A comparison of three microindentation hardness scales at low and ultralow loads

Indentation hardness tests were performed on thick, fine-grained, electro-formed deposits of copper and nickel using Knoop, Vickers, and Berkovich indenters. The latter type of indenter was used for shallow penetrations (85–1750nm), and results are reported in terms of nanoscale hardness (NH) numbers. Knoop and Vickers indenters were used with applied loads of between 0.15 and 0.98 N, and at the lowest load, produced indentation depths comparable to the larger ones obtained with the Berkovich indenter. The NH numbers became very sensitive to penetration depth when the penetration depth was less than certain critical values. NH numbers for Cu and Ni were higher than those for Knoop and Vickers testing at comparable penetration depths. Applying indenter area function corrections to calculate hardness numbers (i.e., considering projected area versus facet contact area) resulted in a closer correlation between microhardness and nanohardness scales; however, changes in the tip shape because of wear or other imperfections can lead to inaccurate calculation of NH numbers at the lowest loads. Results also suggest that the interconversion of lowload hardness numbers from one scale to another can be material-dependent.     

Scale factor in determining the hardness of metal materials

The method and the results of investigations into the effect of the scale factor on the hardness characteristics measured by the Vickers and Brinell methods at the macro- and microlevels of indentation of standard steel plates with different hardness values are described. The forcing-in load and the indenter diameter at which the hardness values increase abruptly are determined. Dependences are proposed for converting the Vickers hardness values at different forcing-in loads and the Brinell hardness values at different diameters of the indenter on condition of an equal degree of loading or an equal ratio between the diameters of the indentation and the indenter.     

Kraft-Eindringtiefe-Messungen mit verschiedenen pyramidenförmigen Indentern

Depth-sensing indentation measurements with different pyramidal indentors Depth-sensing indentation measurements are performed with a Vickers, a Berkovich and a Knoop indentor on bulk samples of ceramic, glass, metalls and of a polymer. The load-indentation data are evaluated in terms of an indentor specific energy density which is designated as hardness equivalent. A transformation principle for the different indentor specific hardness equivalents is introduced. The principle and the required transformation parameter is shown to be independent of the material investigated. The principle is based on the determining character of the displaced volume for the material resistance against the penetration of the indentor.     

Indentation testing of nuclear-waste glasses

The fracture properties of several nuclear-waste glasses were determined by indentation techniques. The fracture toughness,K _Ic, was calculated from the measurement of radial cracks around Vickers diamond indentations as a function of applied load, and the results agree quite satisfactorily with values obtained by the Hertzian indentation technique. The fracture toughness of the waste glasses containing simulated fission products ranged from 0.9 to 1.1 MN m^–3/2 in air, with slightly higher values measured in dry nitrogen. The hardness was also obtained from the Vickers indentations and the ratioH/E was determined from the elastic recovery of Knoop diamond indentations. The values ofE deduced fromH andH/E were within 15% of values measured by ultrasonic tests. The results along with the limitations of the different techniques are discussed in detail.Supported by the US Department of Energy.     

Application of an indentation method to the fracture mechanics study of a polycrystalline graphite

None of the conventional indentation techniques are applicable to carbon and graphite materials for determining fracture mechanics parameters because of the difficulty in introducing well-defined median/radial cracks. A novel indentation method is proposed in this work for fracture mechanics studies and then applied to a polycrystalline graphite fracture. The most prominent advantage of the indenter designed is that the residual stresses beneath the indentation impression, which prevail in conventional indentation methods (Knoop and Vickers indentations) and lead to crucial difficulties in fracture mechanics analysis, are negligibly small. This makes possible a quantitative study on the microstructural interaction between the indentation-induced micro-flaw and the natural intrinsic flaws of the material. The dependence of flexural strength of a polycrystalline graphite on the indentation-induced surface flaw size is also discussed by examining the microstructural scaling transition of fracture origin from the indentation-induced to the intrinsic flaws with diminishing indentation surface flaw. An important role of the Mrozowsky micro-crack system in the scaling transition is emphasized.     

