Instrumented indentation and ultrasonic velocity techniques for the evaluation of creep cavitation in silicon nitride

Instrumented indentation and ultrasonic wave velocity techniques combined with precise density change measurements and transmission electron microscopy (TEM) were used to investigate the changes of elastic moduli in silicon nitride after tensile deformation up to 3%. Linear dependencies on strain were also found for the degradation of the indentation modulus, longitudinal and transverse ultrasonic wave velocities, Young's, shear and bulk moduli and Poisson's ratio. The results obtained by indentation technique and ultrasonic method were essentially identical. TEM observation confirmed that multigrain junction cavities were responsible for the density changes and the elastic moduli degradation. The density changes were linearly proportional to tensile strain with the slope of 0.75. Thus, cavitation is the dominant creep mechanism in silicon nitride studied. Instrumented indentation and ultrasound velocity techniques are suitable for non-destructive monitoring of creep damage accumulation in ceramic components.     

An Inverse Approach for Extracting Elastic-plastic Properties of Thin Films from Small Scale Sharp Indentation

An inverse method for extracting the elastic-plastic properties of metallic thin films from instrumented sharp indentation has been proposed in terms of dimensional analysis and finite element modeling.A wide range of materials with different elastic modulus,yield strength,and strain-hardening exponent were examined.Similar to the Nix-Gao model for the depth dependence of hardness H,(H/H0)2=1+h*Hh,the relationship between elastic modulus E and indentation depth h can be expressed as(E/E0)4=1+h*Eh.By combining these two formulas,we find that there is a relationship between yield stress σ y and indentation depth h:σy = σy0·(1+h*Hh)f(n)·(1+h*Eh)[0.25-0.54f(n)],where σ y0 is the yield strength associated with the strainhardening exponent n,the true hardness H0 and the true elastic modulus E0.f(n)= 1/2(1-n) is constant,which is only related to n,and h*H and h*E are characteristic lengths for hardness and elastic modulus.The results obtained from inverse analysis show that the elastic-plastic properties of thin films can be uniquely extracted from the solution of this relationship when the indentation size effect has to be taken into account.     

Analysis of data from various indentation techniques for thin films intrinsic hardness modelling

Due to the influence of the substrate, direct measurement of the hardness of thin films by standard micro-indentation tests is not always possible. In such situation, determination of the intrinsic film hardness requires the analysis of a set of experimental apparent hardness values obtained for different indentation loads. A number of mathematical equations based on various assumptions were proposed in literature for that purpose.Most of the models were established on the basis of standard Vickers indentation. Using these models to process the data obtained by Knoop indentation does not provide the same intrinsic hardness value, even after Knoop/Vickers standard conversion, than the one obtained from Vickers indentation. The same problem arises when processing the data coming from depth-sensing indentation. A method to obtain comparable hardness values is proposed in the present work by considering an “equivalent” Vickers hardness in the case of Knoop indentations and the corresponding Martens hardness for depth-sensing indentation. This method has been used to determine the intrinsic hardness of titanium nitride film.     

X-ray diffraction line profile analysis for defect study in Zr-2.5% Nb material

The microstructure characterization by X-ray line profile analysis is possible for determination of dislocation density, micro-strain within grains due to dislocation and average coherent domain size (subgrain) within the grain. This study presents the X-ray diffraction peaks shape analysis and their broadening with different thermal treatments in Zr-2.5% Nb pressure tube material. The peak shape is analysed using Fourier transformation and information about coherent domain size, micro-strain and dislocation density could be obtained from the Fourier coefficients of the peak. Analysis of broadening of the peaks by integral breadth method also gives the coherent domain size, dislocation density and micro-strain present in the material. The results from the X-ray techniques are comparable to those obtained from direct observation of transmission electron microscopy. The measured yield strength increases with dislocation density. An empirical relationship is obtained for the yield strength from the dislocation density of the material. The measured strength is in agreement with the one calculated from dislocation density.     

Assessment of a modification to the Brinell method for determining solid wood hardness

Purpose of this study was to assess a modification to the hardness determination method in order to mitigate the effect of visual measurements on the consistency of Brinell method and accuracy of the results. The amendment has been previously proposed by other researchers and refers to the automated determination of indentation diameter and relies on the ability of modern testing machines to accurately measure indentation depth, through which the calculation of indentation diameter is possible. From the results of this study it was shown that the hardness values acquired by the proposed modification presented statistically significant difference compared to those acquired using the visual method described in EN1534 (Wood and parquet flooring—determination of resistance to indentation (Brinell)—test method, 2000). Moreover, compared to the standard methodology, the application of the proposed amendment led to hardness values which are better correlated to density as well as Janka hardness for the six different solid wood species tested. Furthermore, the proposed modification resulted to hardness values which seem to be less affected by the presence of varnish coatings.     

