Indenter Displacement Research Articles

Quasi-static indentation analysis on three-dimensional printed continuous-fiber sandwich composites

Fiber reinforced sandwich structures are widely used as structural elements due to their lightweight and high load-bearing capacity. In this paper, effort is taken to fabricate fiber facesheet (0°/90° orientation) and corrugated cores (trapezoidal vertical pillared, core-1 and sinusoidal vertical pillared, core-2) of the sandwich structure using fused filament fabrication and Inkjet printing techniques, respectively. Firstly, the quasi-static indentation properties of the additively manufactured facesheet, cores, and sandwich structures were investigated. In addition, acoustic emission signals were monitored during quasi-static indentation testing and the resulting hits data were correlated with quasi-static indentation test results. The quasi-static indentation test results showed that sinusoidal sandwich structures have the highest load-bearing capacity of 1.79 kN until crack initiation and a total energy-absorption capacity of 20.05 J. Acoustic emission hits recorded in the range of 1–30, 30–100, and above 100 represented crack initiation, crack propagation, and specimen failure, respectively. Lastly, micro-computed tomography analysis was performed on the sandwich structures at intermediate indentation displacements, thus leading to the identification of hard to detect failure points and damage propagation. Fracture surface morphology of the sandwich structures showed that fiber pullout and core shear were the dominant damage mechanisms.

Contribution of interferometry to Vickers indentation toughness determination of glass and ceramic glass

Cracking resistance or fracture toughness of brittle materials, such as optical glasses, can be determined by Vickers indentation, which allows generating cracks along the diagonals of the indent whose length depends of the loading rate. Subsequently, a relationship between the crack length and the corresponding indentation load is applied to calculate the indentation fracture toughness. As a result, the precision of the fracture toughness will depend on the accuracy of the crack length measurement. To minimize the uncertainties of this parameter, we propose its measurement more precisely by a profilometric method. On the other hand, as the glass surface roughness is recognized to have an important influence on the crack growth, different surface preparations are studied to minimize this roughness effect. In this work, four types of glasses are studied, namely Classical Crown K5, Borosilicate Crown BK7, Dense Flint SF2, and Ceramic Zerodur® glasses. The surface polishing is performed by using CeO2 pellets, which allow obtaining a roughness value for Ra to be <10 nm. Vickers instrumented indentation tests, allowing the plot of the applied load as a function of the indenter displacement, are performed with various maximum applied loads of up to 90 N. Different relationships based on assumptions on the crack shape (half-penny/median or Palmqvist cracks) are then used to calculate the indentation fracture toughness. Additionally, to accurately measure the crack length, we present an original approach based on the analysis of the interferometry map obtained with an optical profilometer using a monochromatic wavelength.

Failure analysis and mechanical behavior of dented pipeline dent caused by indenter

Dented defects pose a great threat to the safety of oil and gas pipeline transportation. In this paper, dent behavior of a pipeline caused by a spherical indenter was investigated. Effects of thickness, indenter displacement, indenter radius and pipeline internal pressure on the stress, strain and depth of the pipeline dent are discussed. The results show that internal pressure has a great effect on the pipeline dent. When the internal pressure increases, folds appear on the pipeline wall. With the increasing of wall thickness and indenter displacement, the stress, plastic strain and dent depth increase. But the radius of the indenter has a little effect on the dent’s stress and strain. In general, the strain and the depth of the dent achieve an extreme point or maximum near the edge of the dent.

The hardness and modulus of polycrystalline beryllium from nano-indentation

Nanoindentation was used to compare properties of four industrial beryllium grades with different purity. An extremely high variation of hardness was observed in all samples which obscured differences between samples. Analysis of the nanoindentation data in combination with SEM/EBSD measurements demonstrated that the crystallographic orientation of the indented grain was the major source of the wide variation in hardness, which was 2.5 times higher when the indentation direction was close to the [0001] c-axis of beryllium compared to indentation along the [112¯0] or [11¯00] directions. The most noticeable difference between tested grades were observed for the “soft” orientations: hardness of less pure structural grades was 15–30% higher compared to the pure nuclear grade. Crystal plasticity finite-element (CPFEM) simulations indicated how the hardness anisotropy of beryllium arises from the anisotropy in the plastic deformation. Experiments and simulations also demonstrated that localised plastic deformation of the surface around the indent (pile-up or sink-in) was highly crystallographically dependent: during indentation into “soft” orientations, pile-up dominated increasing the contact area; while sink-in behaviour was dominant during indentation into “hard” orientation reducing the contact area. This implies that the hardness values calculated from indenter displacement and indenter profile using the standard Oliver-Pharr approach, without considering pile-up/sink-in effects, will be incorrect. Several contact area correction methods were applied and compared. In contrast the indentation modulus was similar for all investigated grades and was not found to have any strong crystallographic dependence. Crystal plasticity finite element analysis indicates that this is due to the complex 3-dimensional nature of the elastic interaction between the indenter and the sample, and also since, for the chosen indentation depth, the elastic interaction volume is much larger than the materials’ grain size.

