Bending-induced crack propagation in a 4% CuAl alloy with reference to acoustically propagated fatigue cracks

The growth rates of bending-induced fatigue cracks in bare and clad 4% CuAl alloy sheets typical of those used for aircraft skins are determined as a function of the crack tip stress intensity. Although the emphasis of the work is on crack growth at load reversal rates characteristic of the acoustic fatigue situation (175 reversals/second) comparison is made with crack growth rates at relatively low load reversal rates (4 reversal/ second). Data applicable to both sinusoidal and narrow band random loading is presented and the relationship between growth rates under these two forms of loading is examined.     

The effects of substructure on fatigue crack propagation

The correlation between the initiation and propagation of fatigue cracks and the substructure formation was examined using aluminium specimens. The effects of substructures introduced by static and alternating stresses and those of the recovery of the substructure on the propagation rates of fatigue cracks were also studied. Observations of the substructures were made by means of the X-ray micro-beam technique. The principal results obtained are as follows:

1. At the time of fatigue crack initiation a definite substructure develops at the root of a notch made on the specimen edge.
2. The rate of fatigue crack propagation has a relation to the characteristics of the substructures at the tip of the fatigue cracks.
3. While the rates of propagation are retarded by static pre-strains, they increase in proportion to the degree of substructure formation due to alternating stresses.
4. The rates are usually reduced by the recovery after alternating deformation.

On the basis of the above results, the significance of substructures for fatigue fracture is discussed.     

基于散射矩阵法的飞机壁板声学优化设计

采用散射矩阵法分析夹层板结构声学特性,并对典型的夹层板结构即飞机壁板进行声学优化,预计飞机壁板隔声特性,获得蒙皮、隔声隔热层、内饰板及它们的组合结构的声学性能。针对尾吊飞机客舱后部噪声过大问题,通过增加铺设隔热隔声层以及部分区域优化安装阻尼层等一系列被动降噪处理方法,对主要传递路径的飞机壁板结构进行优化,降低客舱后部噪声水平,并进行试验验证。试验结果表明:散射矩阵法可快速准确获得夹层结构的隔声性能,并与混响室法测试结果吻合较好;在厚度不变的前提下,改变隔热隔声层的铺设方式和材料密度对壁板隔声性能影响较小,但在蒙皮内侧粘贴阻尼层能在一定频段范围提高壁板隔声性能;将优化的壁板构型应用到飞机后舱段侧壁板,舱内噪声水平可降低约3 dB。     

VIBRATION-BASED DIAGNOSTICS OF FATIGUE DAMAGE OF BEAM-LIKE STRUCTURES

The analytical investigation of vibration of damaged structures is a complicated problem. This problem may be simplified if a structure can be represented in the form of a beam with corresponding boundary and loading conditions. In this connection, free vibrations of an elastic cantilever Bernoulli-Euler beam with a closing edge transverse crack is considered in the present work as a model of a structure with a fatigue crack. The modelling of bending vibrations of a beam with a closing crack is realized based on the solutions for an intact beam and for a beam with an open crack. The algorithm of consecutive (cycle-by-cycle) calculation of beam mode shapes amplitudes is presented. It is shown that at the instant of crack opening and closing, the growth of the so-called concomitant mode shapes which differ from the initially given mode shape takes place. Moreover, each of the half-cycles is characterized by a non-recurrent set of amplitudes of concomitant modes of vibration and these amplitudes are heavily dependent on the crack depth.The vibration characteristics of damage based on the estimation of non-linear distortions of the displacement, acceleration and strain waves of a cracked beam are investigated, and the comparative evaluation of their sensitivity is carried out.     

Experimental investigations to establish acoustic fatigue design charts

The investigations presented in this paper show that the acoustically induced stresses in stiffened panels can be estimated with sufficient accuracy. Due consideration is given to the effect of the parameters aspect ratio, stringer pitch, curvature, skin thickness and skin doublers. The stresses can be evaluated by means of random SN curves for different joining techniques.     

