Indenter Radius Research Articles

Molecular dynamics simulation of gradient alloying distribution on the nano-mechanical properties of Nb-Zr alloys

Abstract In this work, a nano-indentation process of homogeneous Nb-Zr alloy and gradient Nb-Zr alloy was simulated using molecular dynamics simulation. The effects of Zr content, system temperature, indentation radius on the mechanical properties and micro-deformation were investigated. Comparing the homogeneous and gradient alloys, it was revealed that the gradient alloy had a smoother mechanical performance. The results showed that the effect of Zr content on the hardness of Nb-Zr homogeneous alloy was not linear. The hardness rose followed by a decline with increasing Zr content and the turning point came at 1.5 wt.%. Under high temperatures, the Nb-Zr homogeneous alloy and gradient alloy layer retained extremely high hardness, exhibiting excellent mechanical properties. Due to the entanglement of multiple dislocations in gradient Nb-Zr alloy at high temperatures, the hardness still increased with increasing temperature at high temperatures. The influence of indentation size on nano-indentation experiments was mainly affected by the curvature of the indented part. It was worth noting that gradient alloys could disperse stress faster and reach a stable state during the loading process. The hardness of the Nb-Zr homogeneous alloy layer first increased and then decreased as the Zr content changed from 1.0 wt.% to 2.0 wt.%, as verified by the experiments. This study provided the reference for the preparation of high-temperature applications alloy by constructing Nb-Zr gradient alloy.

Calibration of the spherical tip radius of Rockwell hardness diamond indenters using a confocal laser scanning microscope

Abstract The precise form of an indenter is an essential part of hardness testing methods. It is therefore incumbent upon a user to ensure that the indenter geometry is calibrated before performing a hardness test. A geometric change of the tip radius by ±5 μm can cause a change of approximately 0.6 units of Rockwell hardness C scale (HRC) in a material with a hardness of 65 HRC. Keeping in mind that the measurement uncertainty is typically of the order of 0.3 HRC, it is critical to know the true value of the tip radius. Typically, tactile methods are used to determine the tip radius of a Rockwell hardness diamond indenter from the measured surface topography. Two main drawbacks of tactile measurements are the long duration of measurement and the limitation in capturing surface features of sizes smaller than the probe tip radius of 2 μm. Both could be overcome by using an optical 3D measurement. Confocal laser scanning microscopes (CLSM) allow a fast contactless 3D-mapping of the surface of Rockwell hardness diamond indenters and can be used to obtain geometric information such as the tip radius. The accuracy of these 3D measurements is still under question. Within this work, some of the influencing factors for fast 3D surface measurement are investigated. Using a CLSM with a 50x objective lens and a numerical aperture of 0.95, typical shape deviations of Rockwell diamond indenters are shown. Furthermore, an improved 3D based point cloud method for the evaluation of the indenter radius is presented. The aim of this paper is to explore the capabilities and limits of CLSM to obtain the 3D surface of a Rockwell hardness diamond indenter in order to calibrate the tip radius and compare their results with measurements from traceable stylus instruments.

Conical indentation over a transversely isotropic and layered elastic half-space

We propose a novel method for solving the static response of a conical indenter on a transversely isotropic and layered elastic half-space. The newly developed Fourier-Bessel series (FBS) system of vector functions, along with the unconditionally stable dual-variable and position method, is employed to derive the Green's function in the transversely isotropic and layered elastic half-space under a vertical ring load on the surface. To calculate the response at different field points on the surface, we apply discrete love numbers within the FBS vector system. The load densities in the discretized rings within the contact radius of the conical indenter are determined using the integral least-square method, along with a self-adaptive algorithm developed in this study. Finally, the relationship between the indentation depth (vertical displacement) and the applied load is obtained through force balance between the external load and the summed contact traction. The developed scheme is validated using existing exact solutions for the reduced homogeneous half-space case. Selected numerical results clearly demonstrate the effect of anisotropic material and layering on the indentation response. It is observed that, regardless of whether the structure is a stratified half-space or a layered structure with a rigid substrate, the material properties in the top layer have the most significant influence on the indentation behavior. In the case of a layered structure with an underlying elastic half-space, the material properties in the interlayer and bottom layer could also affect the indentation behaviors.

