Hardness results for computing optimal locally Gabriel graphs

Delaunay and Gabriel graphs are widely studied geo-metric proximity structures. Motivated by applications in wireless routing, relaxed versions of these graphs known as Locally Delaunay Graphs (LDGs) and Lo-cally Gabriel Graphs (LGGs) have been proposed. We propose another generalization of LGGs called Gener-alized Locally Gabriel Graphs (GLGGs) in the context when certain edges are forbidden in the graph. Unlike a Gabriel Graph, there is no unique LGG or GLGG for a given point set because no edge is necessarily in-cluded or excluded. This property allows us to choose an LGG/GLGG that optimizes a parameter of interest in the graph. We show that computing an edge max-imum GLGG for a given problem instance is NP-hard and also APX-hard. We also show that computing an LGG on a given point set with dilation ≤k is NP-hard. Finally, we give an algorithm to verify whether a given geometric graph G= (V, E) is a valid LGG.

CHARACTERIZATION AND HARDNESS OF Co-P COATINGS OBTAINED FROM DIRECT CURRENT ELECTRODEPOSITION USING GLUCONATE BATH

Direct current electrodeposition of Co-P alloy coatings were carried out using gluconate bath and they were characterized by employing techniques like XRD, FESEM, DSC and XPS. Broad XRD lines demonstrate the amorphous nature of Co-P coatings. Spherical and rough nodules are observed on the surface of coatings as seen from FESEM images. Three exothermic peaks around 290, 342 and 390 degrees C in DSC profiles of Co-P coatings could be attributed to the crystallization and formation of Co2P phase in the coatings. As-deposited coatings consist of Co metal and oxidized Co species as revealed by XPS studies. Bulk alloy P (P delta-) as well as oxidized P (P5+) are present on the surface of coatings. Concentrations of Co metal and P delta- increase with successive sputtering of the coating. Observed microhardness value is 1005 HK when Co-P coating obtained from 10 g L-1 NaH2PO2 is heated at 400 degrees C that is comparable with hard chromium coatings.

Nanoindentation behavior of nanotwinned Cu: Influence of indenter angle on hardness, strain rate sensitivity and activation volume

The influence of strain on the mechanical properties and deformation kinetic parameters of nanotwinned (at) copper is investigated by a series of nanoindentation experiments, which were performed by employing sharp indenters with five varying centerline-to-face angles (psi). Comparison experiments were also conducted on (1 1 0) single crystalline Cu. Experimental results indicate that, unlike coarsegrained materials, nt-Cu is prone to plastic flow softening with large material pile-up around the indentation impression at high levels of strains. Localized detwinning becomes more significant with decreasing psi, concomitant with reduced strain-rate sensitivity (m) and enhanced activation volume (V*). The m of nt-Cu is found to depend sensitively on psi with a variation of more than a factor of 3, whereas V* exhibits a much less sensitive trend. This paper discusses the validation of the experimental techniques and the implications of various deformation kinetic parameters on the underlying deformation mechanisms of nt-Ca. 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Solubility-Hardness Correlation in Molecular Crystals: Curcumin and Sulfathiazole Polymorphs

Curcumin and sulfathiazole exist as three and five polymorphs, respectively. We correlate solubility and mechanical properties in these polymorphic systems. It is seen that hardness (H) is inversely proportional to the solubility of a polymorph. H of the polymorphs is explained on the basis of slip planes in the crystal structure, the Schmid factor (m), and the relative orientation of molecules with respect to the nanoindenter direction. Effectively, H is a useful parameter (compared to melting point, T-m, and density, rho) that correlates well with the solubility of a polymorph. Such a correlation is helpful in systems like curcumin and sulfathiazole in which the Gibbs free energy of the polymorphs are close to one another. To summarize, a softer polymorph is more soluble.

