Dynamic optical visualization on the interaction between propagating crack and stationary crack

Dynamic interactions between the propagating crack and the static crack in PMMA material are studied by combining high-speed Schardin camera with optical caustic method. A series of dynamic optical bifocal patterns (the specimen-focused image and the off-focused image) around the propagating crack tip and the static crack tip are recorded for PMMA thin strip which contains two collinear-edge-cracks subjected to tensile loading, the variations of the caustic diameter and the distortion of the caustic shape are revealed due to the influence of local stress singularity at the crack tip. Interactions between the moving crack and the static crack are analyzed by means of the evolution of dynamic fracture parameters. The influence of crack interaction on fracture parameters is discussed based on both a K-dominance assumption and a higher order transient crack-tip expansion. These results will be useful to the evaluation of dynamic properties and the design of structures in the cracked polymer material.     

Elastic wave surfaces for the (111) plane of cubic crystals

The nature of inverse velocity surfaces as well as energy surfaces for elastic wave propagation in the (111) plane have been studied for a number of cubic crystals. The sections of inverse velocity surfaces by the (111) plane exhibit six-fold symmetry in all cases. Cuspidal edges are exhibited with a six-fold symmetry by both the slow transverse and fast transverse shear modes in the (111) plane, unlike the case of the (100) and (110) planes for which only the slow transverse shear mode exhibits cuspidal edges. The slow transverse mode energy surface exhibits cuspidal edges along direction or an equivalent symmetry direction. The inverse velocity surfaces of the A-15 compounds exhibit unusually large inflexions for the slow transverse mode, whereas their energy surfaces have large cuspidal edges which intersect each other resulting in common regions of cusps.     

Crack propagation in amorphous polymers and their composites

The fracture energy of a polymer depends strongly on the viscoelastic responses of the material, and therefore is a function of temperature and crack velocity. The toughness of a composite is determined by the way in which the reinforcing filler modifies the energy dissipating mechanisms of the polymeric matrix.

The fracture toughness of a variety of polymeric glasses and their composites with glass beads, glass fibers, and rubber particles was measured. The velocity of rapidly moving cracks and the crack propagation rates under controlled loading conditions were also measured.

It was found that the crack propagation velocities in unfilled and glass bead filled materials were controlled by the longitudinal stress waves in the matrix and that the only effects of the glass beads were to blunt the crack tip and limit the viscous deformation. The effect on fracture toughness was relatively small and either positive or negative, depending on which of the above two factors dominated.

The presence of rubber particles as a second phase lowered terminal crack propagation velocities and greatly increased the fracture toughness, indicating a crack retarding effect of the rubber particles. This is related to the induction of crazes in the matrix by the rubber phase.

Glass fibers had a tendency to bridge the tip of a propagating crack, thereby greatly increasing the fracture toughness. In this case the work of fracture comes from a combination of the elastic strain energy stored in the fibers, the energy dissipated in debonding the fibers from the matrix, and the fracture energy of the matrix itself.     

Spin-axis-dependent magnetic properties of FePt and CoPt

A theoretical study of the magnetic properties of the CoPt and FePt ordered alloys has been performed. The calculation is done as a function of the spin-quantization axis by means of both the local spin density and the generalized-gradient approximations in conjunction with the full-potential linear muffin–tin orbital method. Both approximations produced similar results for the FePt and CoPt compounds. The band structure and the total density of states have been calculated and it was confirmed that all electronic states contribute to the magneto-crystalline anisotropy energy; the magnetization axis is along the [0 0 1] direction. The Fe and Co orbital magnetic moments decrease with respect to the angle γ between the [0 0 1] axis and the spin quantization axis, but for the [1 0 0] axis the orbital moment is comparable to the [0 0 1] moment. The Pt orbital moments are of the same order of magnitude as those of Fe and Co moments due to the large spin–orbit splitting parameter of Pt and show a similar behavior with the angle γ.     

