Spherical Indenter Research Articles

An adaptive spherical indentation test integrating targeted testing scenarios, data acquisition, and model selection for uniaxial mechanical property predictions

An adaptive spherical indentation test integrating targeted testing scenarios, data acquisition, and model selection for uniaxial mechanical property predictions

Stress–Strain Curve Estimation from Load–depth Curve of Spherical Indentation Test Based on Finite Element Analysis and Optimization

Stress–Strain Curve Estimation from Load–depth Curve of Spherical Indentation Test Based on Finite Element Analysis and Optimization

Spherical Indentation Method for Measuring Biaxial Residual Stresses Without Using Stress-Free Sample

Spherical Indentation Method for Measuring Biaxial Residual Stresses Without Using Stress-Free Sample

Numerical analyses of spherical indenter intrusion into sandstone: From laboratory tests to numerical simulations

To explore the mechanical mechanisms of rock fracturing under compression during ball milling. The study investigates the effects of intrusion depth and indenter diameter on the evolution of stresses and plastic strains, integrating laboratory tests and numerical predictions. The results reveal a reduction in both axial and radial stresses with increasing intrusion depth into the rock. Shear stress experiences an initial rise followed by a decline, while circumferential stress demonstrates an initial increase followed by a rapid decrease in the radial direction. As the intrusion deepens, the predominant influence on plastic strain of rock shifts from shear stress dominance to a combined dominance of shear and circumferential stresses. The influence of the indenter diameter on the stress field diminishes following an exponential decay pattern. In terms of the plastic strain field, smaller indenters are more likely to induce plastic failure due to shear and circumferential stresses, larger indenters are more prone to plastic failure induced solely by shear stresses. As the number of indenters increases, the integration of the stress and plastic strain fields is enhanced. This implies that introducing more spherical indenters amplifies the collaborative effect, leading to a more cohesive fracturing of the rock.

Micromechanical investigation of DLC based coating systems by means of combined characterization and simulation methods

The assessment of the elastic-plastic material behavior is imperative for benchmarking the performance of thin coating systems. Linear-elastic approaches can lead to deviating results and experimental investigations, such as fatigue tests, frequently overlook the intricacies of the failure mechanism. Therefore, the elastic-plastic material behavior of DLC based coating systems with CrN support interlayer, deposited on 100Cr6 substrates and Si, was investigated. Using an inverse approach, a nanoindentation simulation with spherical indenter geometry was iteratively optimized to experimental curves by adjusting the material parameters Young's modulus E, yield strength Y, hardening coefficient K and hardening exponent n for DLC and CrN layers. Mechanical parameters were measured and the yield strength of DLC was analyzed with a scratch procedure to implement appropriate initial values. The results showed an overall good agreement between the measured and optimized force-displacement curves with reasonable determined material parameters. The control parameter Y exhibited nearly identical outcomes for scratch measurements and the calculated value from simulations although DLC was deposited on different substrates. The employment of a spherical indenter tip mitigates the influence of the microstructure in the CrN layer through homogenization effects and a larger affected area of the plastic zone. Furthermore, enhancing the performance of the coating systems can be achieved by increasing the DLC or CrN interlayer thickness.

Contact damage response of alumina-based layered architectures under different loading configurations

Hertzian contact damage upon spherical indentation is investigated in alumina-based ceramics designed with embedded textured compressive layers. The effect of the location of the embedded layer and the testing configuration (parallel or normal to the layer orientation) on the sub-surface damage evolution is explored. An acoustic emission system for crack detection and post-mortem cross sectioning are employed to evaluate the onset and extension of damage in the different samples. Distinct acoustic signals detected at different contact loads are correlated with the onset of the ring crack, cone crack propagation and quasi-plastic deformation within the textured layer. The distinct damage mechanisms are influenced by the location of the embedded textured compressive layer and the loading orientation with respect to the layers. The design of layered ceramics for contact applications should consider the loading orientation as well as the contact stress field with respect to the “protective” layer to enhance damage tolerance.

