Indentation Results Research Articles

Study of the plastic deformation of metals by indentation method

All-Russian Scientific Research Institute of Aviation Materials, 17, ul. Radio, Moscow, 105005 Russia; e-mail: 89639619741@mail.ruPlastic deformation is a type of material damage which can disrupt the normal operation of the structure. In this regard, the method for assessing the degree of damage to a metal sample has been developed. A corset sample for tensile tests was made from an aluminum alloy of the Al – Zn – Mg – Cu system. The ANSYS finite element complex was used to simulate an inhomogeneous stress state occurred in the sample working zone due to the variable cross-section upon tension. First, the hardness of the corset sample was measured, then it was tested for tension until the onset of necking and the load drop on the deformation diagram. After unloading along the sample working area, the Brinell hardness and surface roughness were measured. The results of the hardness measurements showed that in the areas where the tensile stresses are below the conditional yield stress of the material, the hardness value corresponds to the hardness of the starting material. In the areas where the tensile stresses are higher than the conventional yield stress, the hardness increases and reaches the maximum value in the center of the specimen, i.e., in the zone of the minimum cross-section. Thus, the damageability of the material can be assessed through the change in the hardness and roughness of the surface along the sample length. Proceeding from the results of instrumental spherical indentation, a technique for assessing the mechanical characteristics of the material was developed. The method consists in testing one sample for hardness and tensile strength with subsequent construction of the correlation dependences of tensile and indentation loads using the experimental results to obtain calculated tensile diagrams from the indentation diagrams of the material under study.

Analysis of the methods for determination of strength characteristics of NPP main equipment metal from the results of hardness and indentation measurements

The authors have considered the current situation with determining the mechanical characteristics of metals from the results of hardness measurements. The particular features of hardness measurement regarding harmonization of national standards with international standards are specified. Moreover, there is a need for a comparative analysis of existing regulatory documents for determining the characteristics from the hardness measurement results to improve their accuracy. Particular attention is paid to the reliability and accuracy of hardness measurements considering the international practice and many years of the accumulated experience. The validity of the use of some measuring devices requires an additional investigation. The main trends in the development of the determination of mechanical characteristics using the method of instrumented indentation are analyzed. The necessity of comparative analysis of existing determination methods of mechanical characteristics from the indentation results is indicated. It is required to develop a normative document, which regulates the application of instrumented indentation to current control for the materials of Ukrainian NPP main equipment.

Micromechanical properties and character of fracture after cross-bending of the SHS composite by the Fe-Ni-Ti-C-B system

Based on the result of instrumental indentation, the micromechanical properties of a monolithic SHS-composite of the Fe-Ni-C-B system are determined. The matrix of the composite is austenite, the hardening phases are TiC, TiB2, the particles of which are randomly placed in the matrix. Regions of the eutectic structure “γ-Fe + Fe2B” were found in the matrix. They are the most plastic and are characterized by the maximum values of hmax, φ, CIT. The maximum values of strength indices (E*, Re, HIT/E*, HIT3/E*2) are typical for the regions “γ-Fe + TiC” and “γ-Fe + TiB2 + TiC”. Composite specimens after bending tests fractured ductilely with a high fracture work. The axes of the Fe2B dendrites in the “γ-Fe + Fe2B” eutectic are deformed in the process of testing up to the destruction of the samples.

Determination of the plasticity of metals by impact indentation of a spherical indenter

The problems of measuring the plastic characteristics of metals are considered. It is shown that the characteristics of materials used to compare their plasticity are not comparable and depend in the different degrees on the values of strain, strain rate, and modulus of elasticity. At the same time, the value of plasticity is more physically substantiated, which is determined by the ratio of plastic strain to total strain. It is shown that one of the optimal methods for measuring plasticity (plasticity index) is indentation. The possibility of using impact microindentation for this purpose is studied and expressions are proposed that allow calculating the plasticity based on the results of a single indentation of a spherical indenter. The specialties of the calculation of strain for this type of testing are shown. It was found that the values of plasticity obtained from the ratios of the depths of the plastic and elastic penetration of the indenter are equivalent to the values calculated from the energy ratios upon impact. Experimental studies have been carried out on metals with different hardness and type of crystal lattice. For the first time, the effect of strain rate, deformation, and impact energy (initial impact velocity) on the calculated value of plasticity when a sphere is impressed with strain rates of ~ 103 s–1 is shown. It is shown that when the strain corresponding to the onset of full plasticity during indentation is reached, the maximum sensitivity of the measured plasticity parameter for various metals is achieved.

