An X-ray radial distribution study of amorphous calcium phosphate

A series of amorphous calcium phosphate and hydroxyapatite samples synthesized under different preparative conditions were studied by the x-ray radial distribution method. The results indicate that amorphous calcium phosphate has a reproducible structure independent of a wide variety of preparation conditions. Detail in the RDF of amorphous calcium phosphate diminishes rapidly for atomic separations greater than 9.5 A, suggesting ordered domains or clusters of about this size. It is proposed that amorphous calcium phosphate is an amorphous cluster or microcrystallite material rather than a random network structure. Small-angle x-ray scattering and dehydration studies indicate that the ACP water of constitution is interstitial to the domains. Finally, hydroxyapatite prepared at 25°C has lower perfection of atomic order than material prepared at 100°C.     

Stress corrosion cracking of Al-Zn-Mg alloy AA-7039 by slow strain-rate method

The stress corrosion behaviour of Al-Zn-Mg alloy AA-7039 in an aqueous 3.5 wt % Nad solution (pH=1) was studied with the specimens under constant strain rate as function of ageing state and cold working. The tests were carried out at temperatures of 30 and 45°C and strain rates between 7.6×10^–7 and 7.6×10^–6 sec^–1 and the apparent activation energy for mechanical deformation in oil and stress corrosion cracking (SCC) process in NaCl solution were determined. The fracture energy in NaCl solution under constant strain rate, as compared with experiments in oil, was lowered in the overaged specimens and markedly lowered in sequence of the peak-aged and the underaged specimens. The values of fracture energy for peak-aged and overaged specimens were nearly similar to those in oil at the higher strain rate of 7.6×10^–6 sec^–1. The relative fracture energy was comparatively lowered in the fine-grained specimens, as compared to coarsegrained specimens. The apparent activation energy for mechanical processes in oil was found to be 103 kJ mol^–1 in the peak-aged and 96.5 kJ mol^–1 in the overaged specimens. Those for SCC processes in NaCl solution were 47.5 kJ mol^–1 in the peak-aged and 51.5 kJ mol^–1 in the overaged specimens. The results suggest that stress corrosion (SC) cracks are initiated by electrochemical dissolution of grain boundaries (gbs) and propagated by mechanical processes such as creep.     

The asymptotic behaviour of second-order stochastic Volterra series models of slow drift response

The paper presents a detailed study of the structure and asymptotic behaviour of a second-order stochastic Volterra series model of the slow drift response of large volume compliant offshore structures subjected to random seas. A long standing challenge has been to develop efficient and accurate methods for calculating the response statistics of compliant offshore structures to random seas. Recent work has revealed that the statistical properties of the response process, which consist of a linear, first-order component and a nonlinear, second-order component, is surprisingly complex. The goal of the research work presented here is to complement efforts to develop numerical procedures to calculate the statistics of the response process.     

An asymptotic model for elastoplasticity

This paper describes the asymptotic analysis of a model for one-dimensional elastoplastic compression at high stress. We identify a new wave phenomenon that can occur when a singular asymptotic limit reduces the order of a nonlinear hyperbolic system.     

An asymptotic theory of sandwich plates

Elastic plates can be described by a two-dimensional theory, if the characteristic length of the stress state along the plate, l, is much larger than the plate thickness, h. If all elastic moduli of a laminated plate are of the same order, no matter how many lamina the plate has, then the normal to the mid-surface of the plane remains normal in the course of deformation, and the deformation of the plate can be described by the classical plate theory. The situation changes, when the elastic moduli are of different orders of magnitude. This occurs, in particular, for the hard-skin plates, i.e. the sandwich plates the faces of which are very hard. Due to the low deformability of the skin, normal fibers cannot remain normal to the mid-surface in the course of deformation. The deviations are characterized by transverse shear. The difference from the theory of transverse shear, introduced by Timoshenko and Reissner, is that the transverse shear effects are not the corrections to classical plate theory; they are the effects of the leading order. That is caused by the presence of an additional small parameter, the ratio of elastic moduli of the core and the skin. The additional small parameter changes the character of the asymptotics. In this paper, the governing two-dimensional equations for sandwich plates are derived by an asymptotic analysis of linear three-dimensional elasticity. We show that the classical plate theory works only within a certain range of parameters. Beyond that range the asymptotic theory differs from the classical one. We focus especially on the hard-skin plates, but obtain also the universal relations, which can be applied for any values of elastic moduli and the relative thickness of the skin and the core. As an example four-point bending problem is discussed.     

