Asymptotic analysis of growing plane strain tensile cracks in elastic-ideally plastic solids

An exact asymptotic analysis is presented of the stress and deformation fields near the tip of a quasistatically advancing plane strain tensile crack in an elastic-ideally plastic solid. In contrast to previous approximate analyses, no assumptions which reduce the yield condition, a priori, to the form of constant in-plane principal shear stress near the crack tip are made, and the analysis is valid for general Poisson ratio ν. Specific results are given for ν = 0.3 and 0.5, the latter duplicating solutions in previous work by L.I. Slepyan, Y.-C. Gao and the present authors. The crack tip field is shown to divide into five angular sectors of four different types ; in the order in which these sweep across a point in the vicinity of the advancing crack, they are : two plastic sectors which can be described asymptotically (i.e., as r → 0, where r is distance from the crack tip) in slip-line terminology as ‘constant stress’ and ‘centered fan’ sectors, respectively ; a plastic sector of non-constant stress which cannot be described asymptotically in terms of slip lines; an elastic unloading sector; and a trailing plastic sector of the same type as that directly preceding the elastic sector. Further, these four different sector types constitute the full set of asymptotically possible solutions at the crack tip. As is known from prior work, the plastic strain accumulated by a material point passing through such a moving ‘centered fan’ sector is O(ln r) as r → 0 ; it is proved in the present work that the plastic strain accumulated by a material point passing through the ‘constant stress’ sector ahead of a growing crack must be less singular than In r as r → 0. As suggested also in earlier studies, the rate of increase of opening gap δ at a point currently at a distance r behind, but very near, the crack tip is given for crack advance under contained yielding by

$\text{δ}\text{?}\text{=}\text{α}\text{J}\text{?}\text{σ}{}_0\text{+β(}\text{σ}{}_0\text{E}\text{)}\text{a}\text{?}\text{ln(}\text{R}\text{r}\text{)}$

where a is crack length, σ0 is tensile yield strength, E is Young's modulus, J is the value of the J-integral taken in surrounding elastic material, and the parameters α and R are undetermined by the asymptotic analysis. The exact solution for ν = 0.3 gives β = 5.462, which agrees very closely with estimates obtained from finite element solutions. An approximate analysis based on use of slip line representations in all plastic sectors is outlined in the Appendix.     

Synthesis and characterisation of luminescent rhenium tricarbonyl complexes with axially coordinated 1,2,3-triazole ligands

A series of 1-alkyl-4-aryl-1,2,3-triazoles (1-methyl-4-phenyl-1,2,3-triazole (1a); 1-propyl-4-phenyl-1,2,3-triazole (1b); 1-benzyl-4-phenyl-1,2,3-triazole (1c); 1-propyl-4-p-tolyl-1,2,3-triazole (1d)) have been prepared through a one-pot procedure involving in situ generation of the alkyl azide from a halide precursor followed by copper catalysed alkyne/azide cycloaddition (CuAAC) with the appropriate aryl alkyne. Cationic Re(I) complexes [Re(bpy)(CO)(3)(1a-d)]PF(6) (2a-d) were then prepared by stirring [Re(bpy)(CO)(3)Cl] with AgPF(6) in dichloromethane in the presence of ligands 1a-d. X-ray crystal structures were obtained for 2a and 2b. In the solid state, 2a adopts a highly distorted geometry, which is not seen for 2b, in which the plane of the triazole ligand tilts by 13° with respect to the Re-N bond as a result of a π-stacking interaction between the Ph substituent and one of the rings of the bpy ligand. This π-stacking interaction also results in severe twisting of the bpy ligand. Infrared spectra of 2a-d exhibit ν(CO) bands at ～2035 and ～1926 cm(-1) suggesting that these ligands are marginally better donors than pyridine (ν(CO) = 2037, 1932 cm(-1)). The complexes are luminescent in aerated dichloromethane at room temperature with emission maxima at 542 to 552 nm comparable to that of the pyridine analogue (549 nm) and blue shifted relative to the parent chloride complex. Long luminescent lifetimes are observed for the triazole complexes (475 to 513 ns) in aerated dichloromethane solutions at room temperature.     