Filled elastomers sliding over smooth obstacles: Experiments and modeling in large deformations

The objective of this paper is to shed light on the mechanical response of filled elastomers in sliding contact. Compared to situations encountered by tires in breaking conditions, the study only considers smooth obstacles in order to analyse the contribution of finite deformations and of the complex viscosity of filled elastomers without facing all the complexity of surface roughness. For this purpose, a new experiment is introduced that allows to measure the friction on the surface of a filled elastomer that is subjected to large local deformation through a cyclic contact loading applied by sliding indenters. The setup uses smooth spherical indenters sliding on the material of interest within a temperature controlled water tank. The relevance of adhesion forces is reduced by using Teflon as a dry lubricant and Sinnozon as a surfactant. To analyze the experimental results, full-field simulations of the experiments are carried out within the setting of finite viscoelastodynamics by making use of two types of viscoelastic constitutive models for the filled elastomer: (i) a classical viscoelastic model combining a Mooney–Rivlin equilibrium elasticity and Maxwell branches with constant viscosities and (ii) an internal-variable-based viscoelastic model that was introduced in (Kumar and Lopez-Pamies, Comptes Rendus Mecanique 344, 102-112) for unfilled elastomers and that is extended herein to account for the more complex viscous response of filled elastomers.

ОПЕРАТИВНЫЙ КОНТРОЛЬ ВЕЛИЧИНЫ ИСТИННОГО СОПРОТИВЛЕНИЯ РАЗРЫВУ СТАЛЕЙ

The paper presents the method proposed by the authors for non-destructive determination of true tensile strength of steels by the parameters of elastic-plastic indentation of a spherical indenter. Acceptable accuracy of the method for engineering evaluation of the properties of carbon and alloy structural steels is shown.

Nanoindentation-induced serrated flow behavior and deformation mechanism in metallic glass: A combined experiments and molecular dynamics simulation

In this study, the deformation behaviors of bulk metallic glass (BMG) during the nanoindentation are presented via the experiments and molecular dynamics (MD). The relationship between shear transformation zone (STZ) formation and serrated flow dynamics are developed to explain the deformation characterization evolution of BMG. It is found that as the peak load increases, the hardness and elastic modulus significantly decrease. Creep behavior at room temperature was also revealed by analyzing the creep displacement curve and the stress index under different peak loads.The accumulation of free volume during the deformation process promotes more uniform creep deformation. Furthermore, the serrated flow behaviors were analyzed innovatively using the shear stress drops further statistically. At lower loads, the occurrence of serrated retention is due to energy exceeding the potential barrier required for flow unit activation, ultimately released in the form of kinetic energy. At higher loads, the transition from intermittent curve to smooth curve exhibits a typical self-organized critical (SOC) state dynamic characteristics, and ISE phenomenon is also observed. The results also suggested that the shear deformation of the spherical indenter is more pronounced, with the shear band forming at a 45° angle to the direction of the downward pressure. And based on the Cooperative shear model (CSM) theory, the STZ size was estimated and verify that the increment of STZ makes it easier to generate stronger plastic strain to dissipate STZ, ultimately leading to complete plastic deformation. Combining five fold symmetry and gradient atoms, the majority of atoms with five fold symmetry (LFFS>0.5) have stronger resistance to plastic deformation when the load rate is low.

DEM modelling of surface indentations caused by granular materials: application to wheel–rail sanding

The presented surface indentation model is one step towards building a DEM model for wheel–rail sanding. In railways, so-called low-adhesion conditions can cause problems in traction and braking, and sanding is used to overcome this problem. Sand grains are blasted towards wheel–rail contact, fracture repeatedly as they enter the nip and are drawn into the contact and then increase adhesion. Research on this topic has mostly been experimental, but focussed on adhesion enhancement measurement. Thus, physical mechanisms increasing the adhesion are not well understood. Previous works involved experiments and DEM modelling of single sand grain crushing tests under realistic wheel–rail contact pressures of 900 MPa, focusing on sand fragment spread and formation of clusters of solidified fragments. In the experiments, indents in the compressing steel plates were also observed, which are also observed on wheel and rail surfaces in railway operation. These are now modelled by adapting an existing surface indentation model from literature to the case of surface indentations caused by granular materials. Two test cases are studied, and experimental spherical indentation tests for model parametrisation are presented. In a proof of concept, the mentioned single sand grain crushing tests under 900 MPa pressure are simulated including the surface indentation model. This work contributes to DEM modelling of wheel–rail sanding, which is believed to be a good approach to deepen the understanding of adhesion increasing mechanisms under sanded conditions.

