Propagation properties of rectangular Laguerre–Gaussian-correlated Schell-model beams in atmospheric turbulence

Based on the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function (WDF), the analytical expressions for the cross-spectral density (CSD) and the propagation factor of a rectangular Laguerre–Gaussian-correlated Schell-model (LGCSM) beam propagating in atmospheric turbulence are derived. The statistical properties, such as the average intensity, the spectral degree of coherence (SDOC) and the propagation factor, of a rectangular LGCSM beam in free space and atmospheric turbulence are comparatively analysed. It is illustrated that a rectangular LGCSM beam exhibits self-splitting and combing properties on propagation in atmospheric turbulence, and the self-splitting properties of such beam are closely related to its beam orders m and n, which is quite different from other self-splitting beams. In addition, the rectangular LGCSM beam has an advantage for reducing the turbulence-induced degradation compared with the conventional partially coherent beams.     

A Model for Non-Rayleigh Scattering Statistics

The independent-scatterer K -distribution model, which has been introduced to describe a variety of scattering situations, is extended to include the effects of correlation between scatterers and finite illumination size. A model in which the array of scatterers is represented by a Γ -lorentzian cross-section fluctuation is proposed. In the appropriate limits this reduces to the independent K -distribution model. Following scattering by the Γ -lorentzian surface, the autocorrelation function and moments of the detected intensity for radiation of arbitrary beamwidth and wavefront curvature are derived. The results are compared with the predictions of the independent K -distribution model and the implications of the differences, which reflect the fact that the independent model cannot represent spatial averaging over the correlations within the surface, are discussed.     

Coupling characteristics and kurtosis parameter of partially coherent beams in turbulent atmosphere

Coupling properties and kurtosis parameter (K parameter) of arbitrary beams propagating through atmospheric turbulence are investigated. A correlation factor (C⁴-factor) is introduced to describe the influence of turbulence on coupling characteristics. The general analytical expression for C⁴-factor of arbitrary beams in atmospheric turbulence is derived. It is shown that C⁴-factor of arbitrary beams in the turbulent atmosphere depends on the initial second-order moments and fourth-order moments and turbulence quantities. Taking the partially coherent anomalous elliptical hollow Gaussian (PCAEHG) beam as an example, we can obtain that C⁴-factor decreases as structure constant of the refractive index fluctuations and inner scale increase, and waist width and transverse coherence length decrease when z?>?5?km. Moreover, K parameter of PCAEHG beam in turbulent atmosphere converges to 2 when propagation distance is large enough. It indicates that the profile of PCAEHG beams in turbulent atmosphere finally evolves into fundamental Gaussian distribution.     

Kurtosis parameter K of arbitrary electromagnetic beams propagating through non-Kolmogorov turbulence

General analytical formulae for the kurtosis parameters K (K parameters) of the arbitrary electromagnetic (AE) beams propagating through non-Kolmogorov turbulence are derived, and according to the unified theory of polarization and coherence, the effect of degree of polarization (DOP) of an electromagnetic beam on the K parameter is studied. The analytical formulae can be given by the second-order moments and fourth-order moments of the Wigner distribution function for AE beams at source plane, the two turbulence quantities relating to the spatial power spectrum, and the propagation distance. Our results can also be extended to the arbitrary beams and the arbitrary spatial power spectra of Kolmogorov turbulence or non-Kolmogorov turbulence. Taking the stochastic electromagnetic Gaussian Schell-model (SEGSM) beam as an example, the numerical examples indicate that the K parameters of a SEGSM beam in non-Kolmogorov turbulence depend on propagation distance, the beam parameters and turbulence parameters. The K parameter of a SEGM beam is more sensitive to effect of turbulence with smaller inner scale and generalized exponent parameter. A non-polarized light has the strongest ability of resisting turbulence (ART), however, a fully polarized SEGSM beam has the poorest ART.     

A fracture mechanics analysis on the fatigue behaviour of cruciform joints of duplex stainless steel

The paper presents the results of an experimental and numerical study on the fatigue behaviour of cruciform load carrying joints made from the duplex stainless steel and failing from the weld root through the weld metal. Fatigue crack growth (FCG) data, obtained in specimens of the weld metal, are presented, as well as threshold data, both obtained for R= 0 and 0.5. The influence of stress ratio is discussed, and the FCGR results are compared with data for low carbon structural steels. S–N data were obtained in the joints, both for R= 0.05 and 0.5, and the fatigue cracking mechanisms were analysed in detail with the SEM. It was found that the cracks propagated very early in the lifetime of the joints, under mixed mode conditions (I + II), but the mode I component was found to be predominant over mode II. The geometries of the cracks were defined in detail from measurements taken in the fracture surfaces. A 2D FE analysis was carried out for the mixed mode inclined cracks obtained at the weld root, and the J‐integral formulations were obtained as a function of crack length and crack propagation angle. The values of the crack propagation angle, θ_i, were obtained for the J_max conditions, and it was found that, in the fatigue tests, the cracks propagated in directions very close to the predicted directions of maximum J. K_I and K_II formulations were obtained, and the K_I data were compared with the formulations given in the PD6493 (BS7910) document, and some differences were found. A more general formulation for K under mixed mode conditions was derived. The derived K solutions were applied to predict the fatigue lives of the joints under crack propagation, and an extremely good agreement was found with the experimental results obtained in the fatigue tests.     

