Fatigue strength of Al7075 notched plates based on the local SED averaged over a control volume

When pointed V-notches weaken structural components,local stresses are singular and their intensities are expressed in terms of the notch stress intensity factors(NSIFs).These parameters have been widely used for fatigue assessments of welded structures under high cycle fatigue and sharp notches in plates made of brittle materials subjected to static loading.Fine meshes are required to capture the asymptotic stress distributions ahead of the notch tip and evaluate the relevant NSIFs.On the other hand,when the aim is to determine the local Strain Energy Density(SED)averaged in a control volume embracing the point of stress singularity,refined meshes are,not at all,necessary.The SED can be evaluated from nodal displacements and regular coarse meshes provide accurate values for the averaged local SED.In the present contribution,the link between the SED and the NSIFs is discussed by considering some typical welded joints and sharp V-notches.The procedure based on the SED has been also proofed to be useful for determining theoretical stress concentration factors of blunt notches and holes.In the second part of this work an application of the strain energy density to the fatigue assessment of Al7075 notched plates is presented.The experimental data are taken from the recent literature and refer to notched specimens subjected to different shot peening treatments aimed to increase the notch fatigue strength with respect to the parent material.     

Fracture assessment of polymethyl methacrylate using sharp notched disc bend specimens under mixed mode I + III loading

Mixed mode I/III behavior of Perspex (polymethyl methacrylate (PMMA)) is studied experimentally and theoretically in this research using a new and simple laboratory test configuration. The specimen is a circular disc containing a sharp V-notch along the diameter that is loaded by the conventional three-point bend fixture. The critical values of notch stress intensity factors (K _I ^V and K _III ^V ) were obtained for the whole combinations of modes I and III simply by changing the notch inclination angle relative to the loading rollers. The value of notch fracture toughness under pure or dominantly tension loads was greater than its corresponding value under mode III or dominantly torsion loads. The experimental results were also predicted very well by employing the local strain energy density (SED) criterion.     

Notch fatigue of Cu_(50)Zr_(50) metallic glasses under cyclic loading: molecular dynamics simulations

Molecular dynamics simulation is performed to simulate the tension–compression fatigue of notched metallic glasses(MGs), and the notch effect of MGs is explored. The notches will accelerate the accumulation of shear transition zones, leading to faster shear banding around the notches' root causing it to undergo severe plastic deformation. Furthermore, a qualitative investigation of the notched MGs demonstrates that fatigue life gradually becomes shorter with the increase in sharpness until it reaches a critical scale. The fatigue performance of blunt notches is stronger than that of sharp notches. Making the notches blunter can improve the fatigue life of MGs.     

A study on the effect of stress state on damage evolution in hot deformation of free cutting steels using double notched bars

The effect of stress state on the initiation of damage for leaded free cutting steel has been investigated under hot rolling conditions. Double notched (DN) circumferential tension samples were designed and used to simulate damage development at different stress states and deformation conditions using a Gleeble (3800) thermal-mechanical testing system. Two DN sample geometries with varying notch profiles were used to account for different states of stress. To simulate the conditions of hot rolling the samples were tested at high temperatures (900–1200 °C) and moderate strain rates (0.1–1 s^?1). After testing to failure, which normally occurs at one notch of the specimen, the unfailed notch of each sample was sectioned to examine the sites where damage occurs since the material has been captured in a state very close to failure. Two of the cases examined have shown definitive damage paths occurring from ‘outside–in’ for a sharp notch deformed at T = 900 °C and from ‘inside–out’ for a blunt notch tested at T = 1200 °C for the same strain rate of 0.1 s^?1. The experimental results of the failure initiation sites were compared with computed values of the stress fields around the notch profiles, obtained from FE analysis using a set of viscoplastic constitutive equations calibrated for free cutting steel. The temperature profiles from high temperature mechanical testing were used in the FE calculations of the stress state.     

