Spherical Indenter Research Articles

Evaluation of adhesive damage in a nitrided stainless steel under cyclic contact loading

In this study, adhesive damage in a nitrided AISI 316L stainless steel is evaluated by cyclic contact loading. The AISI 316L steel was hardened by the salt bath nitriding process at a constant temperature (580 °C) and three different exposure times (1 h, 3 h and 5 h). Mechanical properties such as Young's modulus (E) and hardness (H) were obtained by nanoindentation testing, where the H3/E2 ratio was used as an indicator of the fracture resistance of the nitride layers. Cyclic contact loads were applied to the nitrided steels using a spherical indenter of 3 mm in diameter. The layer/substrate systems were evaluated under 50,000 load cycles and a constant frequency of 5 Hz. Adhesive damage was observed at the interface between the compound-layer and the diffusion zone, where the samples with a thicker nitride layer showed more severe damage. In addition, the finite element method was used to obtain the stress field in the nitrided AISI 316L steel caused by cyclic contact loading, where both the maximum principal stress and the maximum shear stress were related to the adhesive damage observed in the experimental test.

Mechanism and Method of Testing Fracture Toughness and Impact Absorbed Energy of Ductile Metals by Spherical Indentation Tests

To address the problem of conventional approaches for mechanical property determination requiring destructive sampling, which may be unsuitable for in-service structures, the authors proposed a method for determining the quasi-static fracture toughness and impact absorbed energy of ductile metals from spherical indentation tests (SITs). The stress status and damage mechanism of SIT, mode I fracture, Charpy impact tests, and related tests were first investigated through finite element (FE) calculations and scanning electron microscopy (SEM) observations, respectively. It was found that the damage mechanism of SITs is different from that of mode I fractures, while mode I fractures and Charpy impact tests share the same damage mechanism. Considering the difference between SIT and mode I fractures, uniaxial tension and pure shear were introduced to correlate SIT with mode I fractures. Based on this, the widely used critical indentation energy (CIE) model for fracture toughness determination using SITs was modified. The quasi-static fracture toughness determined from the modified CIE model was used to evaluate the impact absorbed energy using the dynamic fracture toughness and energy for crack initiation. The effectiveness of the newly proposed method was verified through experiments on four types of steels: Q345R, SA508-3, 18MnMoNbR, and S30408.

Parameter determination of anisotropic yield function using neural network-based indentation plastometry

Understanding the impact of plastic anisotropy on the formability of sheet metals is crucial for their industrial application and high-precision forming simulation. Existing multiple uniaxial tensile tests for measuring the plastic flow of anisotropic materials, however, are costly, time-consuming, and destructive. Therefore, it is more efficient to focus on indentation plastometry, a simple, nondestructive test that can quickly extract tensile properties. The objective of this work is to directly derive the parameters of the advanced Poly6 yield criterion and hardening, which describes strong plastic anisotropy, using indentation plastometry basd on a neural network (NN) system. The identification process for these parameters through conventional tensile tests is inherently complex, thereby determining the parameters directly from indentation data presents an unprecedented challenge. We trained NNs using a database generated from verified finite element (FE) simulations of spherical indentations. To systematically iterate these FE simulations, we designed a strategy generating a set of input anisotropic parameters that ensure the convexity of the yield function. We considered the radial and vertical displacement fields around the indentation mark along with the load-depth curve as indentation responses. Through a comprehensive analysis of the correlation between displacement profiles, we have proposed an optimal feature extraction method for NN training. The developed FE-NN model was evaluated by comparing the predicted parameters from the indentation responses of the target materials with those measured from tensile tests. These parameters were expressed as the yield locus and directional properties. The results demonstrated that the FE-NN modeling approach is robust and can accurately capture the anisotropic plastic flow from indentation responses.

Study on Friction Behaviors of Soft Materials Considering Sliding-Caused Deformation

Accurate and quantitative characterization of friction behavior is of critical importance for material design and manufacture, especially for soft materials. It is mainly because the sliding-caused deformation of soft materials has always been neglected during characterization. Here, a modified model considering sliding-caused deformation was proposed to characterize the friction behavior between a spherical glass indenter and silicon rubber. A novel friction apparatus consisting of a transparent spherical indenter connected with a camera was used in real-time to measure the friction contact status. The contact shape and area during friction were then extracted by a proposed shape function. Experimental results show that shrinking and expanding of the contact area occur simultaneously when a spherical-rigid indenter slides on a soft substrate due to sliding-caused deformation of soft materials. Based on these results, this study built a modified model considering the shape change and the accompanying deformation component of friction, which is an effective method for evaluating the friction behavior of soft materials.