An asymptotic theory of guided waves

Summary A procedure is developed for finding asymptotic expansions at high frequencies of the solutions of Helmholtz's equation subject to boundary conditions on certain guiding surfaces. This includes surface waves along surfaces of rather general shapes, and wave-guide modes in a class of non-uniform waveguides. Guided waves have some features of both eigenvalue (mode) and radiation problems. The method of this paper combines the two techniques, finding modes that propagate along rays in the general waveguide region and whose amplitudes vary along the paths of propagation. The phases of these modes are found from two coupled equations, one analogous to the eiconal equation of geometrical optics, and the other analogous to the eigenvalue or transverse resonance equation of waveguides. The amplitudes are asymptotic series in inverse powers of the wavenumber, and the coefficients satisfy a set of ordinary differential equations that can be solved recursively. It is found that the ray paths are not only functions of the refractive index (as in pure radiation problems), but depend also on the local geometrical properties of the guiding surface.     

Necking and radial cracking around perforations in thin sheets at normal incidence

The formation of multiple necks and cracks around perforations in ductile materials is investigated. Expressions are obtained for the number of plane-strain radial necks formed by conical penetrators (with or without starter holes in the flat target), and also by round-ended projectiles into flat targets having starter holes or, in plain targets with no starter holes, after fracture of the initial circumferential neck has detached a circular cap of material (“discing”). Likewise, expressions are derived for the number of radial cracks which form subsequently in both cases and lead to “petalling”. The number of cracks is smaller than the number of necks. Experiments seem to agree with the analyses, although accurate counting of necks in thin sheets is illusory.     

An analytical study of two-phase helium flow within a radial rotating duct

A study was made of the behaviour of separated two-phase helium flow within a radial rotating duct. The liquid film thickness, phase velocities, heat-exchange coefficients, pressure and temperature differences were evaluated. The plots obtained for helium flow in thermodynamic equilibrium are used to calculate the radius dependence of pressure and quality at a given rotational frequency and inlet duct conditions. The equilibrium pressure model is presented which describes pressures not too close to the critical values.     

The question of corrosion cracking of metals under a constant load and slow tension

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 5, pp. 47–51, September–October, 1990.     

Investigation of caustic stress corrosion cracking of a carbon steel by slow strain rate testing

Abstract

This paper presents results of an experimental investigation of stress corrosion cracking (SCC) of a carbon steel in a typical synthetic Bayer liquor (SBL), employing a slow strain rate testing (SSRT) technique. Fractographic details of SCC crack propagation of specimens tested in SBL and an inert environment have been compared.     

An asymptotic matching approach to shallow-notched structural elements

Fracture in brittle material specimens with V-notches is satisfactorily described assuming as governing parameter the generalized (or notch) stress intensity factor, whose anomalous physical dimensions depend on the notch opening angle. Its critical value, i.e. the generalized toughness, can then be linked to the material strength and toughness according to a number of fracture criteria available in the literature. However, all these criteria provide an infinite failure load as the notch depth tends to zero, this undesirable property being shared with Linear Elastic Fracture Mechanics when applied to vanishing cracks. Aim of the present paper is to overcome this shortcoming. The analysis of the notched specimens is carried out by means of a multiscale approach according to which the problem is solved separately in the region far away from the notch (the outer field) and in the region close to the notch (the inner field). Hence, the asymptotic matching technique can be exploited to achieve the overall solution. Although the procedure is general, i.e. it may be applied to any notch shape, numerical computations refer to sharp V-notches with a re-entrant corner equal to 120°. Comparison with experimental data obtained by testing polystyrene specimens turns out to be more than satisfactory.     