Towards Simpler Modelling Expressions for the Mechanical Characterization of Soft Materials

Aims: The aim of this paper is to develop a new, simple equation for deep spherical indentations. Background: The Hertzian theory is the most widely applied mathematical tool when testing soft materials because it provides an elementary equation that can be used to fit force-indentation data and determine the mechanical properties of the sample (i.e., its Young’s modulus). However, the Hertz equation is only valid for parabolic or spherical indenters at low indentation depths. For large indentation depths, Sneddon’s extension of the Hertzian theory offers accurate force-indentation equations, while alternative approaches have also been developed. Despite ongoing mathematical efforts to derive new accurate equations for deep spherical indentations, the Hertz equation is still commonly used in most cases due to its simplicity in data processing. Objective: The main objective of this paper is to simplify the data processing for deep spherical indentations, primarily by providing an accurate equation that can be easily fitted to force-indentation data, similar to the Hertzian equation Methods: A simple power-law equation is derived by considering the equal work done by the indenter using the actual equation. Results: The mentioned power-law equation was tested on simulated force-indentation data created using both spherical and sphero-conical indenters. Furthermore, it was applied to experimental force-indentation data obtained from agarose gels, demonstrating remarkable accuracy. Conclusion: A new elementary power-law equation for accurately determining Young’s modulus in deep spherical indentation has been derived.

Experimental investigations on characterizing the uniaxial mechanical property variations along the thickness of hydrogenation reactor welded joints by spherical indentation tests

To meet the demands for non-destructive testing of uniaxial mechanical properties of welded joints of thick-wall hydrogenation reactors, this study provides an experimental investigation on whether the spherical indentation tests (SITs) can accurately characterize the uniaxial mechanical property variations along the thickness of welded joints. The phenomenologically summarized empirical method (i.e., the Kwon method) and the semi-analytical method (i.e., the simplified-IIEM) were selected as representatives, and their reliability was judged from the viewpoints of stress-strain prediction, the inversion accuracy and repeatability of strength, and the ability to characterize the variation of uniaxial mechanical properties along the thickness of welded joints. Characteristics of the inverse predictions were analyzed, and the source of errors in each method were extensively investigated. This study provides a theoretical and technical guidance for the engineering application and promotion of SITs.

Inverse Method to Determine Parameters for Time-Dependent and Cyclic Plastic Material Behavior from Instrumented Indentation Tests.

Indentation is a versatile method to assess the hardness of different materials along with their elastic properties. Recently, powerful approaches have been developed to determine further material properties, like yield strength, ultimate tensile strength, work-hardening rate, and even cyclic plastic properties, by a combination of indentation testing and computer simulations. The basic idea of these approaches is to simulate the indentation with known process parameters and to iteratively optimize the initially unknown material properties until just a minimum error between numerical and experimental results is achieved. In this work, we have developed a protocol for instrumented indentation tests and a procedure for the inverse analysis of the experimental data to obtain material parameters for time-dependent viscoplastic material behavior and kinematic and isotropic work-hardening. We assume the elastic material properties and the initial yield strength to be known because these values can be determined independently from indentation tests. Two optimization strategies were performed and compared for identification of the material parameters. The new inverse method for spherical indentation has been successfully applied to martensitic steel.

Ad Hoc Modeling of Rate-Dependent Adhesion in Indentation Relaxation Testing.

