Cylindrical Indenter Research Articles

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.

The revisited phase-field approach to brittle fracture: application to indentation and notch problems

In a recent contribution, Kumar et al. (J Mech Phys Solids 142:104027, 2020) have introduced a comprehensive macroscopic phase-field theory for the nucleation and propagation of fracture in linear elastic brittle materials under arbitrary quasistatic loading conditions. The theory can be viewed as a natural generalization of the phase-field approximation of the variational theory of brittle fracture of Francfort and Marigo (J Mech Phys Solids 46:1319–1342, 1998) to account for the material strength at large. This is accomplished by the addition of an external driving force—which physically represents the macroscopic manifestation of the presence of inherent microscopic defects in the material—in the equation governing the evolution of the phase field. The main purpose of this paper is to continue providing validation results for the theory by confronting its predictions with direct measurements from three representative types of experimentally common yet technically challenging problems: (i) the indentation of glass plates with flat-ended cylindrical indenters and the three-point bending of (ii) U-notched and (iii) V-notched PMMA beams.

Effects of surface stress on the indentation response of an elastic half-space

Nanoindentation technique, which is based on Hertzian contact theory and Sneddon's solutions for the contact between a rigid indenter and an elastic half-space, has been widely investigated due to its practical importance in localized mechanical test of submicron structures. However, both the Hertzian contact theory and Sneddon's solutions do not take into account the contribution of surface stress to contact deformation. In this work, we study the effect of surface stress without the out-of-plane term on the indentation deformation of an elastic half-space by rigid, axisymmetric indenters, including flat-ended cylindrical, conical and spherical indenters. In contrast to classical theories, which are based on physically admissible condition of finite normal stress at contact edge, an alternative condition of geometrical continuity at contact edge is used to determine the contact radius. The numerical results reveal the combinational effects of the surface stress and Poisson's ratio on the load-displacement relationship for the indentation of the elastic half-space. The surface stress causes significant change in shear stress and modest variation in normal stress in the direction normal to the surface of the elastic half-space. The numerical method used in this work offers a feasible approach to study the effect of surface stress on the contact deformation of elastic substrates.

An initial study on the impression creep behaviour of stir-cast GNP reinforced AA6061 composite (AMMC)

Impression creep testing technique is used to screen out creep behaviour of materials as it is relatively faster method, requires small volume of the specimen, and is relatively material non-invasive technique when compared to conventional uniaxial tensile creep test method. This technique also possesses the benefit of maintaining constant stress throughout the experiment because a flat cylindrical indenter is used to apply load on the specimen. Owing to commercial unavailability of the materials under development such as metal matrix composites (MMC), the impression creep testing approach for such materials becomes a best method. In present work, creep behaviour of stir-cast graphene nanoplatelets (GNP) reinforced AA6061 composite (AMMC) is studied by using impression creep tests. The AMMC was prepared by adding GNPs in AA6061 through stir casting process by melting the alloy up to 1073 K. The impression creep experimentation included stress levels of 140 MPa, 170 MPa, and 200 MPa at a temperature of 573 K, 603 K and 633 K. The tests were conducted at constant stress by varying the temperature and vice-versa in vacuum. Two distinct regions i.e., primary and secondary/steady-state were observed and minimum creep strain rate was obtained in steady-state region. Tertiary region was absent, since the load/stress applied was compressive. During the experiment, depth of indentation of 0.03 mm to 0.14 mm was produced in the specimen. The microstructure of the composite has been analyzed using optical microscope and scanning electron microscope (SEM) to correlate with impression creep behaviour of the studied materials.

