Maximum Indentation Depth Research Articles

Determination of the Mechanical Properties of PIN–PMN–PT Bulk Single Crystals by Nanoindentation

The present study aimed to experimentally evaluate the mechanical properties of Pb(In1/2Nb1/2)O3–Pb(Mg1/3Nb2/3)O3–PbTiO3 (PIN–PMN–PT) bulk single crystals with different crystallographic directions using the nanoindentation technique. The load–indentation depth curves, elastic and plastic deformations, hardnesses, and Young’s moduli of [100]- and [110]-oriented 0.28PIN–0.43PMN–0.29PT bulk single crystals were investigated. Our results show that with an increase in the maximum indentation depth hmax, the plastic residual percentage increased for both the [100]- and the [110]-oriented single crystals. At each hmax, the plastic residual percentage of the [100]-oriented PIN–PMN–PT single crystals was less than that of the [110]-oriented PIN–PMN–PT single crystals. At hmax from 500 nm to 2000 nm, the plastic deformation was larger than the elastic deformation, and the plastic residual percentage was larger than 50% for both the [100]- and the [110]-oriented single crystals. This means that the plastic deformation dominated in the indentation process of PIN–PMN–PT single crystals. The indentation size effect on the hardness of the PIN–PMN–PT single crystals was apparent in the nanoindentation process. Both the hardness and the Young’s modulus of the [100]-PIN–PMN–PT single crystals were greater than those of the [110]-PIN–PMN–PT single crystals, which indicates that the PIN–PMN–PT single crystals had anisotropic mechanical characteristics.

Insight into the microphysics of antigorite deformation from spherical nanoindentation.

The mechanical behaviour of antigorite strongly influences the strength and deformation of the subduction interface. Although there is microstructural evidence elucidating the nature of brittle deformation at low pressures, there is often conflicting evidence regarding the potential for plastic deformation in the ductile regime at higher pressures. Here, we present a series of spherical nanoindentation experiments on aggregates of natural antigorite. These experiments effectively investigate the single-crystal mechanical behaviour because the volume of deformed material is significantly smaller than the grain size. Individual indents reveal elastic loading followed by yield and strain hardening. The magnitude of the yield stress is a function of crystal orientation, with lower values associated with indents parallel to the basal plane. Unloading paths reveal more strain recovery than expected for purely elastic unloading. The magnitude of inelastic strain recovery is highest for indents parallel to the basal plane. We also imposed indents with cyclical loading paths, and observed strain energy dissipation during unloading-loading cycles conducted up to a fixed maximum indentation load and depth. The magnitude of this dissipated strain energy was highest for indents parallel to the basal plane. Subsequent scanning electron microscopy revealed surface impressions accommodated by shear cracks and a general lack of dislocation-induced lattice misorientation. Based on these observations, we suggest that antigorite deformation at high pressures is dominated by sliding on shear cracks. We develop a microphysical model that is able to quantitatively explain Young's modulus and dissipated strain energy data during cyclic loading experiments, based on either frictional or cohesive sliding of an array of cracks contained in the basal plane. This article is part of a discussion meeting issue 'Serpentinite in the earth system'.

Диссипация механической энергии в осциллирующем адгезионном контакте между жестким индентором и эластомером

A model of hysteresis in an adhesive contact under oscillating loading is proposed, based on the chemical inhomogeneity of the indenter surface. Results of numerical simulation are compared with experimental data obtained with a setup allowing direct observation of the dynamics of contact area. It is shown that the hysteresis almost disappears if the amplitude of the oscillating load is smaller than a critical value depending on the maximum indentation depth.

Adhesive contact of a diamond sphere with an iron substrate caused by interatomic interaction

By incorporating the adhesive force as a body force in the finite element method, the adhesive contact between a diamond sphere and the iron substrate is studied. The adhesive force is derived from Morse potential by integrating the pair potential function over the spherical domain. Based on the tensile behaviors of iron nanowires, the elastic and elastoplastic material parameters are obtained for the substrate. As the radius of the sphere is larger than 320 nm and the maximum depth of indentation is one-tenth of the radius of the sphere, the adhesion caused by interatomic interaction between diamond and iron is small enough to ignore. Then take the sphere whose radius is 20 nm as an example, the results of a single load–unload cycle and multiple load–unload cycles are discussed. In the contact process between the sphere and the surface, the phenomena jump-to-contact and jump-off-contact were observed. Further, the stress distributions inside the substrate and the pressure distribution are investigated. With the analysis of the results, the proposed method can be used to simulate the mechanical behaviors under micro-nano scale contact.

