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.     

基于数字图像处理的布氏硬度压痕直径测量方法

在分析布氏硬度试验压痕图像的基础上,提出了基于数字图像处理的布氏硬度压痕直径测量方法.利用CCD相机获取压痕图像,通过图像分割、目标区域处理、压痕圆拟合等步骤完成图像处理,由此实现对压痕尺寸的自动精确测量.     

Improved core model of indentation and its application to measure diamond hardness

A model of the indentation using conical and pyramidal indenters has been proposed, in which not only a sample but the indenter as well are elastoplastically deformed and their materials obey the Mises yield condition. These conditions are characteristic of the measuring of diamond hardness through a diamond indenter. The model that has been proposed generalizes and refines the known simplified Johnson’s model, which uses an elastically deformed indenter. The proposed model makes it possible to determine approximately the sizes of elastoplastic zones in the indenter and sample, the effective apex angle of the loaded indenter and effective angles of the indenter and imprint after unloading. Based on this model a procedure of the determination of the sample and indenter yield strengths (Y _s and Y _i , respectively) has been developed, in which the relations that use the experimental values of the effective angle of the sample imprint and measured values of the Meyer hardness, HM (mean contact pressure) are added to theoretical relations of the indentation model. The developed computational procedure was applied in indentation experiments on synthetic diamond at the temperature 900°C (at which diamond exhibits a noticeable plastic properties) using natural diamond pyramidal indenters having different apex angles. According to the proposed model, the stress-strain states of samples and indenters have been investigated and their yield strengths and plasticity characteristics were defined. The stress–strain curve of the diamond in the stress-total strain coordinates has been constructed. The strain hardening of diamond was also studied.     

Hardness of bi-layer films on a leadframe substrate

The indentation hardness and elastic modulus of leadframe materials that consist of Cu alloy substrate and Ni/Pd bi-layer films of differing thicknesses are characterised using the micro-hardness and nano-indentation tests. The true hardness of the individual substrate and film layers is evaluated based on the empirical relationship between the measured composite hardness and the volume of plastically deformed material of film layers. It is found that the composite hardness determined from the nano-indentation test increases rapidly toward a peak at extremely low indentation depth of less than about 20–30 m for all materials studied, due mainly to the finite value of the indenter tip radius and the rough surface of the specimen on the nano-scale. The composite hardness for the coated specimens decreases with further increasing indentation depth toward the hardness value of the substrate, because of the strong influence of the film/substrate interaction and the indentation size effect. The nano-indentation test in general gives higher true hardness values than those obtained from the micro-hardness test. Nevertheless, the relative hardness values of the substrate and films determined from the two tests are consistent. The hardness of Ni film is about 20 to 50% greater than that of Cu alloy, whereas the hardness of Pd film is 7 to 11 times the Ni film in the nano-indentation test.     

基于机器视觉的某种弹弹体硬度检测技术研究

目的 解决某种弹弹体硬度检测过程中人工读取硬度圆直径存在的问题。方法 应用材料的布氏硬度检测原理,设计基于机器视觉的某种弹弹体硬度检测装置,并制定某种弹弹体硬度的视觉检测算法。根据所提出的算法应用Maltlab实现对某种弹弹体硬度圆特征的提取和直径的计算。结果 通过T检验法对所提出的机器视觉检验方法与人工检测的结果进行对比分析,其结果为2种检测结果无差异性。结论 本文所设计的机器视觉检测装置和提出的视觉检测算法的具有较高的可靠性和正确性,可以应用于某种弹弹体的硬度检测。     

Indentation creep of lead and lead-copper alloys

Stress exponent values have been determined in Pb and Pb-Cu alloys with small Sn, Se and Pd additions by indentation methods (long time hardness tests) to evaluate their applicability as compared with tensile tests. Homogeneous, fine grained alloys were obtained by induction melting and thermo-mechanical treatments. Grain size was 38–60 m in alloys and 183 m in pure lead. Stress exponent values, i.e. of 11–12 agree between different methods of derivation and, in fine grained material, with tensile methods. The largest differences in pure lead, i.e. 10–11 versus 7–8 are attributed to high strain rates when indentation size is comparable to grain size. In all cases indentation and tensile tests indicate the same deformation mechanism, namely slip creep. The indentation test is thus considered useful, within limits, to acquire information on the deformation mechanism.     

