Flat-tip Indenter Research Articles

Development of a continuum-based, meshless, finite element modeling approach for representation of trabecular bone indentation

Implant subsidence into the underlying trabecular bone is a common problem in orthopaedic surgeries; however, the ability to pre-operatively predict implant subsidence remains limited. Current state-of-the-art computational models for predicting subsidence have issues addressing this clinical problem, often resulting from the size and complexity of existing subject-specific, image-based finite element (FE) models. The current study aimed to develop a simplified approach to FE modeling of subject-specific trabecular bone indentation resulting from implant penetration.Confined indentation experiments of human trabecular bone with flat- and sharp-tip indenters were simulated using FE analysis. A generalized continuum-level approach using a meshless smoothed particle hydrodynamics (SPH) approach and an isotropic crushable foam (CF) material model was developed for the trabecular bone specimens. Five FE models were generated with CF material parameters calibrated to cadaveric specimens spanning a range of bone mineral densities (BMD). Additionally, an alternative model configuration was developed that included consideration of bone marrow, with bone and marrow material parameters assigned to elements randomly according to bone volume (BV%) measurements of experimental specimens, owing to the non-uniform nature of trabecular bone tissue microstructure.Statistical analysis found significant correlation between the shapes of the numerical and experimental force-displacement curves. FE models accurately captured the bone densification patterns observed experimentally. Inclusion of marrow elements offered improved response prediction of the flat-tip indenter tests.Ultimately, the developed approach demonstrates the ability of a generalizable continuum-level SPH approach to capture bone variability using clinical bone imaging metrics without needing detailed image-based geometries, a significant step towards simplified subject-specific modeling of implant subsidence.

Inferring mechanical properties of the SARS-CoV-2 virus particle with nano-indentation tests and numerical simulations

The pandemic caused by the SARS-CoV-2 virus has claimed more than 6.5 million lives worldwide. This global challenge has led to accelerated development of highly effective vaccines tied to their ability to elicit a sustained immune response. While numerous studies have focused primarily on the spike (S) protein, less is known about the interior of the virus. Here we propose a methodology that combines several experimental and simulation techniques to elucidate the internal structure and mechanical properties of the SARS-CoV-2 virus. The mechanical response of the virus was analyzed by nanoindentation tests using a novel flat indenter and evaluated in comparison to a conventional sharp tip indentation. The elastic properties of the viral membrane were estimated by analytical solutions, molecular dynamics (MD) simulations on a membrane patch and by a 3D Finite Element (FE)-beam model of the virion's spike protein and membrane molecular structure. The FE-based inverse engineering approach provided a reasonable reproduction of the mechanical response of the virus from the sharp tip indentation and was successfully verified against the flat tip indentation results. The elastic modulus of the viral membrane was estimated in the range of 7–20 MPa. MD simulations showed that the presence of proteins significantly reduces the fracture strength of the membrane patch. However, FE simulations revealed an overall high fracture strength of the virus, with a mechanical behavior similar to the highly ductile behavior of engineering metallic materials. The failure mechanics of the membrane during sharp tip indentation includes progressive damage combined with localized collapse of the membrane due to severe bending. Furthermore, the results support the hypothesis of a close association of the long membrane proteins (M) with membrane-bound hexagonally packed ribonucleoproteins (RNPs). Beyond improved understanding of coronavirus structure, the present findings offer a knowledge base for the development of novel prevention and treatment methods that are independent of the immune system.

Characterization of Anisotropy of Strength in API-X80 Line Pipe Welds Through Instrumented Indentation

In this work, an instrumented indentation technique with a nearly flat tip indenter was used to measure the yield strength of API-X80 line pipe weld. Using this technique, the yield strength can be estimated directly from the indentation load–displacement response. The yield strength of the weld metal was measured in the transverse (hoop) and longitudinal (long) directions of the weld, and the results indicated that the weld metal exhibits anisotropy in terms of the yield strength by as much as 100 MPa, which could lead to a non-conservative estimate when strength mismatch is considered. Conventional tensile testing obtained strength values to within 4.6% of the indentation measurements and confirmed the results. Hardness maps also show a 20 HV0.5 difference in the two directions of the weld, which supports anisotropy of yield strength. The microstructure analysis using SEM reveals a slight difference in the grain size, which partially explains the differences in properties.

