Finite element study of an interface crack between an elastic-perfectly plastic solid and a rigid substrate

The near-tip asymptotic stress fields around an interface crack between an elastic-perfectly plastic solid and a rigid substrate are members of a family parameterized by ₀, which depends on the phase angle and magnitude of the complex stress intensity factor and bimaterial properties. A new family of three-sector slip-line solutions is found in addition to the existing two-sector field and the family of four-sector fields. The finite element study confirms the existence of this new family, the two-sector solution, and only one member in the four-sector family. The finite element analysis also confirms the existence of elastic sectors near the interfacial crack tip.     

Dynamic emission of dislocations from a crack tip — a computer simulation

The behavior of dynamic emission of dislocations from the tip of a stationary crack under mode II or mode III loading is examined. A critical stress intensity factor, K _D is assumed for dislocation emission. After emission, the dislocation moves with a velocity which varies with the effective shear stress to the third power. The effective shear stress is due to the applied stress , modified by the presence of the crack and all other dislocations minus the lattice friction stress, ^F. The effects of K _D, , and ^F on the rate of emission, the plastic zone strain rate, the plastic zone size, the dislocation distribution, and the dislocation-free zone are reported.

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Résumé On a examiné le comportement d'une émission dynamique de dislocations depuis l'extrémité d'une fissure stationnaire. On suppose que l'émission de dislocations est caractérisée par un facteur critique d'intensité de constrainte K _D. Après son émission, la dislocation se meut avec une vitesse qui varie avec le cube de la constrainte effective de cisaillement. Celle-ci résulte de la constrainte appliquée , modifiée par la présence de la fissure et de toutes les autres dislocations, et sous déduction de la contrainte de friction du réseau, ^F.On étudie les effects de K _D, et ^F sur la vitesse d'émission des dislocations, la vitesse de déformation plastique, la taille de la zone plastique, la distribution des dislocations, et sur la zone qui en est dépourvue.

     

The Ni3Al-Ni3Cr-Ni3Ru section of the Ni-Cr-Al-Ru system

An investigation is reported of the 75 at% nickel section of the Ni-Cr-Al-Ru system at 1523 and 1273 K. Constitutional data obtained by electron probe microanalysis, X-ray diffraction and microscopical examination are presented as partial isothermal sections. At 1523 K, the major part of the section consists of phase, while the aluminium-rich region contains a and+ region; the extent of the solid solution of chromium and ruthenium in totals ~ 4 at%. The ruthenium-rich corner of the section shows a two-phase region consisting of + ruthenium-rich solid solution. At 1273 K the,+ and + ruthenium regions increase in extent. The/ mismatch values in the equilibrated alloys studied lie in the range ~ –0.08 to –0.39%. Constitutional features of as-cast alloys are also reported.     

Simulating Crack Trajectories from a radially loaded hole

A procedure for determining the trajectory of growth of a crack in the neighbourhood of a stress-raising feature is described, The method relies on first determining the underlying stress field, and then formulating an integral equation along the (generally) curvilinear contour of the crack, which ensures that its surfaces remain traction free. The crack tip stress intensities are calculated, from which an increment of growth is found using the ^max criterion. The technique is then applied to the determination of the growth trajectory for a crack growing from a circular hole loaded by pressing a pin against its boundary.     

Dielectric properties of chemically treated wood

Dielectric properties along the grain for absolutely dried untreated and seven kinds of chemically treated Sitka spruce (Picea sitchensis Carr.) woods were measured. Cole-Cole's circular arc law was applied to the results of the relaxation due to the motions of methylol groups. The following changes were caused by chemical treatments. In polyethylene glycol (PEG) impregnation, the distribution of relaxation times became very narrow, the generalized relaxation time (_m) was considerably decreased, and the relaxation magnitude (₀ – ) was slightly increased. In acetylation, the distribution of relaxation times became very broad, _m was considerably increased, and (₀ – ) was remarkably decreased. In propylene oxide treatment, the distribution of relaxation times became slightly narrow and _m was decreased. _m was slightly decreased in formalization, phenol-formaldehyde (PF) resin treatment and wood methyl methacrylate (MMA) composite. (₀ – ) was decreased in formalization and PF-resin treatment and was hardly changed in wood-MMA composite and heat treatment. The distribution of relaxation times was almost unchanged in formalization, PF-resin treatment, wood-MMA composite and heat treatment.     