Finite Element Analysis of Impression Creep on P91

Impression creep is a versatile technique that is used nowadays for studying the creep deformation of different materials and there is no tertiary stage in this method; it's a non-destructive process. The present work deals with finite element analysis of plastic deformation corresponding to the impression creep deformation of P91 steel. In the FE model, a 3D deformable body is used as a specimen along with a rigid hollow cylindrical indenter with a 0.07 fillet. The effect of sizes of the specimen and indenter was studied, the diameter of the specimen was changed from 10mm,15mm, and 20mm whereas the indenter diameter was changed from 1mm,1.5mm, and 2mm respectively. Moreover, it was found that when punch diameter is increased the induced stress is reduced. It is observed that there is no effect on the diameter of the specimen, however, when the diameter of the indenter is increased from 1mm to 1.5mm and 1.5mm to 2mm, induced stress is reduced by approximately 10% and 20%, respectively. The simulation was run for 100 hours. Furthermore, the optimum distance between two impressions in P91 steel was studied and the distance between two indenters was altered from 10mm,8mm,6mm and 4mm respectively with the same loading and boundary conditions, and the same mesh size. It was observed that for P91 there is no contact between two deformations at 4mm.For P91 steel we can perform two impression creep tests from 4mm apart.

Failure behavior of sandwich beams with glass fiber-reinforced epoxy/aluminum laminates face-sheets and aluminum honeycomb core under three-point bending

The failure behavior and energy absorption performance of aluminum honeycomb sandwich beams with glass fiber-reinforced epoxy/aluminum laminates (GLARE) face-sheets under three-point bending are experimentally and numerically studied. The experimental specimens consists of 2/1 (2 aluminum sheets and 1 glass fiber/epoxy laminates) GLARE and aluminum honeycomb core. The effects of core height (8 mm, 20 mm, 40 mm) and indenter shape (cylindrical indenter and flat indenter) on bending failure behavior are tested in quasi-static three-point bending. Six sandwich beam specimens (300 mm-long and 40 mm-wide) were prepared. The initial failure modes of GLARE sandwich beams are observed, i.e. core shear and indentation. The numerical model considering geometric nonlinearity is established by ABAQUS/Explicit software and its effectiveness is verified by the experimental results of specimens with the same size and loading conditions. The effects of geometric and material parameters on the load-carrying capacity and energy absorption of the GLARE sandwich beams are discussed in details. It is shown that increasing the face-sheet thickness, honeycomb wall-thickness, the ratio of the core height to span length and the elasticity effect of metal materials or reducing the side length of the honeycomb cell can improve the load-carrying capacity and energy absorption of GLARE sandwich beams. The work can provide the guidance for the design of the GLARE sandwich structure with honeycomb core.

Force relaxation of contact between a flat-ended cylindrical indenter and a poroviscoelastic layer

Interpreting the contact force relaxation between an indenter and a poroviscoelastic material at a fixed displacement to obtain the materials properties is a challenging task, because both fluid drainage and solid viscoelasticity contribute to the relaxation. In this research, the indentation of a poroviscoelastic layer caused by a flat-ended cylindrical indenter is formulated analytically by the displacement functions in the Laplace-transformed domain. The contact force of the indenter at a fixed displacement was expressed by a closed-form in the transformed domain and numerically inverse-transformed to the time domain. The force relaxation is analyzed for combinations of three drainage conditions prescribed on the layer top and two boundary conditions prescribed on the layer bottom. The closed-form solution can approach that of the flat-indentation on a poroviscoelastic half-space, when the layer is very thick compared to the indenter radius. In addition, finite element simulations of the flat-indentation on poroviscoelastic layers were carried out as a comparison for the semi-analytical results. The relaxation ratios at the limits of the drained-nonviscoelastic state, the nondrained-viscoelastic state and the drained-viscoelastic state are shown for different ratios of the layer thickness to the indenter radius, and verified with the corresponding elastic solutions. The effects of the viscoelastic characteristic time on the force relaxations are also presented for different viscoelastic properties and boundary conditions.

Buckling of dented bi-material pipe under bending Part I: Experiments and simulation