Finite element modeling of spherical indentation behavior of 3D mesh fabric at the yarn level

This paper reports an experimental and numerical study on the spherical indentation behavior of three-dimensional (3D) warp-knitted mesh fabrics. A full-size finite element (FE) model of a typical 3D mesh fabric is established at the yarn level based on the realistic monofilament architecture from micro-computed tomography (μCT) scanning and verified with experiments. The structural change of the fabric in the spherical indentation process is quantitatively analyzed in terms of fabric global deformation, local deformation, mesh deformation, and spacer monofilament deformation from the FE simulation. The numerical results show that the fabric shrinks walewise and expands coursewise from the spherical indentation of the continuous intermeshed monofilament architecture, showing counterintuitive partial auxeticity. The coursewise symmetry and walewise asymmetry of the 3D mesh fabric produce relatively symmetrical coursewise deformation and asymmetrical walewise deformation under spherical indentation. The symmetrical coursewise deformation includes even widening, good fitting of the indenter, and almost identical mesh sizes in the coursewise direction. Walewise asymmetry leads to uneven shortening, inferior fitting of the indenter, and considerably varied mesh sizes in the walewise direction. Spacer monofilaments in different positions relative to the spherical indenter have different deformations. The closer to the indenter, the greater bending and twisting of the spacer monofilament. The spacer monofilament knitted earlier of the tested fabric has smaller deformation than that knitted later due to the walewise asymmetry. The coursewise symmetry and walewise asymmetry of the inhomogeneous 3D mesh fabric structure result in a highly nonlinear spherical indentation behavior.

The Study Influence Analysis of the Mathematical Model Choice for Describing Polymer Behavior.

The article considered the three types of description of the material behavior model: elastic, elastic-plastic, and viscoelastic. The problem is considered in the framework of deformable solid mechanics. The paper considers the possibility of describing modern polymeric and composite materials used as antifriction sliding layers in the viscoelasticity framework. A numerical procedure for finding the coefficients to describe the viscoelastic material behavior using the Prony model has been implemented. Numerical results and experimental data are compared. The model problem of spherical indenter penetration into polymer half-space is realized. The influence of the system discretization on the numerical solution is analyzed. The influence of the polymer behavior description in static and dynamic problem formulations is analyzed.

A New Elementary Method for Determining the Tip Radius and Young's Modulus in AFM Spherical Indentations.

Atomic force microscopy (AFM) is a powerful tool for characterizing biological materials at the nanoscale utilizing the AFM nanoindentation method. When testing biological materials, spherical indenters are typically employed to reduce the possibility of damaging the sample. The accuracy of determining Young's modulus depends, among other factors, on the calibration of the indenter, i.e., the determination of the tip radius. This paper demonstrates that the tip radius can be approximately calculated using a single force-indentation curve on an unknown, soft sample without performing any additional experimental calibration process. The proposed method is based on plotting a tangent line on the force indentation curve at the maximum indentation depth. Subsequently, using equations that relate the applied force, maximum indentation depth, and the tip radius, the calculation of the tip radius becomes trivial. It is significant to note that the method requires only a single force-indentation curve and does not necessitate knowledge of the sample's Young's modulus. Consequently, the determination of both the sample's Young's modulus and the tip radius can be performed simultaneously. Thus, the experimental effort is significantly reduced. The method was tested on 80 force-indentation curves obtained on an agarose gel, and the results were accurate.

Application of Extended Finite Element Method for Studying Crack Propagation of Welded Strip Steel in the Cold Rolling Process.

In the cold rolling process, edge cracks, particularly those near the welded zone, can inadvertently lead to strip rupture. This study employed the extended finite element method (XFEM) to analyze the crack propagation behavior in welded strip steel during cold rolling. Various tests such as the tensile test, essential work of fracture (EWF) test, spherical indentation method, and elastoplastic finite element simulations were conducted to determine the maximum principal stress and fracture energy utilized in XFEM for the base metal and weld metal, respectively. A continuous cold rolling model was established to investigate the crack propagation behaviors in the base metal, weld metal, and the interface between the base and weld metal. In the continuous rolling process, the crack propagation and expansion speed in the base metal are much larger than that of the weld zone. In addition, the base metal at the back end of the rolled piece is more prone to fracture than the base metal at the front end.