Relationship of hardness to load on the indentor and hardness with a fixed diagonal of the indentation

For high-hardness materials, particularly for ceramics, the relationship of hardness to load is revealed very strongly. An equation is proposed for conversion of Vickers hardness from one load to another: $$HV = HV_1 \left( {\frac{P}{{P_1 }}} \right)^{1 - 2/n}$$ where HV and HV₁ are the hardness with loads on the indentor of P and P₁ respectively. The parameter n is determined from the equation P = const dⁿ, where d is the indentation diagonal. The parameter n may also be determined on the basis of a normalized curve of the value of HV/E (E is Young's modulus). The physical nature of the relationship of hardness to load is discussed and the hardness \(HV_{d_f }\) is introduced with a fixed indentation diagonal d_f (and not with a fixed load) calculated using the equation $$HV_{d_f } = HV\left( {\frac{d}{{d_f }}} \right)^{2 - n}$$ . The introduction of \(HV_{d_f }\) makes it possible to unify measurement of microhardness for different materials at different temperatures. Curves are given simplifying conversion of hardness from one load to another and determination of the hardness \(HV_{d_f }\) .     

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.     

Interrelation between Strains and Parameters of Metal Strengthening upon Tension and Indentation in Plastic Region

This article discusses analytical dependences of uniform elongation δ_p and ratios of yield strength to ultimate strength of metal on parameter of strain strengthening n in the Meyer equation. These dependences are verified experimentally for carbon and pearlitic steels upon determination of n using oblique illumination in a microscope for measurement of indentation diameter. The Meyer equation cannot be applied for some austenite steels because of structural phase transformations in deformed metal under indentation.     

Rate-dependent indentation behavior of solder alloys

Finite element (FE) simulations of visco-plastic indentation in Sn-37Pb eutectic solder alloy are performed to investigate the influence of loading rate on its creep characteristic. The resulting indentation load-displacement curves are rate-dependent and have varying creep penetration depths during the same hold time. Creep indentation hardness H, defined from the concept of work of indentation, varies with volume strain occurring during the creep hold time, which is a measure of creep strain rate _cr. Thus, creep stress sensitivity can be determined from the H versus _cr curve. This analysis can be verified by the good agreement between the derived value and the predefined value, and then be used to analyze the Berkovich indentation load-displacement curves of Sn-3.5Ag-0.75Cu lead-free solder. Such indentation tests and physical analysis provide a cheaper and more convenient method to determine the mechanical properties of the upcoming lead-free solder alloys.     

A model for crack initiation in elastic/plastic indentation fields

A model is proposed for the initiation of microfracture beneath sharp indenters. Using a simple approximation for the tensile stress distribution in the elastic/plastic indentation field, in conjunction with the principle of geometrical similarity, fracture mechanics procedures are applied to determine critical conditions for the growth of penny-like median cracks from sub-surface flaws. The analysis provides a functional relationship between the size of the critical flaw and the indentation load necessary to make this flaw extend. Initiation is well defined (unstable) only if the critical flaw lies within a certain size range; outside this range, large flaws can extend stably but small flaws can not extend at all. No flaws can extend below a characteristic minimum load, values of the indentation variables at this load accordingly providing useful threshold parameters. These quantities involve the intrinsic deformation/fracture parameters, hardness and toughness, in a fundamental way, thereby establishing a basis for materials selection in fracture-sensitive applications.     

Examination of the relationship between cracking resistance,hardness, and strength of steels at different temperatures and strain rates

The results are presented of measurements of Brinell hardness HB of 15Kh2NMFA and 10G2FB steels in the temperature range 77 T 373K. The resultant HB values are compared with strength, impact toughness, and cracking resistance in the entire temperature range examined. The relationship between cold brittleness of the steels and the form of the HB-T curves is analyzed on the basis of the concept of the characteristic temperature of contact deformation. The results show that the relationship between hardness and yield limit depends in a complicated manner on the test temperature and is determined by the plastic deformation mechanisms operating in each individual case. Correlation dependences are presented for determining the height of the stretching zone and stress intensity factor on the basis of HB values at different temperatures and strain rates. A criterion K_Ic/HB is introduced to predict the cracking resistance inside the examined temperature range on the basis of the values of K_Ic and HB at the boundaries of this range.Translated from Problemy Prochnosti, No. 2, pp. 14–17, February, 1991.     