Clinical research on corneal biomechanical changes after keratoconus collagen cross-linking

Objective To observe corneal biomechanical changes in patients with keratoconus after corneal collagen cross-linking. Methods Prospective self-control study. Twenty-three eyes of 17 patients with primary keratoconus from Jan. 2018 to Jun. 2018 in Zhengzhou Second Hospital were analyzed. The age of patients ranged from 13 to 28 years, with average of (16.4±2.8) years. All cases were treated with riboflavin/ultraviolet A (UVA)-induced rapid epithelium-off corneal collagen cross-linking. All cases were observed with Corvis ST visualized corneal biomechanical measurement instrument and followed up for 12 months. Results The best corrected visual acuity (LogMAR) after operation increased from 0.42±0.19 to 0.29±0.15 (t=-8.043, P=0.000). The equivalent spherical diopter and the maximum curvature of the anterior corneal surface were decreased (t=-4.183, -5.188, P=0.000, 0.000). The thinnest corneal thickness postoperative was decreased compared with that before operation(t=-3.984, P=0.001). The first flattening time postoperative increased (t=7.793, P=0.000). The second flattening time and the maximum indentation depth decreased (t=-9.075, P=0.000, t=-3.280, P=0.003). Conclusion The visual acuity, corneal morphology and biomechanical parameters after the rapid epithelium-off corneal collagen cross-linking in patients with primary keratoconus are ameliorated significantly. Key words: Keratoconus; Cross-linking, collagen, corneal; Biomechanics, cornea

Mechanical behavior of anti-oxidation coatings on C/C composites at elevated temperature: An in-situ indentation study

Mechanical behavior of anti-oxidation coatings at high temperatures has an important influence on service safety of C/C composites. In this study, an in-situ high temperature indentation method was firstly adopted to study mechanical behavior of Hf-based anti-oxidation coatings in air up to 1000 °C. The indentation tests at room temperature, 800 and 1000 °C were conducted on the surface of the coatings. The maximum indentation depth and modulus increased and decreased with increasing temperature, respectively. And they both changed at a slower rate ranging from room temperature to 800 °C and a faster rate ranging from 800 to 1000 °C. It is also found that a smooth thin glass layer was formed on the surface of the coatings and had little influence on the mechanical behavior of the coatings at 800 °C. However, the oxidation became severe and some voids came into being at 1000 °C. The mechanical behavior was seriously affected, and the plasticity was obviously enhanced, resulting in a significant reduction in the modulus of the coatings.

Determination of the linear elastic regime in AFM nanoindentation experiments on cells

Atomic force microscopy nanoindentation method has been extensively used for the determination of cells’ mechanical properties. The data processing is usually performed using contact mechanics models at the linear elastic regime such as the Hertz model. It should be noted that the cells’ response can be considered as linearly elastic only for a limited range of indentation depths. Although there are in literature proposed values of the maximum allowed nanoindentation depth for most of the cell types, these values have been mostly derived empirically. As a result, the use of these empirically obtained findings can result in significant errors regarding Young’s modulus calculations. A large number of measurements, using spherical and conical indenters, showed errors in the range of 4−10% with respect to the Young’s modulus calculation. In this paper, a new mathematical approach is proposed that enables the identification of the optimum load - indentation data range for the application of the Hertz contact theory. The results presented in this paper indicate that the optimum choice of the maximum indentation depth can vary greatly even in the same sample. For example, 64 load indentation curves on the same cell using a spherical indenter showed that the maximum indentation depth is (553 ± 43)nm (mean value ± standard deviation). As a consequence, the determination of a specific maximum indentation depth for indentation experiments on a specific cell will lead to significant errors regarding Young’s modulus values. Hence, the selection of the linear elastic regime must be performed individually for each load—indentation curve to accurately determine the cell’s mechanical response.

Influence factors of pop-in in the nanoindentation micromechanical property measurement of gas-bearing shale

Abstract Studying the micromechanical properties of gas-bearing shale is very important for understanding it. In the nanoindentation measurement of gas-bearing shale, the load-displacement curve often shows pop-in at the loading stage, namely the change of load is small but the change of penetration depth is large. Pop-in can introduce a large error in the calculation of the mechanical parameter. To investigate the influence factors of pop-in, the maximum load, load rate and sample characteristics have been addressed. The results show that pop-in is related to cracks and pores in the shale. Due to the heterogeneity of shale, pop-in cannot be avoided, but can be reduced by choosing reliable load modes and test parameters. Pop-in can increase the maximum indentation depth and decrease the elastic modulus and hardness. The influence of pop-in on hardness is larger than on the elastic modulus. At a high load rate it is easy to induce pop-in. The influence of the load rate on pop-in is larger than that of the maximum load.