Three-dimensional vibrations of cylindrical elastic solids with V-notches and sharp radial cracks

This paper provides free vibration data for cylindrical elastic solids, specifically thick circular plates and cylinders with V-notches and sharp radial cracks, for which no extensive previously published database is known to exist. Bending moment and shear force singularities are known to exist at the sharp reentrant corner of a thick V-notched plate under transverse vibratory motion, and three-dimensional (3-D) normal and transverse shear stresses are known to exist at the sharp reentrant terminus edge of a V-notched cylindrical elastic solid under 3-D free vibration. A theoretical analysis is done in this work utilizing a variational Ritz procedure including these essential singularity effects. The procedure incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of “edge functions” that explicitly model the 3-D stress singularities which exist along a reentrant terminus edge (i.e., α>180°) of the V-notch. The first set of polynomials guarantees convergence to exact frequencies, as sufficient terms are retained. The second set of edge functions—in addition to representing the corner stress singularities—substantially accelerates the convergence of frequency solutions. This is demonstrated through extensive convergence studies that have been carried out by the investigators. Numerical analysis has been carried out and the results have been given for cylindrical elastic solids with various V-notch angles and depths. The relative depth of the V-notch is defined as (1−c/a), and the notch angle is defined as (360°−α). For a very small notch angle (1° or less), the notch may be regarded as a “sharp radial crack.” Accurate (four significant figure) frequencies are presented for a wide spectrum of notch angles (360°−α), depths (1−c/a), and thickness ratios (a/h for plates and h/a for cylinders). An extended database of frequencies for completely free thick sectorial, semi-circular, and segmented plates and cylinders are also reported herein as interesting special cases. A generalization of the elasticity-based Ritz analysis and findings applicable here is an arbitrarily shaped V-notched cylindrical solid, being a surface traced out by a family of generatrix, which pass through the circumference of an arbitrarily shaped V-notched directrix curve, r(θ), several of which are described for future investigations and close extensions of this work.     

A review on coupled modes in V-notched plates of finite thickness: A generalized approach to the problem

Mode 1, 2 and 3 cannot exist in isolation. One mode provokes the existence of a coupled mode which, in some conditions, can be more dangerous than the generating mode itself. This means that three-dimensional problems are automatically at least dual scale. While for a crack this effect was known to exist for a long period of time, it was largely ignored in theoretical studies of V-shaped notches subjected to in-plane and out-of-plane loading as well as in practical fracture problems associated with such geometries. Only recently, some numerical investigations confirmed that highly localized coupled modes do exist in the close vicinity of the notch tip. The present paper is aimed to briefly review important features of these recently identified singular coupled modes. The most significant results from a comprehensive three-dimensional numerical study are presented here to describe the contribution of these modes into the overall stress state in the close vicinity of the notch tip and discuss the implementation of these new results to the failure and integrity assessment of plate structures with sharp notches.     

The Features of the Structural and Magnetic Characteristics of Low-Dimensional Thin-Film Systems Based on Cobalt and Copper

The results of investigation of the structural and magnetic characteristics of Co/Cu/Co thin-film systems obtained by magnetron sputtering on glass substrates are presented. The thickness of the cobalt layer in all samples was 5 nm and the thickness of the copper layer was varied from 0.5 to 4 nm. The saturation field H _S of the studied samples was found to oscillate in magnitude with changes in the copper-layer thickness with a period on the order of 1 nm. The maximum values of H _S are observed for the thin-film systems with t_Cu = 1.4, 2.2, and 3.2 nm. The hysteresis loops measured for these systems in a magnetic field applied along the easy magnetization axis of the samples have a two-stage shape, while for the samples with other values of tCu the hysteresis loops are rectangular. These data are explained by the presence of exchange coupling between the ferromagnetic layers through a copper spacer and its oscillating behavior with changing t_Cu.     

