Hardness Anisotropy Research Articles

Thermomagnetic processing of liquid-crystalline epoxy resins and their mechanical characterization using nanoindentation.

A thermomagnetic processing method was used to produce a biphenyl-based liquid-crystalline epoxy resin (LCER) with oriented liquid-crystalline (LC) domains. The orientation of the LCER was confirmed and quantified using two-dimensional X-ray diffraction. The effect of molecular alignment on the mechanical and thermomechanical properties of the LCER was investigated using nanoindentation and thermomechanical analysis, respectively. The effect of the orientation on the fracture behavior was also examined. The results showed that macroscopic orientation of the LC domains was achieved, resulting in an epoxy network with an anisotropic modulus, hardness, creep behavior, and thermal expansion.

Hardening mechanism of commercially pure Mg processed by high pressure torsion at room temperature

Coarse-grained Mg in the as-cast condition and fine-grained Mg in the extruded condition were processed by high pressure torsion (HPT) at room temperature for up to 16 turns. Microstructure observation and texture analysis indicate that to fulfil the Von Mises criterion, the non-basal slip is activated in the as-cast Mg and tension twinning is activated in the as-extruded Mg. Although the deformation mechanism is different in the as-cast Mg and the as-extruded Mg during HPT, their hardening evolutions are similar, i.e. after 1/8 turn of HPT, microhardness of the as-cast Mg and the extruded Mg both show a significant increase and further HPT processing does not significantly further increase the microhardness. Texture strengthening can explain the rapid hardening. Hardness anisotropy and texture data results suggest that texture strengthening plays an important role for both types of samples. Texture strengthening weakens with decreasing grain size.

Study of Knoop microhardness anisotropy on the (001), (100) and (010) faces of gadolinium calcium oxyborate single crystals

The Knoop microhardness anisotropy of monoclinic gadolinium calcium oxyborate single crystals was investigated on the (001), (100) and (010) faces. The experimental results of the microhardness anisotropy were analysed for different slip systems using a model based on the effective resolved shear stress. The results obtained for all three faces revealed hardness anisotropy consisting of one maximum or minimum in the 180° range of indenter orientation. From experimental data and computed effective resolved shear stress it was found that the {101} and {011} slip planes are active during the indentation deformation of all three faces whereas the {110} slip planes are also active during the indentation of the (001) and (100) faces of gadolinium calcium oxyborate crystals.

Structural, electronic and mechanical properties of Imma-carbon

A theoretical investigation on mechanical and electronic properties of Imma-carbon was performed by employing first-principles calculations based on the density functional theory. The stability at ambient condition is approved by phonon dispersion and elastic constants calculations. The analysis of elastic anisotropy and hardness anisotropy shows that Imma-carbon is nearly mechanical isotropy. The large elastic constants and ideal strength indicate Imma-carbon is a potential superhard material. Ideal strength studies show that (010) plane is the easy cleavage plane for Imma-carbon, and the cleavage mechanism was discussed in detail. The calculated band structure is a direct band gap semiconductor with 2.97 eV gap at Γ-point.

Metallization and softening of B6O at high pressure

Structural stability, elastic and electronic properties of boron suboxide, B6O, up to 300GPa were investigated by first-principles calculations. Structural searching and enthalpy differences calculations identify a high-pressure phase for B6O with monoclinic Cc structure (denoted as β-B6O), which is energetically preferable to the known R-3m-type phase above 245GPa. β-B6O phase forms a three-dimensional covalent network mainly composed of pentagonal pyramids and zig-zag O–B1–O chains extended along c-direction. β-B6O phase is found to be stable examined by the calculated elastic constants and phonon dispersion and exhibits metallic behavior and greater elastic and hardness anisotropy, totally different from the semiconducting character and relative isotropy of ground state structure. Moreover, β-B6O is predicted to soften significantly with a Vicker’s hardness of about 20.7GPa.

Ab initio calculation of the structural and elastic properties, anisotropy, and hardness of nitrogen-doped diamond

The elastic properties of nitrogen-doped diamond are studied with the use of the density functional theory in the plane-wave basis, the electron density gradient approximation, and ultrasoft pseudopotentials. It is established that doping increases the lattice parameter and decreases the elastic constants, elasticity moduli, elastic wave velocities, and the anisotropy of elastic properties and hardness. It is shown that the hardness of the (111) face exceeds that of the (100) face in both pure and nitrogen-doped diamond.

