Microhardness studies on nonlinear optical L-alanine single crystals

Vickers and Knoop microhardness tests were carried out on grown L-alanine single crystals by slow evaporation technique over a load range of 10–50 g on selected broad (2 0 3) plane. Vickers (H _v ) and Knoop (H _k ) microhardness for the above loads were found to be in the range of 60–71 kg/mm² and 35–47 kg/mm², respectively. Vickers microhardness number (H _v ) and Knoop microhardness number (H _k ) were found to increase with increasing load. Meyer’s index number (n) calculated from H _v shows that the material belongs to the soft material category. Using Wooster’s empirical relation, the elastic stiffness constant (c ₁₁) was calculated from Vickers hardness values. Young’s modulus was calculated using Knoop hardness values. Hardness anisotropy has been observed in accordance with the orientation of the crystal.     

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.     

Hardness anisotropy in niobium carbide

Measurements of hardness anisotropy by Knoop diamond indentation on the {100} surfaces of Nb₆C₅ crystals show that the hardness is determined by crystallographic slip on {111} 〈1¯10〉 and {110} 〈1¯10〉 systems. {111} is the preferred slip plane for Nb₆C₅ and crystals with higher carbon content which show a marked decrease in Knoop hardness. The carbon atom/vacancy arrangement in these crystals is shown, by electron diffraction, to possess short-range order. Crystals annealed at low temperatures contain domains of non-cubic long-range order which increase the Knoop hardness and eliminate the anisotropy in hardness. Dislocation arrangements around Knoop indentations have been directly observed by electron microscopy in an attempt to confirm the slip processes deduced from hardness anisotropy.     

Influence of visco-elasto-plastic properties of magnetite on the elastic modulus: Multicyclic indentation and theoretical studies

In the present work, we study the indentation behaviour of the magnetite coexisting with hematite in a natural dual-phase crystal. In particular we show the influence of cycling indentation conditions on the elastic modulus measurement in relation to the visco-elasto-plastic properties of the material. Elastic properties of Fe₃O₄ are investigated using Oliver and Pharr's technique, which is based on depth-sensing indentation (DSI) analysis. Depending on the visco-elasto-plastic properties of the material, the indentation test conditions (monotonic, cyclic, loading and unloading rates, dwell time at peak load, …) can modify the shape of the load–depth curve and, subsequently, the results. Molecular dynamics simulation based on shell model potential, is used to determine elastic quantities including elastic modulus, bulk modulus and Young modulus.     

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.     

Finite element modeling of nanoindentation on C–S–H: Effect of pile-up and contact friction

In this paper we computationally study the indentation response of a rigid axisymmetric indenter on a semi-infinite elasto-plastic material of the Mohr–Coulomb type. The finite element method is used to quantify the effect of material properties (E, c, φ) and contact friction (μ) on the indentation response of C–S–H phases. The high E/c-ratio for both C–S–H phases, together with their cohesive-frictional behavior, leads to pile-up phenomena around the penetrated probe. The influence of all these parameters on the actual area of contact and its subsequent effect on commonly extracted quantities of the indentation test, namely indentation modulus (M) and indentation hardness (H), is investigated. It is shown that contact friction affects the contact area between the indenter and indented material and as a consequence interferes, to a certain extent, with the procedure for estimating elastic and plastic material properties. The effect is more pronounced for the hardness measurements.     

High cycle fatigue damage mechanisms in cast aluminium subject to complex loads

This article is dedicated to the high cycle fatigue behaviour of cast hypo-eutectic Al–Si alloys. In particular, the AlSi7Cu05Mg03 alloy is investigated. It presents the results of a vast experimental campaign undertaken to investigate the fatigue behaviour, and more specifically the fatigue damage mechanisms observed under complex loading conditions: plane bending with different load ratios, fully reversed torsion and equibiaxial bending with a load ratio of R = 0.1. A specific test set-up has been designed to create an equibiaxial stress state using disk shaped specimens. A tomographic analysis is also presented with the aim of characterising the micro-shrinkage pore population of the material.It is shown that two distinct and coexisting fatigue damage mechanisms occur in this material, depending on the presence of different microstructural heterogeneities (i.e. micro-shrinkage pores, Silicon particles in the eutectic zones, Fe-rich intermetallic phases, etc.). Furthermore, it is concluded that the effect of an equibiaxial tensile stress state is not detrimental in terms of high cycle fatigue. It is also shown that the Dang Van criterion is not able to simultaneously predict the multiaxial effect (i.e. torsion and equibiaxial tension) and the mean stress effect for this material.     

