A BOUNDARY ELEMENT MODEL OF PLASTICITY-INDUCED FATIGUE CRACK CLOSURE

This paper describes a plane stress boundary element model of plasticity-induced fatigue crack closure. A simple Dugdale-type strip yield zone is used and quadratic programming techniques are employed to establish crack shape, stress and plastic deformation. The technique is extremely effective and the model can be readily implemented on a personal computer. Predictions of crack closure behaviour are produced for cracks growing under constant amplitude loading, and also following an overload or overload/underload cycle. These results are compared with an empirical R-ratio correction due to Walker and with experimental measurements taken from the literature. The model is found to give good predictions of crack behaviour under constant amplitude loading. Predictions for crack closure levels following an overload cycle give qualitative agreement with experimental results; the differences observed may well be due to the different definition of crack closure in the experiments.     

Modelling of growth of three-dimensional cracks by a continuous distribution of dislocation loops

This paper is concerned with a numerical simulation of growth of fatigue cracks in a three-dimensional geometry. A continuous distribution of infinitesimal dislocation loops is employed to model the crack faces, so that the crack problem can be formulated as a set of singular integral equations. A numerical procedure based on an analytical treatment of the associated finite part integral is developed to solve the singular integral equations. The Paris law is then used to predict the rate of crack growth, so that the evolution of the crack shape under fatigue can be traced by a step-by-step algorithm. Various crack growth problems, e.g., the growth of a subsurface crack in a surface treated specimen, are analyzed using the technique, providing new data for several cracks of practical interest.     

INITIATION AND GROWTH OF FRETTING FATIGUE CRACKS IN THE PARTIAL SLIP REGIME

Abstract— —Recent work addressing the problems of fretting fatigue crack initiation and propagation under a carefully controlled axi-symmetric Hertzian contact is described. Both experimental work, enabling the fretting damage, sites of initiation, and crack trajectory to be viewed, and theoretical work, permitting a prediction of those processes are presented. Good correlation between the two strands of work is found. In particular, the initiation criterion proposed by Ruiz, Boddington and Chen for a very different geometry is found to work well, and would seem to indicate its potential as a design tool.     

Large-signal dynamic behavior of distributed-feedback lasersincluding lateral effects

The large-signal behavior of DFB lasers is analyzed, including lateral as well as longitudinal variations in carrier density, photon density, and refractive index. The effective index method and other approximations are used to reduce the complex three-dimensional problem to one dimension. The coupled wave and carrier rate equations are then solved in a self-consistent manner. Lateral spatial carrier hole burning and lateral diffusion are found to affect the relaxation oscillation frequency and damping rate of DFB lasers, depending on their detailed structure. The effective time-averaged linewidth enhancement factor is also affected. In symmetric AR-coated λ/4 phase-shifted lasers the side mode suppression ratio can be deteriorated significantly by lateral spatial hole burning when kL is large     

Partial closure and frictional slip of 3-D cracks

The effects of partial closure and frictional slip of three-dimensional cracks on the stress intensity factors are studied using the eigenstrain method. The formulation, based on the correct modelling of the boundary conditions on the crack faces, is presented separately for partial closure and frictional slip, and applied to two simpler cases: partial closure of a surface-breaking crack normal to the free surface and under a residual stress field; and frictional slip of a completely closed crack under normal and shear tractions. The evolution of crack closure with the increase of crack depth and its influence on the stress intensity factor are examined and compared with a simple model for the first problem. the effect of coefficient of friction between crack faces on the stress intensity factors is investigated for the second problem.     

The preparation and characterisation of crystalline α-zirconium phosphate

Crystalline α-zirconium phosphate has been prepared by four methods. The products have been characterised by chemical and thermal analysis, X-ray and infrared spectroscopy, surface area, porosity and particle size determinations and electron microscopy. A method is recommended for the preparation of crystalline α-zirconium phosphate.     

Analysis of copper grains in damascene trenches after rapid thermal processing or furnace anneals

The microstructures of Cu lines in damascene trenches annealed at temperatures from room temperature to 425°C using both rapid thermal processing (RTP) and furnace annealing were investigated using an array of characterization techniques including transmission electron microscopy (TEM), focused ion beam, scanning electron microscopy (SEM), and electron backscatter diffraction-orientation-imaging microscopy (EBSD-OIM). It was found that the final grain sizes strongly depend on the annealing process used; RTP generated larger grains than furnace annealing. The Cu line electrical resistance correlated with grain size differences observed for RTP and furnace anneals. The ramping rate, not the annealing time, played the critical role in the grain growth process. In either case, a high density of Σ3 coincident site lattice (CSL) twin boundaries was observed in the Cu lines. Forty-five percent of the grain boundaries measured were found to be Σ3 CSL twins, which are differentiated from random high-angle boundaries by having preferred electrical and diffusion properties. The minimum feature dimension of width or height of the damascene trenches limited the average grain size. Prior to the trench height limitation, the average grain size increased linearly with the trench width. The Cu (111) texture became stronger as the trench width increased up to 0.5 μm; for wider trenches, the texture did not increase further.     

The continental lithospheric mantle: characteristics and significance as a mantle reservoir

The continental lithospheric mantle (CLM) is a small-volumed (ca. 2.5% of the total mantle), chemically distinct mantle reservoir that has been suggested to play a role in the source of continental and oceanic magmatism. It is our most easily identifiable reservoir for preserving chemical heterogeneity in the mantle. Petrological and geophysical constraints indicate that the maximum depth of the CLM is ca. 250 km. There is a clear secular variation of CLM composition, such that CLM formed in the last 2 Gyr is less depleted and therefore less dynamically stable than ancient CLM formed in the Archean. We present new trace-element data for kimberlite-hosted lithospheric peridotites and metasomites. These data, combined with other data for spinel peridotites from non-cratonic regions, show that neither hydrous nor anhydrous lithospheric mantle xenoliths make suitable sources for continental or oceanic basalts. Addition of a hydrous phase, either amphibole or phlogopite, to depleted peridotite results in positive Nb and Ti anomalies that are the opposite of those predicted for some flood-basalt sources on the basis of their trace-element abundances. Overall, the Sr and Nd isotopic composition of cratonic and non-cratonic CLM is close to bulk Earth, with cratonic CLM showing small numbers of extreme compositions. Thus, while the CLM is certainly ancient in many locations, its average composition is not significantly 'enriched' over primitive upper mantle, in terms of either radiogenic isotopes or trace elements. These characteristics, plus a change in lithospheric chemistry with depth, indicate that the elemental and isotopic composition of lithospheric mantle likely to be re-incorporated into convecting mantle via delamination/thermal erosion processes is probably not very distinct from that of the convecting mantle. These observations lead us to question the requirement for CLM participation in the source of oceanic magmas and to promote consideration of a mantle that is chemically heterogeneous on all scales. Hf and Nd isotope compositions identify a distinctive source component in deeply derived alkaline volcanics associated with continents. This component cannot be constrained to the CLM but may originate from a deeper reservoir of ancient, subducted oceanic crust stored in the mantle.     

A further corrigendum

A further corrigendum