Indentation Experiments Research Articles

The Influence of Tilt on Berkovich Indentation of a Steel Sample Using FEM Analysis and Nanoindentation

Abstract The main shape deviations of a Berkovich indenter are the indenter bluntness and indenter tilt. The influence of the Berkovich indenter tilt on the results of the FEM modelling of steel nanoindentation is evaluated in this paper. The indenter tilt has an impact on the indentation curves and contact area. The X5CrNiCuNb 16-4 steel nanoindentation was modelled by FEM and the indentation curves were obtained. The Berkovich indenter was blunted and the tilt of the indenter was changed to determine its influence on the indentation curves. The results showed that growing tilt shifts the indentation curves to higher values of indentation forces and makes unloading curves steeper which is in agreement with a larger contact area. The calculated indentation curves were compared with the experimental indentation curves and the impact of the indenter tilt to the indentation curves was determined.

Experimental and modeling studies on contact mechanics of silicone rubbers

In this paper, the contact behavior of silicone rubbers under spherical and conical indenters is investigated by simulation and experiment. The accuracy and applicability of seven hyperelastic constitutive models are discussed for the contact behavior of silicone rubbers. The stress-strain curves obtained by uniaxial tension/compression experiments are used to fit parameters of hyperelastic constitutive models. Indentation experiments are carried out to compare with simulation results. The fitting accuracy of constitutive models under different strains is analyzed. It is found that the constitutive parameters fitted by the uniaxial compression experiments are the best for simulating the contact behavior of silicone rubbers.

Composition controls soft hydrogel surface layer dimensions and contact mechanics.

Hydrogels are soft hydrated polymer networks that are widely used in research and industry due to their favorable properties and similarity to biological tissues. However, it has long been difficult to create a hydrogel emulating the heterogeneous structure of special tissues, such as cartilage. One potential avenue to develop a structural variation in a hydrogel is the "mold effect," which has only recently been discovered to be caused by absorbed oxygen within the mold surface interfering with the polymerization. This induces a dilute gradient-density surface layer with altered properties. However, the precise structure of the gradient-surface layer and its contact response have not yet been characterized. Such knowledge would prove useful for designs of composite hydrogels with altered surface characteristics. To fully characterize the hydrogel gradient-surface layer, we created five hydrogel compositions of varying monomer and cross-linker content to encompass variations in the layer. Then, we used particle exclusion microscopy during indentation and creep experiments to probe the contact response of the gradient layer of each composition. These experiments showed that the dilute structure of the gradient layer follows evolving contact behavior allowing poroelastic squeeze-out at miniscule pressures. Stiffer compositions had thinner gradient layers. This knowledge can potentially be used to create hydrogels with a stiff load-bearing bulk with altered surface characteristics tailored for specific tribological applications.

Constitutive parameter identification of transtibial residual limb soft tissue using ultrasound indentation and shear wave elastography

Finite element analysis (FEA) can be used to evaluate applied interface pressures and internal tissue strains for computational prosthetic socket design. This type of framework requires realistic patient-specific limb geometry and constitutive properties. In recent studies, indentations and inverse FEA with MRI-derived 3D patient geometries were used for constitutive parameter identification. However, long computational times and use of specialized equipment presents challenges for clinical, deployment. In this study, we present a novel approach for constitutive parameter identification using a combination of FEA, ultrasound indentation, and shear wave elastography. Local shear modulus measurement using elastography during an ultrasound indentation experiment has particular significance for biomechanical modeling of the residual limb since there are known regional dependencies of soft tissue properties such as varying levels of scarring and atrophy. Beyond prosthesis design, this work has broader implications to the fields of muscle health and monitoring of disease progression.

Adhesive depth-sensing indentation tests: Slopes of the force–displacement curves

Depth-sensing indentation experiments are a very important tool for estimating mechanical properties of modern materials. A review of various aspects of contact problems that used as the theoretical basis for interpretation of depth-sensing nanoindentation experiments is presented. Usually, analytical treatment of the indentation tests is based on analysis of the slopes of the force–displacement curves according to the non-adhesive Hertz contact theory. However, molecular adhesion is crucially important for many physical processes at the micro/nano-scales. Here, depth-sensing indentation techniques are reviewed and analyzed using the recent results obtained for adhesive contact problems. Fundamental relations for adhesive nanoindentation tests are derived for both frictionless and no-slip boundary conditions within the contact region. It is argued that the adhesive effects may be very important for treatment of the nanoindentation tests because the slopes of the force–displacement curves may considerably differ from the slopes derived using the non-adhesive contact theory.