As a cost-effective solution for transporting corrosive hydrocarbons, mechanically lined pipe has been used in many offshore and onshore projects. The bonding between the carbon steel carrier and the non-corrosive liner is commonly achieved by mechanical expansion. As typical pipeline damage, the local dent brings deformation to the bimetallic composite, which is expected to undermine the structural integrity. This work investigates the influence of a local dent on the plastic responses and stability of a lined pipe system during bending. Part I presents the results of the experiments and numerical analysis involving a set of small-scale lined tubes. The lined tubes, made of carbon steel Grade GB45 (AISI 1045) and copper Grade T2, are manufactured using a custom hydraulic expansion facility. The products have finished diameters of 50 mm and an overall D/t of 16.5, with 1.0 mm thickness for the liner. A minor transverse dent is introduced to the specimen using a cylindrical indenter. The dented tube is subsequently bent to collapse in a four-point bending facility. It is found that the local dent tends to induce early collapse of both the outer tube and the liner, resulting in a noteworthy reduction of the bending capacity of the composite. Initially, the local dent grows stably instead of collapsing right away. With increasing bending, the liner develops a major buckle and several satellite dimples around it. Subsequently, the manufacture, indentation, and the succeeding bending to collapse are simulated using a custom numerical framework, and the experimental results are reproduced reasonably well. Part II will use the validated numerical model to conduct an extensive parametric study of the important variables of the problem for full-scale lined pipes.

Crash Safety Design for Lithium-ion Vehicle Battery Module with Machine Learning

<div class="section abstract"><div class="htmlview paragraph">Lithium-ion battery systems have been used as the main power source for electric vehicles due to their lightweight and high energy density. The impact safety of these battery systems has been a primary issue. In this work, the crashworthiness design of a typical vehicle battery module is implemented through numerical (finite element) simulations integrated with machine learning algorithms (decision trees). The module with multiple layered porous cells is modeled with a simplified, homogeneous material law, and subjects to the impact of a cylindrical indenter. The main protective component on the module - cover plate is designed as an energy absorbing sandwich structure with a core of cellular solids. Large scale simulations are conducted with various design variable values for the sandwich structure, and the results form a design (simulation) dataset. Based on the dataset, machine learning is applied to the sandwich cover plate design to: (1) correlate the design variables to the response; (2) investigate the complex inter-relationship between design variables; and (3) derive decision-making rules to achieve the designs with highest energy absorbing capability.</div></div>

Contact Nonlinearity in Indenter–Foam Dampers

AbstractIn this paper, the nonlinear response of indenter–foam dampers is characterized. Those dampers consist of indenters pressed on open-cell foams swollen with wetting liquids. Recently, the authors identified the dominant mechanism of damping in those dampers as poro-viscoelastic (PVE) relaxations as in articular cartilage, one of nature’s best solutions to vibration attenuation. Those previous works by the authors included dynamic mechanical analyses of the indenter–foam dampers under small vibrations, i.e., linear regime. The current study features the dynamic response of similar dampers under larger strains to investigate the nonlinear regime. In particular, the indenter–foam dampers tested in this paper consist of an open-cell polyurethane foam swollen with castor oil. Harmonic displacements are applied on the swollen and pre-compressed foam using a flat-ended cylindrical indenter. Measured forces and corresponding hysteresis (force–displacement) loops are then analyzed to quantify damping performance (via specific damping capacity) and nonlinearities (via harmonic ratio). The effects of strain and strain rates on the damping capacity and harmonic ratio are investigated experimentally. The dominant source of the nonlinearity is identified as peeling at the indenter–foam interface (and quantified via peeling index). A representative model consisting of a linear viscoelastic foam and rate-dependent adhesive interface (slider element with limiting adhesive strength) explains the observed trends in peeling and thus nonlinear dynamic response. Possible remedies to suppress those nonlinearities in future designs of indenter–foam dampers are also discussed.

Elastoplastic Indentation Response of Sigmoid/Power Functionally Graded Ceramics Structures

Due to the applicability of new advanced functionally graded materials (FGMs) in numerous tribological systems, this manuscript aims to present computational and empirical indentation models to investigate the elastoplastic response of FG substrate under an indention process with spherical rigid punch. The spatial variation of the ceramic volume fraction through the specimen thickness is portrayed using the power law and sigmoid functions. The effective properties of two-constituent FGM are evaluated by employing a modified Tamura–Tomota–Ozawa (TTO) model. Bilinear hardening behavior is considered in the analysis. The finite element procedure is developed to predict the contact pressure, horizontal displacement, vertical deformation, and permanent deformation of FG structure under the rigid cylindrical indentation. The empirical forms for permanent deformation were evaluated and assigned. Model validation with experimental works was considered. The convergence of the mesh and solution procedure was checked. Numerical studies were performed to illustrate the influence of gradation function, gradation index, and indentation parameters on the contact pressure, von Mises stresses, horizontal/vertical displacements, and permanent plastic deformation. The present model can help engineers and designers in the selection of an optimum gradation function and gradation index based on their applications.