Modeling and simulation of contact parameters of elliptical and cubic nanoparticles to be used in nanomanipulation based on atomic force microscope

Regarding the contact mechanics of smooth nanoparticles, two new geometries, specifically elliptical and cubic are chosen for nanoparticles. The results of elliptical contact simulation show that the JKR theory induces a greater indentation depth in both contact geometries since it includes the adhesion forces. Moreover, the Jamari theory shows a lesser indentation depth because it assumes larger contact area. The results of cubic nanoparticles simulation exhibit a significant difference between the contact of tip and nanoparticle compared to the contact of nanoparticle and surface. This can be attributed to the large contact area between the cubic nanoparticle and the reference surface. The JKR and DMT theories, however, show greater indentation depths in the tip contact with nanoparticle. Furthermore, the Lundberg theory yields the maximum indentation depth in the nanoparticle contact with reference surface. Finally, in order to validate the results, experimental and FEM approaches are incorporated. Concerning the experimental results, a certain number of silver nanoparticles are placed on a polystyrene surface. After obtaining the experimental force-displacement curves, the results of presented models are compared with them. The experimental results indicate that for silver nanoparticles and polystyrene surface, the Hertz theory with 1.11% of error and the JKR theory with 8.7% of error show the best output, respectively. Regarding rough nanoparticles contact, the geometry of roughness are taken as elliptical. Meanwhile, analytical relations are presented to solve force and contact area integrals while noting the problem dimensions. The results of simulation show that the JKR theory yields the highest roughness force, followed by the Hertz and Jamari theories, and regarding rough contact area, the Hertz theory creates the largest contact area, followed by the Jamari and JKR theories. The presented analytical method is compared with numerical results as a means of validation.

Specific energy analysis of rock cutting based on fracture mechanics: A case study using a conical pick on sandstone

In order to further study rock fracture mechanism cutting by conical picks, a number of indentation experiments were undertaken. In these experiments, the chips formation and their shapes were initially observed. Then, a model of specific energy was developed and the effects of relevant cutting parameters on the specific energy were investigated based on Evans’ rock cutting mode and indentation experiments. The results showed that fracture toughness, elasticity modulus of the rock, and depth of cut have significant influence on specific energy. Applications of fracture mechanics to cutting indicated that the maximum indentation depth linearly increases with the increasing of depth of cut. There is positive power correlation between maximum cutting force and depth of cut. The total work done by the pick is approximately proportional to the square of cutting depth. The dataset of specific energy yields on a power fitting curve with the depth of cut. Theoretical analysis and experimental results revealed that there is only approximately 3% of the external work of the pick contributes to the generation of new chipping surfaces while most the external energy is dissipated in producing the crushing zone.

The influence of strain hardening on steel erosion wear studied by analytical modelling of impeller testing

ABSTRACTAbrasive wear of steel is a common problem in the mining industry. It was tackled by many researches using analytical and numerical approaches. Despite the advantages of the analytical models to provide quick and elegant solutions, they were derived using several assumptions limiting their applicability, such as e.g. rigid-plastic flow. However, the consideration of strain hardening during impact is crucial to depict a real behaviour of tool material, which changes its mechanical properties during collision. In this research, a new analytical model is invented describing the impact of steel plate with a solid rock, while the material of the steel plate is hardening during penetration and scratching. The model provides a frame of analytical equations based on the second Newton law and equations of motion in vertical and horizontal directions. The motion in vertical direction is considered as an indentation problem and the motion in the horizontal direction as a scratch problem. This model incorporates the most general Holloman representation of strain-hardening law to capture the relationship between microstructural characteristics of steels and wear resistance. It was shown that the indentation depth, the pile-up height, length of the scratch and erosion ratio directly dependant on the strain-hardening parameters in Holloman equation. The model predicts the maximum indentation depth and scratch length as a function of strength coefficient and strain hardening exponent, but also of impact angle, mass of the rock, position of impact at the surface of steel plate and coefficient of friction during metal movement. The model was tested qualitatively by comparison with impeller-tumbler experiments using different steel plates. The solution obtained from this model could be used for quick and easy evaluation of the steel for mining tools in an industrial environment.