Atomic force microscopy investigations on nanoindentation impressions of some metals: effect of piling-up on hardness measurements

In the indentation test, the hardness and the elastic modulus depend strongly on the estimate of the indenter-material contact area at peak load. However, many elastic–plastic behaviours such as elastic recoveries during unloading and piling-up or sinking-in of surface profiles during indentation affect the determination of the hardness and the elastic modulus. So, atomic force microscopy is a method of utmost importance to provide an accurate knowledge of the indentation impression especially when plastic deformations occur, that leads to errors in the determination of the contact area. Atomic force measurements of vanadium, tungsten, molybdenum and tantalum pure metals as well as stainless steels, often used as substrates for thin films depositions, highlight the difficulties to estimate the contact area. The variation of hardness values determined by atomic force microscopy measurements and nanoindentation test is correlated to the formation of folds of 150 and 100 nm high, around the residual impression of vanadium and tungsten indented at 0.1 N, respectively. Some folds which increase with increasing loads are detected on the residual impressions of both 35CD4 and 30NCD16 stainless steels indented under loads of 0.01 N, only. Such structures are related to piling-up of surface profiles that could lead to an underestimate of the contact area in the indentation test. So, the hardness value of tungsten could be closer to 6 than to 7 GPa whereas the effect of piling-up on the estimation of contact area of vanadium could be lower. Almost no deformation is seen on tantalum and molybdenum. So, the hardness values determined by the various methods are consistent. These results show that atomic force microscopy measurements are quite complementary of the nanoindentation test.     

仪器柔度对压入法测试结果的误差影响与校准

分析了仪器柔度及其标定精度对压人法测试微机电系统（MEMS）材料弹性模量和硬度结果的误差影响规律,并得出了系统误差公式。通过溯源分析,认为柔度标定误差是压人法测试的3个基本源误差之一。利用间接法对微压人测试仪柔度进行了标定和校准,校准后得到的单晶硅（100）弹性模量和硬度测试值分别为151．5GPa和12．8GPa,与文献值符合较好,而未校准直接得到的测试值明显偏低。理论分析和实验结果均表明：仪器柔度的准确标定和位移校准是获得压人法可靠测试结果的必须步骤。     

Relationship between fatigue limit and Vickers hardness in steels

In this work, a method to predict the fatigue limit by using Vickers hardness measurements is proposed. Tests carried out in small regions of different annealed, quenched and quenched-tempered alloy steels allowed an improvement of the empirical Murakami-Endo's equation.In this method, the plastic deformation caused by the indentation is assumed to be the defect from which the process of initiation and propagation of cracks originate, analogously to small cracks.Fatigue limits for four kinds of steels in different metallurgical states (annealed, quenched and quenched-tempered) were estimated in two different ways, and the obtained values were compared to the experimental ones. A good correlation between Vickers hardness and the fatigue limits estimated by direct plastic deformation zone measurements using optical microscopy was envisaged.     

Hertzian analysis of the self-consistency and reliability of the indentation hardness measurements on superhard nanocomposite coatings

The measurement of elastic properties of superhard nanocomposite coatings can be subject to a number of possible errors, such as indentation size effects (indenter tip blunting, non-representative small volume of the material to be tested upon nanoindentation and a too small stress under the indenter which does not reach the yield stress of that material if a too low load is used), the composite effect of the system of superhard coating on a softer substrate, high compressive or tensile stress in the coatings, drifts and/or stiffness of the indenter etc. We shall present a systematic study of these possible artefacts on superhard coatings using a large range of applied loads on a number of super- and ultrahard samples. The hardness values obtained from the indentation measurements are compared with the Vickers hardness calculated from the projected area of the plastic deformation. The data will be also compared with finite element method computer modeling in order to obtain a deeper insight into the complex problems. It will be shown that reliable results can be obtained if sufficiently thick coatings are used which allows one to obtain load independent values of hardness measured at sufficiently large indentation depths. Hertzian analysis of the non-linear elastic response upon unloading provides analytical solutions that can be used in order to check if the hardness values measured on the super- and ultrahard coatings are self-consistent. In particular, it is possible to estimate the maximum tensile stress that the coatings survive without failure. This stress occurs at the periphery of the contact between the coating and the indenter and, in the case of ultrahard coatings, it can reach values in the range of tens of GPa. The results show a very good agreement with the theoretical predictions based on the Universal Binding Energy Relation.     

