On damage tolerance design of fuselage structure (longitudinal cracks)

Aircraft structure is the most obvious example where functional requirements demand light weight and, therefore, high operating stresses. An efficient structural component must have three primary attributes; namely, the ability to perform its intended function, adequate service life and the capability of being produced at reasonable cost. To ensure the safety of aircraft structures, the Air Force requires damage tolerance analysis. This paper focuses its attention on designing a fail-safe fuselage structure. Two types of damage most frequently associated with the structural integrity of the fuselage are longitudinal cracks under high hoop stresses induced by cabin pressurization and circumferential cracks under stresses from vertical bending of the fuselage. The analysis of these types of cracks is complex, first due to the complex structural configuration (i.e. frames, skin longeron and crack stopper straps) and secondly due to the influence of the curvature of the shell. Various analytical and empirical approaches have been used to study the damage tolerance capability of the fuselage structure. Due to the lack of a comprehensive model to calculate the stress intensity factors for the complex structure, experiments usually have been performed to measure the crack growth rates and to demonstrate the residual strength of fuselage-type structural components containing circumferential and longitudinal cracks.

In this paper various analytical and empirical approaches used in evaluating the damage tolerance capability of the fuselage structure are critically evaluated and compared. A model which accounts for the influence of frames, straps and curvature is developed. This model is then used in an example problem having typical military cargo aircraft fuselage structural elements. The Air Force damage tolerance requirements are discussed in detail.     

On damage tolerance design of fuselage structure—circumferential cracks

The aircraft structure is the most obvious example where functional requirements demand light weight and, therefore, high operating stresses. An efficient structural component must have three primary attributes; namely, the ability to perform its intended function, adequate service life, and the capability of being produced at reasonable cost. To ensure the safety of aircraft structures, the Air Force requires damage tolerance analysis. This paper focuses its attention on designing a fail-safe fuselage structure considering circumferential cracks under stresses from vertical bending of the fuselage. The analysis of these types of cracks is complex, first due to the complex structural configuration (i.e. frames, skin longeron and crack stopper straps) and secondly due to the influence of the curvature of the shell. Various analytical and empirical approaches have been used to study the damage tolerance capability of the fuselage structure. Due to lack of a comprehensive model to calculate the stress intensity factors for the complex structure, experiments usually have been performed to measure the crack growth rates and to demonstrate the residual strength of fuselage-type of structural components containing circumferential and longitudinal cracks. In this paper various analytical and empirical approaches used in evaluating the damage tolerance capability of the fuselage structure are critically evaluated and compared. A model which accounts for the influence of frames, straps and curvature is developed. This model is then used in an example problem having typical military cargo aircraft fuselage structural elements. The Air Force damage tolerance requirements are discussed in detail.     

Analysis of crack interactions at adjacent holes and onset of multi-site fatigue damage in aging airframes

Focusing on the geometry of one hot spot in airframes, this paper discusses the onset of the interaction of two collinear cracks at adjacent holes and defines the onset as a criterion for multi-site fatigue damage failure. The finite element method is used to calculate the stress intensity factors at the tips of two collinear cracks at adjacent holes growing towards each other. The stress intensity factor is found to increase rapidly at the onset of interaction. Since a rapid increase in stress intensity factor results in a rapid and unstable growth of the crack, the onset of the interaction is proposed as the point where the multi-site fatigue damage starts. A criterion to avoid multi-site fatigue damage locally is then established based on the separation distance of two crack tips at the onset of the interaction. To speed up the simulation of crack growth under multi-site fatigue damage with the finite element method, a semi-empirical criterion is derived to determine the time at which the stress intensity factors at the tips of the cracks correlate. The numerical examples show that the proposed criterion saves simulation time while incurring negligible relative error in the computation of the final crack length.     

Improvement of damage tolerance of laser beam welded stiffened panels for airframes via local engineering

Damage tolerance of an aerospace grade aluminum alloy was studied using a new design philosophy in skin and stringer geometries. Systematic thickness variations (crenellations) were introduced onto the skin and stringers of the laser beam welded (LBW) stiffened Al2139-T8 large center cracked flat panels to modify the stress intensity factor (SIF) distribution and hence to improve fatigue life. Fatigue crack propagation (FCP) tests (on panels with crenellations) with crack growing perpendicular to the welded stringers were conducted under constant amplitude and spectrum loading conditions. Results were compared with the “classical” LBW stiffened panels (with no crenellations) having equal weight and tested under the same conditions. The new panel design with crenellations showed substantially longer fatigue lives under constant amplitude loading. This gain significantly improved under spectrum (MINI-TWIST) loading fatigue tests. This paper presents the first FCP test results of a comprehensive ongoing program which investigates the efficiency of component design with crenellations to improve damage tolerance behavior of welded Al-alloy and steel structures. Issues including microstructural examinations, numerical investigations, fitness-for-service (FFS) analysis and residual strength aspects of this program will be topics of another communication.     