Δ Degrees of Freedom in Trinuclei with the Argonne V28Q Model

The effects of explicit Δ degrees of freedom on trinuclear binding energy and structure are investigated using the Argonne V28Q Δ model. Separate dispersive effects, one- and two-Δ three-body force effects, and one- and two-Δ probabilities are determined for the triton. Some new results are also given for the Hannover and Argonne V28 Δ models, and V28Q trinuclear Δ effects are compared with those of these other models. Considerable consistency among the models is found, suggesting a coherent qualitative picture of trinuclear Δ effects. Received June 8, 1994; accepted for publication September 27, 1994     

Conformally invariant differential operators on Minkowski space and their curved analogues

This article describes the construction of a natural family of conformally invariant differential operators on a four-dimensional (pseudo-)Riemannian manifold. Included in this family are the usual massless field equations for arbitrary helicity but there are many more besides. The article begins by classifying the invariant operators on flat space. This is a fairly straightforward task in representation theory best solved through the theory of Verma modules. The method generates conformally invariant operators in the curved case by means of Penrose's local twistor transport.S.E.R.C. Advanced Fellow and Flinders University Visiting Research Fellow     

Systematic improvement of variational Monte Carlo using Lanczos iterations

We present a new numerical technique which combines the variational Monte Carlo and the Lanczos methods without suffering from the fermion sign problem. Lanczos iterations allow systematic improvement of trial wavefunctions while Monte Carlo sampling permits treatment of large lattices. As in the usual Lanczos method we find it useful to symmetrize the starting wavefunction in order to accelerate convergence. We apply our method to the 2D AFM Heisenberg model in the fermionic electron representation, which allows us to compare with results from the equivalent bosonic spin representation. Using d-wave RVB states as starting wavefunctions shows that after only one iteration between 70 and 80% of the difference between the variational energy and the ground state energy (as determined by GFMC) is recovered, and a similar improvement is observed in the second iteration. Leaving the spin-singlet sector by introducing antiferromagnetic correlations reduces the symmetry and the relative improvement in energy drops below 50% for one iteration. Our method allows us also to see trends in observables. Relative to the d-wave RVB states we find an enhancement in the spinspin correlations, consistent with the expectation that the true ground state has long-range order.     

Farbstoffe

Ohne Zusammenfassung     

An interlaboratory study of potassium determination in rocks and minerals

Seven laboratories took part in this interlaboratory study which was part of an investigation of the flame-speetrometric determination of potassium in rocks and minerals suitable for potassium-argon age-measurement. Three of these laboratories determined potassium in the following five international reference rocks: tonalite T-1, basalt BCR-1, andesite AGV-1, granite G-2, and granodiorite GSP-1. The other five samples (with the number of laboratories analysing them in parentheses) were: a chlorite rock (7), an altered basic igneous rock (5), an altered basaltic andesite (5), a biotite (6) and a potassium feldspar (7). Details of sample preparation and methods of analysis are given; no laboratory used exactly the same method as any of the other six laboratories. Results have been examined by analysis of variance; larger relative between- and within-laboratory variations occurred for the two samples containing less than 0.1% potassium than for seven of the eight other (higher potassium) samples; between-laboratory variations for the basalt BCR-1 and, to a lesser extent, the andesite AGV-1, were high and of similar magnitude to those for the samples containing less than 0.1% potassium. The causes of any poor interlaboratory agreement in the present study are considered.     

Thermodynamics of the quasi-static growth of Griffith cracks

Restrictions on the quasi-static extension, or healing, of Griffith cracks are developed in the framework of irreversible thermodynamics. It is emphasized that thermodynamics requires that (G ? 2γ)ι ? 0, where ι is crack speed, G the Irwin energy release rate, and 2γ the work of reversible separation of the surfaces to be fractured. Implications for ‘lattice trapping’ models of cracks and for thermally-activated crack motion are discussed, as are the effects on crack growth and healing of a surface-reactive environment, in which case γ must be given a definition appropriate to adsorption-altered surface properties.     

Oscillatory disruptions in the Alcator C tokamak

Periodic disruptions were observed which persisted for as long as 400 ms during plasma discharges. Soft X-ray emissions, T_e, n_e, impurity radiation and plasma position showed the pulsations. The abrupt collapse in X-ray signal (1–2 ms; period ∽10 ms) encompassed a large fraction of the plasma cross section. Plasma conditions associated with the onset of this pattern are examined.     

Elastic scattering of electrons by hydrogen molecules at intermediate energies

Several quantum mechanical calculations of differential cross sections for elastic scattering of electrons by H₂ are compared with the recent experiments by Williams.