Theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation for work-hardening materials

In our previous paper, the expanding cavity model (ECM) and Lame solution were used to obtain an analytical expression for the scale ratio between hardness (H) to reduced modulus (E-r) and unloading work (W-u) to total work (W-t) of indentation for elastic-perfectly plastic materials. In this paper, the more general work-hardening (linear and power-law) materials are studied. Our previous conclusions that this ratio depends mainly on the conical angle of indenter, holds not only for elastic perfectly-plastic materials, but also for work-hardening materials. These results were also verified by numerical simulations.

Age hardening and mechanical properties of Mg-Gd-Er alloy

The Mg-8Gd-0.6Zr-xEr (x = 1, 3 and 5 mass%) alloys were prepared by casting technology, and the microstructures, age hardening behaviors and mechanical properties of alloys have been investigated. Microstructures of the alloys are characterized by the presence of rosette-shaped equiaxed grains. The age hardening behaviors and the tensile properties are enhanced by adding Er element. The maximum aged hardness of Mg-8Gd-0.6Zr-5Er alloy is 97, it is nearly 1.24 times higher than that of Er-free alloy.

Effect of Y for enhanced age hardening response and mechanical properties of Mg-Ho-Y-Zr alloys

In this study, compositional dependence of age hardening characteristics and tensile properties were investigated for Mg-4Ho-xY-0.6Zr alloys (x = 0, 3 5, and 7 wt%). The result showed that with increasing Y content, the hardness of the alloys increased in the as-quenched and aged-peak conditions. Considerable age hardening response was recognized for the alloys. When the alloy containing 7% Y showed the most remarkable age hardening response at aging temperature of 250 degrees C.

Effect of Y for enhanced age hardening response and mechanical properties of Mg-Gd-Y-Zr alloys

In this study, compositional dependence of age hardening response and tensile properties were investigated for Mg-10G(d-x)Y-0.4Zr (x = 1, 3, 5 wt.%) alloys. With increasing Y content, the age hardening response of the alloys enhanced and tensile properties increased. The Mg-10Gd-5Y-0.4Zr alloy exhibited maximum tensile strength and yield strength at aged-peak hardness, and the values were 302 MPa and 289 MPa at room temperature, and 340 MPa and 267 MPa at 250 degrees C, respectively. The strong peak age hardening was attributed to the precipitation of prismatic beta' plates in a triangular arrangement. The cubic shaped beta phase was also observed at grain boundaries. The remarkable improvement in strength is associated with a uniform and high dense distribution of beta' and cubic shaped beta precipitate phases in Mg matrix. Elongation of Mg-10Gd-0.4Zr alloys decreased with increasing Y content, and the elongation of Mg-10Gd-5Y-0.4Zr alloy was less than 3% below 250 degrees C, whereas the alloys containing I wt.% and 3 wt.% Y exhibited higher elongation than 5% at room temperature.

Conducting probe atomic force microscopy investigation of anisotropic charge transport in solution cast PBD single crystals induced by an external field

2-(4-Biphenylyl)-5-(4-tert-butylphenyl)-1,3,4-oxdiazole (PBD) is a good electron-transporting material and can form single crystals from solution. In this work, solution cast PBD single crystals with different crystallographic axes (b, c) perpendicular to the Au/S substrates in large area are achieved by controlling the rate of solvent evaporation in the presence and absence of external electrostatic field, respectively. The orientation of these single crystals on Au/S substrate was characterized by transmission electron microscopy (TEM) and atomic force microscopy (AFM). Conducting probe atomic force microscopy (CP-AFM) was used to measure the charge transport characteristics of PBD single crystals grown on Au/S substrates. Transport was measured perpendicular to the substrate between the CP-AFM tip and the Au/S substrate. The electron mobility of 3 x 10(-3) cm(2)/(V s) for PBD single crystal along crystallographic b-axis is determined. And the electron mobility of PBD single crystal along the c-axis is about 2 orders of magnitude higher than that along the b-axis due to the anisotropic charge transport at the low voltage region.

Effective properties of spherically anisotropic piezoelectric composites

Piezoelectric composites consisting of spherically anisotropic piezoelectric inclusions (i.e., piezoceramic material) in an infinite nonpiezoelectric matrix under a uniform electric field are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials are derived exactly. Taking account of the coupling effects of elasticity, permittivity, and piezoelectricity, formulas are derived for the effective dielectric and piezoelectric responses in the dilute limit. A piezoelectric response mechanism is revealed, in which the effective piezoelectric response vanishes irrespective of how much spherically anisotropic piezoelectric inclusions are inside. Moreover, the effective coupled responses of the piezoelectric composites show that the effective dielectric responses decrease (increase) as the inclusion elastic (piezoelectric) constants increase.