A singularity analysis in Keer’s elastic indentation problem

A non-axisymmetric three-dimensional frictionless contact problem for an elastic half-space and a cylindrical indenter with the face in a wedge form is considered under the assumption of a circular region of contact. Explicit formulas are derived for the critical indenter displacement and contact force that are needed to ensure full contact over the entire contact region. It is shown that the contact pressure beneath the indenter maintains a logarithmic singularity, which is produced by the wedge edge and is similar to the singularity of the contact pressure in the corresponding two-dimensional contact problem for a wedge rigid indenter.

Prediction of Internal Circuit and Mechanical-Electrical-Thermal Response of Lithium-Ion Battery Cell with Mechanical-Thermal Coupled Analysis

The lithium-ion battery (LIB) is widely used as an energy storage device for electric vehicles (EV) due to its advantages, such as high energy density and long lifespan. However, LIB for EV can be exposed to mechanical abuse such as vehicle collision, which causes thermal runaway due to extreme mechanical deformation. Therefore, it is necessary to predict the internal short circuit (ISC) of the LIB cell under mechanical loading conditions and to analyze the mechanical, electrical, and thermal responses after ISC. In this paper, the starting point of ISC is predicted using a two-way mechanical-electrical-thermal coupled analysis method. At the same time, mechanical responses, along with the effects of the ISC area on electrical and thermal responses of the LIB cell, were analyzed. ISC was defined as failure of the separator. The separator’s failure was calculated considering material nonlinearity. Considering the indentation test results, the finite element method (FEM) analysis could accurately predict the starting point of ISC. In the order of cylindrical, hemispherical, and conical indenters, ISC occurred quickly, and the ISC area was large. The larger the ISC area, the greater the voltage drop, current, and joule heat, and the higher the maximum temperature.

Multiscale Analysis and Safety Assessment of Fresh and Electrical Aged Lithium-Ion Pouch Cells Focusing on Mechanical Behavior

Analyzing the impact of electrical aging on the lithium-ion cell’s mechanical behavior and safety is an important factor to assess the crash safety of electric vehicles during their lifetime. In this study, fresh and electrical aged state-of-the-art NCM pouch cells were investigated. Aged cells, which were cycled electrically to 90% state of health, under laboratory conditions in electric vehicle battery modules were used. The used charging/discharging strategy represents real customer behavior based on accelerated driving profiles. First, it is shown that electrical aging has a significant influence on the anodes’ and separators’ mechanical properties, which had a lower mechanical strength and stiffness under tension. Additionally, quasi-static cylindrical indentation and three-point bending tests were performed to investigate aging effects on cell level at varying state of charge (SOC). Aged cells with 0% SOC showed a right-shifted force–displacement curve and a 29% lower maximum force compared to fresh cells. Fully charged, aged cells reached a similar maximum force to fresh cells, but faster temperature increase and higher temperature peaks after internal short circuit. Inductively coupled plasma optical emission spectrometry analyses confirmed an increased lithium content on the anode surface, which is indicated in literature as a reason for the increased exothermic reaction of the aged cells. The results indicate a higher safety risk for the aged investigated pouch cells under mechanical loads based on their changed mechanical properties and thermal runaway behavior.

Characterization of in-situ material properties of pouch lithium-ion batteries in tension from three-point bending tests