Photoelastic investigation of interfacial fracture between orthotropic and isotropic materials

Static and dynamic fracture of interfaces between orthotropic and isotropic materials were studied using photoelasticity. In this study, a bi-material specimen made of PSM-1^® and Scotchply^® 1002, a unidirectional glass fiber reinforced epoxy composite, was used. Two fiber orientations, fibers parallel to the interface (α=0°) and fibers perpendicular to the interface (α=90°) were considered. Center crack bi-material specimens having different crack lengths were loaded quasi-statically and the full-field isochromatics were recorded using a digital camera. The complex stress intensity factor corresponding to each crack length was calculated from the isochromatics and the values were compared to that obtained from boundary collocation method. Dynamic interfacial fracture was studied with an edge crack bi-material geometry for the two different fiber orientations. The isochromatics around the propagating crack were recorded using a digital high-speed camera. The fracture parameters such as crack speed, complex stress intensity factor and energy release rate were extracted from the isochromatics using the asymptotic stress field equations. The complex stress intensity factor obtained from the static experiments was in close agreement with that calculated using the boundary collocation method. The results also indicated that the fiber orientation with respect to the interface influences the fracture parameters for stationary and propagating cracks.     

Surface gravity waves in deep fluid at vertical shear flows

Special features of surface gravity waves in a deep fluid flow with a constant vertical shear of velocity is studied. It is found that the mean flow velocity shear leads to a nontrivial modification of the dispersive characteristics of surface gravity wave modes. Moreover, the shear induces generation of surface gravity waves by internal vortex mode perturbations. The performed analytical and numerical study show that surface gravity waves are effectively generated by the internal perturbations at high shear rates. The generation is different for the waves propagating in the different directions. The generation of surface gravity waves propagating along the main flow considerably exceeds the generation of surface gravity waves in the opposite direction for relatively small shear rates, whereas the latter wave is generated more effectively for high shear rates. From the mathematical standpoint, the wave generation is caused by non-self-adjointness of the linear operators that describe the shear flow.     

Polarization of plane wave propagating inside elastic hexagonal system solids

Based on the reported physical parameters for hexagonal system solids,we have calculated the effects of anisotropy on polarization of plane P-wave propagation.Herein we report the results of calculations and the newly observed physical phenomena.It is found that,for a given propagation,if the polarization is parallel to the wave vector,so also to the Poynting vector.In such a case,the phase velocity is identical to the energy velocity;the quasi P-wave degenerates to a pure P-wave along the propagation.It is also noted that if the polarization is parallel to the Poynting vector but not to the wave vector,the propagating wave cannot be a pure P-wave.Furthermore,the polarization in a quasi P-wave may deviate from the wave vector for more than 45°,but the deviation from the Poynting vector is always less than 45°.The energy velocity of a quasi SV-wave can be larger than that of the quasi P-wave in some propagation directions,even though the phase velocity of a quasi SV-wave may never be larger than either the phase velocity or energy velocity of the quasi P-wave.Finally,in case of parameters ε=0 and δ*≠0,the polarization of a quasi P-wave has an observed symmetry at a 45°phase angle.The anisotropy of a hexagonal system solid determines if a pure P-wave can be created and what the propagation direction is for a plane wave propagating inside such a hexagonal system solid.     

Transverse-longitudinal coherence function of a sound field for line-of-sight propagation in a turbulent atmosphere

Using the narrow-angle and Markov approximations, a formula for the transverse-longitudinal coherence function of a sound field propagating in a turbulent atmosphere with temperature and wind velocity fluctuations is derived. This function, which applies to observation points that are arbitrarily located in space, generalizes the transverse coherence function (coherence when the observation points are in a plane perpendicular to the sound propagation path), which has been studied extensively. The new result is expressed in terms of the transverse coherence function and the extinction coefficient of the mean sound field. The transverse-longitudinal coherence function of a plane sound wave is then calculated and studied in detail for the Gaussian and von Kármán spectra of temperature and wind velocity fluctuations. It is shown, for relatively small propagation distances, that the magnitude of the coherence function decreases in the longitudinal direction but remains almost constant in the transverse direction. On the other hand, for moderate and large propagation distances, the magnitude of the coherence decreases faster in the transverse direction than in the longitudinal. For some parameters of the problem, the coherence function has relatively large local maxima and minima as the transverse and longitudinal coordinates are varied. With small modifications, many results obtained in the paper can be applied to studies of electromagnetic wave propagation in a turbulent atmosphere.     