Characterization of Anisotropy in Hardness and Indentation Modulus by Nanoindentation

This paper provides a useful guide how to characterize material anisotropy by nanoindentation. Hardness and indentation modulus of austenitic stainless steel (grade A304) were characterized by instrumented indentation at the grain scale (at low indentation load and depth of penetration). We applied the grid indentation method on an area containing several grains with different crystallographic orientation which was simultaneously characterized by electron back-scatter diffraction. Hardness and indentation modulus dependencies on crystallographic orientation were then evaluated and compared with single crystal Young’s modulus and finite element simulations.

Stability and elastic properties of Y–C binary compounds investigated by first principles calculations

The first principles calculations based on density functional theory (DFT) were adopted to investigate the stability, elastic constants, hardness, Debye temperature and mechanical anisotropy properties of Y–C binary compounds. The cohesive energy and formation enthalpy of these compounds indicate that they are thermodynamically stable structures. The elastic parameters Cij were calculated, and then the bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio σ were evaluated by Voigt-Reuss-Hill (VRH) approximation. The largest B, G, E values and hardness are ascribed to β-Y2C3 among all YxCy binary compounds. The hardness of compounds was estimated using a semi empirical hardness theory, and the results showed that hardness for all the calculated compounds was less than 17GPa. The mechanical anisotropy was characterized by calculating several different anisotropic indexes and factors. The calculated anisotropy factors indicate that the YxCy binary compounds show anisotropic mechanical properties and YC2 is largely shear isotropic.

Stability and mechanical properties of C2N2X (X=O, NH and CH2) from first-principles calculations

The structural stability and mechanical properties such as elastic constants, mechanical moduli, Vickers hardness and mechanical anisotropy of C2N2X (X=O, NH and CH2) are calculated by first principles calculations based on the density functional theory. The calculated lattice parameters, elastic constants of C2N2X (X=O, NH and CH2) are in good agreement with the experimental data and previous calculated values. C2N2X (X=O, NH and CH2) are also found to be thermodynamically and mechanically stable. The mechanical moduli (bulk modulus, shear modulus and Young's modulus) are evaluated by Voigt–Reuss–Hill approach. The hardness of C2N2X (X=O, NH and CH2) is calculated using both the ab initio and semiempirical model calculations. The Vickers hardness of C2N2X (X=O, NH and CH2) is approximate to 40GPa of the superhard materials. In conclusion, these materials can be regarded as potential candidate of ultra-incompressible and hard materials. Furthermore, the mechanical anisotropy is also discussed in details.

Studies on mechanical properties of titanium aluminium nitride coatings

Vickers and Knoop microhardness studies have been carried out on titanium aluminium nitride (TiAlN) hard coatings deposited on WC-12Co substrates. The microhardness test has been studied as a function of applied loads varying from 0.49 to 9.8 N. The normal indentation size effect has been observed in Vickers and Knoop microhardness test. It follows that increase in microhardness at lower loads (up to 9.8 N) depends inversely on elastic modulus of the hard coatings. Knoop microhardness test shows that microhardness values decrease with increase in applied load. The elastic stiffness constants have been calculated using Wooster’s empirical relation. Young’s modulus is found to be 378.18 GPa. Also hardness anisotropy has been performed with respect to the orientation of the TiAlN coatings from Knoop microhardness test. Morphology of indented imprints of the coatings has been examined using scanning electron microscopy.

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.

Effects of Different Modes of Hot Cross-Rolling in 7010 Aluminum Alloy: Part II. Mechanical Properties Anisotropy

The influence of microstructure and texture developed by different modes of hot cross-rolling on in-plane anisotropy (AIP) of yield strength, work hardening behavior, and anisotropy of Knoop hardness (KHN) yield locus has been investigated. The AIP and work hardening behavior are evaluated by tensile testing at 0 deg, 45 deg, and 90 deg to the rolling direction, while yield loci have been generated by directional KHN measurements. It has been observed that specimens especially in the peak-aged temper, in spite of having a strong, rotated Brass texture, show low AIP. The results are discussed on the basis of Schmid factor analyses in conjunction with microstructural features, namely grain morphology and precipitation effects. For the specimen having a single-component texture, the yield strength variation as a function of orientation can be rationalized by the Schmid factor analysis of a perfectly textured material behaving as a quasi-single crystal. The work hardening behavior is significantly affected by the presence of solute in the matrix and the state of precipitation rather than texture, while yield loci derived from KHN measurements reiterate the low anisotropy of the materials. Theoretic yield loci calculated from the texture data using the visco-plastic self-consistent model and Hill’s anisotropic equation are compared with that obtained experimentally.