Microstructure-hardness-fretting wear resistance correlation in ultrafine grained Cu-TiB2-Pb composites

The retention of the desired combination of mechanical/tribological properties in ultrafine grained materials presents important challenges in the field of bulk metallic composites. In order to address this aspect, the present work demonstrates how one can achieve a good combination of hardness and wear resistance in Cu-Pb-TiB2 composites, consolidated by spark plasma sintering at low temperatures ( < 500 degrees C). Transmission electron microscope (TEM) studies reveal ultrafine grains of Cu (100-400 nm) with coarser TiB2 particles (1-2 mu m) along with fine scale Pb dispersoid at triple junctions or at the grain boundaries of Cu. Importantly, a high hardness of around 2.2 GPa and relative density of close to 90% relative density (rho(theo)) have been achieved for Cu-15 wt% TiB2-10 wt% Pb composite. Such property theo, combination has never been reported for any Cu-based nanocomposite, by conventional processing route. In reference to the tribological performance, fretting wear tests were conducted on the sintered nanocomposites and a good combination of steady state COF (0.6-0.7) and wear rate (10-4 mm(3)/N m) were measured. An inverse relationship between wear rate and hardness was recorded and this commensurates well with Archard's relationship of abrasive wear. The formation of a wear-resistant delaminated tribolayer consisting of TiB2 particles and ultrafine oxide debris, (Cu, Fe, Ti)(x)O-y as confirmed from subsurface imaging using focused ion beam microscopy has been identified as the key factors for the low wear rate of these composites. (C) 2014 Elsevier B.V. All rights reserved.

Hardness Alternation in alpha,omega-Alkanedicarboxylic Acids

The variation of hardness as a function of the number of carbon atoms in alpha,omega-alkanedicarboxylic acids, CNH2N-2O4 (4 <= N <= 9), was examined by recourse to nanoindentation on the major faces of single crystals. Hardness exhibits odd-even alternation, with the odd acids being softer and the even ones harder; the differences decrease with increasing chain length. These variations are similar to those seen for other mechanical, physical, and thermal properties of these diacids. The softness of odd acids is rationalized due to strained molecular conformations in them, which facilitate easier plastic deformation. Relationships between structural features, such as interplanar spacing, interlayer separation distance, molecular chain length, and signatures of the nanoindentation responses, namely, discrete displacement bursts, were also examined. Shear sliding of molecular layers past each other during indentation is key to the mechanism for plastic deformation in these organic crystals.

Nano-hardness Techniques and Its Applications in Mechanical Property Measurements for Surface Engineering

结合纳米硬度技术测量各类薄膜和块体材料表层的纳米压痕硬度、弹性模量、断裂韧性、膜厚、微结构的弯曲变形,采用纳米划痕硬度技术测量各类薄膜和块体材料的粗糙度、临界附着力、摩擦系数、划痕横剖面.纳米硬度计是检测材料表层微米乃至几十纳米力学性能的先进仪器,可广泛应用于表面工程中的质量检测.

Evaluation of the Effectiveness of Representative Methods for Determining Young's Modulus and Hardness from Instrumented Indentation Data

The effectiveness of Oliver & Pharr's (O&P's) method, Cheng & Cheng's (C&C's) method, and a new method developed by our group for estimating Young's modulus and hardness based on instrumented indentation was evaluated for the case of yield stress to reduced Young's modulus ratio (sigma(y)/E-r) >= 4.55 x 10(-4) and hardening coefficient (n) <= 0.45. Dimensional theorem and finite element simulations were applied to produce reference results for this purpose. Both O&P's and C&C's methods overestimated the Young's modulus under some conditions, whereas the error can be controlled within +/- 16% if the formulation was modified with appropriate correction functions. Similar modification was not introduced to our method for determining Young's modulus, while the maximum error of results was around +/- 13%. The errors of hardness values obtained from all the three methods could be even larger and were irreducible with any correction scheme. It is therefore suggested that when hardness values of different materials are concerned, relative comparison of the data obtained from a single standard measurement technique would be more practically useful. It is noted that the ranges of error derived from the analysis could be different if different ranges of material parameters sigma(y)/E-r and n are considered.