The role of the cortex in indentation experiments of animal cells

We present a model useful for interpretation of indentation experiments on animal cells. We use finite element modeling for a thorough representation of the complex structure of an animal cell. In our model, the crucial constituent is the cell cortex—a rigid layer of cytoplasmic proteins present on the inner side of the cell membrane. It plays a vital role in the mechanical interactions between cells. The cell cortex is modeled by a three-dimensional solid to reflect its bending stiffness. This approach allows us to interpret the results of the indentation measurements and extract the mechanical properties of the individual elements of the cell structure. During the simulations, we scan a broad range of parameters such as cortex thickness and Young’s modulus, cytoplasm Young’s modulus, and indenter radius, which define cell properties and experimental conditions. Finally, we propose a simple closed-form formula that approximates the simulated results with satisfactory accuracy. Our formula is as easy to use as Hertz's function to extract cell properties from the measurement, yet it considers the cell’s inner structure, including cell cortex, cytoplasm, and nucleus.

Microstructural characteristics and mechanical properties of Si-B alloys for functional and structural ultra-high temperature applications

Silicon boron alloys have been recognized as important materials for e.g. a direct usage in ultra-high temperature latent heat thermal energy storage systems or as a batch materials for processing boron enhanced silicide-based composites. In this work, we put new experimentally driven insights on a structure of selected Si-B binary alloys. For this reason, four Si-xB alloys (x = 2.5; 8, 13.5; 86 (at%)) were fabricated from pure elements by using a crucible-less electric arc melting technique. Nominal compositions of the alloys were selected in accordance to Si-B phase diagram as hypoeutectic, eutectic, hypereutectic and corresponding to the stoichiometric composition of SiB6 intermetallic phase, respectively. The fabricated Si-xB alloys were subjected to a detailed structural characterization. Additionally, a hardness, elastic moduli and fracture toughness of each phase constituent were examined through a micro-indentation technique. A co-existence of various silicon borides, namely SiB4, SiB6 and SiBn, has been experimentally documented. Obtained results allows receiving a description of each alloy in terms of microstructure, crystal structure and mechanical properties of involved phases. It was found that mechanical properties (both microhardness and Young modulus) increases with raising boron content in recognized Si-B phases. The fracture toughness of silicon borides assessed through indentation experiments was found to be in the rage of 2.13–3.29 MPa·m1/2.

From LUVs to GUVs─How to Cover Micrometer-Sized Pores with Membranes.

Pore-spanning membranes (PSMs) are a versatile tool to investigate membrane-confined processes in a bottom-up approach. Pore sizes in the micrometer range are most suited to visualize PSMs using fluorescence microscopy. However, the preparation of these PSMs relies on the spreading of giant unilamellar vesicles (GUVs). GUV production faces several limitations. Thus, alternative ways to generate PSMs starting from large or small unilamellar vesicles that are more reproducibly prepared are highly desirable. Here we describe a method to produce PSMs obtained from large unilamellar vesicles, making use of droplet-stabilized GUVs generated in a microfluidic device. We analyzed the lipid diffusion in the free-standing and supported parts of the PSMs using z-scan fluorescence correlation spectroscopy and fluorescence recovery after photobleaching experiments in combination with finite element simulations. Employing atomic force indentation experiments, we also investigated the mechanical properties of the PSMs. Both lipid diffusion constants and lateral membrane tension were compared to those obtained on PSMs derived from electroformed GUVs, which are known to be solvent- and detergent-free, under otherwise identical conditions. Our results demonstrate that the lipid diffusion, as well as the mechanical properties of the resulting PSMs, is almost unaffected by the GUV formation procedure but depends on the chosen substrate functionalization. With the new method in hand, we were able to reconstitute the syntaxin-1A transmembrane domain in microfluidic GUVs and PSMs, which was visualized by fluorescence microscopy.