Unloading Model of Elastic-Plastic Half-Space Contacted by an Elastic Spherical Indenter.

A new unloading contact model of an elastic-perfectly plastic half-space indented by an elastic spherical indenter is presented analytically. The recovered deformation of the elastic indenter and the indented half-space has been found to be dependent on the elastic modulus ratio after fully unloading. The recovered deformation of the indented half-space can be calculated based on the deformation of the purely elastic indenter. The unloading process is assumed to be entirely elastic, and then the relationship of contact force and indentation can be determined based on the solved recovered deformation and conforms to Hertzian-type. The model can accurately predict the residual indentation and residual curvature radius after fully unloading. Numerical simulations are performed to demonstrate the assumptions and the unloading model. The proposed unloading model can cover a wide range of indentations and material properties and is compared with existing unloading models. The cyclic behavior including loading and unloading can be predicted by combining the proposed unloading law with the existing contact loading model. The combined model can be employed for low-velocity impact and nanoindentation tests and the comparison results are in good agreement.

Spherical Indentation and Implementation of S3/P for yield stress determination of brittle materials

A mathematically transparent and robust experimental method has been developed to estimate the yield stress of brittle materials through the analysis of depth-sensing spherical indentation. Employing Hertzian contact mechanics, an elastically invariant ratio based on the simple equation S3/P=6REr2, (where S and P are contact stiffness and indentation load, respectively) has been derived that enables more accurate and confident determination of the transition from elastic to inelastic deformation; a transition that the yield stress dictates and represents. Using two diamond spheres with radii of 3.2 and 8.6 μm, the indentation test method and analyses are applied to two vitreous silicates: Corning's HPFS 7980® fused silica and Vitro's Starphire® soda-lime silicate. The estimated yield strengths are 8.15 GPa ± 2.5 % for the fused silica and 6.1 GPa ± 3.3 % for the soda-lime silicate, and both were independent of indenter radius. Verification of this new experimental method is demonstrated with an as-drawn titanium by showing equivalence of measured yield stress by its spherical indentation and that from uniaxial compression testing. This method will enable easier and more confident estimation of yield stress in brittle materials - a property that historically has been elusive to measure for these materials using common laboratory mechanical test methods.

Graphene oxide under the nanoscope: A comprehensive study of nanoindentation behavior

Graphene oxide membranes are expected to become one of the most important materials for technological applications due to their highly reactive surface, being directly related to their atomistic configuration. The understanding of its structure and physicochemical properties under mechanical deformation is becoming crucial in the development of new applications; however, the role of the different functional groups in the membrane and their response to external factors like indentation is still unclear. Nanoindentation experiments show elastic behavior when the penetration is small compared to the indenter radius and the membrane diameter. Molecular Dynamics simulations for large 3-layer graphene oxide membranes were carried out for a 50% oxidation content and the inclusion of epoxy and hydroxy groups. Simulations showed an elastic modulus similar to experimental values. After the elastic regime, the mechanical behavior is dominated by the evolution of functional groups. A quasi-elastic regime is uncovered, where unloading leads to self-healing of broken bonds. Finally, large indenter penetration leads to fracture, with fracture stress similar to experimental values.

Atomistic simulation of nanoindentation behavior of amorphous/crystalline dual-phase high entropy alloys

High-entropy alloys (HEAs) are a new type of multi-principal metal materials that exhibit excellent mechanical properties. However, the strength–ductility balance in the HEAs remains a challenge that needs to be addressed. The amorphous/crystalline (A/C) structure is a new design strategy to achieve high strength and excellent ductility of the HEAs. Here, the influences of amorphous layer spacing, indenter velocity, and indenter radius on the mechanical properties and microstructure evolution of the A/C dual-phase CoCrFeMnNi HEAs under nanoindentation were investigated by molecular dynamics (MD) simulation. The results indicate that the plastic deformation mechanism of the monocrystalline HEAs is mainly dominated by the nucleation and slip of dislocations, while the plastic deformation mechanism of the dual-phase HEAs is mainly dominated by the interaction between dislocations and amorphous phases. The results show that the average indentation force of the dual-phase HEAs increases with the increase of the amorphous layer spacing. The amorphous layer in the HEAs can hinder the expansion of dislocations, limiting them to the crystalline matrix between the two amorphous layers. The results also indicate that Young's modulus of the HEAs increases with the increase of the indentation velocity and indentation radius. However, the hardness of HEAs is positively correlated with the indenter velocity, and negatively correlated with the indenter radius. It should be noted that the critical indentation depth and critical indentation force for the plastic deformation of the dual-phase HEAs decrease with the increase of indenter velocity, which is opposite to that of the single-phase crystalline HEAs.