Selective role of bainitic lath boundary in influencing slip systems and consequent deformation mechanisms and delamination in high-strength low-alloy steel

We elucidate here the deformation behaviour and delamination phenomenon in a high-strength low-alloy bainitic steel, in terms of microstructure, texture and stress evolution during deformation via in situ electron back-scattered diffraction and electron microscopy. Furthermore, the selective role of bainitic lath boundary on slip systems was studied in terms of dislocation pile-up and grain boundary energy models. During tensile deformation, the texture evolution was concentrated at {1 1 0}<1 1 1> and the laths were turn parallel to loading direction. The determining role of lath on the deformation behaviour is governed by length/thickness (l/t) ratio. When l/t > 28, the strain accommodates along the bainite lath rather than along the normal direction. The delamination crack initiated normal to (0 1 1) plane, and become inclined to (0 1 1) plane with continued strain along (0 1 1) plane and lath plane. This indicated that the delamination is not brittle process but plastic process. The lack of dimples at the delaminated surface is because of lack of strain normal to the direction of lath. The delaminated (0 1 1) planes were associated with cleavage along the (1 0 0) plane.     

A high-speed photographic study of fast cracks in shocked diamond

Six fracture surfaces have been observed extending at velocities between c_R (the Rayleigh wave velocity) and 1.3c_R in high-speed photographs of four diamond specimens. The diamonds were embedded in a transparent polymer and shocked in plate impact experiments. The measured velocities exceed limiting velocities proposed in theoretical and practical studies of single mode I cracks in diamond. The fracture surfaces probably extend by initiation and coalescence of multiple tensile fractures along a single cleavage plane. This mechanism is dependent on the suppression of cracks branching from the {111} growth plane in diamond and considers the population of flaws near a propagating crack tip.     

Local adsorption sites and bondlength changes in Ni(1 0 0)/H/CO and Ni(1 0 0)/CO

The local adsorption geometry of CO adsorbed in different states on Ni(1 0 0) and on Ni(1 0 0) precovered with atomic hydrogen has been determined by C 1s (and O 1s) scanned-energy mode photoelectron diffraction, using the photoelectron binding energy changes to characterise the different states. The results confirm previous spectroscopic assignments of local atop and bridge sites both with and without coadsorbed hydrogen. The measured Ni–C bondlengths for the Ni(1 0 0)/CO states show an increase of 0.16 ± 0.04 Å in going from atop to bridge sites, while comparison with similar results for Ni(1 1 1)/CO for threefold coordinated adsorption sites show a further lengthening of the bond by 0.05 ± 0.04 Å. These changes in the Ni–CO chemisorption bondlength with bond order (for approximately constant adsorption energy) are consistent with the standard Pauling rules. However, comparison of CO adsorbed in the atop geometry with and without coadsorbed hydrogen shows that the coadsorption increases the Ni–C bondlength by only 0.06 ± 0.04 Å, despite the decrease in adsorption energy of a factor of 2 or more. This result is also reproduced by density functional theory slab calculations. The results of both the experiments and the density functional theory calculations show that CO adsorption onto the Ni(1 0 0)/H surface is accompanied by significant structural modification; the low desorption energy may then be attributed to the energy cost of this restructuring rather than weak local bonding.     

Impulsive fracture of silicon by elastic surface pulses with shocks

During nonlinear evolution of surface acoustic waves (SAWs) stress increases with propagation, and may cause fracture of brittle materials. This effect was used to evaluate the strength of crystalline silicon with respect to impulsive load in the nanosecond time scale without using seed cracks. Short SAW pulses propagating in the [11(macro)2] direction on the Si(111) plane induce fracture at significantly lower SAW amplitudes than the mirror symmetric wave propagating in the [112(macro)] direction. This effect is explained by the differences in elastic nonlinearity of the two propagation directions.     

Molecular dynamics simulation of brittle fracture in silicon

Brittle fracture in silicon is simulated with molecular dynamics utilizing a modified embedded atom method potential. The simulations produce propagating crack speeds that are in agreement with previous experimental results over a large range of fracture energy. The dynamic fracture toughness is found to be equal to the energy consumed by creating surfaces and lattice defects in agreement with theoretical predictions. The dynamic fracture toughness is approximately 1/3 of the static strain energy release rate, which results in a limiting crack speed of 2/3 of the Rayleigh wave speed.     

Hydrodynamic instability of premixed flame propagating in narrow planar channel in the presence of gas flow

The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.     

