Effect of electric current on the evolution of plastic strain near a crack tip

The effect of direct current on the evolution of plastic strain near the tip of a crack in a crystal in tension is studied. The plastic strain near the crack tip in the loaded specimen is the result of motion of dislocations in the active slip planes of the crystal under the action of shear stresses caused by external loading and electric current. The Joule heat, Thomson effect, and electron wind (electroplastic effect) are taken into account in calculations. The plastic strain and stress distributions near the crack tip are determined at different moments of time for a given magnitude ofelectric current. The effect of the plastic zone on the stressintensity factor of the crack is studied. It is found that the plastic strain is affected largely by the Joule heat released upon passage of the electric current. A numerical analysis is performed for an Fe crystal.     

The effect of the sheet rigidity on strength of the spot weld tension shear joint

This paper presents some test and analysis results for a spot welded joint subjected to tensile and alternate load. The effect of sheet rigidity on the tensile strength and fatigue life of the spot welded joint is studied by using the stress intensity factorsK _I,K _II,K _III and an effective stress intensity factor K_max calculated by the finite element method for crack around the nugget. The results show that the effective stress intensity factor K_max is an essential parameter for estimating the fatigue life of the spot welded joint.     

EXACT SOLUTIONS OF NEAR CRACK LINE FIELDS FOR MODE I CRACK UNDER PLANE STRESS CONDITION IN AN ELASTIC－PERFECTLY PLASTIC SOLID

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Closure of microcracks during unloading and the formation of reverse dislocations

Conclusion During unloading, local closure of the crack is followed by the emission of the first pair of reverse dislocations. The formation of an area of local contact during unloading occurs with a bang; the critical SIF of the external loads at this moment coincides with the value of the overall SIF of the field of the primary sessile dislocations. There is always a free gap between the crack tip and the area of local contact. External loads acting in the crack plane and not resulting in a stress concentration at the crack front play an important role in the emission of reverse dislocations (in particular, they may block their departure from the S-structure).Pacific Oceanological Institute, Academy of Sciences of the USSR, Vladivostok. Translated from Prikladnaya Mekhanika, Vol. 24, No. 7, pp. 3–18, July, 1988.     

Effect of electric current on migration of point defects near a crack tip

The effect of direct current on migration of point defects dissolved in a crystal near the tip of a crack in tension is estimated. Calculations are carried out with allowance for the plastic strain near the crack tip of a loaded specimen, caused by the motion of dislocations in the active slip planes of the crystal, the Joule heat released, and the effect of gas exchange on the crack edges on the evolution of distribution of interstitial impurity atoms. A numerical analysis is performed for an Fe crystal.     

Dynamic crack resistance of acrylic plastic

The dependence of the stressintensity factor near the tip of a growing crack in an SO120 acrylic plastic on the crackpropagation velocity K_I(:v) within the range of 10^–5 –300 m/sec is determined. Specific features of crack propagation associated with the shape of the curve K_I(v), which has discontinuities and nonuniqueness intervals, are discussed.     

Fatigue crack propagaion under mixed mode loading

Mixed model fatigue crack propagation is analyzed in this paper, using a centre cracked plate geometry, loaded under un-iaxial cyclic tension. Based on maximum principal stress criterion, a modified Paris expression of fatigue crack growth rate is derived in terms of ΔK and crack angle β_α for an inclined crack. It is also shown that it is more convenient to express the Paris equation by means of crack length projected on the x -axis, α_x rather than the actual length, α itself. The crack trajectory due to cyclic loading is predicted, β is varied from 29° to 90°. Experimental data on Type L3 aluminium agree fairly well with predicted values when β_α exceeds 30°.     

Stresses in a conical tube under sudden loading

The paper considers a thickwalled long conical tube from an ideal plastic material whose inner surface is suddenly subjected to timeconstant, uniformly distributed pressure or is given a velocity. An idealplastic zone propagates from the inner conical surface. It is assumed that the material of the tube is incompressible in both the elastic and plastic zones. The plastic material obeys the Houber–Mises plasticity condition.     