Fracto-mechanoluminescence and mechanics of fracture of solids

The present paper explores the correlation between fracto-mechanoluminescence and fracture of solids and thereby provides a clear understanding of the physics of fracto-mechanoluminescence. When a fluorescent or non-photoluminescent crystal is fractured impulsively by dropping a load on it, then initially the mechanoluminescence (ML) intensity increases linearly with time, attains a maximum value I_m at a particular time t_m and later on it decreases exponentially with time. However, when a phosphorescent crystal is fractured impulsively by dropping a load on it, then initially the ML intensity increases linearly with time, attains a maximum value I_m at a particular time t_m and later on it decreases initially at a fast rate and then at a slow rate. For low impact velocity the value of t_m is constant, however, for higher impact velocity t_m decreases logarithmally with the increasing impact velocity. Whereas the peak ML intensity I_m increases linearly with the impact velocity, the total ML intensity I_T, initially increases linearly with the impact velocity and then it tends to attain a saturation value for higher values of the impact velocity. The value of t_m increases logarithmally with the thickness of crystals, I_m increases linearly with the area of cross-section of crystals and I_T increases linearly with the volume of crystals. Generally, the ML of non-irradiated crystals decreases with increasing temperature of crystals. Depending on the prevailing conditions the ML spectra consist of either gas discharge spectra or solid state luminescence spectra or combination of the both. On the basis of the rate of generation of cracks and the rate of creation of new surface area of crystals, expressions are derived for the ML intensity and they are found to explain satisfactorily the temporal, spectral, thermal, crystal-size, impact velocity, surface area, and other characteristics of ML. The present investigation may be useful in designing of damage sensors, fracture sensors, ML-based safety management monitoring system, fuse-system for army warheads, milling machine, etc. The present study may be helpful in understanding the processes involved in earthquakes, earthquake lights and mine-failure as they basically involve fracture of solids.     

Transient behaviour of the mechanoluminescence induced by impulsive deformation of fluorescent and phosphorescent crystals

When a crystal is fractured impulsively by the impact of a moving piston, then initially the mechanoluminescence (ML) intensity increases quadratically with time, attains a peak value and later on it decreases with time. Considering that the solid state ML and gas discharge ML are excited due to the charging and subsequent production of electric field near the tip of moving cracks, expressions are derived for the transient ML intensity I, time t_m and intensity I_m corresponding to the peak of ML intensity versus time curve, respectively, the total ML intensity I_T, and for fast and slow decays of the ML intensity. It is shown that the decay time for the fast decrease of the ML intensity after t_m, is related to the decay time of the strain rate of crystals, and the decay time of slow decay of ML, only observed in phosphorescent crystals, is equal to the decay time of phosphorescence. The value of t_m decreases with the increasing impact velocity, I_m increases with the increasing impact velocity, and I_T initially increases and then it tends to attain a saturation value for higher values of the impact velocity. The values of t_m, I_m and I_T increase linearly with the thickness, area of cross-section and volume of the crystals, respectively. So far as the rise, attainment of ML peak, and fast decay of ML are concerned, there is no any significant difference in the time-evolution of solid state ML, gas discharge ML, and the ML emission consisting of both the solid state ML and gas discharge ML. From the time-dependence of ML, the values of the time-constant for decrease of the surface area created by the movement of a single crack, the time-constant for the decrease of strain rate of crystals, and the decay time of phosphorescence of crystals can be determined. A good agreement is found between the theoretical and experimental results. The importance of fracto ML induced by impulsive deformation of crystals is discussed.     

Molecular dynamics simulation of stress and grain evolution

A three-dimensional molecular dynamics simulation is carried out to study the evolution of grains and stresses during the deposition of atoms on the (100) plane of a fcc regular crystal, using the cubic system with x–y periodic boundary conditions. At the bottom an atomic surface and at the top a reflecting wall are assumed. Atoms in the system interact via the Lennard–Jones potential. During simulation the films grow according to the Volmer–Weber mode and exhibit specific shape of the stress curves. When the film becomes continuous, the stress during the growth possesses a maximum value, but later new grain boundaries are formed. Individual atoms in the grain boundaries generate compressive stress in the films.     

Cohesive zone modelling of anodic dissolution stress corrosion cracking induced by corrosion product films

Damage mechanics based on the cohesive zone model were applied to study the anodic dissolution stress corrosion cracking (SCC) in flat and U-shaped edge-notched specimens. The simulation results show that corrosion product films (CPFs) facilitate crack initiation in SCC due to the CPF-induced stress and CPF rupture. In the flat specimen, SCC susceptibility increases with the CPF thickness and CPF Young’s modulus, while it decreases with CPF fracture strength. For the U-shaped edge-notched specimen, the normalised threshold stress intensity factor K_ISCC/K_IC decreases with the CPF thickness and notch depth.     