Microscale interfacial adhesion assessment in a multilayer by a miniaturised four-point bending test

Microscale techniques capable of selectively isolating and delaminating embedded multilayer interfaces in a stable manner have the potential to be powerful characterisation tools for improving the reliability of microelectronic devices. Here we propose an analytical approach to assess the steady-state strain energy release rate during the delamination of an embedded multilayer interface, initiated by our recently developed miniaturised four-point bending technique. Stable delamination of a SiN-GaAs interface was initiated via nanoindentation induced bending of microbridges that had been milled into the surface of an Al-SiN-GaAs multilayer using a focused ion beam. Analytical models quantify the strain energy released within a section of a microbridge using the load-displacement relation obtained during delamination. The models are validated by demonstrating their capacity to approximate the experimentally observed linear-elastic deformation of a reference microbridge under both three- and four-point bending. We find that deformation of the clamped-ends as well as indenter penetration of a microbridge contribute significantly to the total indenter displacement. We then show this can be accounted for through a combination of Euler–Bernoulli beam and Hertzian contact theory. A mean steady-state strain energy release rate of G¯SS=2.20±0.36Jm−2 is obtained for the SiN–GaAs interface.

On the value of test data for reducing uncertainty in material models: Computational framework and application to spherical indentation

We present a conceptual framework and the computational tools to study the value of the material responses in designing material characterization tests to identify the material model under uncertainty. A computational framework is first developed to estimate the information gained by observing a material response as a measure of the value of the experiment. The proposed framework is then extended to estimate the mutual information between the material response space and the material model space as a basis for ranking the available material response candidates as they relate to reducing the uncertainty of the inferred model. We then define a design problem where a tunable parameter, referred to as the design parameter, is identified so as to render two different material responses to be of the same value from an information content point of view. We finally study the value of the material responses, obtained in a spherical indentation test, i.e. reaction force–indenter displacement, maximum indentation load and the residual imprint, where it is shown that the proposed framework offers a computationally affordable and uncertainty-aware platform to design material characterization tests.

Determining of the machine compliance using instrumented indentation test and finite element method

.At present time the importance of indentation measurements once again increases. As modern and perspective measurement method it allows to measure various mechanical properties while only needing micro volumes of materials. While standard hardness measurement methods examine only the plastic response of sampled material, Depth Sensing Indentation (DSI) testing is founded on real-time recording of applied force and resulting travel of indenter. This allows to evaluate both plastic and elastic response of examined material during the indentation process which in turn allows for calculation of various static material properties in very small volumes of samples. The big advantage of this approach is saving of time (especially on sample preparation), however the data analysis – and thus results – could be influenced by certain factors. Those worth noting are surface quality of the sample, wear of the indenter head, its shape and material, and also the compliance of testing machine’s frame. If we consider the frame of testing machine having non-zero compliance, inevitably there will occur not only displacement of indenter but also displacement of frame itself, especially noticeable while using high loads. This negatively influences the results of such measurement. This work’s aim is to calculate the compliance of test machine’s frame using Finite Element Method model and 1 mm in diameter steel ball indenter. The result of this work is addition of virtual spring to the FEM model and fine tuning of its stiffness. This should allow us to minimize the influence of frame’s compliance on the results of future measurements.

Three-dimensional finite element analysis of shallow indentation of rough strain-hardening surface

Three-dimensional finite element modeling of the contact between a rigid spherical indenter and a rough surface is presented when considering both the loading and unloading phases. The relationships among the indentation load, displacement, contact area, and mean contact pressure for both loading and unloading are established through a curve fitting using sigmoid logistic and power law functions. The contact load is proportional to the contact area, and the mean contact pressure is related to the characteristic stress, which is dependent on the material properties. The residual displacement is proportional to the maximum indentation displacement. A proportional relationship also exists for plastically dissipated energy and work conducted during loading. The surface roughness results in an effective elastic modulus calculated from an initial unloading stiffness several times larger than the true value of elastic modulus. Nonetheless, the calculated modulus under a shallow spherical indentation can still be applied for a relative comparison.