A Bilayer Method for Measuring Toughness and Strength of Dental Ceramics

The ever-increasing usage of ceramic materials in restorative dentistry necessitates a simple and effective method to evaluate flexural strength σF and fracture toughness KC. We propose a novel method to determine these quantities using a bilayer specimen composed of a brittle plate adhesively bonded onto a transparent polycarbonate substrate. When this bilayer structure is placed under spherical indentation, tunneling radial cracks initiate and propagate in the lower surface of the brittle layer. The failure analysis is based on previous theoretical relationships, which correlate σF with the indentation force P and layer thickness d, and KC with P and mean length of radial cracks. This work examines the accuracy and limitations of this approach using a wide range of contemporary dental ceramic materials. The effect of layer thickness, indenter radius, load level, and length and number of radial cracks are carefully examined. The accuracy of the predicted σF and KC is similar to those obtained with other concurrent test methods, such as biaxial flexure and 3-point bending (σF), and bending specimens with crack-initiation flaws (KC). The benefits of the present approach include treatment for small and thin plates, elimination of the need to introduce a precrack, and avoidance of dealing with local material nonlinearity effects for the KC measurements. Finally, the bilayer configuration resembles occlusal loading of a ceramic restoration (brittle layer) bonded to a posterior tooth (compliant substrate).

Size effects in spherical indentation of single crystal copper

A study of the size effects in the spherical indentation test of a copper single crystal is carried out. The main novelty of the approach is the analysis of a wide spectrum of parameters measured in the test that are predicted by the proposed model, and the prediction is verified experimentally for six different tip radii. Load-penetration depth curves, nominal hardness, pile-up and sink-in profiles, and the rotation and rotation gradient of the crystallographic lattice in the cross-section beneath the indenter have been measured and also calculated using 3D finite element simulations on the micro- and nanometer scale. Two gradient-effects are examined numerically within the Cosserat elastoplasticity framework with the gradient-enhanced hardening law. It is shown that a good prediction of the experimentally observed size effect on nominal hardness is achieved using the conventional power-hardening law, calibrated from the standard uniaxial compression test, enhanced with a term dependent on the lattice spin gradient term with no adjustable parameter. Furthermore, it has been found that the observed distribution of lattice rotation and decrease in the rotation magnitude with decreasing indenter radius can be qualitatively modelled by adjusting the coefficient of accumulated lattice curvature energy within the same framework.

On the superelastic behavior during spherical nanoindentation of a Ni-Ti shape memory alloy

Nanoindentation, the most widely-used probe for small-scall mechanical property evaluation, has been increasingly adopted for exploring the local behavior of shape memory alloys (SMAs). Herein, we explore the influence of the testing parameters (i.e., peak load, indenter radius, loading/unloading rate, and cyclic loading) on the superelastic behavior of a Ni-Ti SMA at room temperature, at which it is in the austenitic state, during spherical nanoindentation. The possible underlying mechanisms for measured response due to each of the testing parameters are discussed in terms of the roles of forward/reverse stress-induced phase transformations, dislocation activity, latent heat evolution, and geometric compatibility of the interfaces during the post-yield deformation.