A peridynamic elasto-plastic damage model for ion-irradiated materials

This study presents the novel peridynamic constitutive relations formulated in order to predict the plastic deformation and damage evolution in irradiated materials. The plastic behaviour of the material in which radiation induced defects contribute to the defined peridynamic porosity is described by the Gurson–Tvergaard–Needleman (GTN) yield criterion with irradiation hardening. The definition of peridynamic porosity is proposed as a volume of discontinuities created in the volume of peridynamic particles. The new constitutive relations for irradiation hardening based on the dilatational part of elastic strain energy are formulated. The physical relevance of coupling the porosity with the nonlinear irradiation hardening is discussed. The expressions for the yield function, kinetics of evolution of radiation induced porosity, irradiation hardening and plastic flow rule are derived in terms of the peridynamics variables. The peridynamic predictions are calibrated based on the experimental data obtained during the advanced experimental campaigns dedicated to irradiated materials to verify the validity of the proposed constitutive model. Ion irradiation campaigns were carried out to mimic the effects of neutron irradiation. A series of indentation experiments were conducted to elucidate the effects of material structure modification and assess the hardening effect originating from radiation defects.

Effect of Zr content on microstructure and hardness of ODS-FeCrAl alloys

Oxide dispersion strengthened (ODS) Fe-12Cr-5Al-2 W-xZr (x = 0, 0.3, 0.6, 1.0 wt%) alloys were produced by mechanically alloying and spark plasma sintering. The size and distribution of grain, number density, size distribution and types of nanoscale oxides as well as hardness of the ODS alloys were analyzed by EBSD, TEM, HRTEM and an indentation experiment, respectively. The results showed that the grain size is not sensitive to Zr content, but the increase of Zr content is helpful for the homogenization of grain size. With the increase of Zr content from 0 to 0.6 wt%, the number density of oxides is increased from 1.66 × 1021 m−3 to 9.94 × 1022 m−3, while the mean size of oxides is decreased from 21.2 nm to 11.1 nm. The coarsening of oxides occurs when Zr is up to 1 wt%. In Zr-free alloy, nano-oxides are YAlO3 with perovskite structure (YAP) and α-Al2O3. In Zr-containing ODS alloys, the trigonal δ-phase Y4Zr3O12, YAP and α-Al2O3 are observed. An appendage oxide, Y4Zr3O12/YAP/α-Al2O3, is found in the alloy with 1.0 wt% Zr and the possible formation mechanism is briefly analyzed. The hardness of 6.03 GPa is achieved in the 0.6 wt% Zr alloy.

Star Crack Formation via Low-Velocity Impact on Glass Windows

The resistance to crack formation induced by gravel impacts on laminated glass windshields is a crucial issue for windshield manufacturers. It is proposed to study the star crack formation on polyvinyl butyral (PVB) laminated glass by designing a new highly-instrumented device that can break the glass under dynamic loading. The set-up is composed of a spring-loaded projectile that mimics a gravel momentum and an input bar equipped with strain gauges, whose end is an indenter initially in contact with the laminated glass sample. A synchronized high-speed camera allows for the observation of the crack growth. A unidimensional model introduces the local non-linear behavior of the indented zone. Crack monitoring synchronized with the Force and Velocity measurements are presented. Live-indentation depth measurements are performed. Experimental results are used in a dynamic simulation to analyze the non-linear damage behavior under the indenter tip. Dynamic and well-instrumented indentation experiments on the laminated glass are performed to investigate the star-shaped crack formation and describe the indented zone. This work is a prelude to the crack length prediction on windshields submitted to gravel pitting.

Size-dependent geometrically necessary dislocation structures in single-crystalline tungsten

Wedge indentation experiments were conducted to study the depth dependence of geometrically necessary dislocation (GND) structures in single-crystalline tungsten. Single-crystalline tungsten exhibits a pronounced indentation size effect (ISE), which can be rationalized based on GNDs. The dislocation mechanisms, however, are still under debate. Due to the plane strain condition during the wedge indentation, the dislocations in the cross sections underneath indents could be analyzed based on the Nye tensor and the lattice rotations determined using transmission Kikuchi diffraction. The dislocation structures depend on the size of the indent confirming the different hardness regimes and the bilinear ISE reported recently. For shallow indents, the dislocations are rather localized at the tip of the indent, while with increasing depth the dislocation volume expands; subgrains and distinct rays of increased dislocation density form. At larger depths, the indentation-induced deformation fields exhibit characteristics similar to the kink-type shear at a stationary crack tip.Graphical abstract