Strength of the pyroceram So115M under lengthy static loading

The article presents the results of long-time strength tests of the casting pyroceram SO115M at room temperature by the method of three-point bending. We obtained the power dependence of the time to failure _f on the applied load : _f ^–11.7.Translated from Problemy Prochnosti, No. 1, pp. 102–104, January, 1996.     

On type-II superconductors with a first-order transition at the lower critical field

The free energy of a superconductor in the mixed state is obtained to first order in 1–(T/T _c) and – in terms of the solutions of the Ginzburg-Landau equations for = . The circular cell approximation is used to evaluate the lower critical field and the discontinuity in the magnetization at this field for those type-II materials displaying a first-order transition at the field of first flux penetration; the cases of both singly quantized and doubly quantized vortices are considered. The main result of the numerical calculations is that the critical value of for a first-order transition is identical to the critical value of for an attractive interaction between widely separated vortices.Supported in part by the National Research Council of Canada.     

Heat capacity of titanium hydride at millikelvin temperatures

The heat capacity C of a TiH_1.98 bulk sample in zero and 72 mT magnetic fields has been measured at 8 mKT 600 mK. In zero magnetic field the sample shows metallic behavior. In a magnetic field the protons give an additional nuclear heat capacity contribution, whose value is in good agreement with the calculated one. From our data we also obtain an upper limit for the nuclear spin-lattice relaxation time ₁ and for the molecular hydrogen impurity concentration in the sample. ForT 10 mK, no superconducting or any other phase transition has been observed.     

The edge interface crack

An analysis of a crack lying along an interface between two elastically dissimilar quarter-planes, and breaking the free surface is given. The method of distributed dislocations is employed and the nominal stress field is taken to be uniform along the length of the line of the crack. Models for crack tip behaviour are discussed and it is shown that a simplified quadrature can be used to extract the crack extension force for cases where small-scale contact obtains. Values of the crack extension force are given, displayed on the , diagram.     

A note on the μ-zeros of combinations of cross-product bessel functions

Summary In the problem of diffraction of elastic waves in annular circular, or cylindrical (doubly connected) domains, the zeros of complicated combinations of cross-products of cylinder functions as analytic functions of the index =n+i (in general complex) are required. In this note, the imaginary -zeros of two such combinations of cross-products of two identical doubly connected domains, however with two different boundary conditions on one boundary, are asymptotically computed and graphically displayed. It is shown that even for such a comparison of different boundary conditions, one can obtain with a minimum effort in mathematics asymptotic distributions and the relative dispositions of the respective -zeros. It is then rather simple to determine with a computer the exact positions of the -zeros.

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Zusammenfassung Bei der Behandlung des Beugungsproblems elastischer Wellen in kreisringförmigen oder zylindrischen (zweifach zusammenhängenden) Bereichen werden die Nullstellen komplizierter Produktkombinationen von Zylinderfunktionen benötigt, und zwar als analytische Funktionen ihrer im allgemeinen komplexen Ordnung =n+i . In dieser Arbeit werden die imaginären -Nullstellen zweier solcher Produktkombinationen in zwei identischen, zweifach zusammenhängenden Bereichen, jedoch mit an einem Rand verschiedenen Randbedingungen, asymptotisch berechnet und graphisch dargestellt. Es wird gezeigt, daß man selbst bei einem solchen Vergleich verschiedener Randbedingungen mit einem Minimum an mathematischem Aufwand asymptotische Verteilungen und die relativen Lagen der entsprechenden -Nullstellen erhalten kann. Es ist dann ziemlich einfach, mit Hilfe eines Rechners die exakten Lagen der -Nullstellen zu bestimmen.