Stress-intensity factors for a semi-infinite plane crack with a wavy front

The stress-intensity factors for a semi-infinite plane crack with a wavy front are determined when the crack faces are subjected to normal and shearing tractions. The results are derived using asymptotic methods and are valid to O(²) where =A/1; A is the amplitude and is the wavelength of the wavy front. The normal and shearing tractions are in the form of line loads parallel to the crack front.The results are then used to evaluate, in a qualitative manner, the growth characteristics of a semi-infinite plance crack with a wavy front under combined mode loading. This provides a possible explanation of crack front segmentation observed experimentally.     

Deformed particle image pattern matching in Particle Image Velocimetry

The deformation of particle image patterns due to velocity gradients causes errors of velocity measurements and false velocity detections in PIV (Particle Image Velocimetry). A novel technique to overcome those limitations inherent in the conventional PIV by correcting the particle image pattern according to the local velocity gradients in two dimensional flows, i.e. u/x, u/y, v/x and v/y, is proposed and successfully applied to a water flow downstream of a backward facing step.     

On the Path of a Quasi-static Crack in Mode III

A method for finding the path of a quasi-static crack growing in a brittle body is presented. The propagation process is modelled by a sequence of discrete steps optimizing the elastic energy released. An explicit relationship between the optimal growing direction and the parameters defining the local elastic field around the tip is obtained for an anti-plane field. This allows to describe a simple algorithm to compute the crack path. Mathematics Subject Classifications (2000) 74R05, 74B05, 74G70.Gerardo E. Oleaga: Supported by EU-Project Front Singularities University of Leipzig and the Max Planck Institute MIS. Partial support was also provided by the Spanish DGES project BFM2000-0605.     

The onset of Taylor-like vortices in the flow induced by an impulsively started rotating cylinder

The onset of instability in the flow by an impulsively started rotating cylinder is analyzed under linear theory. It is well-known that at the critical Taylor number T_c=1695 the secondary flow in form of Taylor vortices sets in under the narrow-gap approximation. Here the dimensionless critical time _c to mark the onset of instability for TT_c is presented as a function of the Taylor number T. Available experimental data of water indicate that deviation of the velocity profiles from the primary flow occurs starting from a certain time 4_c. It seems evident that during _c4_c the secondary flow is very weak and the primary state of time-dependent annular Couette flow is maintained.     

Fiducial grid for measuring microdeformation ahead of fatigue crack tip near aluminum bicrystal interface

Fiducial grids have been applied to measure micro-deformation near interfaces in aluminum bicrystals and to study mechanisms of fatigue crack transfer across the interface under loading in a scanning electric microscope (SEM). Three types of aluminum bicrystals were designed to allow the primary slip to induce different incompatible plastic strain at the interface. An inclined notch was spark cut along the primary slip band on one edge of each specimen to initiate a crack smoothly. This paper also describes the means to produce fiducial grids of evaporated gold with 7-m square mesh size and 0.3-m line width in a place of interest on a specimen surface, usually ahead of a crack tip near the interface. Interface cracking and width increase of persistent slip band (PSB) induced by an approached transvese crack have been identified by comparing two photos of fiducial grid patterns taken, respectively, at maximum and minimum cyclic stress in a SEM. Grids were also used to measure both cyclic shear strain at a crack tip and crack growth rate, which decreases as the crack approaches an incompatible interface.is presently Visiting Professor     

Finite strains at the tip of a crack in a sheet of hyperelastic material: I. Homogeneous case

This paper describes an asymptotic analysis of the strain and stress fields at the tip of a crack in a sheet of incompressible hyperelastic material. The investigations are carried out within the framework of finite elastostatics and for the class of Generalized Neo-Hookean materials. Both the symmetric (mode I) and non-symmetric (mixed-mode) cases are considered. It is shown that the latter situation corresponds locally to a rigid body rotation of the symmetric fields. The effect of the hardening parameter on crack tip blunting is investigated analytically and numerically.     