Evaluation of the tensile properties of a material through spherical indentation: definition of an average representative strain and a confidence domain

In the present article, a new method for the determination of the hardening law using the load displacement curve, F–h, of a spherical indentation test is developed. This method is based on the study of the error between an experimental indentation curve and a number of finite elements simulation curves. For the smaller values of these errors, the error distribution shape is a valley, which is defined with an analytic equation. Except for the fact that the identified hardening law is a Hollomon type, no assumption was made for the proposed identification method. A new representative strain of the spherical indentation, called “average representative strain,” ε _aR was defined in the proposed article. In the bottom of the valley, all the stress–strain curves that intersect at a point of abscissa ε _aR lead to very similar indentation curves. Thus, the average representative strain indicates the part of the hardening law that is the better identified from spherical indentation test. The results show that a unique material parameter set (yield stress σ _y, strain hardening exponent n) is identified when using a single spherical indentation curve. However, for the experimental cases, the experimental imprecision and the material heterogeneity lead to different indentation curves, which makes the uniqueness of solution impossible. Therefore, the identified solution is not a single curve but a domain that is called “solution domain” in the yield stress–work hardening exponent diagram, and “confidence domain” in the stress–strain diagram. The confidence domain gives clear answers to the question of uniqueness of the solution and on the sensitivity of the indentation test to the identified hardening laws parameters.     

Using a modified Knoop Indentation Technique to estimate the cavitation erosion resistance of NiTi

An Ni-rich (50.8 at.% Ni) NiTi alloy was heat treated with different aging temperatures to obtain specimens possessing different cavitation erosion resistance. A modified Knoop Indentation Technique that combines indentation measurements and thermal recovery has been used to determine the total-recovery/deformation ratio for the heat-treated NiTi specimens. This ratio, which reflects both superelasticity and pseudoplasticity, has been found to correlate well with the cavitation erosion resistance for NiTi. The technique thus serves as a simple method for estimating the performance of NiTi against cavitation erosion.     

Effects of mixed-mode ratio and step-shaped micro pattern surface on crack-propagation resistance of carbon-fiber-reinforced plastic/adhesive interface

This study investigated the effects of the mixed-mode ratio of applied loads (G_II/G) and aspect ratio A of step-shaped micro patterns on the crack-propagation resistance of a carbon-fiber-reinforced plastic (CFRP)/adhesive interface fabricated by in-mold surface modification. Experiments showed that the fracture behaviors change and that the apparent mixed mode fracture toughness G_C increases with G_II/G and A. We used the Benzeggagh–Kenane (B–K) failure criterion for the mixed-mode fracture toughness considering the transition of the failure mode of the step-shaped micro patterns. The B–K criterion agreed well with the improvement of G_C due to an increase in G_II/G for various fixed values of A. We clarified the relationship between the aspect ratio A and the parameter η, which is required to describe the B–K criterion, and therefore, η can be estimated from A. Consequently, it was verified that G_C of the CFRP/adhesive interface with step-shaped micro patterns can be predicted for arbitrary G_II/G and A values by substituting the η–A relationship in the B–K criterion.     

The microhardness indentation load/size effect in rutile and cassiterite single crystals

The microhardness indentation load/size effect (ISE) on the Knoop microhardness of single crystals of TiO₂ and SnO₂ has been investigated. Experimental results have been analysed using the classical power law approach and from an effective indentation test load viewpoint. The Hays/Kendall concept of a critical applied test load for the initiation of plastic deformation was considered, but rejected to explain the ISE. A proportional specimen resistance (PSR) model has been proposed that consists of the elastic resistance of the test specimen and frictional effects at the indentor facet/specimen interface during microindentation. The microhardness test load, P, and the resulting indentation size, d, have been found to follow the relationship $$P = a_1 d + a_2 d^2 = a_1 d + (P_c /d_0^2 ) d^2$$ The ISE is a consequence of the indentation-size proportional resistance of the test specimen as described by a ₁. a ₂ is found to be related to the load-independent indentation hardness. It consists of the critical indentation load, P _c, and the characteristic indentation size, d _o.     