Depth-dependent hysteresis in adhesive elastic contacts at large surface roughness

Contact force–indentation depth measurements in contact experiments involving compliant materials, such as polymers and gels, show a hysteresis loop whose size depends on the maximum indentation depth. This depth-dependent hysteresis (DDH) is not explained by classical contact mechanics theories and was believed to be due to effects such as material viscoelasticity, plasticity, surface polymer interdigitation, and moisture. It has been observed that the DDH energy loss initially increases and then decreases with roughness. A mechanics model based on the occurrence of adhesion and roughness related small-scale instabilities was presented by one of the authors for explaining DDH. However, that model only applies in the regime of infinitesimally small surface roughness, and consequently it does not capture the decrease in energy loss with surface roughness at the large roughness regime. We present a new mechanics model that applies in the regime of large surface roughness based on the Maugis–Dugdale theory of adhesive elastic contacts and Nayak’s theory of rough surfaces. The model captures the trend of decreasing energy loss with increasing roughness. It also captures the experimentally observed dependencies of energy loss on the maximum indentation depth, and material and surface properties.

Characterization of strut indentation during mechanical thrombectomy in acute ischemic stroke clot analogs

BackgroundAlthough it is common practice to wait for an ‘embedding time’ during mechanical thrombectomy (MT) to allow strut integration of a stentriever device into an occluding thromboembolic clot, there is...

Copper foam enhanced Sn58Bi solder joint with high performance for low temperature packaging

The brittle Sn58Bi solder was modified with the ductile copper foam (Cu-F) with high plasticity to improve its mechanical properties. It is observed that the coarse microstructure of Sn58Bi solder is notably refined by the uniform distribution of copper foam. Moreover, it is found that the shear force of Sn58Bi soldered sample increases sharply with increasing shear distance and brittle fracture occurs once the shear force reaches the maximum value. However, thanks to the existence of large amount of copper frameworks in Sn58Bi + Cu-F soldered sample, significant plastic deformation is generated after reaching the maximum shear force and no fracture is observed. Also, the Sn58Bi + Cu-F soldered sample demonstrates a higher resistance to elastoplastic deformation as the average maximum indentation depth decreases from 2.48 μm to 1.80 μm compared to the Sn58Bi solder. In addition, the creep of soldered samples becomes stable after 200 s, and a lower creep rate is gained in Sn58Bi + Cu-F soldered sample.

Alterations in the microhardness of a titanium alloy affected to a series of nanosecond laser pulses

The alterations in the microhardness of a titanium alloy Ti85.85Al6.5Zr4Sn2Nb1Mo0.5Si0.15 subjected to laser treatment were investigated. Laser processing consists of a series of pulses with durations 20 ns. We used various methods of laser processing, which differed in power density, wavelength, geometrical pattern of irradiation and so on. The dependences of the microhardness on the load on the indenter were found. The laser processing modes providing the increased microhardness are determined. The investigations were carried out at loads from 0.49 N to 4.9 N, with maximum indentation depth of the Vickers pyramid up to 12 μm. Vickers microhardness can be increased by 20 – 40 %. At the same time, the plastic properties of the hardened layer are improved. The probability of crack formation during indentation of the initial alloy increased with a load on the indenter and reached 0.52 for a load of 4.9 N. In two of the treated areas of the three presented, crack formation was not recorded at any load. The mechanisms of hardening of the material surface layer under the influence of a laser pulse are discussed. Using the methods of computational mathematics, the character of sample heating under the influence of a single laser pulse is determined. The perspectives for the development of the proposed processing method are permitting to obtain the optimal mechanical properties of the hardened layer are discussed.

Determining suitable parameters for inverse estimation of plastic properties based on indentation marks

Tensile elastoplastic properties are extensively used in engineering applications; however, sample preparation for tensile tests is time-consuming. Therefore, a technique to estimate the tensile properties from an indentation test, with relatively easy sample preparation, is useful to reduce effort and accelerate the evaluation of advanced materials. Previously proposed techniques for the inverse estimation of elastoplastic properties used plural load-displacement curves. In this study, the authors proposed an estimation technique based on a single indentation involved using three-dimensional information of an indentation mark in addition to a load-displacement curve. To determine the parameter suitable for use in the inverse estimation of elastoplastic properties, the sensitivity and experimental variation in parameters extracted from the indentation results were investigated. The maximum pile-up height normalized by the maximum indentation depth, Zmax/hmax, was determined as the suitable parameter for inverse estimation owing to its high sensitivity compared to experimental variations. Moreover, the stress-strain curve obtained using this technique agreed with that obtained using dual indenters.