Effects of ion implantation on the mechanical behavior of GaN films

The effects of ion implantation on the response to indentation in epitaxially grown hexagonal GaN films were studied by means of the static microindentation technique, utilizing Knoop and Vickers indenter geometries. Mg, O, Au, Xe and Ar ions were used as projectiles for the implantation process. Heavily damaged polycrystalline epilayers showed enhanced microhardness values and normal indentation size effect (ISE). Amorphised epilayers showed lower microhardness values, while they presented reverse ISE. The shape of the Knoop indentation print as a function of the implanted species revealed that reverse ISE is connected with plastic behavior. Implantation was also found to render films more receptive to fracture. Normal ISE curves were explained using models such as Meyer's law, Hays-Kendall approach, proportional specimen resistance (PSR), modified PSR and elastic/plastic deformation (EPD) models.     

角焊缝维氏硬度压痕直线行排列试验的新操作方法

根据设计和标准的要求,在角焊缝中心位置45°角处均匀测量维氏硬度,必须保证硬度压痕间隔为1 mm,角焊缝、热影响区和母材等部位的维氏硬度压痕呈直线行排列。笔者选用了HV-120型维氏硬度计,载荷98 N。为了达到标准要求,在硬度计工作平台上放置两块方型磁铁,以固定试样上、下不可移动,用游标卡尺的精度来保证压痕的间隔为1 mm,用45°角的三角板来确保角焊缝的中心线为45°。用这种方法进行维氏硬度试验,操作简单,压痕成为直线行排列均匀,测试结果准确可靠,满足了设计和标准的要求。     

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.     

Hardness testing of ceramic materials

This paper reviews the applicability of hardness test methods to polycrystalline ceramics. It is concluded that Rockwell Superficial HR45N tests are appropriate high-load tests for dense ceramics, because the indentation depth recorded is not confused by local cracking. In contrast the degree of cracking and spalling around Vickers or Knoop indentations limits loads to 2.5 kgf (25 N) or less in order to measure indentation diagonals accurately. However, at loads of less than 1 kgf (10 N), indentation dimensions in hard ceramics become small and subject to considerable scatter in size as a result of the locally anisotropic hardness. Operator biases and practical limits of resolution limit the accuracy and repeatability of results for purposes of materials comparison and specification.     

Die wechselseitige Umrechnung von Vickers-und Knoop-Härtewerten im Kleinlastbereich

Interconversion of Vickers and Knoop hardness numbers obtained in low load testing . In the industrial field the Vickers indenter has been largely applicated for hardness testing at low loads; in recent times the Knoop indenter came into use more and more. Consequently the question was raised, whether on the basis of some fundamental assumptions and experimental results equations could be deduced for interconversion of hardness numbers on Vickers and Knoop scales. Subsequently, a set of equations representing the connection between these above mentioned scales is given. The parameters of these equations were computed applying methods of statistical estimation.     

Wichtige Gesichtspunkte für die Härtemessung nach Vickers und nach Knoop im Bereich der Kleinlast- und Mikrohärte

Important aspects for low load testing of Vickers and Knoop hardness . There are various factors, which can affect the hardness number obtained in low load testing. Both, the Vickers and the Knoop indenter, are widespread applicated for hardness testing at low loads. Subsequently, in respect of these above mentioned hardness testing methods, it is given a summary concerning the most important factors, which, if they are not eliminated, can bring about serious errors in the test results.     

Mechanical characterization of calcium-modified lead titanate ceramics by indentation methods

The microstructural dependence of the mechanical properties of Ca-modified lead titanate piezoelectric ceramics were studied. To this end, a combination of the Vickers and Knoop indentation techniques at different applied loads was used as simple method for mechanical characterization of these ceramics. The influence of porosity, grain size and tetragonal distortion on hardness, Young's modulus and toughness is discussed. An attempt to obtain internal stresses from toughness variation reveals the limitations of the method.     