On a study of the superposition effect of diffracted X-rays by a liquid column and the optimum thickness for X-ray diffraction

A measure of intensity due to the superposition of diffracted X-rays from elementary regions in the line of X-ray path has been calculated on the basis of Gaussian distribution of intensity from every element. This gives the optimum thickness for maximum intensity implicitly by the relation. Μt₀=α?′(αt₀)/?(αt₀) where ? is the error integral and α is a characteristic of the liquid which determines the Gaussian distribution form for the particular liquid. Good agreement between the theoretical relations and the experimental values have been observed.     

The effect of the boundary conditions on in-plane and out-of-plane stress field in three dimensional plates weakened by free-clamped V-notches

Dealing with the material microstructure an analytical multiscale model has recently been developed by Sih. Physically, the different orders of the stress singularities are related to the different constraints associated with the defect thought as a microscopic V-notch at the tip of the main crack. Irregularities of the material microstructure tend to curl the crack tip being the clamped-free boundary conditions the more realistic and general representation of what occurs on the microscopic V-notch. As a result, mixed mode conditions are always present along the V-notch bisector line.It is known for a long time that at the antisymmetric (mode II) stress distribution ahead of the crack tip generates a coupled out-of-plane singular mode. Recent theoretical and numerical analyses have demonstrated that this out-of-plane mode due to three-dimensional effects occurs also in the case of large V-notches where the mode II stress field is no longer singular. In addition, when the notch opening angle is non-zero, the three-dimensional singular stress state is strongly influenced by the plate thickness.The aim of this paper is to investigate the effect of free-fixed boundary conditions along the notch edges in three dimensional plates weakened by pointed V-notches and quantify the intensity of the out-of-plane singularity occurring under this constraint configuration. For the sake of simplicity a macronotch is considered rather than a micronotch. A synthesis of the magnitude of the stress state through the plate thickness is carried out by using the mean value of the strain energy density over a given control volume embracing the notch tip. The capability of the strain energy density to capture all the combined effects due to the out-of-plane mode make it a powerful parameter at every scale levels.     

Effect of film morphology on the magnetic properties for Nd-Fe-B thin films

The microstructure and magnetic properties of Nd-Fe-B thin films with a particulate structure were investigated. The nominal thickness of the Nd-Fe-B layer (t_N) was varied from 2 to 50 nm on a (0 0 1) Mo buffer layer. The films were grown with their c-axis perpendicular to the plane, and the morphology of the film with t_N=2 nm was shown to be particulate from an atomic force microscope image. The slope of the initial magnetization curve became steeper by increasing the t_N value in the initial magnetization curve, indicating that the film morphology composed of single domain particles changed to that of multi-domain particles with growth. The film with t_N=8 nm, which had a structure consisting of a mixture of single and multiple domain particles, showed the maximum value of the coercivity measured in the direction perpendicular to the film plane (H_c) as 19.5 kOe.     

Impact toughness of EK-181 ferritic-martensitic chromium (12%) steel under loading by concentrated bending

The low-temperature fracture of a high-temperature low-activated ferritic-martensitic EK-181 chromium (12%) steel (RUSFER-EK-181: Fe-12Cr-2W-V-Ta-B) is studied using impact and static concentrated bending tests as a function of the specimen dimensions (standard, small), the type of stress concentrator (V-shaped notch, fatigue crack), and the temperature (from −196 to +100°C). The ductile-brittle transition temperature falls in the range from −85 to +35°C. The temperature dependences of stress-intensity factor K _Ic and fracture toughness J _Ic are determined. The severest type of impact toughness tests is represented by tests of V-notched specimens with an additional fatigue crack and two lateral V-shaped notches (three-sided V-shaped notch with a central fatigue crack). The fracture energy of the steel depends on the type of stress concentrator and the specimen dimensions and is determined by the elastic energy and the plastic deformation conditions in the near-surface layers of a specimen, which are controlled by the lateral notches. At the same test temperature, the impact toughness and the fracture toughness are interrelated. Irrespective of the type of specimen (including notches and a fatigue crack), the ferritic-martensitic steel exhibits the same fracture mechanism.     

