Viscosity-induced mode splitting and potential energy criterion for mode stability

This paper points out that viscosity can induce mode splitting in a uniform infinite cylinder of an incompressible fluid with self-gravitation, and that the potential energy criterion cannot be appropriate to all normal modes obtained, i.e., there will be stable modes with negative potential energy (<0). Therefore the condition >0 is not necessary, although sufficient, for the stability of a mode in an incompressible static fluid or magnetohydrodynamics (MHD) system, which is a correction of both Hare's [Philos. Mag. 8, 1305 (1959)] and Chandrasekhar's [Hydrodynamic and Hydromagnetic Stability (Oxford U.P., Oxford, 1961), p. 604] stability criterion for a mode. These results can also be extended to compressible systems with a polytropic exponent.

Initiation and propagation of short fatigue cracks in a weld metal

Fatigue tests were performed using a purpose designed triangular shaped specimen to investigate the initiation and propagation of short fatigue cracks in a weld metal. It was observed that short fatigue cracks evolved from slip bands and were predominantly within ferrite grains. As the test progressed, the short crack density increased with minor changes in crack length. The growth of short cracks, in the early stage resulted mainly from coalescence with other existing cracks. The mechanism of short crack behaviour is discussed.

Prediction of mixed-mode cracking direction in random, short-fibre composite-materials

The prediction of cracking direction in composite materials is of significance to the design of composite structures. This paper presents several methods for predicting the cracking direction in the double grooved tension-shear specimen which gives mixed-mode cracking. Five different criteria are used in this analysis: two of them have been used by other investigators and the others are proposed by the present authors. The strain energy density criterion proposed by G.C. Sih is modified to take account of the influence of the anisotropy of the strength on the direction of crack. The two failure criteria of Tsai-Hill and Norris are extended to predict the crack orientation. The stress distributions in the near-notch zone are calculated by using the 8-node quadrilateral isoparametric finite element method. The predictions of all the criteria except one are in good agreement with the experimental measurement. In addition, on the basis of the FEM results, the size of the zone in which the singular term is dominant is estimated.

Additional response: Additional discussion of “Mixed mode ductile fracture using the strain energy density criterion”

boundary-layer flows, the skin friction and wall heat-transfer are higher and the

Theory of local mode excitation in polyatomics by frequency-modulated lasers

that the Stokes-interaction relation is reasonable qualitatively but not correct

Effect of grain size on slow fatigue crack propagation and plastic deformation near crack tip

Fatigue crack growth and its threshold are investigated at a stress ratio of 0.5 for the three-point bend specimen made of Austenitic stainless steel. The effect of grain size on the crack tip plastic deformation is investigated. The results show that the threshold value Δkth increases linearly with the square root of grain size d and the growth rate is slower for materials with larger grain size. The plastic zone size and ratio for different grain sizes are different at the threshold. The maximum stress intensity factor is kmax and σys is the yield strength. At the same time, the characteristics of the plastic deformation development is discontinuous and anti-symmetric as the growth rate is increased from 2·10—8 to 10−7 mm/cycle.

Evolution and propagation of density waves on galactic disk .1. General evolution equation of wavelet and discussion of its solution

This paper presents a general self-consistent theory of evolution and propagation of wavelets on the galactic disk. A simplified model for this theory, i. e. the thin transition-layer approximation is proposed.There are three types of solutions to the basic equation governing the evolution of wavelets on the disk: (ⅰ) normal propagating type; (ⅱ) swing type; (ⅲ) general evolving type. The results show that the first two types are applicable to a certain domain on the galactic disk and a certain region of the wave number of wavelets. The third is needed to join the other two types and to yield a coherent total picture of the wave motion. From the present theory, it can be seen that the well-known "swing theory" of the G-L sheet model holds only for a certain class of basic states of galaxies.

Evolution and propagation of density waves on galactic disk .2. An approximation of the thin transition layer

In this part of the present work, a simplified model—the thin transition layer theory is proposed. The comparison of this model with the G-L sheet model is made.

Ductile crack propagation with the strain-energy density criterion

The strain energy density criterion is used to characterize subcritical crack growth in a thin aluminum alloy sheet undergoing general yielding. A finite element analysis which incorporates both material and geometrical nonlinear behaviors of the cracked sheets is developed to predict fracture loads at varying crack growth increments. The predicted results are in excellent agreement with those measured experimentally, thus confirming the validity of the strain energy density criterion for characterizing ductile crack propagation.

Mixed-mode fracture mechanisms near the fatigue threshold of aisi-316 stainless-steel

Near threshold, mixed mode (I and II), fatigue crack growth occurs mainly by two mechanisms, coplanar (or shear) mode and branch (or tensile) mode. For a constant ratio of ΔK_I/ΔK_II the shear mode growth shows a self-arrest character and it would only start again when ΔK_I and ΔK_II are increased. Both shear crack growth and the early stages of tensile crack growth, are of a crystallographic nature; the fatigue crack proceeds along slip planes or grain boundaries. The appearance of the fracture surfaces suggest that the mechanism of crack extension is by developing slip band microcracks which join up to form a macrocrack. This process is thought to be assisted by the nature of the plastic deformation within the reversed plastic zone where high back stresses are set up by dislocation pile-ups against grain boundaries. The interaction of the crack tip stress field with that of the dislocation pile-ups leads to the formation of slip band microcracks and subsequent crack extension. The change from shear mode to tensile mode growth probably occurs when the maximum tensile stress and the microcrack density in the maximum tensile plane direction attain critical values.

The asymptotic near-tip solution for mode-iii crack in steady growth in power hardening media

Two local solutions, one perpendicular and one parallel to the direction of solar gravitational field, are discussed. The influence of gravity on the gas-dynamical process driven by the piston is discussed in terms of characteristic theory, and the flow field is given quantitatively. For a typical piston trajectory similar to the one for an eruptive prominence, the velocity of the shock front which locates ahead the transient front is nearly constant or slightly accelerated, and the width of the compressed flow region may be kept nearly constant or increased linearly, depending on the velocity distribution of the piston. Based on these results, the major features of the transient may be explained. Some of the fine structure of the transient is also shown, which may be compared in detail with observations.