Dislocation Analysis of 3C-SiC Nanoindentation with Different Crystal Plane Groups Based on Molecular Dynamics Simulation

To explore the deformation law of nanoindentation dislocations of different crystal plane groups of 3C-SiC by cube indenter. The molecular dynamics simulation method is used to construct the different crystal plane family models of 3C-SiC, select the ensemble, set the potential function, optimize the crystal structure, and relax the indentation process. The radial distribution function, shear strain, and dislocation deformation of nanoindentation on (001), (110), and (111) planes were analyzed, respectively. In the radial distribution function, the change in g r in the (110) crystal plane is the most obvious. Shear strain and dislocation occur easily at the boundary of square indentation defects. During the indentation process, the shear strain is enhanced along the atomic bond arrangement structure, (001) crystal plane shear strain is mainly concentrated around and below the indentation defects and produce a large number of cross dislocations, (110) the crystal plane shear strain is mainly concentrated in the shear strain chain extending around and below the indentation defect, which mainly produces horizontal dislocations, and (111) the crystal plane shear strain is mainly concentrated in four weeks extending on the left and right sides in the direction below the indentation defect and produces horizontal and vertical dislocations. The direction of shear stress release is related to the crystal structure. The crystal structure affects the direction of atomic slip, resulting in the results of sliding in different directions. The final dislocation rings are different, resulting in different indentation results.

Nano-scale fracture toughness of fly ash incorporated hydrating cementitious composites using experimental nanoindentation technique

Instrumented nanoindentation technique has proven its strength by providing incredible insight into the material microstructure of homogeneous materials. Its success has led to its implementation in heterogenous materials such as cementitious composites. The implementation of instrumented nanoindentation on cement paste composites has proven to be very fruitful as it has enabled the evaluation of fundamental properties including Young’s modulus, hardness, creep at multiscales. However, there are more complex properties like fracture toughness which are crucial to characterize the material at macro scales. This characterisation would be benefitted by studies at micro-, nano- scales of the complex properties; but they are seldom reported. Cement-based materials have extremely complex, multiscale structures that are initiated from the chemical reactions of the hydration process and then continue to evolve with time. Also, preparing the surface of hydrating cementitious composites requires special consideration as it can greatly affect the indentation results. To explore the microstructural composition and its fracture toughness, an experimental grid nanoindentation protocol has been put forward. This experimental protocol has been implemented on three cement pastes, i.e., plain Ordinary Portland Cement (OPC), OPC + 20% fly ash, and OPC + 40% fly ash during their early stages as well as near complete stages of hydration. Since measuring the micro cracks around the indent is virtually near impossible, the load vs. displacement curves recorded by the indentations have been utilized in an energy-based method to evaluate the energy release rate and fracture toughness. The evaluated values of fracture toughness property of the individual microstructural phases will help in shedding a light on the development and spread of fracture toughness in cement-based materials. In this study the different methods for fracture toughness evaluation at the micro scales using nanoindentation technique are reported on and the method suitable for cementitious materials is implemented to evaluate fracture toughness of the microstructural phases.

Reduced delamination and improved cutting performance of TiAlSiN multilayer coated cutter by tailoring the adhesion layers and intermediate layers