Heat and entropy in nonextensive thermodynamics

The concepts of the quantity of heat and work are deduced in the context of non-extensive statistical mechanics, following steps parallel to those employed in extensive statistical mechanics.Received: 31 January 2003, Accepted: 6 May 2003, Published online: 21 November 2003PACS: 05.70.-a, 05.30.-d, 05.90. + m     

Modelling of heat transfer by conduction in a transition region between a porous medium and an external fluid

We study the modelling of purely conductive heat transfer between a porous medium and an external fluid within the framework of the volume averaging method. When the temperature field for such a system is classically determined by coupling the macroscopic heat conduction equation in the porous medium domain to the heat conduction equation in the external fluid domain, it is shown that the phase average temperature cannot be predicted without a generally negligible error due to the fact that the boundary conditions at the interface between the two media are specified at the macroscopic level.Afterwards, it is presented an alternative modelling by means of a single equation involving an effective thermal conductivity which is a function of point inside the interfacial region.The theoretical results are illustrated by means of some numerical simulations for a model porous medium. In particular, temperature fields at the microscopic level are presented.Roman Letters _sf interfacial area of thes-f interface contained within the macroscopic system m² - A _sf interfacial area of thes-f interface contained within the averaging volume m² - C _p mass fraction weighted heat capacity, kcal/kg/K - g vector that maps to _s , m - h vector that maps to _f , m - K _eff effective thermal conductivity tensor, kcal/m s K - l _s,l _f microscopic characteristic length m - L macroscopic characteristic length, m - n _fs outwardly directed unit normal vector for thef-phase at thef-s interface - n outwardly directed unit normal vector at the dividing surface. - R ₀ REV characteristic length, m - T _i macroscopic temperature at the interface, K - error on the external fluid temperature due to the macroscopic boundary condition, K - T ^* macroscopic temperature field obtained by solving the macroscopic Equation (3), K - V averaging volume, m³ - V _s,V _f volume of the considered phase within the averaging volume, m³. - _mp volume of the porous medium domain, m³ - _ex volume of the external fluid domain, m³ - _s , _f volume of the considered phase within the volume of the macroscopic system, m³ - dividing surface, m² - x, z spatial coordinates Greek Letters _s, _f volume fraction - ratio of the effective thermal conductivity to the external fluid thermal conductivity - ^* macroscopic thermal conductivity (single equation model) kcal/m s K - _s, _f microscopic thermal conductivities, kcal/m s K - spatial average density, kg/m³ - microscopic temperature, K - ^* microscopic temperature corresponding toT ^*, K - spatial deviation temperature K - error in the temperature due to the macroscopic boundary conditions, K - ^* _i macroscopic temperature at the interface given by the single equation model, K - spatial average - ^s , ^f intrinsic phase average.     

Group Classification of Equations of the Form y″ = f(x,y)

The problem of classification of ordinary differential equations of the form y = f(x,y) by admissible local Lie groups of transformations is solved. Standard equations are listed on the basis of the equivalence concept. The classes of equations admitting a oneparameter group and obtained from the standard equations by invariant extension are described.     

On the Ellipticity of the Middle Surface of a Shell and its Application to the Asymptotic Analysis of ‘Membrane’ Shells

We consider a surface S = (), where ² is a bounded, connected, open set with a smooth boundary and : ³ is a smooth map; let () denote the components of the two-dimensional linearized strain tensor of S and let 0 with length 0 > 0. We assume the the norm ,|| ()||0, in the space V0() = { H¹() × H¹() × L²(); = 0 on 0 } is equivalent to the usual product norm on this space. We then establish that this assumption implies that the surface S is uniformly elliptic and that we necessarily have 0 = .