High pressure sintering of diamond-SiC composite

Sintered polycrystalline compacts in the system diamond-10–50 wt% SiC having average grain size of less than 1 m were prepared at pressure of 6 GPa and temperature between 1400 and 1600 °C. Knoop indentation hardness of the compacts increased with diamond content and sintering temperature, and specimens with a Knoop indentation hardness greater 40 GPa were obtained. It was found that small amount of Al addition into the starting diamond-SiC powder was effective to improve relative density and Knoop indentation hardness of the compacts. The formation of graphite was also suppressed by the addition of Al. Microstructure observation by SEM and TEM suggested that Al segregated at the grain boundary and promoted the bonding between grains. Thin microtwins were observed in diamond grains, whereas fine wavy structures with slightly different orientations were observed in SiC grains, with or without Al addition.     

Hardness measurements of thin films

A simple technique is presented to obtain the characteristic microhardness values of surface coatings that are too thin for the values to be directly measured. The application of the technique requires conventional microhardness measurements on both coated and uncoated substrates and a knowledge of the film thickness. The film hardness is obtained from these data by the use of a simple formula which is based on a physical model of film deformation during indentation. The model is verified for chromium films on four different substrate materials. Hardness values of the film material can be obtained from films with a thickness of more than 2000 Å with this technique.     

Indentation modulus extrapolation and thickness estimation of ta-C coatings from nanoindentation

Coatings used in tribological applications often exhibit high hardness and stiffness to achieve high wear resistance. One coating characterization method frequently used is nanoindentation which allows the determination of indentation hardness and indentation modulus among other material properties. The indentation modulus describes the elastic surface behavior during indentation and is, among hardness, a direct indicator for wear resistance. To obtain the true indentation modulus of a coating, it must be measured with varying loads and then extrapolated to zero load. Current recommendation of the standard ISO 14577-4:2016 is a linear extrapolation which fits poorly for nonlinear curves. Such nonlinear curves are commonly found for high hardness mismatches between coating and substrate, for example, superhard tetrahedral amorphous carbon coatings (ta-C) on a steel substrate. In this study, we present a new empirical fit model, henceforth named sigmoid. This fit model is compared to several existing fit models described in the literature using a large number of nanoindentation measurements on ta-C coatings with wide ranges of indentation modulus and coating thickness. This is done by employing a user-independent and model agnostic fitting methodology. It is shown that the sigmoid model outperforms all other models in the combination of goodness of fit and stability of fit. Furthermore, we demonstrate that the sigmoid model’s fit parameter directly correlates with coating thickness and thus allows for a new approach of determining ta-C coating thickness from nanoindentation.

     

Hardness and tensile strength of multifilamentary metal–matrix composite superconductors for the Large Hadron Collider (LHC)

Conventional indentation hardness measurements to obtain load independent Vickers hardness values for the different phases in multifilamentary superconducting (SC) wires are described. The concept of composite hardness is validated for a binary metal–matrix metal–filament Nb–Ti/Cu composite wire. The tensile materials properties of the individual wire components are estimated from their indentation hardness. The potential and limitations of this approach are critically discussed, based on a comparison with ensile test results obtained for wires and extracted Nb–Ti filaments.     

Hardness,indentation fracture toughness and compositional formula of X-phase sialon

The hardness and indentation fracture toughness,K _IC of sintered X-phase sialon, produced by simultaneous carbothermal reduction and nitriding of kaolinitic clays, are determined. By comparing the values obtained for the sialon with those for a commercially pure mullite, it is suggested that X-phase sialon is a material with potential for similar applications to those in which mullite is currently used. On the basis of the oxygen/nitrogen ratios of the sialon determined by the inert gas fusion method, the analysis of the energy of the dispersed X-rays (EDAX) from thinned samples in the transmission electron microscope (TEM) and the aluminium/silicon ratios, also determined by the TEM EDAX method, a modified compositional formula is proposed for X-phase.     

Some features of indentation creep of LiF single crystals

The dependence of the size of the indentation and dislocation rosettes on loading time was investigated on the (001) plane of LiF single crystals. The measurements were performed in temperature range from room temperature to 170° C. The indentation time was varied from 0.2 to 10³ sec. It was revealed that the change of the indentation size during creep was more significant than the change in dislocation ensemble tracks in the field of the concentrated load. It was shown that the dependence of the length of the dislocation rosette edge arms on loading time, when plotting in double logarithmic scale, was linear. This fact allowed the determination of parameterm, characterizing the dependence of the dislocation velocity on stress, using creep experiments. The values ofm proved to be in good agreement with the results obtained by different methods.     