Contact behaviors involving a nanobeam with surface effect by a rigid indenter

In this study, we present a novel surface model that utilizes surface energy density to predict the surface effect in nanobeam contact problems. To address the issue of a finite-length elastic nanobeam being indented by a rigid cylindrical indenter, we propose an equivalent substitution method. This method allows us to formulate analytical relations between the load and contact half-width for two different boundary cases. The explicit expressions of the contact-zone width, the pressure distribution in the contact zone, the deflection outside the contact zone, and the load–displacement relation are obtained for the nanobeam with surface effect and are compared with classical results in detail. The results show that the influence of the surface effect is very significant for nanobeam contact behavior, especially when the half-width of the contact zone increases and the contact zone becomes two independent symmetric strips. It is also found that the length-height ratio of nanobeam and the end support conditions have a fairly obvious effect on the normalized pressure distribution, which deviates significantly from the one predicted by the classical results due to the surface effect. However, for a given beam length and indenter radius, the ratio of the width of the contact zone to the beam thickness is almost constant, independent of the indenter load and beam boundary conditions. Meanwhile, the model predicts that the contact pressure distribution after the normalization of the average indentation pressure is almost independent of the indentation load and beam boundary conditions, but obviously depends on the surface effect parameters. The present method and result should be helpful not only to the measurement of mechanical properties of the indentation nanobeam but also to the design of the nanobeam-based devices.

Multi-objective optimization of sawblade multi-spot pressure tensioning process based on backpropagation neural network and genetic algorithm

ABSTRACT Resources scarcity has created strict requirements for efficient wood processing. Multi-spot pressure tensioning can effectively stabilize the sawblade and reduce cutting losses, but it is difficult to apply in practice due to the complexity of the process. In this study, the elastic-plastic solid model of multi-spot pressure tensioning was established, which was simplified to a thermal expansion shell model, and the mapping relationship between the two models was determined. The feasibility of the mapping method was verified by experiments. The backpropagation neural network (BPNN) was trained on a database composed of 8160 working conditions and the relative error was found to be less than 5%. Indenter displacement, pressing point quantity, and indenter radius were shown to change the degree of tension to varying extent. The pressing-point-distribution radius determines the development direction of sawblade performance. Increasing the number of pressing point circles can expand the adjustment range for sawblade performance. Both sawblade performance and tensioning energy consumption can be optimized by the genetic algorithm (GA). The optimal process parameters for different applications can be obtained. The combination of finite element method, BPNN, and GA can effectively optimize the multi-spot pressure tensioning process to improve the sawblade performance.

Dynamic response of concrete-filled square steel tubular columns under lateral impact load at flat or corner zone

The dynamic response of columns under lateral impact is of great significance for guiding structural design under accidental loads. The present study aims to investigate the effect of different impact directions on the dynamic response of square concrete-filled steel tubular (CFST) columns by conducting drop hammer tests at flat or corner zones. The main experimental parameters included hammer mass, drop height, indenter radius, built-in steel bars, shear span ratio, width-thickness ratio, and column sizes. The experimental results showed that the impact zone has a significant effect on the dynamic response of CFST specimens. Under higher impact energies, specimens impacted at corner zones were more likely to fracture on the tensile side of the steel tube than specimens impacted at flat zones. And the specimens impacted at the corner zone were more sensitive to the change of indenter radius. Smaller shear span ratios, built-in steel bar, and larger column sizes improved the impact resistance of tested specimens. The 3D finite element models were developed and analyzed by ABAQUS/Explicit to explore dynamic behavior further.

Probing soft fibrous materials by indentation.

Indentation is often used to measure the stiffness of soft materials whose main structural component is a network of filaments, such as the cellular cytoskeleton, connective tissue, gels, and the extracellular matrix. For elastic materials, the typical procedure requires fitting the experimental force-displacement curve with the Hertz model, which predicts that f=kδ1.5 and k is proportional to the reduced modulus of the indented material, E/(1-ν2). Here we show using explicit models of fiber networks that the Hertz model applies to indentation in network materials provided the indenter radius is larger than approximately 12lc, where lc is the mean segment length of the network. Using smaller indenters leads to a relation between force and indentation displacement of the form f=kδq, where q is observed to increase with decreasing indenter radius. Using the Hertz model to interpret results of indentations in network materials using small indenters leads to an inferred modulus smaller than the real modulus of the material. The origin of this departure from the classical Hertz model is investigated. A compacted, stiff network region develops under the indenter, effectively increasing the indenter size and modifying its shape. This modification is marginal when large indenters are used. However, when the indenter radius is small, the effect of the compacted layer is pronounced as it changes the indenter profile from spherical towards conical. This entails an increase of exponent q above the value of 1.5 corresponding to spherical indenters. STATEMENT OF SIGNIFICANCE: The article presents a study of indentation in network biomaterials and demonstrates a size effect which precludes the use of the Hertz model to infer the elastic constants of the material. The size effect occurs once the indenter radius is smaller than approximately 12 times the mean segment length of the network. This result provides guidelines for the selection of indentation conditions that guarantee the applicability of the Hertz model. At the same time, the finding may be used to infer the mean segment length of the network based on indentations with indenters of various sizes. Hence, the method can be used to evaluate this structural parameter which is not easily accessible in experiments.