X-ray Diffraction Method in the Study of a Metal Surface Stress State Under Static and Impact Deformation

Study of the stress field in a plastic imprint and around it is of great practical importance. Processes similar to indentation are used in shot blasting to harden the surface of materials and generate compressive stresses in the surface layers. The purpose of this work was to study the change in the stress-strain state in the area of the plastic imprint with increasing load, in the transition from small to large deformations, as well as to study the change in stress at different strain rates.X-ray diffraction method was used to study the field of residual stresses generated on the surface of a plastically deformed region – in the zone of an imprint formed when a spherical indenter is pressed into the metal. An analysis of the change in the stress distribution with increasing load in the range of plastic imprint depths of 10–60 µm for steels and aluminum was made. Influence of the loading rate on the change in the values of residual stresses under normal contact of colliding bodies was studied. It is shown that the stress distribution has a complex character with areas of compression and tension of the metal and is determined by the ratio of the indentation depth to its diameter.The obtained experimental data make it possible to determine the choice of optimal modes of shot blasting, including for increasing the endurance limit of products.

Indentation of living cells by AFM tips may not be what we thought!

The models used to calculate Young's moduli from atomic force microscopy (AFM) force curves consider the shape of the indentation. It is then assumed that the geometry of the indentation is identical to the geometry of the indenter, which has been verified for hard materials (E > 1 MPa). Based on this assumption, the force curves calculated by these models, for the same object with a given Young's modulus, are different if the indenter geometry is different. On the contrary, we observe experimentally that the force curves recorded on soft living cells, with pyramidal, spherical, or tipless indenters, are almost similar. This indicates that this basic assumption on the indentation geometry does not work for soft materials (E of the order of 5 kPa or less). This means that, in this case, the shape of the indentation is therefore different from the shape of the indenter. Indentation of living cells by AFM is not what we thought!

On determination of elastic modulus and indentation hardness by instrumented spherical indentation: influence of surface roughness and correction method

Although, surface roughness can influence the determination of elastic moduli and indentation hardness to some extent by instrumented spherical indentation test, limited work has been done to quantitatively reveal and minimize these influences. In the present work, through a large number of finite element (FE) simulations and analyses, we clarified the evolution trend of determined elastic moduli and indentation hardness corresponding to different normalized indentation depths (h/R) and normalized roughness (S q/R). On this basis, an area correction method was proposed to improve the measurement accuracy in the elastic moduli and indentation hardness. The FE results show that, with the newly proposed correction method, the maximum relative error in determined elastic moduli is reduced from about ±7% to ±2%, and that in the determined indentation hardness is reduced from about ±13% to ±5%, when S q/R ≤ 2.2 × 10−3 and h/R = 5%. Applications were then illustrated on four typical metallic materials (i.e., AA 7075, AA 2014, steel 316 L, and copper T2). The experimental results demonstrate that the proposed correction method is able to mitigate the effects of surface roughness on the determination of elastic moduli and indentation hardness to obtain more correct results.

Analysis of failure characteristics and mechanical mechanisms of sandstone during spherical indenter intrusion based on acoustic emission experiment

This paper aims to investigate the effects of steel ball diameter on failure characteristics and mechanical mechanisms of sandstone during the spherical indenter intrusion process. By using equipment such as acoustic emission (AE), the process of spherical indenter intrusion into sandstone was monitored and recorded for analysis of the fracture characteristics, load-depth relationship, and specific energy of sandstone under spherical indenters with different diameters. The results showed that as the diameter of the spherical indenter increased, the peak load of the sandstone increased continuously, and the failure mode transitioned from “jump-type” to plastic, with the acoustic emission count exhibiting a staged variation characteristic. During this process, the accumulated acoustic emission count, intrusion coefficient, and specific energy of intrusion all exhibited a “parabolic” law of first decreasing and then increasing, all of which reached minimum values when the ratio of the diameter of indenter to sandstone was close to 1.0. This indicated that as the diameter of the indenter approaches that of the sandstone, the intrusion process becomes more facile and efficient. Finally, the study revealed the formation mechanism of dense core and crack inside the sandstone during intrusion, and discussed the law of the crushing rate in ball milling from the perspective of compression. The conclusions contribute to revealing the fragmentation mechanics of rocks in the ball milling process and aid in determining the ball loading parameters in the milling process based on rock properties, aiming to achieve energy-saving and cost reduction.