Longitudinal shear of a crack in a multi-material circular cylinder

This is an article dealing with the longitudinal shear of a crack contained in a circular cylinder, which is embedded in and fixed by perfect bonding to a composed hollow circular cylinder, consisting of a number of hollow sub-cylinders of different materials. A rigorous solution to the problem is developed. With the material and geometric constants of the composed hollow circular cylinder as parameters, numerical values of stress intensity factors for the crack are worked out. The delicate behavior in the variation of the stress intensity factors, when the number of the hollow sub-cylinders becomes large, is analyzed and discussed. The solution is developed by utilizing a simplified and improved technique using complex variables.     

Near-threshold fatigue crack propagation of several high strength steels

In support of Douglas Aircraft Co. structural damage tolerance analysis, crack propagation rates were measured in humid air from 10^?8 to 10^?3 mm/cycle of several high strength martensitic steels at stress ratios of $\text{R = 0.1}$ and $\text{R = 0.5}$. Increasing the stress ratio was found to decrease the threshold stress intensity. Increasing the tensile yield material strength in these quench and tempered steels resulted in a nearly linear inverse relationship with the threshold stress intensity. The threshold stress intensity appeared to be independent of the fracture toughness of the alloy steel.     

Examination of the Mode II fracture behaviour of wood with a short crack in an asymmetric four-point bending test

Asymmetric four-point bending tests of agathis specimens with a short crack along the neutral axis in a tangential–longitudinal system were conducted onto analyse the failure behaviour of wood with a short crack. The nominal shear strength and Mode II critical stress intensity factors of the specimens with various crack lengths were measured, and the influence of crack length on these properties was examined. The nominal shear strength of the cracked specimens was significantly lower than the strength of a crack-free specimen, even when the crack was extremely short. This finding suggests that the fracture mechanics theory is effective for analysing the failure behaviour of wood with a very short crack in this loading condition. However, the Mode II critical stress intensity factor still depends on the crack length. When the crack length was corrected with considering the formation of fracture process zone ahead of the crack tip, the critical intensity factor could be predicted effectively as well as the nominal shear strength.     

Investigation of the kinetics of cracks in polymethyl methacrylate by dynamic photoelasticity

Methods have been developed for experimental investigation of the kinetics of fast cracks in plates of optically active model material making it possible to load by pulsed pressure varying the amplitude and length of the pulse and also to use the photoelastic method for recording dynamic processes with use of a superfast motion picture camera. The relationship of the dynamic stress intensity factor to crack growth rate and plate thickness was obtained taking into consideration the influence of longitudinal and transverse elastic waves. A clear relationship between stress intensity factor and v_cr was established. It was shown that with a fast crack growth rate (v_cr < 270 m/sec) the uniqueness between stress intensity factor and v_cr is disturbed by the action of reflected waves. The character of action on the stress intensity factor and crack growth rate of longitudinal and transverse waves reflected from the boundaries of the plate and also the influence of inertial effects caused by stress waves, high crack growth rates, and a change in the stressed and strained state with an increase in plate thickness were determined. It was determined that in polymethyl methacrylate in incidence on a crack at an angle of 90° a longitudinal wave increases the stress intensity factor and v_cr (with v_cr<625 m/sec) while a transverse wave decreases these characteristics.Translated from Problemy Prochnosti, No. 9, pp. 40–46, September, 1991.     

COMPARISON OF FATIGUE LIFE PREDICTIONS IN WELDED JOINTS USING 2D AND 3D K SOLUTIONS

The paper presents the results of fatigue life predictions in non-loaded carrying tee and cruciform joints and also longitudinal seams of tubes, obtained with 2D and 3D stress intensity factor solutions. The 2D computational method uses the standard Bueckner weight function solution to obtain the 2D values of the stress magnifying factor M_K. In the 3D approach a modified 3D weight function solution was used in conjunction with the Raju and Newman base stress intensity formulation. Comparison of results is shown between the 2D and 3D fatigue life predictions and experimental results of fatigue strength obtained by the authors. Results are also given showing the influence of crack aspect ratio, thickness and the ratio of tube radius to tube thickness.     