Indentation toughness of ceramics: A modified approach

The indentation toughness equation proposed by Anstis et al. was re-examined with a particular emphasis on the definition of the hardness parameter used. It was shown that, because of the existence of the well-known indentation size effect (ISE), the apparent hardness defined as the ratio of the applied load to the projected area of the resultant indentation usually varies with the applied load and seems not to be suitable for use in indentation toughness determination. A new equation for determining indentation toughness, in which a load-independent hardness number was incorporated, was proposed.     

Dislocations in energetic materials

An assessment has been made of the primary dislocation slip systems in the explosives pentaerythritol tetranitrate (PETN) and cyclotrimethylene trinitramine (RDX) using a combination of dislocation etching and microhardness indentation techniques. Hardness measurements were made on all major habit faces as a function of temperature and load. These showed that, within the attainable temperature range (PETN 293 to 353 K, RDX 293 to 373 K) no change in hardness occurred which could be associated with the development of deformation mechanisms additional to those operating at room temperature. The hardness values of both materials were consistent with values obtained in some previous measurements (PETN 17 kg mm^–2, RDX 39 kg mm^–2). Solvent etching with acetone (5 sec at 274 K) proved to be an excellent method for revealing the emergent ends of growth and mechanically induced dislocations in PETN. Etching of microhardness indentations confirmed that observable slip traces comprised dislocations. These migrated up to 160m (20g load) from the indentation point on both {110} and {101} faces. The alignments defined a {110} primary slip plane. Parallel experiments with RDX yielded evidence of highly localized slip around the indentation mark (90m, 50g load). Two alignments of etch pits were noticeable. The better defined of these lay at the intersection of the (010) plane with the habit faces. The second could not be defined absolutely but most probably corresponds to the intersection of either the (011) or (012) plane with the surfaces. Consideration of the Burgers vectors of dislocations which are likely to glide in these planes lead us to speculate that the primary slip systems are, PETN {110} [001], and RDX (010) [001]. Such an assignment would be consistent with the relative hardness of the two materials.     

Critical comments to the Oliver–Pharr measurement technique of hardness and elastic modulus by instrumented indentations and refinement of its basic relations

A critical analysis was made of the Oliver and Pharr method for determination of the hardness and elastic moduli of materials by instrumented indentations with the continuous recording of the P–hdiagrams (P is the force acting on the indenter, h is the approach of the indenter and a sample). Mistakes and insufficient justification were revealed in the basic theoretical relations of this method. In particular, this refers to an incorrect definition of the depth of the elastic contact h_c, which is the base of these relalations. New refined basic relations and formulas for the determination of hardness and elastic modulus are given, in which the above defects are eliminated and which are based only on the assumption of elastic unloading of the indenter according to the classic theories of the elastic contact. In addition to the foregoing, using the data of the P–h diagram measured in the arbitrary laboratory coordinate system, an improved method of the stable determination of the contact stiffness S = dP/dh at the P–h diagram position have been proposed in the commonly accepted theoretical coordinate system in which its basic classic model relations are recorded. These refinements have been derived without additional assumptions to hypotheses to the Oliver and Pharr method and additional experimental measurements.     

Influence of particulate fillers on the indentation hardness of a glassy cross-linked polymer

The indentation hardness of a glassy cross-linked network was decreased to a minimum value by a low volume fraction (0.03 to 0.05) of each of six fillers having rigid particles varying in size and surface. This minimum effect was eliminated after specimens were more highly cross-linked by prolonged exposure to -rays. These results are consistent with an earlier suggestion that filler particles act as stress concentrators which may cause increased localized plastic deformation and hence a decreased indentation hardness. In the case of larger particles, morphological evidence of localized plastic deformation was obtained by fractography.     