Instrumented and Vickers Indentation for the Characterization of Stiffness,Hardness and Toughness of Zirconia Toughened Al_2O_3 and SiC Armor

Instrumented and Vickers indentation testing and microstructure analysis were used to investigate zirconia toughened alumina(ZTA) and silicon carbide(SiC).Several equations were studied to relate the Vickers indentation hardness,Young's modulus and crack behavior to the fracture toughness.The fracture in SiC is unstable and occurs primarily by cleavage leading to a relatively low toughness of 3 MPa m~(1/2),which may be inappropriate for multi-hit capability.ZTA absorbs energy by plastic deformation,pore collapse,crack deviation and crack bridging and exhibits time dependent creep.With a relatively high toughness around 6.6 MPa m~(1/2),ZTA is promising for multi-hit capability.The higher accuracy of mediar equations in calculating the indentation fracture toughness and the relatively high c/a ratios above 2.5suggest median type cracking for both SiC and ZTA.The Young's modulus of both ceramics was most accurately measured at lower indentation loads of about 0.5 kgf,while more accurate hardness and fracture toughness values were obtained at intermediate and at higher indentation loads beyond 5 kgf respectively.A strong indentation size effect(ISE) was observed in both materials.The load independent hardness of SiC is 2563 HV,putting it far above the standard armor hardness requirement of 1500 HV that is barely met by ZTA.     

Study of the concept of representative strain and constraint factor introduced by Vickers indentation

The application of the concept of the representative strain is often used in the stress–strain curve determination from indentation test because it can significantly simplify the analysis of the indentation response. A new methodology for determining the representative strain for Vickers indentation is presented in this article. Following a procedure based on finite element simulations of indentation of elastoplastic materials, two representative strains are defined: the representative strain characteristic of the mean pressure and the representative strain characteristic of the Martens hardness or the indentation loading curvature. The results obtained from this methodology show that there is no universal value of representative strain independent of the mechanical parameters of materials indented by Vickers indentation. It is also shown that the representative strain, obtained by Vickers indentation is much lower when it is obtained from the relationship between the applied force and the penetration depth, F-h, rather than from the relationship between the applied force and the contact radius, F-a. The values of the calculated representative strains show that simultaneous measurement of relationships F-a and F-h make it possible to characterize the hardening law with two unknown parameters by Vickers indentation.     

用于测量陶瓷断裂韧性的Vickers和Knoop压痕裂纹技术

采用 Vickers 压痕裂纹测量法或 Knoop 压痕～强度法等压痕技术进行了陶瓷的断裂韧性测量。反应烧结 Si_3N_4,热压 Si_3N_4和 SiC 等结构陶瓷用于研究显微结构非均质性和热残余应力对断裂韧性值的影响。人工水晶用于研究晶体学取向和断裂韧性之间的关系。研究发现,Knoop 压痕～强度法比 Vickers 压痕裂纹测量法更适合于非等轴晶系的晶体断裂韧性测量。其原因是 Knoop 压痕的主裂纹和缺口试样的裂纹都沿着同样的晶面扩展,而 Vickers 径向裂纹对却须沿着相互正交的晶面扩展,仅其中的一个晶面与缺口试样的裂纹扩展面一致。在 Vickers 压痕裂纹技术的基础上,用以计算 K_(1c)值不含弹性模量 E 项的 Evans 式(21),似乎能显示出显微结构对 K_(1c)值的影响;含有弹性模量 E 项的 Evans 式(22),似乎能反映出残余热应力对 K_(?)值的影响。所有上述的陶瓷材料,除了反应烧结 Si_3N_4,其压痕和裂纹关系 a~2～C~(3/2)的线性回归相关系数都相当,甚至>0.99。这表明了 Vickers 压痕技术在测定陶瓷的断裂韧性方面具有一定的实用性。     

Examination of local variations in viscous,elastic, and plastic indentation responses in healing bone