Investigating the mechanical and optical properties of thin PDMS film by flat-punched indentation

We investigated mechanical and optical properties of a thin polydimethylsiloxane (PDMS) film through a flat-punched indentation experiment and a finite element simulation. A microscopic imaging method was used to measure the compressive strain of thin PDMS films, and its corresponding bulk refractive index (RI) was estimated using the relation between density and refractive index. A total internal reflection (TIR) experiment was conducted to estimate the local RI values near the bottom surface of PDMS film. We obtained the correlations between force and indentation displacement in thin PDMS films (10–70 micron). Stress-strain curves present the non-linear deformation of PDMS film with the instantaneous modulus depending on the load and the thickness. Poisson's ratio of PDMS film is estimated by fitting with Yang's asymptotic solution and is inversely proportional to the aspect ratio between the radius of the flat punch probe and the film thickness. RI of PDMS film increases with the decreasing film thickness as well as the increasing load. The bulk RI was increased up to 1.476 by the compressing load while the bottom-surface RI was increased only up to 1.435. This difference is explained qualitatively through the localized stress-strain distribution from finite element analysis. An inhomogeneous stress-strain distribution is observed in the simulation with lower strain at the bottom of the film, corresponding to experiment. A lower strain leads to lower local density resulting in a lower refractive index. Our research provides fundamental insights into the correlation between mechanical and optical properties of thin polymer films.

Asymmetric indentation of an elastic beam by a rigid cylinder

A simple method is proposed to analyze asymmetric indentation of a supported elastic beam by a rigid cylinder placed at an arbitrary position on the beam. A key advantage of our method over existing methods is that a single governing Kerr-type differential equation, which gives the relation between contact pressure and the normal deflection of the pressured surface of the beam, is applied both inside and outside the contact zone. With the present method, the two ends of contact zone will be determined as part of the solution, in contrast to the existing related studies which were all based on a simplifying assumption that the contact zone is geometrically symmetric about the tip of the indenter. Indeed, our results confirm that the contact zone is generally geometrically non-symmetric about the indenter tip, and even the whole contact zone can locate on one side of the indenter tip in some cases. Asymmetric indentation behaviors are demonstrated with numerical examples, with an emphasis on asymmetric contact pressure distribution inside the contact zone. Explicit formulas for the contact-zone width–displacement, force–displacement and moment–displacement relations are derived and illustrated with numerical examples. In particular, the present model predicts that as the indentation displacement exceeds a critical value, the indenter will lose contact with the beam inside the contact zone, which implies that the actual contact zone becomes two separate contact strips. Validity and accuracy of the present method are demonstrated by comparing its predictions with known results for some special cases. New features of asymmetric indentation as compared to symmetric indentation are summarized at the end of the paper.

Design and Fabrication of a Portable 1-DOF Robotic Device for Indentation Tests

There are many tactile devices for indentation examinations to measure mechanical properties of tissue. The purpose of this paper is to develop a portable indentation robotic device to show its usability for measuring the mechanical properties of a healthy abdominal tissue. These measurements will help to develop suitable mathematical models representing abdominal tissue. A 1-DOF portable robotic device has been designed to be placed on the patient’s body. The device presses sensor plate on the abdomen. Force and position sensors measure the indentation force and displacement, respectively. Due to tissue time-dependent behavior, linear viscoelastic models with three, five and seven parameters have been selected for mathematical modeling. Nonlinear Least Squares (NLS) method is adopted to fit viscoelastic models with experimental data obtained from stress relaxation tests. Using Finite Prediction Error (FPE) criterion, viscoelastic model with five parameters has been selected as the optimal model. The results of the present paper can be used in abdominal tissue simulators to facilitate teaching palpation examinations.

An Approximate Solution to the Plastic Indentation of Circular Sandwich Panels

The plastic indentation response of circular sandwich panels loaded by the flat end of a cylinder is investigated employing a velocity field model. Using the principles of virtual velocities and minimum work, an expression for the indenter load in relation to the indenter displacement and displacement field of the deformed face sheet is derived. The analytical solutions obtained are in good agreement with those found by simulations using the ABAQUS code. The radial tensile strain of the deformed face sheet and the ratio of energy absorption rate of the core to that of the face sheet are discussed.