Effect of Poisson’s ratio on material property characterization by nanoindentation with a cylindrical flat-tip indenter

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Mechanical Behavior of Undoped n-Type GaAs under the Indentation of Berkovich and Flat-Tip Indenters.

In this research, the mechanical behavior of undoped n-type GaAs was investigated by nanoindentation experiments using two types of indenters—Berkovich and flat-tip—with force applied up to 1000 mN. From the measured force-depth curves, an obvious pop-in phenomenon occurred at force of 150 mN with the flat-tip indenter representing elastic–plastic transition. The Young’s modulus and hardness of GaAs were calculated to be 60–115 GPa and 6–10 GPa, respectively, under Berkovich indenter. Based on the observation of indent imprints, the fracture characteristics of GaAs were also discussed. A recovery of crack by the next indentation was observed at 1000 mN with Berkovich indenter. In the case of flat-tip indentation, however, surface material sank into a wing shape from 400 mN. In this sinking region, a density of fork-shaped sinking, slip lines, and crossed pits contributed to the slip bands, and converging crossed twinning deformations inside the GaAs material were generated. Since cracks and destructions on GaAs surface took place more easily under the flat-tip indentation than that of Berkovich, a machining tool with a sharp tip is recommended for the mechanical machining of brittle materials like GaAs.

In situ frustum indentation of nanoporous copper thin films

Mechanical properties of thin films are often obtained solely from nanoindentation. At the same time, such measurements are characterized by a substantial amount of uncertainty, especially when mean pressure or hardness are used to infer uniaxial yield stress. In this work we demonstrate that indentation with a pyramidal flat tip (frustum) indenter near the free edge of a sample can provide a significantly better estimate of the uniaxial yield strength compared to frequently used Berkovich indenter. This is first demonstrated using a numerical model for a material with an isotropic pressure sensitive yield criterion. Numerical simulations confirm that the indenter geometry provides a clear distinction of the mean pressure at which a material transitions to inelastic behavior. The mean critical pressure is highly dependent on the plastic Poisson ratio νp so that at the 1% offset of normalized indent depth, the critical pressure pmc normalized to the uniaxial yield strength σ0 is 1 < pmc/σ0 < 1.3 for materials with 0<νp<0.5. Choice of a frustum over Berkovich indenter reduces uncertainty in hardness by a factor of 3. These results are used to interpret frustum indentation experiments on nanoporous (NP) Copper with struts of typical diameter of 45 nm. An estimate of the yield strength of NP Copper is obtained 230 MPa <σ0 < 300 MPa. Edge indentation further allows one to obtain in-plane strain maps near the critical pressure. Comparison of the experimentally obtained in-plane strain maps of NP Cu during deformation and the strain field for different plastic Poisson ratios suggest that this material has a plastic Poisson ratio of the order of 0.2–0.3. However, existing constitutive models may not adequately capture post-yield behavior of NP metals.

Effects of angular misalignment on material property characterization by nanoindentation with a cylindrical flat-tip indenter

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Characterization of materials' elasticity and yield strength through micro-/nano-indentation testing with a cylindrical flat-tip indenter

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Low temperature fracture toughness of PMMA and crack-tip conditions under flat-tipped cylindrical indenter

Fracture toughness of a PMMA (poly(methyl methacrylate)) plate was measured at −20°C, −40°C and −80°C, using a newly-developed flat-tip indentation method, and compared with the room temperature results. A flat-tipped cylindrical indenter with a sharp edge, made from hardened steel, was used for the experiments. For comparison, indentation damage and crack patterns from a tungsten-carbide tip with a microscopically-chipped edge were also examined. The zigzag imprint front shows indentation cracking can indeed be generated under a flat-tipped indenter, as implied by the theoretical singular stress field at the contact edge of a sharp-edged and flat-tip indenter. Finite element analysis (FEA) simulations were used to confirm the theoretical fracture toughness equations for pure elastic stress fields, and were used to determine the elastic stress field at the indentation crack-tip following the theoretically-determined cracking angle to illustrate the nature of the mixed-mode elastic fracture. However, as shown by optical cross-section observations, plastic damage in PMMA at the contact edge alters the cracking/damage pattern.