Fracture toughness measurement with fatigue-precracked single edge-notched beam specimens of WC-Co hard metal

The plain-strain fracture toughness of WC-8%Co hard metal, K _IC, was measured using single edge-notched beam (SENB) specimens with fatigue precrack. The fatigue precrack was introduced with compressive fatigue cycling in four-point bending at room temperature. Since stable fatigue-crack propagation was obtained from the notch tip, it was easy to control the fatigue-precrack length. A reasonable K _IC value of 13.3 MPa m^1/2 was obtained with the fatigue-precracked SENB specimens in four-point bending. The compressive fatigue-precracking technique in four-point bending was simple and convenient, and is therefore applicable to precracking in a variety of brittle materials prior to fracture-toughness measurements.     

The stress intensity factor for grooved DCB specimens loaded by splitting forces

An approximate analysis is used to obtain the stress intensity factors K for DCB specimens with a groove, loaded by splitting forces P. A review is given for the various approaches that have been taken to obtain the stress intensity factor for an ungrooved DCB specimen. The accuracy of the results is evaluated using the exact solution of K, which was finally obtained by Foote and Buchwald [1]. A so-called improved beam analysis is used to obtain K for a rectangular grooved DCB specimen. When the specimen is loaded by bending moments M, the solution of the stress intensity factor is given by Wu et al. [4].     

Evolution of decentred laser beams propagating through atmospheric turbulence

The changes of the average intensity, the centre of beam gravity and the position of intensity maximum of decentred laser beams propagating through atmospheric turbulence are examined in detail. It is shown that the decentred intensity distribution is amended gradually with increasing the propagation distance and the strength of turbulence, and it becomes an off-axis Gaussian-like beam when the propagation distance and the strength of turbulence become large enough. The centre of beam gravity is independent of both the propagation distance and the strength of turbulence. On the other hand, there are two intensity maxima, and their positions are symmetrical around the propagation z-axis when the propagation distance z is small. With increasing z, there is only one intensity maximum. As z further increases, position of the intensity maximum is further shifted towards the z-axis. When z is large enough, the position of the intensity maximum is unchanged. The unchanged position of the intensity maximum moves further away from the z-axis with an increase in the refraction index structure constant, the decentred parameter and the waist width.     

Multiscale fatigue crack growth modelling for welded stiffened panels

The influence of welding residual stresses in stiffened panels on effective stress intensity factor (SIF) values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstructural crack nucleation and propagation is taken into account using molecular dynamics simulations as well as a Tanaka–Mura approach for the analysis of the problem. Mode I SIFs, K_I, were calculated by the finite element method using shell elements and the crack tip displacement extrapolation technique. The total SIF value, K_tot, is derived by a part due to the applied load, K_appl, and by a part due to welding residual stresses, K_res. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.     

A new push‐pull sample design for microscale mode 1 fracture toughness measurements under uniaxial tension

A sample geometry is proposed for performing microscale tensile experiments based on a push‐pull design. It allows measuring mode 1 fracture toughness under uniform far‐field loading. Finite element simulations were performed to determine the geometry factor, which was nearly constant for Young's moduli spanning 2 orders of magnitude. It was further verified that mode 1 stress intensity factor K_I is nearly constant over the width of the tension rods and an order of magnitude higher than K_II and K_III. Notched samples with different a/w ratios were prepared in (100)‐oriented Si by a combination of reactive ion etching and focused ion beam milling. The mode 1 fracture toughness K_I,q was constant with a/w and in average 1.02 ± 0.06 MPa√m in good agreement with existing literature. The geometry was characterized and experimentally validated and may be used for fracture toughness measurements of all material classes. It is especially interesting when a uniaxial, homogeneous stress field is desired, if crack tip plasticity is important, or when positioning of the indenter is difficult.     