Analysis of transverse elastic modulus and compressive deformation mechanism of cellulose crystals based on molecular dynamics

Cellulose nanocrystals (CNCs) have been widely used as reinforcing agents for composite materials due to their excellent mechanical properties. CNC composites are inevitably deformed by external forces during use. In order to reduce the damage of CNC composites in application and improve their service life, their mechanical properties and deformation mechanisms need to be studied in depth. In this study, cellulose Iβ crystals were selected for molecular dynamics simulation of nanoindentation to predict the transverse elastic modulus of cellulose crystals. The simulation results were compared with existing nanoindentation tests to verify the simulation accuracy. The impact of the loading depth, loading speed, and radius of the spherical indenter on elastic modulus and surface deformation of a system was explored. The results show that the loading depth and loading speed of the indenter have weak influence on the elastic modulus, and the small radius of the indenter (1 nm) will lead to the distortion of the elastic modulus. The compression deformation mechanism of cellulose crystal at the molecular level was analyzed by analyzing changes in cellulose crystal indentation morphology, molecular potential energy and hydrogen bond number during compression simulation. As the indenter radius and loading depth increase, the deformation degree of cellulose crystal also increases, whereas the loading speed within the 50–150 m/s range does not significantly influence on the deformation degree of cellulose crystal. These results may guide the production of nanocomposites with cellulose crystal reinforcements, which can be useful for preventing material damage and enhancing material efficiency.

Research on Determining Elastic-Plastic Constitutive Parameters of Materials from Load Depth Curves Based on Nanoindentation Technology.

It is of great significance for structural design and engineering evaluation to obtain the elastic-plastic parameters of materials. The inverse estimation of elastic-plastic parameters of materials based on nanoindentation technology has been applied in many pieces of research, but it has proved to be difficult to determine the elastic-plastic properties of materials by only using a single indentation curve. A new optimal inversion strategy based on a spherical indentation curve was proposed to obtain the elastoplastic parameters (the Young's modulus E, yield strength σy, and hardening exponent n) of materials in this study. A high-precision finite element model of indentation with a spherical indenter (radius R = 20 µm) was established, and the relationship between the three parameters and indentation response was analyzed using the design of experiment (DOE) method. The well-posed problem of inverse estimation under different maximum indentation depths (hmax1 = 0.06 R, hmax2 = 0.1 R, hmax3 = 0.2 R, hmax4 = 0.3 R) was explored based on numerical simulations. The results show that the unique solution with high accuracy can be obtained under different maximum press-in depths (the minimum error was within 0.2% and the maximum error was up to 1.5%). Next, the load-depth curves of Q355 were obtained by a cyclic loading nanoindentation experiment, and the elastic-plastic parameters of Q355 were determined by the proposed inverse-estimation strategy based on the average indentation load-depth curve. The results showed that the optimized load-depth curve was in good agreement with the experimental curve, and the optimized stress-strain curve was slightly different from the tensile test, and the obtained parameters were basically consistent with the existing research.