Prediction of a domain-drag effect in uniaxial,non-compensated,ferromagnetic metals

An electric current is predicted to exert a dragging force on ferromagnetic domain walls. The effect arises from the non-uniform current distribution, recently predicted and observed at 4·2 K in the neighborhood of a wall in metals (Co, Ni) with large Hall angle. When the average current density j? exceeds a certain “coercive” value j?_c, the domains are set into motion in the same direction as the charge carriers. When j?j?_c, the wall speed approaches the drift speed of the carriers. Ohm's law fails when the walls move. The limits of very small and of very large Hall angle are both considered, using the single-wall model of Williams, Shockley and Kittel, and also the stratified-medium model of Herring. We assume B = M_s inside each domain; this is appropriate if the sample thickness t in the direction of the saturation magnetization M_s, and the wall spacing a, obey t > a. Materials with large anisotropy field H_A (h.c.p. Co, Gd) are necessary if the field H of the current is not to remove all walls normal to the current. For similar reasons, the sample should be in the shape of a flat ribbon (or rod) normal to M_s, of thickness (or diameter) t obeying t < dH_A/H_c, where H_c is the coercive field and d the wall length in the direction normal to the current and to M_s.     

Change in the resonance frequency of surface plasmons in copper nanoparticles excited by femtosecond laser pulses

Changes in the optical density ΔD(t), halfwidth ΔH/2(t), and spectral position of the maximum Δλ_SP(t) of the surface plasmon band in Cu nanoparticles after their excitation by femtosecond laser pulses have been investigated. The Δλ_SP(t) dependence appears to be alternating and is accompanied by a nonmonotonic variation in ΔH/2(t) in the time interval 0–5 ps. The results are explained in a model based on the evolution of the dielectric response of such a composite medium excited by intense laser pulses.     

Boltzmann'sH theorem and the Loschmidt and the Zermelo paradoxes

The Umkehreinwand of Loschmidt and the Wiederkehreinwand of Zermelo have been reexamined. The former paradox depends on the augument that for a dynamical system, upon the reversal of the velocities of all the molecules, theH function retraces its sequence of values so thatdH/dt will change its sign. The latter paradox depends on the argument that theH function returns infinitely close to its value after a Poincare' quasi-period and therefore cannot be decreasing all the time. While the main contention of the two paradoxes is correct, that theH theorem is inconsistent with classical dynamical laws, the arguments there can be considerably simplified and the “paradoxes” answered more directly. If the distribution functionf(q _K ,p _K ,t) is governed by an equation which is time-reversal invariant (such as the Liouville equation for a closed dynamical system), then it can be shown immediately thatdH/dt=0,H=cons. In this case, both paradoxes disappear, but together with them, thedH/dt<0 part of theH theorem also has disappeared, i.e., there is no second law of thermodynamics. Iff(q _K ,p _K ,t) is governed by an equation which is not time-reversal invariant (such as the Boltzmann equation, or the Master Equation for Markovian processes), then (1) there is no argument forf andH(t) to retrace their sequence of values upon the reversal of all the velocities of the system, (2) there is no quasiperiod in whichf andH(t) return to their earlier values. In this case, both paradoxes disappear also, but then one must go beyond classical dynamics in order to maintain theH theorem.     

The critical phenomenon and the re-entrance phenomenon in the anti-tumor model induced by the time delay

The effects of time delay τ on an anti-tumor model driven by a multiplicative noise and a periodic signal are investigated. The results obtained from the small delay approximation and numerical simulations indicate: (i) For the absence of the periodic signal in the system, the two-peak structure of the stationary probability distribution transforms into the single-peak structure with the increasing τ, and τ exists a critical value τc. For τ<τc, the stationary mean value 〈x〉_st of the cell population decreases as the noise intensity D increases, however, for τ>τc, the 〈x〉_st increases as the D increases; (ii) For the presence of the periodic signal in the system, the structure of the signal-to-noise ratio with changes of the D exhibits the transitions of one peak → two peaks → one peak as τ increases.     

Effect of tensile stress on the variation of magnetic field of low-alloy steel

The surface magnetic field intensity H_p(y) of low-carbon steel plate specimen was measured after tensile test and unloading; variation of H_p(y) was studied. It was found that H_p(y) signals first decreased with increase in stress, and then reversed to the initial field when the stress was greater than 160 MPa. Under yield stress, H_p(y) reached its maximum, and then decreased slightly with further increase in stress. The initial magnetic signals have great impact on the variation of magnetic field.