Nano-Hardness Tester and its Application in MEMS

微机电系统(MEMS)技术的迅速崛起,推动了对其所用材料和结构的力学性能研究。简要介绍纳米硬度技术的发展展、理论模型和MTS公司的Nano Indenter XP系统的配置、测量原理及功能。并根据我们的一些研究结果,说明它在微机电系统中的应用。

Relationships between hardness, elastic modulus, and the work of indentation

The work done during indentation is examined using dimensional analysis and finite element calculations for conical indentation in elastic-plastic solids with work hardening. An approximate relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work in indentation is found. Consequently, the ratio of hardness to elastic modulus may be obtained directly from measuring the work of indentation. Together with a well-known relationship between elastic modulus, initial unloading slope, and contact area, a new method is then suggested for estimating the hardness and modulus of solids using instrumented indentation with conical or pyramidal indenters.

What is indentation hardness?

Using dimensional analysis and finite element calculations, we derive simple scaling relationships for loading and unloading curve, contact depth, and hardness. The relationship between hardness and the basic mechanical properties of solids, such as Young's modulus, initial yield strength, and work-hardening exponent, is then obtained. The conditions for 'piling-up' and 'sinking-in' of surface profiles during indentation are determined. A method for estimating contact depth from initial unloading slope is examined. The work done during indentation is also studied. A relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work is discovered. This relationship offers a new method for obtaining hardness and elastic modulus. Finally, a scaling theory for indentation in power-law creep solids using self-similar indenters is developed. A connection between creep and 'indentation size effect' is established.

Revelation of a Functional Dependence of the Sum of Two Uniaxial Strengths/Hardness on Elastic Work/Total Work of Indentation

Dimensional and finite element analyses were used to analyze the relationship between the mechanical properties and instrumented indentation response of materials. Results revealed the existence of a functional dependence of (engineering yield strength sigma(E,y) + engineering tensile strength sigma(E,b))/Oliver & Pharr hardness on the ratio of reversible elastic work to total work obtained from an indentation test. The relationship links up the Oliver & Pharr hardness with the material strengths, although the Oliver & Pharr hardness may deviate from the true hardness when sinking in or piling up occurs. The functional relationship can further be used to estimate the SUM sigma(E,y) + sigma(E,b) according to the data of an instrumented indentation test. The sigma(E,y) + sigma(E,b) value better reflects the strength of a material compared to the hardness value alone. The method was shown to be effective when applied to aluminum alloys. The relationship can further be used to estimate the fatigue limits, which are usually obtained from macroscopic fatigue tests in different modes.

Influence of Indenter Tip Roundness on Hardness Behavior in Nanoindentation

In this paper. the effect of indenter tip roundness on hardness behavior for two typical elastic perfectly plastic materials is studied by means of finite element simulation. A rigid conical indenter of semi apex angle 70.3 degrees fitted smoothly with a spherical tip is employed. It is shown that as the indentation depth increases hardness first rises from zero, reaches a maximum and then decreases slowly approaching asymptotically the limiting value equal to that due to a conical indenter of ideally sharp tip. The range within which hardness varies appreciably is comparable to the radius of the indenter tip. The difference between the maximum value and the limiting value depends on the yield stress over the Young's modulus ratio. The smaller this ratio the greater the difference is. Numerical simulation also provides an opportunity for checking the accuracy and limitations of the widely used Oliver-Pharr method.

Experimental Verification And Theoretical Analysis Of The Relationships Between Hardness, Elastic Modulus, And The Work Of Indentation

The relationship between hardness (H), reduced modulus (E-r), unloading work (W-u), and total work (W-t) of indentation is examined in detail experimentally and theoretically. Experimental study verifies the approximate linear relationship. Theoretical analysis confirms it. Furthermore, the solutions to the conical indentation in elastic-perfectly plastic solid, including elastic work (W-e), H, W-t, and W-u are obtained using Johnson's expanding cavity model and Lame solution. Consequently, it is found that the W-e should be distinguished from W-u, rather than their equivalence as suggested in ISO14577, and (H/E-r)/(W-u/W-t) depends mainly on the conical angle, which are also verified with numerical simulations. (C) 2008 American Institute of Physics.