The phenomenon of rate-dependent adhesion has long been recognized as an intricate problem, and the so-far-developed physics and mechanics-based approaches resulted in analytical relations between the implicit form between the work of adhesion and the contact front velocity which are difficult to implement in practice. To address this issue in the framework of spherical indentation, the adhesion relaxation test in a nominal point contact is introduced to estimate the rate-dependent adhesion. Based on a stretched exponent approximation for the contact radius evolution with time, a relatively simple four-parameter model is proposed for the functional relation between the work of adhesion and the contact front velocity, and its fitting performance is compared to that of the known Greenwood-Johnson and Persson-Brener models.

Master Curves for Poroelastic Spherical Indentation With Step Displacement Loading

Abstract Theoretical and numerical analyses are conducted to rigorously construct master curves that can be used for interpretation of displacement-controlled poroelastic spherical indentation test. A fully coupled poroelastic solution is first derived within the framework of Biot’s theory using the McNamee–Gibson displacement function method. The fully saturated porous medium is assumed to consist of slightly compressible solid and fluid phases and the surface is assumed to be impermeable over the contact area and permeable everywhere else. In contrast to the cases in our previous studies with an either fully permeable or impermeable surface, the mixed drainage condition yields two coupled sets of dual integral equations instead of one in the Laplace transform domain. The theoretical solutions show that for this class of poroelastic spherical indentation problems, relaxation of the normalized indentation force is affected by material properties through weak dependence on a single-derived material constant only. Finite element analysis is then performed in order to examine the differences between the theoretical solution, obtained by imposing the normal displacement over the contact area, and the numerical results where frictionless contact between a rigid sphere and the poroelastic medium is explicitly modeled. A four-parameter elementary function, an approximation of the theoretical solution with its validity supported by the numerical analysis, is proposed as the master curve that can be conveniently used to aid the interpretation of the poroelastic spherical indentation test. Application of the master curve for the ramp-hold loading scenario is also discussed.

Micro/Nanomechanical Characterization of ScAlMgO4 Single Crystal by Instrumented Indentation and Scratch Methods.

ScAlMgO4 (SCAM), which can be used as an epitaxial substrate material of GaN in power devices, faces the challenge of achieving a high-quality surface by ultra-precision polishing due to its brittle and easily cleaved characteristics, which are closely associated with its mechanical properties. The micromechanical properties of SCAM single crystals were evaluated by nanoindentation and microscratch tests using different indenters. The elastic modulus EIT and the indentation hardness HIT of SCAM obtained by nanoindentation were 226 GPa and 12.1 GPa, respectively. Leaf-shaped chips and the associated step-like planes of SCAM can be found in the severely damaged regime during scratching by Berkovich and Vickers indenters with sharp edges due to the intersection of intense radial and lateral cracks. The fracture toughness (Kc = 1.12 MPa·m1/2) of SCAM can be obtained by using a scratch-based methodology for a spherical indenter based on linear elastic fracture mechanics (LEFM) under an appropriate range of applied loads. An optimal expression for calculating the fracture toughness of easily cleaved materials, including SCAM, via the Vickers indenter-induced cracking method using a Berkovich indenter was recommended.

Finite Element Analysis of the Mechanical Response for Cylindrical Lithium-Ion Batteries with the Double-Layer Windings

The plastic properties for the jellyroll of lithium-ion batteries showed different behavior in tension and compression, showing the yield strength in compression being several times higher than in tension. The crushable foam models were widely used to predict the mechanical responses to compressive loadings. However, since the compressive characteristic is dominant in this model, it is difficult to identify distributions of the yield strength in tension. In this study, a simplified jellyroll model consisting of double-layer windings was devised to reflect different plastic characteristics of a jellyroll, and the proposed model was applied to an 18650 cylindrical battery under compressive loading conditions. One winding adopted the crushable foam model for representing the compressive plastic behavior, and the other winding adopted the elastoplastic models for tracking the tensile plastic behavior. The material parameters in the crushable foam model were calibrated by comparing the simulated force–displacement curve with the experimental one for the case where the cell was crushed between two plates when the punch was displaced by 7 mm. A specific cut-off value (10 MPa) was assigned to a yield stress limit in the elastoplastic model. Further, the computational model was validated with two more loading cases, a cylindrical rod indentation and a spherical punch indentation, as the punch was displaced by 6.3 mm and 6.5 mm, respectively. For three loading cases, deformed configurations and plastic strain distributions were investigated by finite element analysis. It was found that the proposed model clearly provides the plastic behavior both in compression and tension. For the crush simulation, the maximum compressive stress approached 222 MPa in the middle of the jellyroll, and the maximum effective plastic strain approached 60% in the middle of the layered roll. For indentation with the cylindrical and the spherical punch, the maximum effective plastic strain approached 52% and 277% in the layered roll, respectively. The local crack or location of a short circuit could be predicted from the maximum effective plastic strain.