Adhesion layers and intermediate layers exert important effects on the adhesion and cutting performance of PVD multilayer coatings. In this work, TiAlSiN multilayer coatings with different combinations of adhesion layers and intermediate layers were deposited, and their microstructure, adhesion and milling performance were assessed. Rockwell indentation and scratch results showed that delamination from the interfaces between the adhesion layers and intermediate layers occurred both for the T1 coating (TiN adhesion layer + Al17.5Ti80Si2.5N intermediate layer) and T2 coating (Al33Ti67N adhesion layer + Al43Ti54Si3N intermediate layer). Synchrotron radiation glancing incidence X-ray diffraction (SR-GIXRD) investigation on T2 coating revealed the discontinuities in lattice constant a and micro-strain at the interfaces between intermediate layer and adhesion layer, which resulted in poor cohesion of them. The T3 coating (Al67Ti33N adhesion layer + Al64Ti34Si2N intermediate layer) exhibited the lower residual stress (−3.7 GPa), and better cohesion and adhesion (Lc2 = 72 N). The T3 coating also had the longer milling life corresponding to a cut length 1700 m, due to its better cohesion and adhesion increased the “steady wear” stage. This improved cohesion and cutting performance of the multilayer coatings could be achieved by using proper combinations of adhesion layers and intermediate layers.

The investigation on the fabrication and microstructure of a novel core-shell structure reinforced iron matrix composite

To make the steel/iron composites with better comprehensive mechanical properties, a novel iron matrix composite reinforced with three-dimensional core-shell structure (CS) reinforcing particulates is designed and fabricated via powder hot-pressing sintering process. Studies have shown that the CS consists of isolated soft W core and dense hard shell, that is, showing the structural characteristics of “inner soft and outer hard”. When the carbon content of the raw material powder Fe–W–C ternary system is 0, 0.5, 1.0, 1.5 and 2.0 wt%, the CS of W@(Fe7W6 + Fe2W), W@Fe3W3C, W@(W2C + WC + Fe3W3C)Ⅰ, W@(W2C + WC + Fe3W3C)Ⅱ, and W@(W2C + WC + Fe3W3C)Ⅲ is formed in the matrix, respectively. The formation of CSs with different characteristics is mainly due to the diffusion of Fe atoms and/or C atoms into the W lattice to undergo a diffusion-type solid state phase transformation to form corresponding compounds and the formation kinetics of different phases determined by different carbon concentrations. Furthermore, the results of nanoindentation and Vickers indentation show that the hardness of the shell layer is much greater than that of the metal W core and matrix, but its plastic deformation rate is much smaller than that of the metal W core and matrix. The metal W core and the iron matrix can significantly inhibit the length of the crack propagation, thereby improving the toughness of the composite. And the hard shell layer with high volume fraction can significantly improve the strength of the composite. Therefore, the iron matrix composite reinforced with three-dimensional CS reinforcing particulates is expected to obtain good toughness and excellent strength, and this work may provide a new strategy for the structural design of steel/iron materials.

Demonstration of a laser powder bed fusion combinatorial sample for high-throughput microstructure and indentation characterization

High-throughput experiments that use combinatorial samples with rapid measurements can be used to provide process-structure-property information at reduced time, cost, and effort. Developing these tools and methods is essential in additive manufacturing where new process-structure-property information is required on a frequent basis as advances are made in feedstock materials, additive machines, and post-processing. Here we demonstrate the design and use of combinatorial samples produced on a commercial laser powder bed fusion system to study 60 distinct process conditions of nickel superalloy 625: five laser powers and four laser scan speeds in three different conditions. Combinatorial samples were characterized using optical and electron microscopy, x-ray diffraction, and indentation to estimate the porosity, grain size, crystallographic texture, secondary phase precipitation, and hardness. Indentation and porosity results were compared against a regular sample. The smaller-sized regions (3 mm × 4 mm) in the combinatorial sample have a lower hardness compared to a larger regular sample (20 mm × 20 mm) with similar porosity (<0.03%). Despite this difference, meaningful trends were identified with the combinatorial sample for grain size, crystallographic texture, and porosity versus laser power and scan speed as well as trends with hardness versus stress-relief condition.