Dielectric response of spherically anisotropic graded piezoelectric composites

A graded piezoelectric composite consisting of a spherically anisotropic graded piezoelectric inclusion imbedded in an infinite nonpiezoelectric matrix, with the physical properties of the graded spherical inclusion having a power-law profile with respect to the radial variable r, is studied theoretically. Under an external uniform electric field, the electric displacement field and the elastic stress tensor field of this spherically anisotropic graded piezoelectric composite are derived exactly by means of displacement separation technique, based on the governing equations in the dilute limit. A piezoelectric response mechanism, in which the effective piezoelectric response vanishes along the z direction (or x,y directions), is revealed in this kind of graded piezoelectric composites. Furthermore, it is found that the effective dielectric constant decreases (or increases) with the volume fraction p of the inclusions if the exponent parameter k of the grading profile is larger (or smaller) than a critical value. (C) 2007 American Institute of Physics.

Dielectric responses of anisotropic graded granular composites having arbitrary inclusion shapes

The transformation field method (TFM) originated from Eshelby's transformation field theory is developed to estimate the effective permittivity of an anisotropic graded granular composite having inclusions of arbitrary shape and arbitrary anisotropic grading profile. The complicated boundary-value problem of the anisotropic graded composite is solved by introducing an appropriate transformation field within the whole composite region. As an example, the effective dielectric response for an anisotropic graded composite with inclusions having arbitrary geometrical shape and arbitrary grading profile is formulated. The validity of TFM is tested by comparing our results with the exact solution of an isotropic graded composite having inclusions with a power-law dielectric grading profile and good agreement is achieved in the dilute limit. Furthermore, it is found that the inclusion shape and the parameters of the grading profile can have profound effect on the effective permittivity at high concentrations of the inclusions. It is pointed out that TFM used in this paper can be further extended to investigate the effective elastic, thermal, and electroelastic properties of anisotropic graded granular composite materials.

汽车覆盖件模具激光表面强化中环带区域的测量及轨迹规划

在模具表面激光强化中,测量及轨迹规划是工艺实现的关键环节。本文针对汽车覆盖件模具表面较为常见的侧壁结构,从中抽取出更为基本的一类型面—环带,提出了一种基于特征线的环带测量及轨迹规划的方法，并且在建立环带数学模型的基础上对误差进行了分析,证明了这种方法不仅简单、高效,而且满足相应的加工工艺要求。

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.

The thermo-visco-plastic instability analysis of saturated soil

A theoretical analysis of instability of saturated soil is presented considering the simple shearing of a heat conducting thermo-visco-plastic material. It is shown that the instability is mainly the consequence of thermal softening which overcomes the strain hardening and the other type of instability is controlled by strain softening. The effects of other factors such as permeability to the instability are discussed in this paper.

Flow Stress of Biomorphous Metal-Matrix Composites

For metal-matrix composites (MMCs), interfacial debonding between the ductile matrix and the reinforcing hard inclusions is an important failure mode. A fundamental approach to improving the properties of MMCs is to optimize their microstructure to achieve maximum strength and toughness. Here, we investigate the flow stress of a MMC with a nanoscale microstructure similar to that of bone. Such a 'biomorphous' MMC would be made of staggered hard and slender nanoparticles embedded in a ductile matrix. We show that the large aspect ratio and the nanometer size of inclusions in the biomorphous MMC lead to significantly improved properties with increased tolerance of interfacial damage. In this case, the partially debonded inclusions continue to carry mechanical load transferred via longitudinal shearing of the matrix material between neighboring inclusions. The larger the inclusion aspect ratio, the larger is the flow stress and work hardening rate for the composite. Increasing the volume concentration of inclusion also makes the biomorphous MMC more tolerant of interfacial damage.

Effects of 'sinking in' and 'piling up' on estimating the contact area under load in indentation

The phenomena of the 'piling up' and 'sinking-in' of surface profiles in conical indentation in elastic-plastic solids with work hardening are studied using dimensional and finite-element analysis. The degree of sinking in and piling up is shown to depend on the ratio of the initial yield strength Y to Young's modulus E and on the work-hardening exponent n. The widely used procedure proposed by Oliver and Pharr for estimating contact depth is then evaluated systematically. By comparing the contact depth obtained directly from finite-element calculations with that obtained from the initial unloading slope using the Oliver-Pharr procedure, the applicability of the procedure is discussed.