A numerical model for calculation of the restitution coefficient of elastic-perfectly plastic and adhesive bodies with rough surfaces

A contact mechanics model based on Boundary Element Method (BEM) is used to simulate the contact of rough spheres having elastic-perfectly plastic adhesive behaviour. The model has been verified for smooth surfaces with the classical Hertz contact behaviour in elastic regime, JKR theory in the adhesive regime and Thornton and Ning's analytical solution in the elasto-plastic adhesive regime. In this paper, the effect of yield stress, interface energy and surface roughness on the Coefficient of Restitution (COR) is investigated and reported. The results show that surface roughness dramatically affects the COR and higher roughness values lead to lower CORs in general. In addition, it is found that in the presence of surface roughness, the COR varies based on different maximum indentation depths in 3 different stages; the asperity dominant, bulk elastic dominant and bulk plastic dominant. Interestingly, it was shown that there is a critical indentation depth beyond which the effect of surface roughness will disappear and rough surfaces act like smooth ones. This critical indentation depth is proportional to the Root Mean Square roughness (Rq) value of the surface. Numerical results suggest that the yield stress influences the COR and higher yields stress results in higher COR for both rough and smooth surfaces. Furthermore, the effect of interface energy on the COR for rough surfaces is minimal and only significant at low indentations.

Indentation hardness, plasticity and initial creep properties of nanosilver sintered joint

The nanoindentation test was conducted in this paper to investigate the indentation hardness, plasticity and initial creep properties of pressure sintered nanosilver joint at various test temperatures. The effects of strain rate on the indentation hardness were first investigated. Then yield stress of nanosilver sintered joint was studied in various pressures sintered joints and the corresponding plastic stress-strain constitutive equations were gained. The maximum indentation depth of nanosilver sintered joint was obviously affected by the test temperature and sintering pressure. The indentation hardness of nanosilver sintered joint decreased with increasing test temperature from 140 to 200°C, which can be attributed to the increased amount of thermal vacancies at high temperatures. However, the indentation modulus exhibited decrease trend as the temperature increased. It is suggested that the distance between adjacent atoms was enlarged at elevated temperatures and furtherly resulted in the decrease of indentation modulus. In addition, the increased sintering pressure from 5 to 30 MPa improved the indentation hardness and modulus of sintered joint. The initial creep was observed in nanosilver sintered joint at temperatures ranged from 140 to 200°C. The increase of sintering pressure improved the resistance to creep of nanosilver sintered joint.

Comment on van Casteren et al. (2018): softer metallic spheres do abrade harder enamel.

Comment on van Casteren et al. (2018): softer metallic spheres do abrade harder enamel.

DETERMINATION OF PARAMETERS FOR THE PLASTICITY MODEL OF VT-22 ALLOY POWDER PARTICLES

A computational and experimental method is proposed to determine the medium model for describing the mechanical properties of powder particles of a high-strength VT-22 titanium alloy obtained by plasma spraying in an inert gas jet. The method is based on the indirect determination of the σs ~ ε strain hardening diagram (yield stress dependence on plastic deformation). A specimen for fullscale tests was prepared as a section of powder particles filled into a special resin. The paper provides the results of Vickers indentation into VT-22 powder particles and the results of computer simulation of this process by the finite element method. The average value of the maximum indentation depth was hmax = 6,56 μm with a maximum loading value of 2 N. The Johnson-Cook elasto-plastic model of a material with nonlinear hardening was used for the volume element considered during the computer simulation. An algorithm for searching coefficients by computational experiment multistage planning was proposed to identify the parameters of the equation sought. Estimated maximum coincidences of experimental and calculated data were chosen as selection criteria, in particular, based on maximum indentation depth. As a result of the study, material model coefficient values that meet search conditions best were chosen from a possible set of such values. According to the algorithm proposed, the result was achieved in 4 calculation cycles. Powder metallographic study was carried out. It was found that particles have a coarse intragranular structure with the dominating b phase formed during plasma spraying. This probably led to a decrease in VT-22 alloy deformation resistance in the powder particles.