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With 1 Figure     

Crack-tip damaged zones in rubber-toughened amorphous polymers: a micromechanical model

The various stages of crack propagation in rubber-toughened amorphous polymers (onset and arrest, stable and unstable growth) are governed by the rate of energy dissipation in the cracktip damaged zone; hence the relationship between the applied stress intensity factorK ₁ and the damaged zone size is of utmost importance. The size of the crack-tip damaged zone has been related toK ₁ via a parameter which is characteristic of the material in given conditions: this factor is proportional to the threshold stress for damage initiation in a triaxial stress field, and has been denoted by ^*. Theoretical values of ^* have been calculated by means of a micromechanical model involving the derivation of the stresses near the particles and the application of damage initiation criteria. The morphology, average size and volume fraction of the rubbery particles have been taken into account together with the nature of the matrix. The calculated values of ^* have been successfully compared with the experimental ones, for a wide set of high-impact polystyrenes (HIPS) and rubber-toughened poly(methyl methacrylate) (RTPMMA).Nomenclature PS; HIPS polystyrene; high-impact polystyrene - PMMA; RTPMMA poly(methyl methacrylate); rubber-toughened PMMA - MI; CS/H; CS/R particle morphologies (multiple inclusion; hard core - rubber shell; rubber core - rigid shell) - K _r;K _g bulk moduli of rubber and glassy materials - G _r;G _g shear moduli of the same materials - v _p particle volume fraction - L mean centre-to-centre distance between neighbouring particles - B; H; W standard names for the dimensions of the compact tension specimen - R _y size of the crack-tip plastic zone in a homogeneous material - h half thickness of the crack-tip damaged zone - r; polar coordinates around the crack tip (Fig. 1) - r;r _p distance from particle centre; particle radius - p normalized distance from the particle (Equation 5) - K ₁;K _1c;K _1p stress intensity factor; critical values ofK ₁ at the onset of and during crack growth - G _1c plane strain energy release rate - _y yield stress in uniaxial tension - _th macroscopic threshold stress for the onset of local damage initiation in a composite material - ^* characteristic parameter (Equation 3) - ⁰; ₁ ⁰ ; ₂ ⁰ ; ₃ ⁰ applied stress tensor and its three principal stresses - ⁰ uniaxial applied stress - ; ₁; ₂; ₃ local stress tensor and its three principal stresses - A tensor which elements are the ratios of those of over those of ⁰ (Equation 4) - v Poisson's coefficient of the matrix - g triaxiality factor of the crack-tip stress field - _e; _p Mises equivalent stress; dilatational stress (negative pressure) - I ₁;I ₂ invariants of the stress tensor - U ₁;U ₂ material parameters for argon and Hannoosh's craze initiation criterion (Equation 12)     

Three-dimensional interactions of a crack front with arrays of penny-shaped microcracks

Three-dimensional interactions of a crack front with arrays of penny-shaped microcracks are considered. The work extends the earlier analysis of 2-D crack-microcrack interactions to the 3-D configurations.After analysing simple elementary interaction events (involving only one microcrack) we solve the interaction problem for a number of sample arrays (containing up to 50 microcracks)-realizations of certain microcrack statistics.Statistical aspects of the problem are examined. The interaction effects are found to fluctuate, even qualitatively (from shielding to amplification) along the crack front: the intervals of reduced stress intensity factors (SIFs) alternate with local peaks of SIFs that enhance local front advances. Thus, no statistically stable effect of stress shielding is found (at least, for the microcrack statistics considered): the toughening by microcracking, if it exists, may be due to a statistics of the microcrack centers which is biased towards shielding configurations or to expenditure of energy on nucleation of new microcracks, rather than elastic interactions with them. Similarly to the 2-D case, stochastic asymmetries in the microcrack field produce noticeable secondary modes on the main crack (i.e., modes II and III under mode I loading); this may be partially responsible for crack kinking and an irregular crack path.The short range interactions (several microcracks closest to the main crack tip) play a dominant role. Their impact on the main crack is quite sensitive to the individual microcrack locations and cannot be adequately reproduced by modelling the short range microcracking zone by an effective elastic material of reduced stiffness.The interaction effects in 3-D are found to be weaker than in 2-D.     