On the evaluation of uniaxial tensile and fracture properties of Ti‐6Al‐4V by spherical indentation tests with different calculation models

AbstractThis study assessed the efficacy of models in predicting uniaxial tensile and fracture properties of Ti‐6Al‐4V (TC4) alloys via spherical indentation tests (SITs). Four models, including one empirical, one numerical, and two analytical, were selected as representatives to evaluate uniaxial tensile properties. A series of experiments were conducted on TC4 alloys obtained from three manufacturing processes: selective laser melting (SLM), forging, and welding. The empirical model underestimated the material's strength, while the other models were mostly conservative, with errors within 10%, acceptable for engineering applications. However, although the incremental model is able to provide a desirable result, it may be inaccurate for calculating the yield strength. Thus, the source of errors in each model was thoroughly investigated through theoretical analysis and finite element calculations. Additionally, based on the results of optimal strength assessment, this study validated the effectiveness of the critical stress model to evaluate the fracture toughness of TC4 alloys.

Implementation of Digital Image processing in Calculating Normal Approach for Spherical Indenter Considering Elastic/Plastic Contact

In this work a study and calculation of the normal approach between two bodies,spherical and rough flat surface, had been conducted by the aid of image processingtechnique. Four kinds of metals of different work hardening index had been used as asurface specimens and by capturing images of resolution of 0.006565 mm/pixel a good estimate of the normal approach may be obtained the compression tests had been done in strength of material laboratory in mechanical engineering department, a Monsanto tensometer had been used to conduct the indentation tests. A light section measuring equipment microscope BK 70x50 was used to calculate the surface parameters of the texture profile like standard deviation of asperity peak heights, centre line average, asperity density and the radius of asperities. A Gaussian distribution of asperity peak height was assumed in calculating the theoretical value of the normal approach in the elastic and plastic regions and where compared with those obtained experimentally to verify the obtained results.

Contact interaction and wear of beam supports resting on a frictional substrate

The frictional contact response of a beam with attached spherical indenters and supported on a plane substrate is considered for periodically varying normal load. An oblique loading case then occurs as the structural load induces both normal and tangential forces on the contact zone. The cyclic tangential sliding and spin of indenter on the substrate are then accompanied by evolving contact zone related to load variation. Rigid-sliding and slip-sliding friction models have been used to describe analytically cyclic contact response, load-deflection hysteretic relation, wear scar evolution and dissipated energy per cycle assuming linear-elastic material model. The analytical solution has been verified by experimental tests providing data on mechanical response, load-deflection diagrams illustrating transient and steady states and wear scar evolution. The effect of wear debris adhesively bonded to the indenter was found to be essential for increasing friction and wear. The relation of wear volume to the dissipated energy is presented. The analysis is aimed to develop a new type of wear tester applicable to oblique loading cases.

Machine learning based dual flat-spherical indentation approach for rough metallic surfaces

Instrumented indentation test (IIT) is regarded as one of the non-destructive test methods for mechanical characterization and safety assessment of engineering components. However, indentation test is very sensitive to surface topography i.e surface roughness, requiring specimens with ideally flat and smooth surface for producing reliable and reproducible test results. Recently, a dual flat-spherical indentation (DFSI) technique was proposed to extract material properties directly from rough metallic surface via indentation tests. Integration of DFSI technique with machine learning (ML) approach can facilitate reliable and fast characterization of rough metallic surfaces. Here, ML models including artificial neural network (ANN) and physics-informed artificial neural network (PI-ANN) are established, and then trained by using a database of indentation parameters generated via DFSI simulations. Spherical indentation techniques available in the literature are used to calculate the physics-informed loss in the PI-ANN model. The performances of trained ANN and PI-ANN models are compared, and an optimal ML model with hyperparameters is suggested based on validation study; PI-ANN model with sigmoid activation function shows a better performance than the ANN model and baseline model. The model performances are evaluated by performing DFSI experiments with SM45C and SS304. The applicability of ML based-DFSI method is demonstrated for extracting the mechanical properties from the rough surface of general metals.