Effects of sorbed water on crack propagation in poly(methyl methacrylate) under static tensile stress

Effects of sorbed water on crack propagation in poly(methyl methacrylate) (PMMA) under static tensile stress have been investigated. The specimens were kept for more than two years in temperature and humidity-controlled conditions. Sorbed water of less than 0.40 wt% scarcely affected K _Ith value (threshold stress intensity factor for crack propagation), however, K _Ith value for the specimens containing water of more than 0.40 wt% increased with the amount of sorbed water. K _Ith values related to the balance among the radius of the curvature of crack tip, crazing stress and craze fibril rupture stress, which are functions of the amount of sorbed water. At a crack propagation rate of more than 1 × 10^–7 m/s, the slopes of K-da/dt curves for the specimens containing water less than 0.40 wt% were gentle, however, that for the specimens containing more than 0.40 wt% was steep; and unstably fractured. It was found that the gentler slopes for the specimens containing little sorbed water may be caused by craze-shear controlled crack propagation mechanisms, while the steeper slopes for the other specimens may be caused by a craze controlled crack propagation mechanism.     

Thermal fatigue crack propagation in massive cylinders during their cyclic heating

Processes that reduce the level of maximum unsteady stresses during thermal fatigue crack propagation in massive bodies during their convective cyclic heating are considered. It is shown that during crack propagation, the stress intensity factor K₁ increases initially to a certain limit K _1max and then decreases. The factor K _1max depends on the initial and boundary conditions of heat exchange as well as on the rates of decrease in the maximum stresses during thermal fatigue crack propagation. It is shown that the asymmetry of boundary and initial conditions of heat exchange can contribute to either acceleration or retardation of crack propagation depending on the material properties and heating conditions. Deceased. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 68–80, July–August, 1999.     

Interfacial fatigue crack growth in foam core sandwich structures

This paper deals with the experimental measurement of face/core interfacial fatigue crack growth rates in foam core sandwich beams. The so-called ‘cracked sandwich beam’ specimen is used, slightly modified, which is a sandwich beam that has a simulated face/core interface crack. The specimen is precracked so that a more realistic crack front is created prior to fatigue growth measurements. The crack is then propagated along the interface, in the core material, during fatigue loading, as is assumed to occur in a real sandwich structure. The crack growth is stable even under constant amplitude testing. Stress intensity factors are obtained from the FEM which, combined with the experimental data, result in standard da/dN versus ΔK curves for which classical Paris’ law constants can be extracted. The experiments to determine stress intensity factor threshold values are performed using a manual load-shedding technique.     

Propagation and far-field beam quality of M × N Hermite–Gaussian beams propagating through atmospheric turbulence

The analytical propagation equation of M×N Hermite–Gaussian (H–G) beams, which are combined incoherently and propagate through atmospheric turbulence, is derived, which enables us to study their propagation properties and far-field beam quality. The propagation of M×N Gaussian beams through atmospheric turbulence and M×N H–G beams in free space are treated as special cases of our general result. The power in the bucket (PIB), β-parameter and Strehl ratio are chosen as the parameters characterizing the beam quality in the far field. The dependence of PIB, β-parameter and Strehl ratio of M×N H–G beams through atmospheric turbulence on the refraction index structure constant C _n ², beam numbers M, N, mode indices m, n and separate distances x_d , y_d is illustrated numerically and interpreted physically. It is found that M×N H–G beams are less sensitive to the effects of turbulence than M×N Gaussian beams.     

Analysis of dynamic characteristics of through‐wall cracks between 2 boreholes in the directed fracture controlled blasting

Through‐wall cracks between 2 boreholes in the directed fracture controlled blasting have been always concerned by researchers. Dynamic characteristics of through‐wall cracks between 2 boreholes and lateral crack propagation of boreholes in the double‐borehole slot mode and the synchronous blasting of boreholes were examined using the explosive loading digital dynamic caustics experiment system. And the effects of borehole loading mode and borehole clearance on through‐wall cracks between boreholes were examined using distinct lattice spring model numerical analysis, based on the experiment model. Findings show that the tips of through‐wall cracks between boreholes did not meet directly but staggered, continuously propagated after meeting, and moved closer to the existing anisotropic crack direction. The velocity and acceleration of crack propagation fluctuated. K_I rapidly decreased from the maximum value, then gradually increased after a repeated volatility, and began to decrease after it reached the second peak. During the process of crack propagation, K_II was basically smaller than K_I. The dynamic energy release rate rapidly decreased from the maximum value, reached the second peak after the volatility, and gradually decreased again. The borehole loading mode and borehole clearance had significant effects on through‐wall cracks between boreholes.     