Analysis of crack propagation data for a strain ageing and a stabilized mild steel tested under R=0 and R=−1 loading conditions

Comparative studies of crack propagation in a strain ageing and a stabilized mild steel were carried out under axial loadings of the R = 0 and R = ?1 types. The results show the rate of fatigue crack propagation is dependent on both the tensile and the compressive stresses in the fatigue cycles, the compression stresses being less effective than the equivalent tensile stresses in causing crack growth. An equation is presented relating the rate of fatigue crack growth to a stress intensity range which is factored to allow for the variations in fatigue damage associated with the tensile and compressive parts of the stress cycle.     

Flexural vibration of non-uniform beams having double-edge breathing cracks

Flexural vibration of non-uniform Rayleigh beams having single-edge and double-edge cracks is presented in this paper. Asymmetric double-edge cracks are formed as thin transverse slots with different depths at the same location of opposite surfaces. The cracks are modelled as breathing since the bending of the beam makes the cracks open and close in accordance with the direction of external moments. The presented crack model is used for single-edge cracks and double-edge cracks having different depth combinations. The energy method is used in the vibration analysis of the cracked beams. The consumed energy caused by the cracks opening and closing is obtained along the beam's length together with the contribution of tensile and compressive stress fields that come into existence during the bending. The total energy is evaluated for the Rayleigh-Ritz approximation method in analysing the vibration of the beam. Examples are presented on simply supported beams having uniform width and cantilever beams which are tapered. Good agreements are obtained when the results from the present method are compared with the results of Chondros et al. and the results of the commercial finite element program, Ansys^©. The effects of breathing in addition to crack depth's asymmetry and crack positions on the natural frequency ratios are presented in graphics.     

CRACK IDENTIFICATION IN VIBRATING BEAMS USING THE ENERGY METHOD

An energy-based numerical model is developed to investigate the influence of cracks on structural dynamic characteristics during the vibration of a beam with open crack(s). Upon the determination of strain energy in the cracked beam, the equivalent bending stiffness over the beam length is computed. The cracked beam is then taken as a continuous system with varying moment of intertia, and equations of transverse vibration are obtained for a rectangular beam containing one or two cracks. Galerkin's method is applied to solve for the frequencies and vibration modes. To identify the crack, the frequency contours with respect to crack depth and location are defined and plotted. The intersection of contours from different modes could be used to identify the crack location and depth.     

Fatigue properties of a S45C steel subjected to ultrasonic nanocrystal surface modification

An ultrasonic nanocrystal surface modification (UNSM) technique, at 3 different vibration strike numbers (34,000 times/mm², 45,000 times/mm², 68,000 times/mm²) was used to modify the surface structure and properties of S45C. These three process conditions respectively produced 2 μm, 12 μm and 30 μm nanocrystal layers. UNSM technique improves the following mechanical properties: microhardness, surface roughness, and compressive residual stress. Also, fatigue life increased with the vibration strike number. UNSM C3 (with the vibration strike number of 68,000 times/mm²) has improved the fatigue strength by as much as 33% for S45C. Optical microscope pictures show that cracks usually initiate from intergranular microcracks on the surface and then extend along the tip traces of UNSM which are considered as process defects. A simple math model (tearing adhesive plaster model) has been made to analyze the initiation and growth of cracks. Though most of the cracks initiate at the surface of specimens, surface nanocrystal layers can help to retard crack initiation. In S45C, the efficiency of crack resistance is more than 48%.the vibration strike number     

Fatigue crack growth in fiber-metal laminates

Fiber-metal laminates(FMLs)consist of three layers of aluminum alloy 2024-T3 and two layers of glass/epoxy prepreg,and it(it means FMLs)is laminated by Al alloy and fiber alternatively.Fatigue crack growth rates in notched fiber-metal laminates under constant amplitude fatigue loading were studied experimentally and numerically and were compared with them in monolithic 2024-T3 Al alloy plates.It is shown that the fatigue life of FMLs is about 17 times longer than monolithic 2024-T3 Al alloy plate;and crack growth rates in FMLs panels remain constant mostly even when the crack is long,unlike in the monolithic 2024-T3 Al alloy plates.The formula to calculate bridge stress profiles of FMLs was derived based on the fracture theory.A program by Matlab was developed to calculate the distribution of bridge stress in FMLs,and then fatigue growth lives were obtained.Finite element models of FMLs were built and meshed finely to analyze the stress distributions.Both results were compared with the experimental results.They agree well with each other.     

Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels

This paper investigates free vibration and dynamic instability of functionally graded cylindrical panels subjected to combined static and periodic axial forces and in thermal environment. Theoretical formulations are based on Reddy's higher order shear deformation shell theory to account for rotary inertia and the parabolic distribution of the transverse shear strains through the panel thickness. Thermal effects due to steady temperature change are included in the analysis. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The panel under current consideration is clamped or simply supported on two straight edges and may be either free, simply supported or clamped on the curved edges. A semi-analytical approach, which takes the advantages of one-dimensional differential quadrature approximation, Galerkin technique and Bolotin's method, is employed to determine the natural frequencies and the unstable regions of the panel. Numerical results for silicon nitride/stainless-steel cylindrical panels are given in both dimensionless tabular and graphical forms. Effects of material composition, temperature rise, panel geometry parameters, and boundary conditions on free vibration and the parametric resonance are also studied.     

Low-cycle fatigue small crack initiation and propagation behaviour of cast magnesium alloys based on in-situ SEM observations

In-situ observations on the initiation and propagation behaviour of low-cycle fatigue small cracks in cast magnesium–aluminium alloys (AM50 and AM60B) were carried out with scanning electron microscopy (SEM) to elucidate the resistance to fatigue cracking and to evaluate the fatigue small crack growth rate accurately and quantitatively. The results indicate that the fatigue small cracks formed preferentially on β-phase (Mg₁₇Al₁₂) boundaries at room temperature. In addition, the effects of the parameters of stress levels in low-cycle fatigue and temperatures as well as microstructure on fatigue small crack propagation behaviour are revealed. The variation of crack open displacement (COD) with stress levels and cycles at elevated temperature shows that it is unsuitable to estimate the fatigue small crack growth rate of cast magnesium alloys using conventional measurement methods such as the plastic-replica technique due to the obvious difference between microscopic cracks in the open and closed states. Stabilized crack propagation behaviour is limited to cases where the physical crack length is less than 1?mm in low-cycle fatigue.     

Comparison of structural response and fatigue endurance of aircraft flap-like box structures subjected to acoustic loading

The results of an extensive test program to characterize the behavior of typical aircraft structures under acoustic loading and to establish their fatigue endurance are presented. The structures tested were the three flap-like box-type of structures. Each structure consisted of one flat (bottom) and one curved (top) stiffener stiffened skin panel, front, and rear spars, and ribs that divided the structures into three bays. The three structures, constructed from three different materials (aircraft standard aluminum alloy, Carbon Fibre Reinforced Plastic, and a Glass Fibre Metal Laminate, i.e., GLARE) had the same size and configuration, with only minor differences due to the use of different materials. A first set of acoustic tests with excitations of intensity ranging from 140 to 160 dB were carried out to obtain detailed data on the dynamic response of the three structures. The FE analysis of the structures is also briefly described and the results compared with the experimental data. The fatigue endurance of the structures was then determined using random acoustic excitation with an overall sound pressure level of 161 dB, and details of crack propagation are reported.     

Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Abstract

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.     

A method for crack sizing using Laser Doppler Vibrometer measurements of Surface Acoustic Waves

The goal of non-destructive testing (NDT) is to determine the position and size of structural defects, in order to measure the quality and evaluate the safety of building materials. Most NDT techniques are rather complex, however, requiring specialized knowledge. In this article, we introduce an experimental method for crack detection that uses Surface Acoustic Waves (SAWs) and optical measurements. The method is tested on a steel beam engraved with slots of known depth. A simple model to determine the cracks size is also proposed. At the end of the article, we describe a possible application: fatigue crack sizing on a damaged slat track. This technique represents a first step toward a better understanding of the crack growth, especially in its early stages (preferably when the cracks can still be repaired) and when it is possible to assume a linear propagation of the crack front. The ultimate goal of this research program is to develop a useful method of monitoring aircraft components during fatigue testing.     