Mechanical Material Tests by the Nanoindentation Method at Various Indenter and Specimen Temperatures

Theoretical and experimental studies have been made of the nonisothermal contact interaction of an unsharpened conical indenter and an elastic material with an inhomogeneous surface layer. A relevant contact problem of thermoelasticity with arbitrarily changed thermomechanical characteristics in the depth of the surface layer has been formulated. To solve the boundary-value problem, the apparatus of integral Hankel transforms is used. With the use of the asymptotic method, a numerical-analytical approximated solution of the problem has been constructed, the values of the corresponding heat flux and of the half-space surface displacement have been determined, and the values of contact stresses beneath the die have been found. The developed model is used to estimate the value of indenter displacement caused by the thermoelastic deformation of the specimen. The results of the experiment on nonisothermal indentation of the prepared specimen of steel 40Kh on a Nanotest 600 facility are presented. The application of nanoindentation for investigations of mechanical properties of materials at high temperatures is discussed.

Analysis of Solvent Effect on Mechanical Properties of Poly(ether ether ketone) Using Nano-indentation

Poly(ether ether ketone) (PEEK) is a high-performance semi-crystalline thermoplastic polymer. Exposure of the polymeric surface to solvents can have a strong effect like softening/swelling of polymeric network or dissolution. In this study, nano-indentation analysis was performed to study the effect of acetone on the surface mechanical properties of PEEK using different exposure time. The experiments were performed with a constant loading rate (10 nm/s) to a maximum indentation displacement (1000 nm). A 30-second hold segment was included at the maximum load to account for any creep effects followed by an unloading segment to 80% unloading. The indentation hardness and the elastic modulus were computed as a continuous function of the penetration displacement in the continuous stiffness mode (CSM) indentation. The experimental data showed that the peak load decreased from ∼5.2 mN to ∼1.7 mN as exposure time in solvent environment increased from 0 to 18 days. The elastic modulus and the hardness of PEEK samples also displayed a decreasing trend as a function of exposure time in the solvent environment. Two empirical models were used to fit the experimental data of hardness as a function of exposure time which showed a good agreement with the experimental values.

Simulation investigation of dent behavior of steel pipe under external load

Abstract Denting, caused by working condition and by rocks or external objects during the laying process, is an important failure mode of steel pipes. To study the failure mechanism of a steel pipe, steel pipe behavior with longitudinal, transverse, and tilted dents were investigated. Effects of the diameter-thickness ratio and indenter displacement on the pipe mechanical behavior were studied. The results showed that plastic deformation occurred mainly at the dent, where there was an obvious stress concentration. The plastic deformation of the pipe continued to increase during the unloading process. The axial strain at the dent location was compressive strain. Dent's rebound rate (depth ratio of the dent after loading and unloading) of the pipe increased with increasing the diameter-thickness ratio and decreased with increasing the indenter displacement. With transverse denting, both sides of the dent were more dangerous than the dent location. The force-displacement curve for the pipe subjected to a tilted dent was different than those for longitudinal and transverse denting. There is no raised effect for the tilted dent.

Berkovich nanoindentation of borosilicate K9 glass

Instrumented indentation was used to investigate the proportional relationships among indentation variables such as the maximum indentation displacement, contact depth, the ratio of load over contact stiffness, and the ratio of permanent displacement over the maximum displacement. Material and indenter were borosilicate K9 glass and a Berkovich indenter, respectively. Results of fused silica under the same indenter were compared. Load–displacement curves of K9 glass were characterized by power-law functions for both loading (power exponent of 2) and unloading (power exponent of 1.36) with hardness, elastic modulus, yield stress, and power strain hardening exponent being 7.72, 82.8, 3.5 GPa, and 0.6, respectively. Experimental results were found to be in agreement with theoretical prediction and dimensional analysis. The results calculated from energy-based method were found to be consistent with those based on Oliver and Pharr’s method. General implications of the scaling relations for indentation variables were discussed (e.g., the scaling expressions can be used to check indentation data).