Crack growth on the basal plane in single crystal zinc: experiments and computations

Crack propagation on the basal planes in zinc was examined by means of in situ fracture testing of pre-cracked single crystals, with specific attention paid to the fracture mechanism. During quasistatic loading, crack propagation occurred in short bursts of dynamic crack extension followed by periods of arrests, the latter accompanied by plastic deformation and blunting of the crack-tip. In situ observations confirmed nucleation and propagation of microcracks on parallel basal planes and plastic deformation and failure of the linking ligaments. Pre-existing twins in the crack path serve as potent crack arrestors. The crystallographic orientation of the crack growth direction on the basal plane was found to influence both the fracture load as well as the deformation at the crack-tip, producing fracture surfaces of noticeably different appearances. Finite element analysis incorporating crystal plasticity was used to identify dominant slip systems and the stress distribution around the crack-tip in plane stress and plane strain. The computational results are helpful in rationalizing the experimental observations including the mechanism of crack propagation, the orientation dependence of crack-tip plasticity and the fracture surface morphology.     

Dissipative viscoplastic deformation in dynamic fracture: tip blunting and velocity selection

Dynamic fracture in a wide class of materials reveals a "fracture energy" Gamma much larger than the expected nominal surface energy due to the formation of two fresh surfaces. Moreover, the fracture energy depends on the crack velocity, Gamma=Gamma(upsilon). We show that a simple dynamical theory of viscoplasticity coupled to asymptotic pure linear elasticity provides a possible explanation to the above phenomena. The theory predicts tip blunting characterized by a dynamically determined crack tip radius of curvature. In addition, we demonstrate velocity selection for cracks in fixed-grip strip geometry accompanied by the identification of Gamma and its velocity dependence.     

Scattering of electromagnetic waves from nonlinear thin dielectric coatings

In this paper the reflection and diffraction properties of nonlinear thin dielectric coatings are investigated. A quite simple geometry consisting of two semi-infinite homogenous linear spaces separated by a non-linear coating is considered. An incident plane wave propagating along the z direction towards the nonlinear thin coating is taken. The nonlinear thin coating is divided into elementary sectors, within each one of which one propagating and one reflected wave exists. The boundary conditions are then applied in order to develop an efficient numerical alogirthm to study the properties of the nonlinear thin coating.     

The instability of streaming fluids with fine dust in porous medium

The instability of the plane interface between two uniform, superposed, and streaming fluids permeated with suspended particles through porous medium is considered. The effect of a uniform horizontal magnetic field on the problem is also studied. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored, whereas for perturbations in all other directions there exists instability for a certain wavenumber range. The instability of the system is postponed by the presence of magnetic field. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference in streaming velocities and the Alfvén velocity. The suspended particles do not affect the above results.     

Hydromagnetic instability of streaming fluids in porous medium

The instability of the plane interface between two uniform, superposed, electrically conducting and counter-streaming fluids through a porous medium is considered in the presence of a horizontal magnetic field. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored. For perturbations in all other directions there exists instability for a certain wavenumber range. The instability of this system is postponed by the presence of magnetic field. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference between the streaming velocities and the Alfvén velocity.This research forms a part of the research project awarded to the first author (R.C.S.) by the University Grants Commission.     

Interactive contribution of grain size and grain orientation to coercivity of melt spun ribbons

During melt spinning process, the improvement of certain grain orientation and the refinement of grain size with surface velocity have interactive and contradictory effects on the magnetic properties. The contributions of these effects have seldom been taken into account and they were discussed in this paper via Fe-2, 4, 6.5 wt% Si alloys. Heat treatment at 1173 K for 1 h was performed to show the annealing impact. The X-ray diffraction patterns show that the high surface velocity and heat treatment increase the intensity ratio of line (2 0 0) to (1 1 0) of A2 phase. The (2 0 0) line corresponds to (2 0 0) plane in 〈0 0 1〉 direction, easy magnetization direction of α-Fe phase in Fe-Si alloy. The improvement of this grain orientation with the surface velocity decreases the coercivity, which should increase due to the grain refinement. It is revealed that the 〈0 0 1〉 texture promoted by the anisotropic heat release during melt spinning process is one factor to improve the magnetic properties and should be considered when preparing soft magnetic materials.