Mechanical properties of magnetite (Fe3O4), hematite (α-Fe2O3) and goethite (α-FeO·OH) by instrumented indentation and molecular dynamics analysis

Hardness and elastic properties of pure (crystal) and complex (product of corrosion) iron oxides, magnetite (Fe₃O₄), hematite (α-Fe₂O₃) and goethite (α-FeO·OH), were determined by means of molecular dynamics analysis (MDA) and instrumented indentation. To determine local mechanical properties by indentation, multicyclic loading is performed by using incremental mode. Moreover to study the influence of visco-elastoplastic behaviour of the material, various load-dwell-times were applied at each loading/unloading cycle. To support the indentation results, molecular dynamics analysis based on shell model potential is performed for pure oxides to determine Young's modulus, bulk modulus, Poisson's ratio and shear modulus. The comparison between experimental and theoretical values both with the literature data allows the evaluation of the mechanical properties of the pure oxides. Subsequently, this allows the validation of the mechanical properties of complex oxides which can only be deduced from indentation experiments.     

A study of indentation annealing of (111)p-type single crystal silicon

The indentation rosette size in (111)p-type Czochralski grown silicon was measured as a function of annealing temperature (450 to 1100° C), time (600 to 9300 sec) and indentation load (0.147 to 2.94 N). The indentations were made with the silicon surface immersed in an electrolytic solution containing Nal ions with concentrations in the range of 10^?5 to 10^?1 MI^?1. The rosette size,2L, was found to depend on the experimental variables as $$\left\langle {2L} \right\rangle = Ct^{1/2} P^{1.15} exp\left( {\frac{U}{{kT}}} \right)$$ whereC is a constant andt, T, P, andU are the annealing time, temperature, indentation load and energy, respectively, andk is Boltzmann's constant. The energy U has at least three different values depending on the annealing temperature interval and varies to a lesser extent on the indentation load.     

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.     

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.     

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.     

Microhardness studies on 4-Dimethylamino-N-methyl 4-Stilbazolium Tosylate (DAST)

The Vickers and Knoop microhardness studies were carried out on the (001) face of 4-Dimethylamino-N-methyl 4-Stilbazolium Tosylate (DAST) crystals grown by the slope nucleation technique. The Vickers microhardness number (H_v) and the Knoop microhardness number (H_k) were found to dwindle with increasing load. The Meyer's index number (n) and hardness were calculated from H_v. The fracture toughness, brittle index and yield strength were calculated. The Young's modulus was calculated using the Knoop hardness value.     

Vickers microindentation hardness studies of β-Sn single crystals

The Vickers microindentation hardness anisotropy profile and load dependence of apparent hardness of white tin (β-Sn) single crystals having different growth directions were investigated. Indentation experiments were carried out on the (001) crystallographic plane at indentation test loads ranging from 10 to 50 mN. Examinations reveal that the degree of the hardness anisotropy decreases with increasing indentation test load. Also, the materials examined exhibit significant peak load dependence (i.e., indentation size effect (ISE)). The traditional Meyer's law, proportional specimen resistance (PSR) model and modified PSR (MPSR) model, were used to analyze the load dependence of the hardness. While Meyer's law can not provide any useful information about the observed ISE, the load-independent hardness (i.e., H_PSR and H_MPSR) values can be estimated for different crystallographic directions, using the PSR and MPSR models. Briefly, for microindentation hardness determinations of β-Sn single crystals, the MPSR model is found to be more effective than the PSR model.     

Microhardness studies of renal calculi

The development of acoustic and other methods of kidney stone fragmentation has given importance to the study of the mechanical properties of such stones. Renal calculi based upon calcium oxalate, calcium phosphate, uric acid, cystine, and magnesium ammonium phosphate have been studied using Knoop microhardness indentation methods. The microhardness of dry stones was found to vary with the calculi chemical composition, yet remained consistent within composition groups. The hardest calculi were found to be calcium oxalates with a Knoop microhardness of 68–88 kg/mm². Other compositions have hardness of up to a factor of two lower than this.