Knoop Hardness Anisotropy Research Articles

Microhardness Indentation Studies of 2‐4‐6 Trinitrotoluene

AbstractThe microhardness of the {001} faces of 2‐4‐6 trinitrotoluene crystals has been investigated using both Vickers and Knoop indentation methods. The Vickers hardness number was found to be 22.5 kg mm−2 independent of crystal orientation and perfection. At ambient temperatures (∼20 °C) the Knoop hardness number varied between 20.5 kg mm−2 and 24.0 kg mm−2 with crystal orientation. At higher temperature (50 °C) the Knoop hardness anisotropy curve retained its shape, although the overall hardness decreased by 10 %. We interpret this change as reflecting a simple temperature dependant loosening of the crystal lattice rather than any change in deformation mechanism. No variation of Knoop hardness was evident with changing load. The hard direction was [010] and the soft [100]. The dominant operative slip system was defined to be {001}[010].

Simulating Knoop hardness anisotropy of aluminum and β-HMX with a crystal plasticity finite element model

We report a crystal plasticity finite element model for simulating the variation of the Knoop hardness number with indenter orientation, i.e., the hardness anisotropy. We propose a modification to the Voce hardening law to include the effects of slip on multiple systems on the hardening rate. The model is validated using single crystal aluminum in a two-step procedure: (a) calibration of the material model with single crystal tension experiments, and (b) prediction of the hardness anisotropy of the {001}, {011} and {021} planes. The predicted hardness anisotropy follows experimental trends very well for the {001} and {021} planes, while for the {011} plane there is a deviation of the predictions from experiments at higher angles of the indenter. The model is then used to simulate the hardness anisotropy of the (010), (011) and (110) planes of β-HMX measured by Gallagher et al. (2015). Due to the lack of single crystal data, we were unable to calibrate the model prior to simulating the hardness anisotropy. Hence, we assumed unknown variables to make predictions for comparison to experiments, including the set of active slip systems and the hardening and twinning behavior. From simulations of the indentation of the (010) plane with the set of slip systems from Barton et al (2009) we found that the hardness anisotropy is inversely proportional to the activity of the slip system (101)[01¯0], and to a lesser extent the twin system. Suppressing the (101)[01¯0] slip system improved the predictions, suggesting that the viable set of slip systems for β-HMX need not include it. The predicted twinning activity did not match well with the observations from Gallagher et al. (2015). Suppressing the twinning resulted in a better prediction of the hardness anisotropy. Due to the simplicity of the twinning part of the model we do not make definite conclusions related to twinning. We report predictions for the hardness anisotropy of the (011) and (110) planes of β-HMX using parameters that maximized agreement between simulations and experimental indentation of (010) plane. These predictions are in reasonable agreement with experiments. In addition, we report the predictions of the hardness anisotropy using the sets of slip systems proposed by Pal and Picu (2018) and Zhou et al. (2012), which both gave inferior agreement with experiments.

Knoop hardness anisotropy in anthracene and phenanthrene single crystals

Microhardness anisotropy in single crystals of anthracene and phenanthrene has been observed by the Knoop indentation technique. The Knoop hardness variation with respect to the [010] direction shows opposite trends. Both these crystals have the same crystal structure and space group. The present observations are explained in terms of orientation and disposition of molecules in the unit cells.

Hardness anisotropy of acetaminophen crystals.

The anisotropy of acetaminophen hardness was demonstrated using both Vickers and Knoop indentation hardness measurements. Based on a model of Knoop hardness anisotropy proposed by Brookes et al. (1), it was concluded that plastic flow in acetaminophen crystals occurs primarily as a result of slip in the (010)<001> system. This conclusion was corroborated with the results of the Vickers indentation tests. The apparent brittleness of acetaminophen was rationalized because only one slip system appeared to be operative. Under these conditions generalized plastic flow cannot occur, since this requires the operation of at least five independent slip systems (2). The high stress concentrations that result from flow lead to fracture. Therefore acetaminophen is more precisely classified as being semiductile. When a material deforms plastically as a result of slip in only one slip system, considerable crystal realignment can occur during compaction. This in turn can facilitate capping during decompression and ejection, since the cleavage plane, (010), would become aligned with the direction of highest tensile stress.

Hardness anisotropies: A new approach

Hardness testing is often the only mechanical property test that can be applied to hard solids. The apparent simplicity of hardness tests belies their true complexity; however, understanding the fundamentals of the responses of the materials to indentation allows considerable information to be extracted from such tests. In particular, anisotropies in hardness, for example the Knoop hardness anisotropy on a single-crystal plane, or differences in hardness between different test planes, have been commonly used to investigate the active slip systems in a wide variety of materials. We describe here a new approach to the analysis of hardness anisotropy results, in which the whole slip pattern around indentations is modelled. The hardness anisotropy is then described in terms of the stresses on the active dislocations, of their efficiency as mechanisms for material transport, and of the possible interactions between them. It will be shown that this approach leads to a full description of the slip patterns and hardness behaviour of a wide variety of crystals and leads to a better understanding of other indentation phenomena, such as plastic recovery and the initiation and propagation of fracture.