Investigation on the mechanical properties of shale subjected to different conditions based on nanoindentation experiments and numerical simulation

Nano indentation has become an important means to study the mechanical properties of rock because of its nondestructive and high efficiency. In this work, the Weibull distribution function is used to statistically analyze the nanoindentation test results and to analyze them mechanically and parametrically. The indentation process was simulated using ABAQUS to investigate the effect of semi-through cracks at the indentation on the indentation results. The experimental and simulated results were also analyzed using the dimensional analysis method. The results show that the elastic modulus, hardness and fracture toughness are positively correlated. The correlation between hardness and fracture toughness is poor. In the simulated indentation experiment, the number, depth, distance and Angle of semi-penetrating cracks have different effects on the indentation results. The proportional coefficients of dimensional analysis fitting curves are 0.464, 0.464, 0.457 and 0.462, respectively, which means that the number and depth of cracks have a great influence on the experimental results.

Mechanical Properties of Macromolecular Separators for Lithium-Ion Batteries Based on Nanoindentation Experiment.

High tensile strength and toughness play an important role in improving the mechanical performance of separator films, such as resistance to external force, improving service life, etc. In this study, a nanoindentation experiment is performed to investigate the mechanical properties of two types of separators for LIBs based on the grid nanoindentation method. During the indentation experiment, the “sink-in” phenomenon is observed around the indenter when plastic deformation of the specimen occurs. The “sink-in” area of the polyethylene (PE) separator is larger than that of the polypropylene/polyethylene/polypropylene (PP/PE/PP) separator, i.e., the plastic area of the PE separator is larger than that of the PP/PE/PP separator. In order to select a suitable method to evaluate the hardness and elastic modulus of these separators for LIBs, three theoretical methods, including the Oliver–Pharr method, the indentation work method, and the fitting curve method, are used for analysis and comparison in this study. The results obtained by the fitting curve method are more reasonable and accurate, which not only avoids the problem of the large contact area obtained by the Oliver–Pharr method, but also avoids the influence caused by the large fitting data of the displacement–force curve and the inaccuracy of using the maximum displacement obtained by the indentation method. In addition, the obstruction ability of the PP/PE/PP separator to locally resist external load pressed into its surface and to resist micro particles, such as fine metal powder, that can enter the lithium-ion battery during the manufacturing process is greater than that of the PE separator. This research provides guidance for studying the mechanical properties and exploring the estimation method of macromolecular separators for LIBs.

Cylindrical Indentation to Selectively Stress Nanoscale CMOS Transistors

Advanced indentation techniques have been introduced to study the effects of multiple stresses on the transistor characteristics with using a cylindrical tip with various alignments. Particularly, controlling the cylinder tip orientation relative to the transistor channel direction is proposed to selectively strain the silicon channels in order to induce very different selectively controlled stresses. Several tip alignments allow to shift the stresses from uniaxial towards biaxial stress as well as to induce shear stress. Ring oscillator circuits based on NAND and NOR gates are used to monitor the stress effects on the characteristic circuit frequency as well as on the individual transistors. Finite Element simulations help to identify optimized setup properties for the targeted application. Comparison with previous indentation experiments derives the specific influence of each stress tensor component on the transistor characteristics.

Effect of heat treatment on the microstructure and properties of CoCrFeNiMo0.2 particles reinforced titanium matrix composites

In this paper, the influence of heat treatment process on the microstructure and properties of CoCrFeNiMo0.2/Ti composites was studied by heat treatment of the composites. The structure and composition of CoCrFeNiMo0.2/Ti composites were characterized by X-ray diffraction and optical microscope. The distribution of elements of the interface layer was explored by electron probe. The mechanical properties of the composites were analyzed by nano indentation experiment and hardness tester. The relationship between irregular particles and the thickness of the interface layer was studied. The results are as follows: when the heat treatment temperature is 770 °C, the morphology of the high entropy alloy does not change significantly. As the temperature rises to 830 °C, the shape of the particles deforms and the thickness of the diffusion layer increases significantly. With the increase of the heat treatment temperature, the Young’s modulus and hardness of the interface layer have increased. When the heat treatment temperature rises to 890 °C, the particles completely diffuse into the matrix. Overall, the distance of the particles from the inscribed circle and the thickness of the interface layer are positively correlated.