Effect of Diagenesis on Geomechanical Properties of Organic‐Rich Calcareous Shale: A Multiscale Investigation

AbstractThis study investigates the nano to core‐scale geomechanical properties of a maturity series of organic‐rich, calcareous shales buried to 100°C–180°C, with a focus on: (a) the mechanical properties of organic matter; (b) the elastic response and anisotropy of the shale composite at micro and core scale; and (c) the creep response. Atomic force microscopy was used to target kerogen at nanoscale resolution, and it was found that the elastic stiffness increased with thermal maturity from 5.8 GPa in an immature sample to 11.3 GPa in a mature sample. Nanoindentation testing of the shale matrix showed that diagenesis is a key factor in determining the bulk elasticity, with increasingly intense carbonate cementation at higher thermal maturities contributing to a stiffer response. A multiscale model was formulated to upscale the elastic properties from nanoscale solid clay minerals to a microcracked composite at core scale, with good predictions of the micro and core‐scale stiffness in comparison to indentation and triaxial results. A negative correlation was found between the creep modulus and clay/kerogen content, with greater creep displacement observed in nanoindentation tests in the immature clay‐ and kerogen‐rich sample compared to samples of higher thermal maturity.

Nanoindentation in cyclotetramethylene tetranitramine (β-HMX) single crystals: the effect of pressure-sensitivity

Cyclotetramethylene tetranitramine (HMX) is a molecular crystal used as explosive in a broad range of civilian and military application. Its mechanical behavior is important as it relates to the initiation of the decomposition reaction though the formation of hot spots. However, the mechanics of the HMX crystal is complex and insufficiently understood. In particular, the pressure sensitivity of the mechanical behavior was largely ignored in the past, despite indications that material properties are strongly dependent on pressure. In this work we develop a pressure-sensitive crystal plasticity model for single crystals of β-HMX which accounts for the dependence on pressure of both the elastic constants and the yield surface, and calibrate it based on results from molecular simulations reported in the literature. The model is implemented in a finite element solver and is used to represent nanoindentation in β-HMX single crystals using a Berkovich tip. It is observed that accounting for pressure sensitivity is required if predictions close to experimental indentation results are to be obtained. The pressure sensitivity of the yield surface has a larger impact on predictions than that of the elastic constants. While these effects are demonstrated here in the context of quasi-static indentation, it is suggested that they become essential under shock loading conditions when stress states with large pressure components result.

Young's modulus of thin SmS films measured by nanoindentation and laser acoustic wave

High quality phase pure samarium sulphide (SmS) thin films with low surface roughness were prepared by electron beam evaporation using a samarium metal source in an H2S atmosphere. SmS shows a strong piezoresistive response due to a phase transition between a semiconducting and metallic state, which can be employed in piezo-electronic devices and stress sensing. Measurement of fundamental mechanical properties such as Young's modulus is thus a major objective to assess the elastic behaviour of SmS under external stress. Nanoindentation was used to measure the elastic modulus of thin semiconducting films with nominal thickness of 100 nm, 200 nm and 400 nm on silicon substrate at different loads. The indentation results were fitted to a modified King's model to exclude the effect of the substrate, giving Young's moduli of the films in the range of 79–82 GPa, consistent with measurements with a Laser Surface Acoustic Wave system (LAwave) and results from literature.

A modified Sneddon model for the contact between conical indenters and spherical samples

Indentation techniques have proven to be effective to characterize the mechanical properties of materials. For the elastic deformation, the commonly used models are Hertz model and Sneddon model. However, neither of them works for indenting the spherical samples using the pyramid or conical indenter. Therefore, one modified Sneddon model has been developed to determine the Young’s modulus of spherical samples from indentation results. In this study, the effects of sample diameter and indenter angles on indentation tests were investigated by finite element method (FEM). The empirical correction parameters in the new mathematical model were introduced based on dimensional analysis and determined by the numerical fitting to FEM results. Experimental tests with different conical indenters have demonstrated that the new model is capable to reliably determine the Young’s modulus of the spherical samples. The new model can fill the gap of the contact mechanics and enrich the experimental solid mechanics for the interpretation of indentation results.Graphic abstract

Poking and bulging of suspended thin sheets: Slippage, instabilities, and metrology