Energy Spectrum of the Random Velocity Field Induced by a Gaussian Vortex Tangle in HeII

Using the Gaussian model of the vortex tangle (VT) arising in the turbulent superfluid Hell, we calculate the energy spectrum E(k) of the 3D random velocity field induced by that VT. If the VT is assumed to be a purely fractal object with Haussdorf dimension H_D, the E(k) is a power-like function E(k)k^-2+HD. A more realistic VT in HeII is a semi-fractal object, behaving as smooth line for small separations R ( is the label coordinate, R is mean curvature) and having a random walk structure for large with H_D=2. For that case calculations give a spectrum E(k) that is k-independent for k smaller than 1/R (but larger than the inverse size of the system) and that scales as k^–1 for larger k. The latter reflects the fact, that for small, scales a vortex filament behaves as a smooth line. Our results agree with recent numerical simulations.     

The critical curve in an antiferromagnetic superconductor with nonmagnetic impurities

The critical curve of a transition of the second kind in an antiferromagnetic superconductor (AFS) with nonmagnetic impurities has been studied. The AFS is described by using the mean-field model given by Nass, Levin, and Grest and assuming a one-dimensional electron band. We find that the points on the critical curve satisfy the thermodynamic stability condition for 0₁/₀5.04 and 0.49H_Q/₀1.64.Here ₁ is the inverse lifetime of a conduction electron for nonmagnetic impurity scattering,H _Q is the antiferromagnetic molecular field, ₀ is the zero-temperature order parameter of a superconductor in the absence ofH _Q and impurities. Further, ₁ and H_Q denote the values of these quantities for points on the critical curve. For ₁/₀>5.04 and H_Q/₀>1.64, the phase transition from the superconducting to the normal state is always of the second kind. Some thermal properties of the system near the critical curve have also been investigated and we find that these depends dramatically on the impurity concentration.     

Fatigue crack growth behaviour of tungsten carbide-cobalt hardmetals

Fatigue crack propagation studies have been carried out on a range of WC-Co hardmetals of varying cobalt content and grain size using a constant-stress intensity factor double torsion test specimen geometry. Results have confirmed the marked influence of mean stress (throughK _max), which is interpreted in terms of static modes of fracture occurring in conjunction with a true fatigue process, the existence of which can be rationalized through the absence of any frequency effect. Dramatic increases in fatigue crack growth rate are found asK _max approaches that value of stress intensity factor ( 0.9K_IC) for which static crack growth under monotonic load (or static fatigue) occurs in these materials. Lower crack growth rates, however, produce fractographic features indistinguishable from those resulting from fast fracture. These observations, and the important effect of increasing mean free path of the cobalt binder in reducing fatigue crack growth rate, can reasonably be explained through a consideration of the mechanism of fatigue crack advance through ligament rupture of the cobalt binder at the tip of a propagating crack.     

Thermodynamic properties of antiferromagnetic superconductors containing nonmagnetic,magnetic, and spin-orbit impurities

Effects of all types of impurities (nonmagnetic, magnetic, and spin-orbit) on an antiferromagnetic superconductor (AFSC) have been investigated by studying the transition temperatureT _c and the specific heat jump. We have assumed a one-dimensional electron band. The impurity scattering is treated within the self-consistent Born approximation. We find that: (a) the molecular fieldH _Q and the magnetic impurities depress superconductivity of AFSC and their pair-breaking effect is additive; (b) the effect of spin-orbit impurities is the same as that of nonmagnetic impurities—these enhance superconductivity by screening the molecular field; and (c) in the extreme dirty limit, the AFSC is described in terms of an effective pair-breaking parameter given by 1/_eff=1/₂+H _Q ² where 1/=1/₁+2/3_so(1/₁, 1/₂, and 1/_so, respectively, are the scattering rates from nonmagnetic, magnetic and spin-orbit impurities).     