Investigating the mechanical properties, creep and crack pattern of Cu6Sn5 and (Cu,Ni)6Sn5 on diverse crystal planes

Cu6Sn5 is an important intermetallic compound (IMC) commonly formed during lead-free soldering. It is known that Cu6Sn5 exhibits significantly different thermo-mechanical deformation behaviour compared to both bulk solder alloys and their substrates. In high-density 3-D electrical packages individual solder joints may contain only a few grains of Cu6Sn5. The knowledge of the mechanical properties, creep and crack behaviour of Cu6Sn5 on different crystal planes is therefore essential to understanding the deformation of lead-free solder joints in service. In this research, the mechanical properties, creep and crack patterns on diverse crystal planes of hexagonal Cu6Sn5 and (Cu,Ni)6Sn5 were investigated using electron back scattered diffraction (EBSD), scanning electron microscopy (SEM) and nanoindentation. It was found that the mechanical properties, creep and crack patterns of hexagonal Cu6Sn5 were strongly related to the crystal orientation. The addition of Ni was found to reduce the anisotropy in hardness and the creep of Cu6Sn5 and had a significant effect on the crack patterns of Cu6Sn5.

Study of Knoop microhardness anisotropy on the (001) face of potassium bichromate single crystals

The Knoop microhardness anisotropy of triclinic potassium bichromate single crystals was investigated on the (001) cleaved face at two values of test load. The experimental results of the microhardness anisotropy were analysed for different slip systems using a model based on the effective resolved shear stress. The results revealed a distinct anisotropy consisting of maxima and minima of microhardness for the 〈100〉 and 〈110〉 indenter orientations. Additionally, a fair anisotropy associated with differences between maxima for indenter oriented in the [110] and [11¯0] directions and minima for the [010] and [100] directions was observed. It was found that the computed effective resolved shear stress based on the {110}〈11¯0〉 slip system explains the experimental results of the hardness anisotropy on the (001) face of potassium bichromate single crystals.

Enhanced mechanical properties in die-upset Nd-Fe-B magnets via die-upsetting process

The mechanical properties of die-upset Nd-Fe-B magnets produced at different die-upset processes were investigated. The results showed that the optimum comprehensive mechanical properties of die-upset Nd-Fe-B magnets were obtained at the deformation temperature of 680 °C. The anisotropy of Vickers hardness was more obvious at the die-upset level of 55%, and the Vickers hardness measured parallel to the c-axis was significantly lower than that perpendicular to the c-axis. The fracture toughness measured parallel to the c-axis first increased, and then decreased with increase in die-upset level. The maximum fracture toughness of Nd-Fe-B magnets was obtained at the die-upset level of 60%. The microstructure showed that the width of defect layers and the average size of large grains increased, and the layered structure of die-upset Nd-Fe-B magnets was obviously different with increase in the die-upset level.

An extensive investigation on nucleation, growth parameters, crystalline perfection, spectroscopy, thermal, optical, microhardness, dielectric and SHG studies on potential NLO crystal – Ammonium Hydrogen l-tartarte

Ammonium Hydrogen l-tartarte (AMT), an organic nonlinear optical crystal was grown by slow evaporation method at ambient temperature. Solubility, metastable zone width and induction period of Ammonium Hydrogen l-tartarte in aqueous solution were determined. Good quality crystals were selected and characterized by Single crystal XRD, HR-XRD, FT-IR, 1H NMR, Mass, TGA-DTA, SEM, EDAX, optical and NLO studies. Single crystal XRD analysis revealed that the crystal system belongs to orthorhombic with cell parameters a=7.65Å, b=7.85Å and c=11.07Å. High-resolution-X-ray diffraction (HR-XRD) analysis was carried out to study the crystalline perfection of the grown crystal. 1H NMR and FTIR spectrum thus confirmed the presence of functional groups of the grown crystal. Molecular mass of AMT was measured accurately by mass spectroscopic analysis. Surface features of the grown crystal were analyzed by SEM, AFM, chemical etching and the presence of elements in the compound was identified by EDAX analysis. Thermal behavior of the grown crystal has been studied by TG/DTA analysis. The recorded UV–Vis-NIR spectrum shows excellent transmission in the region of 190–1100nm. The Vickers and Knoop’s microhardness studies have been carried out on AMT crystals over a range of 10–50g. Hardness anisotropy has been observed in accordance with the orientation of the crystal. Fluorescence spectral studies were carried in the range of 280–500nm for the grown crystal. The SHG conversion efficiency and laser damage threshold were measured using an Nd: YAG laser (1064nm).