Knoop hardness anisotropy and predicted and observed slip patterns in MgO

Abstract Results are presented of the Knoop hardness anisotropy on {001} and {110} faces of MgO. Specimens were etched to show dislocation positions. This etching was repeated after chemical surface stripping, so as to reveal the three-dimensional arrangements of dislocations around indentations made in low-index directions on the two surfaces. These dislocation arrangements are compared with those predicted by two hardness-anisotropy models. Additionally, the influence of elastic recovery and surface pile-up on measured hardness has been investigated.

Knoop hardness anisotropy of single crystals with hexagonal structure

Knoop hardness anisotropy of single crystals with hexagonal structure

Hardness anisotropy of III-V semiconducting compounds and alloys

Knoop hardness anisotropy measurements have been carried out on {100} samples of InP, both undoped and doped with sulfur to 1019 cm−3, InGaAs and InGaAsP, the latter two being in layer form. The results show that the ternary and quaternary alloys share similar hardness anisotropy characteristics characterized by two maxima at about 20° from the 〈110〉 direction, and a minimum close to the 〈100〉 direction, whereas InP shows a single maximum near the 〈100〉 direction and two minima about 6–8° from 〈110〉. Sulfur doping increases the general hardness of InP, but the shape of the curve is maintained. The relative hardness curves are discussed in relation to deformation mechanisms.

Slip systems of Cu2O by Knoop hardness anisotropy measurement

Knoop microhardness tests have been performed at room temperature on Cu 2O cuprous oxide single crystals. Hardness anisotropy analysis indicates that { 110} is the operative slip system.

立方晶金属のヌープかたさの異方性の数式表現とセンダスト合金単結晶への応用

立方晶金属のヌープかたさの異方性の数式表現とセンダスト合金単結晶への応用

Knoop Hardness Anisotropy and Plastic Deformation in Mn‐Zn Ferrite Single Crystals

The Knoop hardness anisotropy and plastic deformation markings around the DPH indentation were investigated for an Mn‐Zn ferrite single crystal. Knoop hardness values, which depended primarily on the crystallographic direction, were represented on a standard stereographic triangle. The hardness was maximum in the &lt;001&gt; direction and minimum in the &lt;111&gt; and &lt;011&gt; directions. The patterns of the plastic deformation markings show that the ferrite deforms plastically at room temperature by {110} &lt;110&gt; and {111} &lt;110&gt; slip.

Deformation and Fracture of MnTe and MnSe‐MnTe Solid Solutions

Single crystals of MnTe and solid solutions in the system MnSe‐MnTe were prepared; selected surfaces were indented with either a Vickers or a Knoop microindenter. Information on mechanical behavior was obtained by observation of slip traces and by study of Knoop hardness anisotropy. Hexagonal NiAs‐type MnTe and MnTe‐rich Mn(Te,Se) solid solutions show plastic deformation attributable to {1012} twinning, basal slip, and pencil glide in 〈1120〉. Fracture occurs as primary {0001} and secondary {1010} cleavage. Vickers and Knoop hardnesses were greater on the basal plane than on prism planes. Cubic MnSe‐rich Mn(Te,Se) solid solutions show both {111}〈110〉 and {110}〈110〉 slip with {100} and {110} fracture in crushed fragments and around surface indentations. Knoop hardness anisotropy is like that in MnSe. The rate of solid solution hardening is greater than for comparable substitutions of sulfide ions in the MnSe matrix.

Slip Behavior and Hardness Indentations in MnSe and MnSe‐MnS Solid Solutions

Single crystals in the solid solution series MnSe‐MnS were prepared, and selected surfaces were indented with either a Vickers or a Knoop microindenter. Information on mechanical behavior was obtained by observation of slip traces around indentations and by study of Knoop hardness anisotropy. Manganous selenide exhibits {111} and {110} as primary and secondary slip mechanisms, respectively, in contrast to the {110} mechanism preferred by MnS. In the system MnSe‐MnS, the primary slip mechanism changes gradually with composition. The {110} mechanism of MnS is much more sensitive to temperature than the {111} mechanism of MnSe, and a large solid solution hardening effect accompanies the substitution of sul‐fide for selenide ions.

The effect of temperature on the hardness anisotropy of beryllium single crystals

The effect of orientation on hardness of beryllium single crystals, in the range of room temperature to 400° C, has been studied using Knoop and Vickers indenters. The variation of Knoop hardness anisotropy with temperature is related to the alternation of deformation modes. The asymmetry of Vickers impression is also explained on the basis of deformation around impressions. There is good agreement between the deformation markings around impressions and the orientation factors for each deformation system.