High cycle fatigue mechanisms in a cast AM60B magnesium alloy

ABSTRACT We examine micromechanisms of fatigue crack initiation and growth in a cast AM60B magnesium alloy by relating dendrite cell size and porosity under different strain amplitudes in high cycle fatigue conditions. Fatigue cracks formed at casting pores within the specimen and near the surface, depending on the relative pore sizes. When the pore that initiated the fatigue crack decreased from approximately 110 µm to 80 µm, the fatigue life increased two times. After initiation, the fatigue cracks grew through two distinct stages before final overload specimen failure. At low maximum crack tip driving forces (K_max < 2.3 MPa√m), the fatigue crack propagated preferentially through the α‐Mg dendrite cells. At high maximum crack tip driving forces (K_max > 2.3 MPa√m), the fatigue crack propagated primarily through the β‐Al₁₂Mg₁₇ particle laden interdendritic regions. Based on these observations, any proposed mechanism‐based fatigue model for cast Mg alloys must incorporate the change in growth mechanisms for different applied maximum stress intensity factors, in addition to the effect of pore size on the propensity to form a fatigue crack.     

Behaviour of α-AI2O3 insulator surfaces under electron irradiation

Cathodoluminescence (CL), Auger electron spectroscopy (AES) and direct crack measurements were performed on-Al₂O₃ samples in order to relate chemical, electrical and mechanical effects induced by electron irradiation of the surface. Electrical discharges and visible luminescence were observed during the excitation of the samples with a 80 keV electron beam. Changes of the surface state and of the toughnessK _Ic were subsequently detected. The results suggest that charging of the sample is related to the presence of defects and corresponding trap levels in the energy gap. The concentration of defects (oxygen vacancies or associated F, F⁺ centres) may be enhanced, especially in the vicinity of the surface, by the electrical discharges induced by the electron irradiation. This leads to an increase of mechanical stresses in the brittle material: a striking example was the fracture of a corundum single crystal in the electron microscope, which cannot be explained by the direct heating effect of the primary electron beam. On the contrary, an advantageous situation for the mechanical properties of the material may be achieved when the defects have a blocking effect on the crack propagation; a subsequent increase of the toughnessK _Ic is then recorded.     

Propagation based on second-order moments for partially coherent Laguerre–Gaussian beams through atmospheric turbulence

Abstract

The Wigner distribution function (WDF) has been used to study the propagation properties of partially coherent Laguerre Gaussian (PCLG) beams through atmospheric turbulence. Based on the extended Huygens–Fresnel principle, an analytical formula of the propagation matrixes in terms of the second-order moments of the WDF for PCLG Beams in the receiving plane is derived. And then the analytical formulae for the curvature radii of PCLG Beams propagating in turbulence are given by the second-order moments of the WDF. The numerical results indicate that the curvature radius of PCLG Beams changes more rapidly in turbulence than that in the free space. The influence of the transverse coherence width and the beam waist width on the curvature radius of PCLG Beams is obvious, while the laser wavelength and the inner scale of turbulence have a slight effect. The study results may be useful for remote sensing and free space optical communications.     

Influence of non‐proportional bending with torsion on fatigue life of 10HNAP steel within the range of crack initiation and propagation

The paper presents a precise analysis of the influence of non‐proportional loading of specimens on fatigue life during initiation and propagation of fatigue cracks. Simulation of the fatigue life of specimens was based on relations describing propagation rate of the fatigue cracks. The Paris and Forman relations were applied; they were integrated after previous introduction of relationships for the equivalent range of the stress intensity factor ΔK_eq and including the phase shift angle ? between amplitudes of the bending moment and the torsional moment. Under bending with torsion, range of the equivalent stress intensity factor ΔK_eq includes ranges of stress intensity factors for loading modes I and III, i.e. ΔK_I and Δ K_III. The performed tests of 10HNAP constructional steel under cyclic bending with torsion allowed us to determine the influence of the phase shift angle ? on the fatigue life. It has been proved that increase of the phase shift angle from ?= 0° to ?= 60° and the ratio of amplitude of the bending moment M_ag to amplitude of the torsional moment M_as equal to 1.33, 2 and 4 cause increase of the fatigue life of the tested specimens. The maximum increase of the fatigue life of specimens made of 10HNAP steel was 73% (M_ag/M_as= 2, ?= 45°).     

Strength Assessment for Butt Joints of Steel 50 by the Fracture Toughness Criteria

We propose an experimental-theoretical engineering procedure for assessing the strength of butt-welded joints using the force (K_Ic) and strain (_c) criteria of the brittle and quasibrittle fracture mechanics, respectively. For this purpose, beam specimens with square and bevel welds and an initial edge crack or notch in the weld metal are tested under three-point bending. The parameter K_Imax controlling fracture of a bent beam with an inclined (Mode I + Mode II) crack is assessed taking into account the values of the stress intensity factors K_I and K_II, and the crack inclination angle ^*. We also studied the plastic zone at the crack tip and the crack propagation kinetics depending on the weld geometry and the V-notch tip radius for butt-welded joints. The data obtained allow one to rate such joints by their strength according to the fracture toughness criteria K_Ic and _c.