Dynamic nanoindentation testing for studying thermally activated processes from single to nanocrystalline metals

Nanoindentation experiments are widely used for assessing the local mechanical properties of materials. In recent years some new exciting developments have been performed for also analyzing thermally activated processes using indentation based techniques. This paper focuses on how thermally activated dislocation mechanisms can be assessed by indentation strain rate jump as well as creep testing. Therefore, a small overview is given on thermally activated dislocation mechanism and how indentation data from pointed indenters can be interpreted in terms of uniaxial macroscopic testing. This requires the use of the indentation strain rate as introduced by Lucas and Oliver as well as the concepts of Taylor hardening together with Johnson expanding cavity model.These concepts are then translated to nanoindentation strain rate jump tests as well as nanoindentation long term creep test, where the control of the indenter tip movement as well as the determination of the contact are quite important for reliable data. It is furthermore discussed, that for a steady state hardness test, the interpretation of the hardness data is straightforward and comparable to macroscopic testing. For other conditions where size effects play a major role, hardness data need to be interpreted with consideration for the microstructural length scale with respect to the contact radius.Finally strain rate jump testing and long term creep testings are used to assess different thermally activated mechanisms in single to nanocrystalline metals such as: Motion of dislocation kink pairs in bcc sx-W, Grain boundary processes in nc-Ni and ufg-Al, and the Portevin-le Chatelier effect in ufg-AA6014.     

两种微纳米硬度测试方法的比较

在对材料微纳米硬度测试中,可利用纳米压痕方法得到载荷-位移曲线,并用相关算法得到接触面积和硬度值;也可通过原子力显微镜测出压痕残余面积,由残余面积和最大载荷得到材料的硬度值.利用这两种方法对塑性材料单晶铝和脆性材料单晶硅做微纳米硬度测试试验,经过比较分析,这两种方法各有优势和不足,得到的材料微纳米硬度都有压痕尺寸效应,但第二种方法得到的微纳米硬度尺寸效应比第一种明显.     

The effect of work-hardening and pile-up on nanoindentation measurements

Nanoindentation is performed on the cross-section of copper samples subjected to surface mechanical attrition treatment (SMAT). The cross-section of the SMAT samples provides a unique microstructure with varying amounts of work-hardening depending on the distance from the SMAT surface. Results show that for a given indentation load the pile-up height decreases and the indentation depth increases as the distance from the SMAT surface increases, both following a power law relationship. Based on image analysis of the indented surface this increase in the pile-up height and decrease in indentation depth is attributed to the localization of plastic strain due to the increased resistance to dislocation motion in the work-hardened region. For a given amount of work-hardening (in terms of distance from SMAT surface), the indentation depth increased with the indentation load obeying a power law relationship with the exponent ranging from 0.58 to 0.68. However, the pile-up height increased linearly with the load, with the rate (slope) increasing with the amount of work-hardening. The observed linear increase in pile-up height with indentation load would naturally introduce an indentation size effect (ISE) if the hardness is corrected for the pile-up. Interestingly, this ISE associated with pile-up increased with an increase in indentation depth, in contradiction to the ISE associated with strain gradient. Deviation of the hardness values corrected for pile-up from the bulk behavior due to surface effect is highlighted and a method to obtain a bulk-equivalent hardness quantity representing the bulk behavior is proposed.     

The relationship between indentation hardness of organic solids and their molecular structure

A model has been developed relating the indentation hardness of organic molecular solids to their cohesive energy density, the length of the Burgers vector, the weakest plane from the crystal structure and crystal structural parameters. Whilst the described model is pragmatic, calculated indentation values for a variety of materials based on the weakest plane using specific Burgers vectors agree well with those from literature data.     

Relationship between the stored energy and indentation hardness of copper after compression test: models and measurements

Utilizing the differential scanning calorimetry (DSC) and Vickers hardness tests, the relationship between the stored energy and indentation hardness of copper after compression test is achieved experimentally. Three dislocation models are utilized to develop the relationships between the stored energy and hardness for justifying the experimental relationship. The relationships show that the stored energy is increased by increasing the hardness, non-linearly. By comparing the models’ results with the experimental data, the validity of each model at different ranges of hardness is determined.