Machine learning method for extracting elastic modulus of cells

The Hertz contact mechanics model is commonly used to extract the elastic modulus of the cell, but the basic assumptions of the model are often not met in cell indentation experiments, which can lead to errors in the obtained elastic modulus of cell. The establishment of theoretical formulas or modification of the Hertz formulas has been proposed to reduce the errors introduced by indentation depth and cell thickness, but errors from cell radius and probe radius are largely neglected. Herein, we build a neural network model in machine learning to extract the elastic modulus of cell, which takes into account of four variables: indentation depth, cell thickness, cell radius, and probe radius. The validity of the model is demonstrated by the indentation experiment. The introduction of machine learning methods provides an alternative solution for extracting the elastic modulus of the cell and has potential for application.

Reinforced mechanical properties of plasma-sprayed Fe-based amorphous composite coatings by in-situ TiNx/TiOy

Ceramic particle-reinforced Fe-based amorphous coatings have received extensive attention due to their excellent strength and wear resistance. In this paper, TiNx/TiOy -enhanced Fe-based amorphous coatings were prepared by reactive plasma spraying technology, and the effect of eggshell-like TiNx/TiOy on the comprehensive mechanical properties of Fe-based amorphous coatings was systematically studied. The results showed that the hardness of the composite coating was significantly higher than that of the amorphous single-phase coating. Moreover, indentation experiments showed that TiNx/TiOy effectively confined crack growth in the amorphous phase. Though the bonding strength of the composite coating was lower than that of the pure amorphous coating, but still maintained a high bonding force of 20.68 MPa. Through the wear experiment, it was found that the wear scar of the composite coatings appeared plastic deformation, the friction coefficient and wear mass loss were both greatly reduced, and the optimal wear performance appeared in the composite coating with 15% Ti addition. In addition, SEM, EDS analysis, and the first-principles simulation results demonstrated the good bonding between Ti-containing compounds and Fe-based alloys.

Finite Element Analysis and Experimental Study on Welding Residual Stress of Heavy-Duty Turning Tool

Because of its characteristics of good rigidity and strong ant-vibration, heavy-duty welding turning tools are widely applied in the rough machining of water chamber heads. However, welding residual stress is induced around the welding seam of the tool. During the heavy-duty machining, cracks easily occur due to an influence of impacts, high-temperature and thermal-mechanical loading, which causes tools failure. In this paper, ANSYS finite element model of heavy-duty cutting tools is established based on thermal elastic-plastic theory in order to analyze thermal stress field distribution in welding process. Secondly, actual welding residual stress distribution is obtained by the nano indentation experiment, verifying that the model can effectively analyze the stress and strain distribution. The welding tool failure mechanism is explored further. Finally, vibration aging and ultrasonic impact treatment methods are adopted to reduce welding residual stress of heavy-duty cutting tools. Two methods are compared for the influence of welding residual stress. Through the above research, finite element model can exactly reflect the welding residual stress distribution. The ultrasonic impact treatment is better than vibration aging treatment to reduce the welding residual stress and then extend their service life.

Indentation of small format Lithium-ion pouch cells: Experiments and modeling

Lithium-ion pouch cells are widely used in applications such as cell phones and electric vehicle battery packs. Here, a series of indentation experiments is performed on 4Ah pouch cells. The experimental program includes hemispherical indentation with six different indenter tip radii as well as indentation with cylindrical indenters with three rod diameters. Aside from varying the shape and size of the indenters, the location and direction of loading is varied including out-of-plane and in-plane loading of the rectangular-prismatic pouch cells. It is found that the force–displacement curves obtained for hemispherical indenters scale linearly with the indenter tip radius, while a scaling with the square root of the radius is observed for the experiments with cylindrical indenters. Finite element simulations are performed of all experiments using an enhanced Deshpande-Fleck plasticity model with two stage hardening. Despite the orthotropic nature of the jelly-stack, it is found that the simulations with an isotropic plasticity model provide reasonable predictions of the force–displacement curves for all experimental configurations. This surprising result is explained through the exceptionally high slenderness of the metallic current collector foils comprised in a pouch cell that respond through early buckling failure instead of contributing to the in-plane compressive load carrying capacity.