Measurement of in-plane elasticity of thin sheets often leverages out-of-plane poking or bulging, also known as indentation or bulge tests. For linear elastic sheets, a load-cubic deflection relation has been frequently assumed so that the stiffness of the sheet could be readily extracted. However, we find that recent results of indentation and bulge tests on 2D materials do not support the assumption, which can be attributed to the slippage of 2D materials against their supporting substrates. Besides, the interfacial slippage could cause instabilities in the sheet such as radial wrinkles in suspended region, with finite lengths. To gain a quantitative understanding, we assume constant interfacial shear traction and study the wrinkling extent and the effective stiffness of thin sheets upon poking and bulging. We identify a single dimensionless parameter governing these mechanical responses—the sliding number—defined by comparing the sheet tension (that drives the slippage) with the interfacial traction (that resists the slippage). We discuss several useful asymptotic behaviors emerging at small and large sliding numbers. These understandings inspire when the effect of the interfacial slippage (as well as other substrate-associated subtleties) can be neglected in these tests. For instance, traditional bulge and indentation tests suffer from complexities caused by the slippage, pretension, Poisson's ratio, substrate roughness, and various interfacial traction-separation laws. Based on such understandings, we propose a simple poking/bulging methodology immune to all of these complexities, enabling an alternative way to measure the sheet stiffness.

ВЕРИФИКАЦИЯ ЗАВИСИМОСТЕЙ, АППРОКСИМИРУЮЩИХ ДИАГРАММЫ ДЕФОРМИРОВАНИЯ БЕТОНОВ ЦЕМЕНТНОГО И ПОЛИМЕРНОГО МЕТОДОМ НОРМИРУЕМЫХ ПОКАЗАТЕЛЕЙ

The article verifies some approximating power-law and hyperbolic dependences between stresses σ and deformations ε for experimental deformation diagrams of cement concrete and polymer concrete. When analyzing the state and residual life of reinforced concrete structures, one has to solve the problem of determining the relationship between stresses and deformations in various design sections of structures. The traditional approach, based on the selection of the approximating function "σ – ε" from the numerical values of the deformation diagram obtained by testing samples (cubes, prisms, cylinders), is practically impossible. Therefore, an alternative approach is proposed based on the selection of an approximating function according to standardized indicators: ultimate strength (σ_bu); modulus of elasticity (E_b0); ultimate deformation (ε_bu). The numerical values of the normalized indicators can be determined at a given point by analyzing the results of indentation of the indenter into the material of structures. As approximating ones, consider the power functions that are most preferable for materials with a fractal structure. Various boundary conditions are considered for determining the constant coefficients α and β according to the system of normalized indicators. The graphs of changes in tangent modules are analyzed.

A compressible plasticity model for pulp fibers under transverse load

In the progress of understanding the mechanical behavior of pulp fibers, advanced material models have to be developed alongside experimental investigations. The transverse behavior of pulp fibers is tested by atomic force microscopy (AFM)-based nanoindentation experiments to record both, the volume reduction and the force-displacement curve. Our measurements clearly indicate a compressible plastic behavior in conjunction with a highly nonlinear elastic behavior, both which are attributed to the nanoporous structure of pulp fibers. We therefore advocate a numerical model based on a compressible plastic model combined with a hyper-foam model. Our evaluation yields three key findings for the transverse behavior of pulp fibers: first, the compression behavior is dominated by plastic deformation and nonlinear elasticity, in agreement with the experimental indentation results; second, we found evidence that a compressible plasticity model is justified, with an estimated Poisson's ratio of 0.23; and third, a good agreement of our numerical model with out-of-plane compaction experiments from the literature for a sheet of paper was achieved.

Constitutive modeling of γ-irradiated silicone rubber foams under compression and shear loading

Under the service conditions of nuclear engineering applications, silicone rubber foams should endure radiation of γ rays accompanied by compression and shear loading. In this paper, the Hyperfoam model is extended to characterize the mechanical behaviors of silicone rubber foams under γ-irradiation. After exposing silicone rubber foams to a wide radiation dose range from 0 to 500 kGy at room temperature, uniaxial compression and simple shear tests were carried out to establish the relationships between the model parameters of Hyperfoam model and radiation dose, and indentation tests were performed to verify the extended Hyperfoam model. The linear radiation dose-related hardening properties of the material are derived using the testing results, including the linear increases of the initial shear modulus, and the compression stress and the shear stress for a given strain condition, which result in the linear radiation dose-dependent relationships for the initial shear modulus-related model parameters and the radiation dose-independent hardening exponent-related model parameters of Hyperfoam model. The performances of the extended Hyperfoam model are demonstrated by comparing the fitted material responses with uniaxial compression and simple shear data. And the prediction ability is verified by comparing the simulated results of indentation using the finite element method with the test data. The extended model is capable of characterizing the coupling stress state of compression and shear in the investigated irradiation dose range, which is expected to aid in evaluating the safety of nuclear engineering structures.