Interaction of fatigue crack with vibration and ultrasound in metallic rod and its use for quantitative characterization

According to the principle of synchronous demodulation,the modulation information in the output signal of vibro-acoustic modulation test was investigated and the nonlinear interaction of sound and vibration with the crack interface in a metallic rod was analyzed.A swept signal excitation was used to obtain a proper high frequency parameter in the test of aluminum rod samples with different sizes of cracks and the modulation information in the output signal was analyzed.It was found that the ultrasound wave in the structure can be separated into two parts.One is the wave which passes through the crack interface modulated by the low frequency vibration,and other wave has no any changes.The nonlinear modulation model was modified and a quantitative method for crack detection was proposed.It is demonstrated by comparing with the ultrasonic C-scanning that this method can be used to estimate the fatigue crack size in the metallic rod.     

Formation and propagation of cracks during cyclic deformation

Summary Starting from observation of the geometric features of formation and propagation of cracks in cycled single crystals of copper a model was developed for fatigue cracking. The only and experimentally well established assumption of the model is that the slip during cyclic deformation tends to be coarse. By the cooperation of stress concentrations at the slip steps and the hardening of slip planes activated locally two slip systems (with different slip planes and Burgers vectors) are activated alternatively so that a crack develops from the slip step. It propagates without monotonically increasing the hardening at the crack tip. The coarse slip produces sharp slip steps at the surface for crack formation and prohibits crack blunting during propagation. In contrast to other models the one described can show how the irreversible process of crack formation and propagation can take place despite completely symmetrical push-pull stresses. The whole crack is formed merely by the motion of dislocations present in the material so that but comparatively small stresses are needed. As, moreover, no thermally activated processes are necessary, fatigue at 4·2°K can be explained too. The strong dependence of fatigue on the state of the surface can also be accounted for since the cracks form at the surface steps. Materials which tend to coarse slip even in unidirectional tests are expected to fatigue easily. This is corroborated experimentally. Finally, many details of crack geometry can be explained in terms of the model.Published in Z. f. Metallkunde58 (1967), 780.     

Coupled horizontal and vertical bending vibrations of a stationary shaft with two cracks

This paper investigates the coupled bending vibrations of a stationary shaft with two cracks. It is known from the literature that, when a crack exists in a shaft, the bending, torsional, and longitudinal vibrations are coupled. This study focuses on the horizontal and vertical planes of a cracked shaft, whose bending vibrations are caused by a vertical excitation, in the clamped end of the model. When the crack orientations are not symmetrical to the vertical plane, a response in the horizontal plane is observed due to the presence of the cracks. The crack orientation is defined by the rotational angle of the crack, a parameter which affects the horizontal response. When more cracks appear in a shaft, then the coupling becomes stronger or weaker depending on the relative crack orientations. It is shown that a double peak appears in the vibration spectrum of a cracked or multi-cracked shaft.Modeling the crack in the traditional manner, as a spring, yields analytical results for the horizontal response as a function of the rotational angle and the depths of the two cracks. A 2×2 compliance matrix, containing two non-diagonal terms (those responsible for the coupling) serves to model the crack. Using the Euler–Bernoulli beam theory, the equations for the natural frequencies and the coupled response of the shaft are defined. The experimental coupled response and eigenfrequency measurements for the corresponding planes are presented. The double peak was also experimentally observed.     

On the aeroelastic instability of two-dimensional panels in uniform incompressible flow

A theoretical and experimental study is presented of the aeroelastic instability of a panel with various boundary conditions on its leading and trailing edges, exposed to air flow over its upper surface or on both sides. The flow is incompressible and two-dimensional (no span-wise deformation of the panel). The case of a panel clamped at its leading edge and free at its trailing edge is investigated both theoretically and experimentally. Agreement between theory and experiment is fair. The aerodynamic theory of steady non-circulatory flow is applied for panels fixed at both ends, and the quasi-steady and full unsteady aerodynamic lifting theories to a cantilevered panel (free at the trailing edge). The analogy with incompressible flow through a long slender tube is pointed out. Theory shows that a panel with both ends fixed loses its stability by divergence, while the instability of a cantilevered panel is of a flutter type. The latter is also confirmed experimentally.