Theoretical model of hardness anisotropy in brittle materials

Anisotropy is prominent in the hardness test of single crystals. However, the anisotropic nature is not demonstrated quantitatively in previous hardness model. In this work, it is found that the electron transition energy per unit volume in the glide region and the orientation of glide region play critical roles in determining hardness value and hardness anisotropy for a single crystal material. We express the mathematical definition of hardness anisotropy through simple algebraic relations. The calculated Knoop hardnesses of the single crystals are in good agreement with observations. This theory, extended to polycrystalline materials by including hall-petch effect and quantum size effect, predicts that the polycrystalline diamond with low angle grain boundaries can be harder than single-crystal bulk diamond. Combining first-principles technique and the formula of hardness anisotropy the hardness of monoclinic M-carbon, orthorhombic W-carbon, Z-carbon, and T-carbon are predicted.

Nanoindentation as a Probe for Mechanically‐Induced Molecular Migration in Layered Organic Donor–Acceptor Complexes

Nanoindentation and scratch experiments on 1:1 donor-acceptor complexes, 1 and 2, of 1,2,4,5-tetracyanobenzene with pyrene and phenanthrene, respectively, reveal long-range molecular layer gliding and large interaction anisotropy. Due to the layered arrangements in these crystals, these experiments that apply stress in particular directions result in the breaking of interlayer interactions, thus allowing molecular sheets to glide over one another with ease. Complex 1 has a layered crystal packing wherein the layers are 68° skew under the (002) face and the interlayer space is stabilized by van der Waals interactions. Upon indenting this surface with a Berkovich tip, pile-up of material was observed on just one side of the indenter due to the close angular alignment of the layers with the half angle of the indenter tip (65.35°). The interfacial differences in the elastic modulus (21%) and hardness (16%) demonstrate the anisotropic nature of crystal packing. In 2, the molecular stacks are arranged in a staggered manner; there is no layer arrangement, and the interlayer stabilization involves C-H···N hydrogen bonds and π···π interactions. This results in a higher modulus (20%) for (020) as compared to (001), although the anisotropy in hardness is minimal (4%). The anisotropy within a face was analyzed using AFM image scans and the coefficient of friction of four orthogonal nanoscratches on the cleavage planes of 1 and 2. A higher friction coefficient was obtained for 2 as compared to 1 even in the cleavage direction due to the presence of hydrogen bonds in the interlayer region making the tip movement more hindered.

Microhardness, chemical etching, SEM, AFM and SHG studies of novel nonlinear optical crystal –l-threonine formate

The crystal l-threonine formate, an organic NLO crystal was synthesized from aqueous solution by slow evaporation technique. The grown crystal surface has been analyzed by scanning electron microscopy (SEM), chemical etching and atomic force microscopy (AFM). SEM analysis reveals pyramidal shaped minute crystallites on the growth surface. The etching study indicates the occurrence of etch pit patterns like striations and step like pattern. The mechanical properties of LTF crystals were evaluated by mechanical testing which reveals certain mechanical characteristics like elastic stiffness constant (C11) and young's modulus (E). The Vickers and Knoop microhardness studies have been carried out on LTF crystals over a range of 10–50g. Hardness anisotropy has been observed in accordance with the orientation of the crystal. AFM image shows major hillock on growth surface. The second harmonic generation (SHG) efficiency has been tested by the Kurtz powder technique using Nd:YAG laser and found to be about 1.21 times in comparison with standard potassium dihydrogen phosphate (KDP) crystals.

Anisotropy of bond projections in simple crystal structures

The nearest-neighbor bond distances represented by the stick-and-ball model of a crystal are projected into planes in order to find the directions from where the projections have maximum or minimum values. The projection directions and their corresponding values of the maxima and minima are presented for simple cubic, body-centered-cubic, face-centered-cubic, sodium chloride, zinc sulfide, diamond, fluorite, cesium chloride, hexagonal close-packed, tungsten carbide, wurtzite, graphite, graphene, and aluminum boride structures. The purely geometrical considerations quantitatively reflect an anisotropy of the bond projections and provide data for a large amount of materials crystallizing in these structures. The presented results can be applied to the description, analysis, and understanding of anisotropic effects related to bond projection in 14 crystal structures. The application of hardness anisotropy for BN, SiC, and TiC is shown.