Stress-strain curve for aluminium from a continuous indentation test

Continuous indentation tests using a 6.35 mm diameter steel ball were carried out on polycrystalline aluminium (99.995%) at forces up to 942 N (96 kg) and a total displacement of 65m. On loading the results were observed to follow the classical Hertz equation until the elastic limit was reached at 4.6±0.2 N (0.47 kg), 1.02±0.05m. The unloading results after plastic indentation were found to fit the Hertz solution for an indenter in a spherical hole. Using the Hertz theory it was possible from the unloading results to determine the mean stress and strain under the ball, together with the indentation diameter, plastic strain, Meyer stress and ratio of elastic to total strain, enabling a stress-strain curve for hardness to be drawn. The elastic limit of aluminium occurred at a stress of 4.7±0.2×10⁸Pa (46kg mm^–2) and a strain of 1.27±.05%. At a total strain of 11.25% the stress was 11.7±0.2×10⁸Pa (115 kg mm^–2).     

Hardness anisotropy of InP

Hardness anisotropy measurements in InP single crystals were made using a Knoop hardness tester. The data indicate that hardness is essentially independent of the direction in the (1 1 1) plane, but shows variation with direction in the (1 0 0) and (1 1 0) planes. Contrary to previous observations in crystals of cubic structure, in which the Knoop hardness depends only on the direction of indentation, the hardness of InP is dependent on both plane and direction. The (0 0 1) 1 1 0 combination shows the maximum Knoop hardness number of 430±10.     

Theory and application of microindentation in studies of glide and cracking in single crystals of elemental and compound semiconductors

The microhardness of Si (MP 1688 K), GaP (1623 K), GaAs (1510 K) and InP (1327 K) single crystals was determined by indentation (Vicker's hardness, VHN) of low-index facets at loads of 5–100g at 296–673 K, complementing earlier work on Ge and InSb. In the brittle range, extending up to about 0.35 T _melt (K), cracking occurred preferentially along the diagonals of the indentations, and was observed at all loads, with the possible exception of the lowest (5 g) in the case of InP at 289 K. At higher temperatures the relative orientations of crack and slip traces on the crystal surface, as observed by SEM, suggested that cracks nucleated preferentially at the slip-band intersection, as was also noted by Hirsch et al. (Phil. Mag. 3 (1985) 759) in GaAs above 600 K. As earlier in Ge, the VHN was found to depend on the load, L, as L ^p , and on the indentation diameter, d, as dⁿ, with p = 1/2 and n = 2, as required by the model of indentation plasticity of Banerjee and Feltham [4, 5], but higher p and n values were found if chipping at the indentation edges was evident. The effect was related to the resulting decrease in indentation diameter due to the work lost, through chipping, by the indenter. Above about 0.35 T _melt (K), relaxation of the dislocation structures entails a decrease of p and n; both parameters tend to zero as T T _melt. Shear and tensile stresses seem to co-operate in the process of plastic deformation, the role of normal stresses, acting across slip planes, predominating in the brittle range.     

The mechanical properties of ceramics from bauxite waste

This paper summarizes the development of engineering ceramics made from bauxite waste (red mud) produced in the alumina industry in Jamaica. Test specimens are fabricated from powders by sintering. For a particle size distribution of less than 75m in the starting powders and firing temperatures in the range of 1000 to 1100° C various mechanical properties are measured. These include fracture toughness (K _Ic), modulus of rupture (MOR), compression strength ( _c) and Brinell hardness. While apparent porosity varies between 40 and 48%, K _Ic is found to vary between 0.39 and 0.68 MN m^–3/2. The values are compared with those measured for commercial ceramic tiles and also with ceramics of magnesia and calcium zirconate. Within the fabrication temperature range studied the MOR ranges between 17.23 and 27.09 MN m^–2, compressive strength between 42.0 and 83.9 MN m^–2 and Brinell hardness between 26.2 and 59.9 kg mm^–2. With the aid of scanning electron microscopy and a basic knowledge of the physicochemical properties of the mud an attempt is made to explain the high strength and toughness achieved. The ready availability of raw material and the relatively low firing temperatures required for suitable engineering products should keep the production costs low for red mud ceramics.