To understand the mechanisms of deformation and failure of lithium-ion batteries in case of a crash, it is necessary to accurately characterize their constitutive properties. Previous studies in the field mainly focused on the homogenized compression properties of the cells, which are dominant in load cases such as local indentations. However, in complex practical loadings, such as bending, tension properties play an equally important role. Such complex loads can lead to rupture of the electrode tabs and external short-circuits, which can cause catastrophic outcomes. In the current literature, tensile properties are characterized using specimens extracted from the cell, outside of their operational environment, which leads to unrealistic values. In this study, for the first time, an analytical characterization method is developed to extract the homogenized tensile properties of a cell from bending tests in in-situ conditions. In the next step, this data is used, along with an elaborative procedure, to calibrate a fully uncoupled anisotropic material model for the pouch cells. The material model is utilized to build a single homogenized finite element pouch cell model which is the first of its kind to be validated in all major loading cases; flat, hemispherical, and cylindrical punch indentations and specifically three-point bending, and in-plane compression. This material characterization and the modeling approach provide a universal tool in predicting the load-displacement, shape of deformation, buckling wavelength, and the trend of failure in complex crash scenarios for the safety assessments of Lithium-ion batteries.

Axisymmetric Problem for Indentation of Multi-Layer Poroelastic Body

We considered the axisymmetric indentation of poroelastic multi-coating bonded to poroelastic substrate indented by a rigid flat-ended cylindrical indenter. The approach that expressed poroelastic solutions in term of two displacement functions and the transfer matrix method which can formulate the effect of multi-layer composite were applied in this study. Furthermore, we adopted the analytic method that using Laplace-Hankel transform and expressing the normal contact stress at the surface layer as an appropriate series with a Chebyshev orthogonal polynomial to reduce dual integral equations to an infinite system of simultaneous equations in Laplace transform domain. The numerical results of time-dependent axial displacement of rigid cylindrical indenter were presented by performing numerical inverse Laplace transform. The results of axial displacement for one-layer bonded to rigid impervious substrate given by this study were good agreement with previously reported results.

The effects of half-space approximation and thickness of the contact bodies on the normal contact force: experiment and simulations

The experimental setup developed for investigation of the normal adhesive contact is described. The results of the experiments concerning the indentation of the spherical and cylindrical indenters into the rubber substrate are discussed. Obtained experimental results were compared with theory and simulations for half-space. As it follows from the performed experiments the thickness of the elastomer must exceed several times the size of the contact area in order to use half-space approximation.

Влияние адгезии на трение качения и скольжения: эксперимент

Normal and tangential contact between a cylindrical steel indenter (wheel) and an elastomer with high adhesive properties is investigated. In the case of indentation in the normal direction, a computer simulation of the process of indentation and detachment was carried out, which shows good coincidence with an experiment. For the rolling friction mode, when analyzing the measured dependences of the tangential component of the contact force on the wheel displacement, the adhesive component of the friction force was determined. The situation of sliding friction, in which the rotation of the wheel was impossible, is considered. In the presence of adhesion, the sliding friction force is proportional to the contact area. In the absence of adhesion (the elastomer is covered with a chalk dust), a stick-slip friction mode is realized. The frequency and amplitude of stick-slip transitions depend on the indentation depth of the indenter into the elastomer.

Cylindrical indentation in micropolar elasticity

Experiments existing in the literature present a scale dependence of the mechanical properties of certain materials. Such scale dependence is observable also in indentation experiments where the attained contact area and average pressure among other experimental outputs show a strong dependence upon the microstructure of the indented material. In this work we will examine the indentation of a rigid cylinder on an elastic half-plane within the context of the micropolar elasticity (also known as Cosserat elasticity). The micropolar theory of elasticity incorporates in addition to the displacement field, an independent kinematical microrotation field. Our results show the dependence of the shape of the pressure distribution, the average pressure and the width of the contact site below the indenter upon the microstructure of the material described through the material length as introduced through the micropolar theory. A comparison of the results with those obtained by the classical theory and the couple stress theory as well as a full field solutions regarding equivalent stresses are presented.

Indentation of a circular hyperelastic membrane by a rigid cylinder

In the paper we investigate the effect of friction on the stress–strain state of a hyperelastic membrane in contact with a massive solid body. We consider the axisymmetric indentation of a thin circular rubber membrane by a cylindrical indenter for different contact conditions: dry contact, liquid lubrication, and gel lubrication. We present experimental results and a mathematical model of the indentation. We use the non-linear theory of elastic membranes and the Coulomb friction model in the simulation. We describe different contact conditions with different friction coefficients. We compare the experimental and theoretical dependences between indentation force and indenter displacement.