Material elastic–plastic property characterization by nanoindentation testing coupled with computer modeling

In this paper, an innovative approach through nanoindentation testing using a Berkovich sharp-tip and a cylindrical flat-tip, respectively, and coupled with computer modeling is proposed as a means of characterizing the elastic–plastic properties of materials within micro/nanoscale. Low carbon steel was selected as a case study material. Nanoindentation tests were carried out to obtain load–depth graphs. For cylindrical flat-tip indentation, a mechanical model was proposed for directly extracting yield strength of the testing material from the corresponding load points, considering a modifier k. Young's modulus was derived from the indentation tests using both tips. The final indentation sites were measured and analyzed using a 3D laser scanning microscope. The nanoindentation solid models were developed, and computer modeling based on finite element analysis was conducted to find the effects of indentation depth, yield strength and strain hardening coefficient on the load–depth graph and the final indentation pileup profiles, taking into account the effects of friction on nanoindentation. The computer modeling nanoindentation data was compared with and validated by the nanoindentation tests.

Study of stress relaxation in polytetrafluoroethylene composites by cylindrical macroindentation

In the present work, the time-dependent mechanical behavior of three materials from the fluorocarbon family, including PTFE without filler, 15vol.% regenerated graphite particles-filled PTFE, and 32vol.% carbon and 3vol.% graphite particles-filled PTFE, was investigated using cylindrical macroindentation. Indentation relaxation experiments with a cylindrical flat-tip indenter having a diameter of 1mm were performed at three different strain levels. The generalized Maxwell model in terms of the Prony series and a time-dependent solution based on the power-law creep equation were used to model the viscoelastic response and to extract the time-dependent properties. The stress relaxation properties were found to improve with the addition of fillers. The unfilled PTFE exhibited the lowest stress–relaxation properties, whereas the 32vol.% carbon and 3vol.% graphite particles-filled PTFE composite showed the highest stress–relaxation properties.

Extending the EGP constitutive model for polymer glasses to multiple relaxation times

The one-mode EGP (Eindhoven glassy polymer) model captures the plastic flow at yield and post-yield quantitatively, but behaves poor in the non-linear viscoelastic pre-yield region. Since a proper description here is important in cases of complex loading and unloading situations, such as e.g. in indentation and scratching, an extension to non-linear modeling is required using a spectrum of relaxation times. It is shown that such a reference spectrum can be obtained from simple tensile tests. It shifts to shorter times under the influence of stress and is independent of the two important time-dependent processes in polymers: the strain rate applied during testing and the aging time during storage and use. The multi-mode model is critically tested and proves quantitative in describing the intrinsic polymer response and, based thereupon, in predicting the correct response in tensile testing, including necking, in flat tip indentation and in notched loading.

Determination of Asphalt Binder Creep Compliance Using Depth-Sensing Indentation

Asphalt binders are common construction materials, however due to time- and temperature- dependence, their mechanical properties are often difficult to characterize. Several standard tests methods exist to describe their complex behavior. This paper presents an exploratory feasibility study of a flat-tip indentation testing to analyze the linear viscoelastic properties of asphalt binders. Depth-sensing indentation testing has been extensively used to characterize the properties of many engineering materials, however the applications to asphalt binders are very limited. This paper presents a simple solution for the creep compliance in tension derived for flat-tipped indenter. This solution was verified with the Finite Element Analysis and then applied to the experimental results from the indentation testing performed on one typical unmodified asphalt binder. The testing was conducted at three different low temperatures and under three different creep load levels to verity the linearity of the response, and to evaluate the robustness and applicability of the indentation method. Furthermore, the creep compliance functions determined from the indentation testing were compared with a more traditional 3-point bending experiments. The results show that there is a non-uniform discrepancy between the two testing methods, most likely due to nonlinear behavior of the asphalt binder at higher temperatures and micro-damage of the binder samples at lower temperatures. Other possible sources of error between indentation and 3-point bending are problems determining the initial tip-specimen contact surface and possible tip-specimen adhesion. It is concluded that flat-tipped indentation at low temperatures should be performed at lower load levels to avoid excessive stress concentrations that leads to micro-damage and nonlinear response of asphalt binders. Alternatively, asphalt binders at low temperatures could be evaluated using different indenter geometries, such as spherical or pyramidal, using corresponding parameter interpretation procedures.