Microscopic elastic structure mapping of frozen tuna (Thunnus orientalis) via scanning haptic microscopy

The mechanical properties of fish are closely related to texture and are generally evaluated by macroscopic tests. During freezing storage, however, mechanical damage, such as the growth of ice crystals, occurs at the microscopic level. In this study, scanning haptic microscopy (SHM) measurements were performed on refrigerated and freeze–thaw tuna fillets to observe the microscopic elastic modulus distribution in food samples. In elastic images of the refrigerated samples, areas of hard myotome membrane and soft muscle were clearly discernible. For the muscle area, the elastic modulus of the freeze–thaw sample was significantly higher than that of the refrigerated sample, which was consistent with macroscopic indentation results. In contrast, there were no significant differences in the elastic modulus due to freezing in the myotome area. Thus, we propose that SHM imaging is useful for the evaluation of microscopic mechanical damage.

Effect of Liquid Carburizing at Lowered Temperature on the Micromechanical Characteristics of Metastable Austenitic Steel

The effect of liquid carburizing at a temperature of 780°C on the micromechanical characteristics of the corrosion-resistant chromium–nickel austenitic steel (in wt %: Cr, 16.80; Ni, 8.44) has been studied in this work. According to instrumented microindentation data, it has been established that carburizing leads to the superficial hardening of the studied steel. An average increase in the indentation hardness HIT is nearly 500%. It has been demonstrated that carburizing also leads to an increase in the contact elasticity modulus of the steel E* that grew by 28% on average compared to E* in the quenched state. The carburized steel surface is characterized by an increased resistance to elastoplastic strain as evidenced by an increase in the parameters Re by 1.3–3.5 times, HIT/E* by 2.4–3.5 times, and $${{H_{{{\text{IT}}}}^{3}} \mathord{\left/ {\vphantom {{H_{{{\text{IT}}}}^{3}} {{{E}^{{*2}}}}}} \right. \kern-0em} {{{E}^{{*2}}}}}$$ by 49–109 times. On the contrary, the plasticity index δA decreases by 20% on average from 0.92–0.93 to 0.70–0.74 after carburizing. It has been shown that the instrumented indentation of the steel in the quenched state and after carburizing at different maximum indentor loads provides the possibility to perform a more precise analysis of the micromechanical characteristics of the gradient layer formed by means of carburizing by comparing them with the characteristics of the quenched steel. Based on the results of indentation at different maximum indentor loads, the gradient of properties in the thin carburized layer of up to 4 µm in depth has also been established.

Studies of crystal growth, structural, spectral and optical properties of solution grown 2-phenylethylaminium p-nitrophenolate monohydrate single crystals for efficient nonlinear optical applications

2-phenylethylaminium p-nitrophenolate monohydrate (2PPNP) single crystals were grown by evaporation of solvent method. Defect free 2PPNP crystal was subjected to single X-ray diffraction analysis and revealed the unit cell parameters, packing style. The molecular geometrical parameters, molecular orbital, first order hyperpolarizability, MEP map, Mulliken atomic charges and thermodynamic properties of 2-phenylethylaminium p-nitrophenolate monohydrate crystal were theoretically investigated by DFT calculations. FTIR, FT-Raman and NMR studies encompasses its functional components precisely to confirm the compound as 2PPNP. Optical transparency of the as-grown crystals was studied by using UV-Vis spectrum and it shows the transparency in the entire visible region. Photo-excitation of 2PPNP was examined to understand its light emitting behavior. Thermal stability of the grown was examined by TG-DTA analysis to understand the withstanding temperature of 2PPNP and its various endothermic reactions. Microhardness property of 2PPNP was evaluated upto 100 g indentation load and results are analyzed. The Z-scan study was made for the polished 2 mm thick 2PPNP defect free single crystal to evaluate its third-order nonlinearity for knowing the usefulness to optoelectronic applications.