Ab initio investigation of the elasticity and stability of aluminium

On the basis of the pseudopotential plane-wave (PP-PW) method in combination with the local density functional theory (LDFT), complete stress-strain curves for the uniaxial loading and uniaxial deformation along the [001] and [111] directions, and the biaxial proportional extension along [010] and [001] for aluminium are obtained. During the uniaxial loading, certain general behaviours of the energy versus the stretch and the load versus the stretch are confirmed; in each case, there exist three special unstressed structures: f.c.c., b.c.c., and f.c.t. for [001]; f.c.c., s.c., and b.c.c. for [111]. Using stability criteria, we find that all of these states are unstable, and always occur together with shear instability, except the natural f.c.c. structure. A Pain transformation from the stable f.c.c. structure to the stable b.c.c. configuration cannot be obtained by uniaxial compression along any equivalent [001] and [111] direction. The tensile strengths are similar for the two directions. For the higher energy barrier of the [111] direction, the compressive strength is greater than that for the [001] direction. With increase in the ratio of the biaxial proportional extension, the stress and tensile strength increase; however, the critical strain does not change significantly. Our results add to the existing ab initio database for use in fitting and testing interatomic potentials.

Closed form solutions of T-stress in plane elasticity crack problems

The T-stress is considered as an important parameter in linear elastic fracture mechanics. In this paper, several closed form solutions of T-stress in plane elasticity crack problems in an infinite plate are investigated using the complex potential theory. In the line crack case, if the applied loading is the remote stress or the concentrated forces, the T-stress can be derived from the basic field. Here, the basic field is defined as the field caused by the applied loading in the infinite plate without the crack. For the circular are crack, the T-stress can be abstracted from a known solution. For the cusp crack problems, the T-stress can be separated from the obtained stress solution for which the conformal mapping technique is used.

Size-Dependent Elastic Modulus And Fracture Toughness Of The Nanofilm With Surface Effects

The effective elastic modulus and fracture toughness of the nanofilm were derived with the surface relaxation and the surface energy taken into consideration by means of the interatomic potential of an ideal crystal. The size effects of the effective elastic modulus and fracture toughness were discussed when the thickness of the nanofilm was reduced. And the dependence of the size effects on the surface relaxation and surface energy was also analyzed.

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.

Free radial oscillation of a sphere in relativistic elasticity theory

The spherically symmetric free radial oscillation in the first post-Newtonian approximation for a homogeneous and isotropic elastic sphere with a constant density is studied. Based on the Xu, Wu, and Soffel formalism, the relation of the oscillation frequency of the sphere with the radius, mass density, and elastic constants of the sphere is derived by using the successive approximation method.

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.

Distribution characteristics of (CS)-C-137 in wind-eroded soil profile and its use in estimating wind erosion modulus

Due to its inert reaction in soil system and distinctive vertical distribution in soil profile, caesium-137 (Cs-137) has been used as a tracer to assess wind erosion. In this study, 62 soil samples were collected from 4 sampling sites in Taipusi County, Inner Mongolia; Caesium-137 activities for those soil samples were measured using a gamma-ray spectrometry in Sichuan University, Chengdu. Distribution pattern of Cs-137 in vertical soil profile was different for different land use and land cover types. Caesium-137 was distributed homogeneously in plow layer of cropland, and negatively exponential in low to medium cover grassland. Distribution pattern in high covered grassland was represented by a peak at 2-4 cm soil depth followed by a negative exponential curve. Based on those findings, simplified mass balance model was chosen to estimate the rate of wind erosion for cropland, while profile distribution model was used for grassland. Estimated wind erosion rates were 7990, 4270 and 1808 Mg(.)km(-2.)a(-1) for cropland, low cover grassland and medium cover grassland, respectively. Wind erosion intensity correlated negatively with plant cover.

Calculation of bulk modulus on carbon nitrides with chemical bond method

The bulk moduli of some superhard materials were calculated by using the chemical bond method. For simple crystals, such as diamonds, c-BN, SiC, Si, BP, and Ge, the calculated results agree with experimental and theoretical values. For crystals of complex structure, such as beta-BC2N crystal and various structural C3N4 crystals, the results indicate that their bulk moduli are large, but do not exceed that of diamond.

Study of elastic modulus and yield strength of polymer thin films using atomic force microscopy

Nanometer-scale elastic moduli and yield strengths of polycarbonate (PC) and polystyrene (PS) thin films were measured with atomic force microscopy (AFM) indentation measurements. By analysis of the AFM indentation force curves with the method by Oliver and Pharr, Young's moduli of PC and PS thin films could be obtained as 2.2 +/- 0.1 and 2.6 +/- 0.1 GPa, respectively, which agree well with the literature values. By fitting Johnson's conical spherical cavity model to the measured plastic zone sizes, we obtained yield strengths of 141.2 MPa for PC thin films and 178.7 MPa for PS thin films, which are similar to2 times the values expected from the literature. We propose that it is due to the AFM indentation being asymmetric, which was not accounted for in Johnson's model. A correction factor, epsilon, of similar to0.72 was introduced to rescale the plastic zone size, whereupon good agreement between theory and experiment was achieved.

Experimental measurement of polyethylene chain modulus by scanning force microscopy

Nanoindentation technique and scanning force microscopy have been used to measure directly the polyethylene modulus along the chain axis. Single crystals of polyethylene were employed in order to obtain well-aligned chain segments. To minimize effects of scanner creep, a Z scan rate of 3 Hz was employed. The "X Rotate" value of 25 degrees was selected to eliminate effects of lateral tip motion. The results were analyzed by the Oliver -Pharr method for which direct observation and measurement of the contact area are not required. Considering the influence of tip roundness on the projected contact area, the nanoindentation results were analyzed by the Sawa method. The chain modulus obtained from the thinner polyethylene single crystal sample was 204 +/- 21 GPa by the Oliver-Pharr method and 168 +/- 17 GPa by the Sawa method. The lower values than expected were due to substrate effects and anisotropy of chain deformation during nanoindentation. An extrapolation of the chain modulus obtained by various strains to zero nanoindentation eliminated the effect of substrate and anisotropy of chain deformation. The corresponding chain modulus obtained from the thicker sample was 278 GPa by the Oliver-Pharr method and 267 GPa by the Sawa method, respectively, in better agreement with the value of 340 Cpa determined theoretically. (C) 2001 Elsevier Science Ltd. All rights reserved.

MECHANICAL-PROPERTIES OF PHENOLPHTHALEIN POLYETHER KETONE - YIELD STRESS, YOUNGS MODULUS, AND FRACTURE-TOUGHNESS

A series of tensile and three-point bending studies was conducted at various temperatures and loading rates using phenolphthalein polyether ketone (PEK-C). Yield stress, Young's modulus, fracture toughness, and crack opening displacement data were obtained for various conditions. In general, both yield stress and Young's modulus increase with decreasing temperature. However, the relationships between fracture toughness, loading rate, and temperature are very complex. This behavior is due to the simultaneous intersection of viscoelasticity and localized plastic deformation. The increased yield stress is the main factor contributing to the reduction in fracture toughness and crack opening displacement. The relationship between fracture toughness and yield stress are discussed. (C) 1995 John Wiley and Sons, Inc.