Effects of lattice distortion and chemical short-range ordering on the incipient behavior of Ti-based multi-principal element alloys: MD simulations and DFT calculations

One of key factors in designing high-performance alloys is to understand their incipient behavior. To get detailed real-time atomic scale evolutions of multi-principal element alloys (MPEAs) during nanoindentation incipient yielding, molecular dynamics (MD) simulations were carried out. Emphases are given to the effects of lattice distortion (LD) and chemical short-range ordering (CSRO) on the initiation of plasticity in body-centered cubic (BCC) MPEAs. The initial plastic mechanism is embryo nucleation assisted and the incipient behavior is strongly affected by LD and CSRO. Specifically, the embryo nucleation load Pe is reduced by LD and CSRO and the incipient drop P0 is lowered by LDI that only comes from atomic size difference and further declined by CSRO. This is because LD and CSRO could boost embryo nucleation, which can act as precursors for dislocation nucleation. This is consistent with the free-end nudged elastic band observations. Although Pe is weakened by LDII generated by introducing extra elements, P0 is intensified because severe LD could dominate the following process. The dislocation starvation mechanism is found in an average-atom (AA) model. However, it is replaced by dislocation interactions due to LD and CSRO. Density functional theory (DFT) calculations suggest that charge density distribution and the amount of directional Al-Al bonding would play a critical role in the onset of plastic deformation. When a larger indenter radius was used in MD simulations, the dislocation starvation mechanism is absent in AA model due to the reduced maximum shear stress. Instead, the dislocation propagation prevails. With respect to the orientation effect, three investigated orientations demonstrate a distinct yielding behavior.

Effect of indenter radius on mechanical properties of B3-GaN in nanoindentation based on molecular dynamics

Molecular dynamics (MD) simulation of nanoindentation was conducted to study the indentation of sphalerite gallium nitride (B3-GaN) according to different radius spherical indenters. The effect of indenter radius on the evolution of dislocations, atomic displacements, Von Mises stresses, and phase transition of B3-GaN was primarily analyzed. The outcomes of the study indicate that the plastic deformation of B3-GaN crystals may be attributed to the propagation of dislocations and amorphization. The pop-in events of load in the load-depth curve is related to dislocation nucleation, amorphization, and phase transition. As the indenter radius increases, the critical load during the elastic-plastic transformation increases, and the hardness decreases gradually. The Burgers vector of dislocations during indentation is almost all 1/2 <110>, and the main slip directions were along the <110> crystallographic direction family. The magnitude and distribution range of atomic displacements and Von Mises stresses increase with the indenter radius, and this further promotes the nucleation and propagation of dislocations in the slip system, thus intensifying the plastic deformation of B3-GaN crystals. The elastic deformation of B3-GaN crystals may be attributed to amorphization and phase transition. During the elastic deformation phase, increasing the indenter radius promotes the phase transition of B3-GaN to fibrillated gallium nitride (B4-GaN) and enhances the amorphization of B3-GaN in the deformation layer. In addition, the increase in the indenter radius delays the generation of amorphous phases and phase transition. The outcomes of the study help us understand the mechanical properties of B3-GaN along with its potential for use in precision finishing.

Molecular Dynamics Simulation on Nanoindentation of M50 Bearing Steel.

M50 bearing steel has great potential for applications in the field of aerospace engineering, as it exhibits outstanding mechanical and physical properties. From a microscopic point of view, bearing wear originates from the microscopic region of the contact interface, which usually only contains hundreds or even several atomic layers. However, the existing researches seldom study the wear of M50 bearing steel on the microscopic scale. This study explored the atomic-scale modeling method of M50 bearing steel. Then molecular dynamics simulations of nanoindentation on the M50 bearing steel model were carried out to study the size effect of the mechanical behaviors. The simulation results show that with the change in the radius of the diamond indenter in the nanoindentation simulation, the calculated nanohardness decreases. According to the size effect, when the indentation radius is 200 nm, the hardness obtained by the simulation is about 9.26 GPa, and that of the M50 sample measured by the nanoindentation is 10.4 GPa. Then nanoindentation simulations were carried out at different temperatures. The main bearings of aero-engines generally work at 300-500 degrees Celsius. When the simulated temperature was increased from 300 K to 800 K, the hardness of the model decreased by 15%, and the model was more prone to plastic deformation. In this study, a new molecular dynamics modeling method for M50 bearing steel was proposed, and then nanoindentation simulation was carried out, and the nanoindentation experiment verified the correctness of the model. These results are beneficial to the basic understanding of the mechanical performance of M50 bearing steel.

Numerical Simulation on Effect of Indenter Radius During Point Load Test

Numerical Simulation on Effect of Indenter Radius During Point Load Test