A viscous-elastic-plastic indentation model was used to assess the local variability of properties in healing porcine bone. Constant loading- and unloading-rate depth-sensing indentation tests were performed and properties were computed from nonlinear curve-fits of the unloading displacement-time data. Three properties were obtained from the fit: modulus (the coefficient of an elastic reversible process), hardness (the coefficient of a nonreversible, time-independent process) and viscosity (the coefficient of a nonreversible, time-dependent process). The region adjacent to the dental implant interface demonstrated a slightly depressed elastic modulus along with an increase in local time-dependence (smaller viscosity); there was no clear trend in bone hardness with respect to the implant interface. Values of the elastic modulus and calculated contact hardness were comparable to those obtained in studies utilizing traditional elastic-plastic analysis techniques. The current approach to indentation data analysis shows promise for materials with time-dependent indentation responses.     

Influence of TiC particle size on the load-independent hardness of Al2O3–TiC composites

Seven samples of Al₂O₃–30 wt.% TiC composites were prepared by hot-pressing the Al₂O₃ powder mixed with TiC particles of different particle sizes. Knoop and Vickers hardness measurements were conducted on these samples, respectively, in the indentation load range from 1.47 to 35.77 N. The load-independent hardness numbers were then determined by analyzing the relationship between the measured indentation size and the applied indentation load. It was found that the load-independent hardness number increases with the increasing TiC particle size, and this experimental phenomenon may be attributed to the effect of the residual internal stress resulting from the mismatch between the thermal expansion of Al₂O₃ matrix and that of the TiC particles.     

Load dependence of the apparent Knoop hardness of SiC ceramics in a wide range of loads

Silicon carbide (SiC) ceramics is a material with increasing use, due to its excellent mechanical properties, especially high hardness. In order to integrate this material into design process, we need to know its hardness as precise as possible. The Knoop hardness number (HK) is calculated using the expression: HK = α·F/d², where F is the applied load, d is the long diagonal of the resulting 1₀indentation and a is the Knoop indenter geometrical constant. In this paper, the Knoop hardness of SiC ceramics was measured in the applied load range from 4.9 to 98.07 N. For some materials measured “apparent” hardness value decreases with increasing applied test load (normal indentation size effect – ISE), while for some materials measured “apparent” hardness increases with increasing applied test load (reverse indentation size effect – RISE). Obtained results show the measured hardness exhibits the ISE. In the literature several models are given for the phenomenon explanation. We used the following models: Meyer's law (F = K·dⁿ), proportional specimen resistance – PSR (F = a₁·d + a₂·d²) and modified proportional specimen resistance – MPSR model (F = a₀ + a₁·d + a₂·d²). Results of regression analysis for all applied models show they can all be used for ISE analysis. “True” hardness was determined based on the PSR and MPSR model (HK_T = α·a₂). The obtained results were similar. If the specimen surface is carefully prepared and the range of loads is wide, the a₀ coefficient from MPSR model reaches small values and can be excluded. Therefore, for the calculation of SiC ceramics Knoop hardness, the simpler model (PSR) can be used.     

Factors affecting the measurement of hardness and hardness anisotropy

By considering the observed hardness anisotropies of two different materials (001) single-crystal MgO and an aligned Al-CuAl₂ eutectic), this paper discusses some of the factors controlling the shapes and sizes of microhardness indentations. Both Vickers and Knoop profile indenters have been used. In the Vickers case, the responses of differing materials along symmetrically equivalent indenter diagonals have been observed while, in the Knoop case, indentations were often observed to have widthlength ratios different from that of the indenter. The observed behaviour has been interpreted in terms of differential elastic recovery on withdrawal of the indenter, and of changes in surface topography resulting from the accommodation of material displaced from the indentation (e.g. pile-up). It is demonstrated that both effects can seriously affect the sizes and shapes of hardness impressions. Further, these extrinsic effects are superimposed upon the intrinsic mechanical response and anisotropy of the test material itself. Thus, measured hardness anisotropies are a superposition of a number of effects, each important in its own right and each with its own anisotropy. Approaches have been devised which attempt to separate these extrinsic and intrinsic components of the observed hardness response. The results allow some important conclusions to be drawn concerning the interpretation of hardness values and hardness anisotropies.     

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.