is rigid and has a profile which can be specified as a polynomial with even powers. Both the spherical and flat-ended cylindrical punches are considered. Formulae for the contact tractions, total load and the penetration depth of the tip of the indenter are found. When the tangential traction vanishes, the well-known solutions for the frictionless contact are recovered.

Indentation of metals by a flat-ended cylindrical punch

The paper reviews the fundamentals of indentation theory for punches with cylindrical geometry, presents a deep-indentation finite element (FE) simulation and discusses an experimental technique for flat-ended cylindrical indentation. This technique is based on the use of cylindrical punches with diameters up to 1 mm and allows pressure–penetration curves to be drawn from which yield stress and elasticity modulus can be determined. Several materials have been tested including pure metals, steels and refractory alloys; yield stress has been determined and compared with literature values. By testing at different temperatures it was also possible to determine the ductile-to-brittle transition temperature (DBTT) for some alloys that show such phenomenon.

Mechanical property extraction through conical indentation of a closed-cell aluminum foam

Deformation and energy absorption characteristics of a closed-cell aluminum foam, ALPORAS, during deep indentation were experimentally investigated by employing frustum of cone shaped indenters with varying cone angles and are compared with those observed in uniaxial compression with an objective of estimating mechanical properties such as shear strength from the indentation experiments. Morphological examination of the indents obtained when the cone angle is 0° (a flat-ended cylindrical punch) reveals crushing of the cells beneath the indenter and tearing of the cells at the periphery. No lateral spread in plastic deformation is observed. When the cone angle is greater than 0°, shearing of the foam at the periphery takes place in addition to tearing, and the shearing increases with the cone angle. An analytical model that incorporates all the three modes of deformation, crushing, tearing, and shearing, is used to describe the force–displacement and energy absorption data as a function of the cone angle. In turn, it was demonstrated that material properties such as the tear energy and shear strength could be extracted from the conical indentation data.

Impression creep of a viscous layer

Impression creep of a flat-ended cylindrical punch pushed into a viscous layer overlaid on a rigid substrate is analyzed. The method developed here permits us to relate the impression velocity to the punching stress in terms of an auxiliary function, which represents the solution of a set of Fredholm integral equations with a continuous symmetrical kernel. By a series of numerical analysis, the influence of the boundary conditions and the effect of the thickness of the layer on the impression velocity are obtained. For infinite thickness (i.e., h/a →∞, where h is the thickness of the layer and a is the radius of the punch), the impression creep is independent of the stick or slip boundary condition at the indenter/layer interface. For finite thickness such as h/a = 20, the boundary conditions have about 5% effect on the impression velocity. For a thin film, the impressing velocity is very sensitive to the boundary conditions. In fact it suggests a possible experimental way to detect debonding at the interface between the thin film and the substrate.