A mechanical model of fatigue crack propagation. Report 2

Conclusions The proposed model of fatigue crack propagation based on the solution of the cyclic elastoplastic problem of the stress-strain state [1] makes it possible to take into account the effect of the triaxial stress state on the deformation of the material at the crack tip. The proposed algorithm of calculations of the state of damage on the basis of the principle of linear damage summation and also the agreement between the calculated and experimental data confirm the assumption on the controlling role of low-cycle damage in the mechanics of crack propagation in cyclic loading described from phenomenological positions. The main advantages of the proposed model are:The possibilities of calculating endurance in crack propagation or calculating the crack propagation rate for cases in which the variation of the range of the stress intensity factor along the crack length in structural members takes place at a variable loading asymmetry;the possibilities of describing the effect of loading asymmetry on the fatigue crack-propagation rate using only the strain criterion (Coffin's equation) since the range of the plastic strain intensity at the crack tip is, as shown in [1], a function of not only the range of the stress intensity factor K but also of its maximum value K_max;the possibilities of describing the dependence of K_th on loading asymmetry based on the assumption on the constancy of the size of the structural element for the given material;the possibilities of describing the crack propagation rate in all the three sections of the dL/dN=f(K) diagram, starting with the values K similar to K_th and ending with the value of K at which monotonic quasistatic fracture becomes the controlling process.Translated from Problemy Prochnosti, No. 8, pp. 14–18, August, 1985.     

Ultra-fine particles of amorphous TiO2 studied by means of positron annihilation spectroscopy

Microscopic structures and mechanical properties of amorphous TiO2 ultra-fine particles have been studied by positron annihilation spectroscopy. A positron lifetime of about 1.5 ns was found as the longest lifetime component 3 which is attributed to the ortho-positronium annihilation in open space. The lifetime 3 and the corresponding intensity I3 was independent of atmosphere: vacuum and various gasses. Accordingly, a micro-void is contained inside the particle as the open space. An intermediate lifetime 2 was approximately 0.4 ns. The intensity I2 was strongly affected by the atmosphere. No effect was found for the particles, the surface of which was coated by silicon dioxide film. This component is arisen from the positron annihilation on the particle surface and the particles contain the surface cracks. When the volume of particles packed in an ampoule was decreased by 1/4 times by compression, the longest component as well as the intermediate one disappeared and only the shortest-lifetime component 1 of about 0.24 ns remained. To conclude, the particles are so soft that the micro-voids and the surface cracks are collapsed by compression.     

Transverse acoustic impedance of normal liquid3He

Both the real and imaginary parts of the transverse acoustic impedance of normal liquid³He have been measured at excitation frequencies of 10 and 30 MHz, fluid pressures from 0.7 to 27 bar, and temperatures from 3 mK to 1 K. The impedance is obtained from the changes in resonance frequency and Q of a quartz crystal, which is electrically driven to oscillate in a thickness shear mode while immersed in liquid³He. These results are compared with the predictions of Fermi liquid theory, which takes into account two contributions to the impedance: (1) incoherent single-quasiparticle excitations, and (2) the excitation of the collective transverse sound mode. At 0.7 bar, our measurements of the impedance are in agreement with the predictions of Fermi liquid theory and imply that the symmetric Fermi liquid parameterF ₂=1.25±0.4 ifF ₁=6.3. At higher pressures, we also observe agreement in the region <0.3, where is the excitation frequency and is the quasiparticle scattering time. However, above 8 bar in the zero-sound regime (1), the impedance is observed to be frequency dependent, at constant . This frequency dependence cannot be explained within the present framework of Fermi liquid theory.This work was supported by the National Science Foundation under Grants DMR 76-02043 and DMR 78-08650.     

Comparison of energy and phase relaxation in metallic wires

We have determined the phase coherence time, , frommagnetoresistance measurements of long, narrow wires ofAu, Ag, and Cu, over the temperature range40 mK-6 K. In the Cu and Au wires, saturates at low temperature. In the Ag wire, continues to increase down to the lowesttemperatures measured; moreover, its temperature dependencebelow about 1 K is consistent with theoreticalpredictions of Altshuler, Aronov and Khmelnitskii published in1982. These results cast doubt on recent assertions thatsaturation of at low temperature is a universalphenomenon in metal wires. We compare these results with thoseof recent experiments on energy relaxation in similar metallicwires. The results of the two experiments are stronglycorrelated, suggesting that a single (unknown) mechanism isthe cause of the enhanced phase and energy relaxation observedin some samples.