An asymptotic theory of guided waves (II)

Summary A method of obtaining high frequency asymptotic expansions for time harmonic waves propagating in non uniform waveguides is presented. Both ordinary asymptotic expansions, which are not valid near turning points, and uniform expansions which are valid across turning points are presented for various types of boundary conditions. The correspondance between these expansions and the asymptotic expansion of the exact solution of a canonical problem is shown. A numerical example demonstrating the usefulness of this method is presented. This paper is a sequel to reference [1].This paper is based on a thesis submitted by the first author in partial fulfillment of the requirements for the degree of M.Sc. in Engineering Science at Tel Aviv University.     

An asymptotic analysis of dynamic crack growth in rubber

Asymptotic analyses of the mechanical fields in front of stationary and propagating cracks are important for several reasons. For example, they facilitate the understanding of the mechanical and physical state in front of crack tips, and they enable prediction of crack growth. Furthermore, efficient modelling of arbitrary crack growth by use of XFEM (extended finite element method) requires accurate knowledge of the asymptotic crack tip fields. The present study focuses on the asymptotic fields in front of a crack that propagates dynamically in rubber. Static analyses of this type of problem have been made in previous studies. In order to be able to compare the present results with these earlier studies, the constitutive model from Knowles and Sternberg (J. Elast. 3:67–107, 1973) was adopted. It is assumed that viscoelastic stresses become negligible compared with the singular elastic stresses close to the crack tip. The present analysis shows that in materials with a significant hardening, the inertia term in the equations of motion becomes negligible in the asymptotic analysis. However, for a neoHookean type of model, inertia comes into play and causes a maximum theoretical crack speed that equals the shear wave speed.     

爆炸法密实砂土地基(Ⅰ)——研究现状

在软基处理的各种方法中,爆炸法处理松散砂土地基以其快速、经济、简单的优点为人们所认同。迄今爆炸密实法应用于地基的处理已有70多年的历史,适合于处理饱和、松散的砂土地基,但在我国地基处理中应用不多也不常见,相应的理论研究和设计方法的研究远远落后于工程实践的要求。本文从爆炸密实法发展简史、加固机理及密实过程、爆炸能量输入与衰减的函数、设计参数、处理效果评价指标等几个方面对爆炸密实法的历史及研究现状进行了回顾,并对已有的研究成果进行了简要的评述。     

An asymptotic solution for large Prandtl number free convection

Summary The set of ordinary differential equations governing free convection boundary layer flow past an isothermal semi-infinite vertical flat plate is solved for large Prandtl numbers by means of the method of matched asymptotic expansions. The analysis leads to an expression for heat transfer which contains the Prandtl number explicitly and which is very accurate for sufficiently large values of the Prandtl number. On the other hand the analysis also has qualitative assets. Before choosing the mathematical method of solution, the physical aspects of the large Prandtl number free convection boundary layer are investigated. The mathematical solution serves to enlarge our understanding of the physical implications of a free convection boundary layer in a large Prandtl number fluid.Nomenclature a_ij coefficient defined by - b_ij coefficient defined by F_j()=b_0j+b_1j +b_2j ²+.... - c coefficient defined by equation (3) - c_p specific heat - f non-dimensional stream function of inner expansion (7) - f_n n-th perturbation of f - F non-dimensional stream function of outer expansion (15) - g non-dimensional stream function (1) - ¯g acceleration due to gravity - Gr_x local Grashof number:g(T_w–T)x³/v² - h non-dimensional temperature (2) - k coefficient of heat conduction - Nu_x local Nusselt number: - T temperature - T_w wall-temperature - T ambient temperature - u longitudinal velocity - x co-ordinate measuring distance from the leading edge - y co-ordinate measuring distance normal to the plate Greek symbols coefficient of thermal expansion - _i expansion parameter (21) - expansion parameter (22) - _i expansion parameter (33) - expansion parameter (34) - expansion parameter: ^–1/2 - inner similarity co-ordinate (9) - non-dimensional temperature of inner expansion (8) - _n n-th perturbation of - non-dimensional temperature of outer expansion (16) - _n n-th perturbation of - similarity co-ordinate (3) - kinematic viscosity - outer similarity co-ordinate (17) - density - Prandtl number:c_p/k - stream function