MARSTRUCT benchmark study on nonlinear FE simulation of an experiment of an indenter impact with a ship side-shell structure

This paper presents a benchmark study on collision simulations that was initiated by the MARSTRUCT Virtual Institute. The objective was to compare assumptions, finite element models, modelling techniques and experiences between established researchers within the field. Fifteen research groups world-wide participated in the study. An experiment involving a rigid indenter penetrating a ship-like side structure was used as the case study. A description of how the experiment was performed, the geometry model of it, and material properties were distributed to the participants prior to their simulations. The paper presents the results obtained from the fifteen FE simulations and the experiment. It presents a comparison of, among other factors, the reaction force versus the indenter displacement, internal energy absorbed by the structure versus the indenter displacement, and analyses of the participants' ability to predict failure modes and events that were observed in the experiment. The outcome of the study is a discussion and recommendations regarding mesh size, failure criteria and damage models, interpretation of material data and how they are used in a constitutive material model, and finally, uncertainties in general.

Mechanical property evaluation of carbon nanotubes reinforced plasma sprayed YSZ-alumina composite coating

Yttria (8%) stabilized zirconia (8YSZ)-alumina-carbon nanotube (CNT) composite coatings were deposited using air plasma spray (APS) technique. Three zirconia alumina (ZA) composite coatings, without CNT reinforcement, and with 1%CNT, 3%CNT reinforcement were deposited using identical process parameters (500A and 66V). Indentation method was used to characterize mechanical behavior of coatings. The CNT reinforced composite coating showed superior mechanical properties as compared to the conventional 8YSZ coating. The addition of alumina and 1%CNTs increased the Young's modulus by around 25% and 40%, respectively. However, the increase in CNT content decreased the Young's modulus as a result of CNT agglomeration. The hardness, fracture toughness increased with addition of alumina and CNT. The fracture toughness increased from 0.55 ± 0.26MPam1/2 for 8YSZ to 1.76 ± 0.65MPam1/2 for 17%alumina-3%CNT reinforcement due to various toughening mechanisms like crack deflection, bridging etc. The maximum displacement of indenter was found to decrease from ~ 176nm for conventional YSZ coating to ~ 120nm for 3% CNT reinforced coating. The surface roughness (Ra) was found to be decrease with alumina addition and CNT reinforced coating. The CNT reinforced coating showed surface roughness of around 6µm. Scanning electron microscopy (SEM) with energy dispersive spectroscopy (EDS) was used to characterize the coating microstructure and elemental composition respectively.

Experimental and numerical penetration response of laser-welded stiffened panels

Ductile fracture in large structures is often resolved with non-linear finite element (FE) simulations employing structural shell elements which are larger than localization zone. This makes solution element size dependent and calibration of material parameters complex. Therefore, the paper explores the ability of numerical simulations to capture the penetration resistance of stiffened panels after determining steel material fracture ductility at different stress states. The numerical simulations are compared with experiments performed with rigidly fixed 1.2 m square panels penetrated with half-sphere indenter until fracture took place. Response of the panels was measured in terms of indentation force versus indenter displacement. In parallel, tensile tests were performed with four different flat specimens extracted from the face sheet of panels to characterize the material fracture ductility at different stress states. Panel simulations were performed with two fracture criteria: one calibrated based on the test data from dog-bone specimen and other calibrated based on the data from all tensile tests. To evaluate the fracture criteria in terms of their capacity to handle mesh size variations, mesh size was varied from fine to coarse. Results suggest that fracture criterion calibrated based on the range of stress states can handle mesh size variations more effectively as displacement to fracture showed considerably weaker mesh size dependence.

Indentation on a transversely isotropic half-space of multiferroic composite medium with a circular contact region

The present paper concerns the contact problem in the context of elasticity of multiferroic composite media. The substrate under consideration is a half-space which is made of magneto-electro-elastic material with transverse isotropy. The magneto-electric properties of the indenter are comprehensively taken into account. The integral equations for four cases are established by means of the general solution and the generalized potential theory method. The corresponding fundamental magneto-electro-elastic field variables in the substrate, which are caused by the generalized indentation displacements following the Dirac-delta distribution in the contact area, are explicitly and exactly obtained in terms of elementary functions. Based on the present fundamental solutions, a general theory of indentation, where the profile of the indenter may be expanded as a Taylor series, is developed. Furthermore, by applying the results of a general theory, two classical concave indenters (conical and parabolic) are considered. Concept of effective penetration depth is proposed for concave indenters. Numerical calculations are carried out in order for various purposes, including validation of the present solutions, demonstration of the coupling effects in multi-phases of the composite medium and effect of the geometry of the indenter on contact behaviors.