Numerical simulation of flat-tip micro-indentation of glassy polymers: Influence of loading speed and thermodynamic state

Flat-tip micro-indentation tests were performed on quenched and annealed polymer glasses at various loading speeds. The results were analyzed using an elasto-viscoplastic constitutive model that captures the intrinsic deformation characteristics of a polymer glass: a strain-rate dependent yield stress, strain softening and strain hardening. The advantage of this model is that changes in yield stress due to physical aging are captured in a single parameter. The two materials studied (polycarbonate (PC) and poly(methyl methacrylate) (PMMA)) were both selected for the specific rate-dependence of the yield stress that they display at room temperature. Within the range of strain rates experimentally covered, the yield stress of PC increases linearly with the logarithm of strain rate, whereas, for PMMA, a characteristic change in slope can be observed at higher strain rates. We demonstrate that, given the proper definition of the viscosity function, the flat-tip indentation response at different indentation speeds can be described accurately for both materials. Moreover, it is shown that the model captures the mechanical response on the microscopic scale (indentation) as well as on the macroscopic scale with the same parameter set. This offers promising possibilities of extracting mechanical properties of polymer glasses directly from indentation experiments.

Temperature Dependent Viscoelastic Properties of Polymers Investigated by Small-Scale Dynamic Mechanical Analysis

The temperature-dependent viscoelastic properties of polymers were investigated by small-scale dynamic mechanical analysis in the range of −100°C to 200°C. The polymers tested included glassy polymer (atactic polystyrene), semicrystalline polymer (high-density polyethylene) and rubbery polymer (polyisobutylene). The small-scale dynamic mechanical analyses were performed by using a flat-tip indenter with an oscillating displacement of amplitude 36 nm. The force amplitude and phase angle were measured, from which the storage modulus E′ and loss tangent tanδ were calculated. The results obtained from indentation experiments are consistent with those obtained from conventional dynamic mechanical analyzer (DMA). It is thus demonstrated that the indentation technique can quantitatively measure the temperature-dependent viscoelastic properties of polymers at small dimensions.

Experimental Analysis of Viscoelastic Behavior in Nanoindentation

Conventional analysis of load displacement curves in nanoindentation experiments determine modulus by using the elastic portion of the unloading slope or power law fitting the unloading slope. For polymeric materials, however, this analysis is not adequate because they behave viscoelastically. In companion research, L. Cheng has developed analytical models for flat tip and spherical tip indentation using a three element Kelvin-Voigt model, with a spring in series with a parallel dashpot and a spring for compressible and incompressible materials. Incompressible (v=0.5) polydimethylsiloxane coatings with thicknesses of 2 and 78 microns, a compressible (v=0.33) bulk polystyrene (PS) and a 16 Jim styrene-acrylate block copolymer coating (v=0.33) have been used to verify the models. The polymers were indented using flat tip and spherical tip indenters with a nanoindentation apparatus in creep (constant load) and relaxation modes (constant depth). The data was fit to the analytical models using a non-linear least squares fit algorithm varying three parameters. In general the fitted elastic and shear moduli compared favorably with conventional rheological and mechanical measurements on the same bulk polymers. However, it appears that the agreement for the thin film analysis can be improved by taking the hydrostatic pressure dependence of the modulus and substrate effects into consideration.