A Correction Function to Improve the Accuracy of Measuring Elastic Modulus by Instrumented Spherical Indentation

Abstract Instrumented indentation combined with the classic Oliver–Pharr method has been widely utilized to measure elastic modulus of various materials. However, the elastic modulus measured by instrumented spherical indentation (ISI) is not as accurate as that measured by instrumented sharp indentation, especially at large indentation depth. In this work, the effect of the maximum indentation depth on measurement of elastic modulus by ISI was deeply investigated through finite element simulations and experiments. It was found that errors in measured elastic moduli increase significantly due to the inaccurate estimation of contact radius and excessive increase in initial unloading stiffness as maximum indentation depth increases. A correction function was then proposed to correct the measured elastic modulus. After correction, the errors were effectively reduced to within ±5 % for most cases. This work contributes to discovery of the error source in the measurement of elastic modulus by ISI, thereby improving the measurement accuracy.

Indentation Behavior Assessment of As-Built, Solution, and Artificial Aged Heat-Treated Selective Laser Melting Specimens of AlSi10Mg

This study was conducted to determine the indentation behavior of thin AlSi10Mg specimens manufactured using Selective Laser Melting (SLM) in the as-built condition along with two post-treatments, namely solution heat treatment and artificial aging. Four different thicknesses of 1 mm, 1.5 mm, 2 mm, and 2.5 mm of SLM specimens, with the different post-treatments, underwent standardized Rockwell hardness tests using a spherical indenter to determine their hardness values and assess the impression using a stereo microscope and scanning electron microscope (SEM). The as-built specimens showed a trend of smaller indentation depths with increasing specimen thickness, and finally creased with 0.1547 mm depth at 2.5 mm. However, the post-treatments altered the behavior of the specimens to a certain degree, giving larger experimental indentation depths of 0.2204 mm, 0.1962 mm, and 0.1798 mm at 1.0 mm, 1.5 mm, and 2.5 mm thickness, respectively, after solution heat treatment. Artificial aging showed a general decrease in indentation depth with increasing specimen thickness in contrast to solution treatment, and resulted in depths of 0.1888 mm and 0.1596 mm at 1.0 mm and 2.5 mm thickness. Furthermore, a material numerical model was made using stress–strain data on ANSYS Workbench to develop a predictive model for the indentation behavior of the specimens in contrast to experimentation. Under multi-linear isotropic hardening, the Finite Element Analysis (FEA) simulation produced indentation geometry with an average accuracy of 95.4% for the artificial aging series.

Study on methods measuring mechanical properties of arterial wall by macroscopic indentation

Accurately evaluating the local biomechanics of arterial wall is crucial for diagnosing and treating arterial diseases. Indentation measurement can be used to evaluate the local mechanical properties of the artery. However, the effects of the indenter's geometric structure and the analysis theory on measurement results remain uncertain. In this paper, four kinds of indenters were used to measure the pulmonary aorta, the proximal thoracic aorta and the distal thoracic aorta in pigs, and the arterial elastic modulus was calculated by Sneddon and Sirghi theory to explore the influence of the indenter geometry and analysis theory on the measured elastic modulus. The results showed that the arterial elastic modulus measured by cylindrical indenter was lower than that measured by spherical indenter. In addition, compared with the calculated results of Sirghi theory, the Sneddon theory, which does not take adhesion forces in account, resulted in slightly larger elastic modulus values. In conclusion, this study provides parametric support for effective measurement of arterial local mechanical properties by millimeter indentation technique.