Effect of ultrasonic vibration on the deformation through indentation test and molecular dynamics simulation

An ultrasonic vibration-assisted indentation device is utilized to implement indentation tests, performed with a spherical indenter under static load and superimposed ultrasonic vibration excitation pressing into the sample to study the volume effect of ultrasonic vibration. The loading forces during the test are acquired by a Kistler force sensor. An indentation molecular dynamics model (IMDM) and an ultrasonic vibration-assisted indentation molecular dynamics model (UIMDM) are developed to study ultrasonic vibration on the microstructure evolution qualitatively. The test results show differences in the effects of ultrasonic vibration on materials with distinct microstructures, where a 17.2% reduction in loading force is observed for the aluminum sample and almost no change for resin. The molecular dynamics results indicate that ultrasonic vibrations do not affect the total potential energy of the model during the elastic deformation stage but increase the total potential energy of the model in the plastic deformation stage, attributed to the absorption of the ultrasonic vibration energy by the generation of dislocations. Simultaneously, ultrasonic vibration reduces the resistance to dislocation motion, the Peierls-Nabarro force, and increases the von Mises stress within the model, the driving force for dislocation motion, thus reducing the loading force required for plastic deformation.

Study of the Applicability of the Vyalov Long-Term Strength Prediction Equation under Freezing and Thawing Conditions

In order to determine the appropriate utilization conditions of the Vyalov long-term strength prediction equation, this study selected three soil samples from the loess region. These samples were subjected to varying numbers of freeze–thaw cycles, namely 0, 4, 6, 8, 10, 50, and 100 cycles. Subsequently, post-test soil samples underwent spherical template indenter press-in tests and grain size determinations. The experimental outcomes demonstrated that the Vyalov long-term strength prediction equation accurately reflected the long-term strength variations of frozen loess after 10 freeze–thaw cycles. A further analysis revealed that the stability of the soil samples’ grain composition played a vital role in ensuring the accuracy of the prediction equation. Notably, a highly significant positive correlation was observed between the silt content of the soil samples and the prediction equation parameter β. Moreover, employing the Vyalov long-term strength prediction equation after 10 freeze–thaw cycles yielded prediction results consistent with the freeze–thaw cycles–time analogy method for durations of 10, 20, and 30 years. This study is beneficial for the construction and operation of projects in loess areas.

Surface effects on the spherical indentation of biological film/substrate structures

Micro-/nano-indentation has been the most popular technique to extract the mechanical characteristics of biological cells and tissues. However, due to surface effects and the existence of substrates, conventional contact models are unable to determine the accurate elastic modulus of biological samples by analyzing the measured load-indent depth data. In this study, the spherical indentation of the film/substrate structure considering the surface energy and large deformations is investigated. The hyperelasticity of biological films and substrates is considered through neo-Hookean constitutive model, and the surface effect is incorporated using the finite element method. The explicit formulas for the relations between load and indent depth are presented for films with two orders of magnitude modulus mismatch to the substrate. It is found that the modulus mismatch between film and underlying substrate would lead to an overestimation of modulus for the film on a stiffer substrate, but an underestimated modulus for that on a softer substrate if the conventional Hertzian theory is directly adopted in the analysis. Moreover, for indentation at micro-/nano-scale, the surface energy would pronouncedly reduce the indent depth under a given load and lead to a seemingly stiffer film. Our results provide the explicit expressions to accurately predict the spherical indentation response of biological film/substrate structures.

Load-induced local phase transformation and modulus of shape memory alloys under spherical indentation by finite element method

Shape memory alloys are a unique class of materials that are capable of large reversible deformations under external stimuli such as stress or temperature. The present study examines the phase transformations and mechanical responses of NiTi and NiTiHf shape memory alloys under the loading of a spherical indenter by using a finite element model. It is found that the indentation unloading curves exhibit distinct changes in slopes due to the reversible phase transformations in the SMAs. The normalized contact stiffness (F/S2) of the SMAs varies with the indentation load (depth) as opposed to being constant for conventional single-phase materials. The load-induced phase transformation that occurred under the spherical indenter was simulated numerically. It is observed that the phase transformation phenomenon in the SMA induced by an indentation load is distinctly different from that induced by a uniaxial load. A pointed indenter produces a localized deformation, resulting in a stress (load) gradient in the specimen. As a result, the transformation of phases in SMAs induced by an indenter can only be partially completed. The overall modulus of the SMAs varies continuously with the indentation load (depth) as the average volumetric fraction of the martensite phase varies. For NiTi (Ea > Em), the modulus decreases with the depth, while for NiTiHf (Ea < Em), the modulus increases with the depth. The predicted young modules during indentation modeling agree well with experimental results. Finally, the phase transformation of the SMAs under the indenter is not affected by the post-yield behavior of the materials.