Damage tolerance analysis of a helicopter component

Fatigue critical helicopter components are, in general, subjected to complex high frequency dynamic loading. Due to these high frequencies small flaws can propagate to failure in a short period of time. Consequently, the demonstration of damage tolerance for those components must include the analysis of near-threshold crack propagation, i.e. growth in the low-to-mid stress intensity factor range (ΔK) regime. To this end this paper presents a fatigue crack growth analysis of a helicopter airframe component, that was used as part of a round-robin study into helicopter fatigue, performed using a non-similitude based crack growth law, termed the Generalised Frost–Dugdale law. The resultant computed crack growth history is in excellent agreement with the measured crack length histories.     

ARALL (Aramidfaserverstärkter Aluminiumschicht-Verbundwerkstoff) - Ein neuer Hybrid-Verbundwerkstoff mit besonderen Schwingfestigkeitseigenschaften

ARALL (Aramid Fibre Reinforced Aluminum Laminate)-A New Fatigue Resistant Hybrid Composite High fuel expenses and the tendency to build larger aircrafts are two main factors forcing the aircraft engineers to develop structures which allow for higher design stress levels. Higher design stress levels require an increasing concern with the fatigue behavior of the structure. One way to solve the problem is to develop new high strength fatigue resistant materials. In this paper a material of this type is presented: ARALL, an aramid fibre reinforced aluminum laminate. This hybrid material consists of thin sheets of a high strength aluminum alloy which are bonded together. Into the bond-line thin layers of aramid fibres are embedded. As soon as fatigue cracks are initiated in the metallic part of the hybrid composite material during the fatigue loading, the strong and fatigue insensitive aramid fibres remain unbroken behind the propagating crack. They hinder the crack opening and reduce the stress intensity factor at the crack tip in the metal part of the hybrid composite. This mechanism leads to a significant reduction of the crack growth and can be enhanced by introducing favourable residual stresses into the hyb- rid material. For an optimized ARALL material an aluminum sheet thickness of about 0.5 mm and an aramid layer thickness of about 0.25 mm (with a fibre volume content of about 40–50%) are chosen. ARALL decreases the crack growth rates by orders of magnitude, as compared to monolithic aluminum sheets, and is an extremely damage tolerant material.     

热暴露对γ-TiAl合金表面缺陷损伤容限的影响

研究了热暴露(700℃,10 000 h)对高强度全片层γ-Ti Al合金Ti-44Al-4Nb-4Hf-0.2Si-1B表面缺陷损伤容限的影响,采用扫描电子显微镜研究了热暴露导致γ-Ti Al合金的显微组织变化,并将之与在交变载荷下的表面短裂纹行为和长裂纹扩展行为联系起来.研究发现,在热暴露后,该合金的疲劳强度提高,且长疲劳裂纹启裂门槛值改善,但热暴露导致该合金短裂纹效应的尺寸范围明显增大.采用Kitagawa-Takahashi线图的形式总结和分析了实验结果,分析了热暴露引起的疲劳强化、疲劳失效的非安全短裂纹的尺寸变化以及长裂纹的启裂门槛值的变化,定量确定了热暴露对表面缺陷的损伤容限.长期热暴露所导致的材料内部应力释放、偏聚缓解、缺陷钝化显著影响裂纹尖端的应力状态,更有利于增大长裂纹的启裂抗力并减缓长裂纹的扩展速率.     

Fatigue crack growth in thick-walled cylinders under pulsating internal pressure

The stress intensity factor is derived for both single and multiple longitudinal, elliptical cracks in the wall of a pressurized thick cylinder of given geometry. For this purpose, it is found necessary to combine known solutions to the stress intensity factor for a straight longitudinal crack with the effects of a curved crack front and multiple cracking. The analysis is appraised from a number of fatigue tests reported for % Ni-Cr-Mo cylinders with diameter ratios of between 2 and 3 under repeated and fluctuating pressure cycles. When cylinders with poorly finished bores are assumed to be initially flawed, it is found that their fatigue lives under high ranges of pressure may be predicted reliably for the single crack propagation failures observed. This analysis employs published WOL or SEN fatigue crack growth data for the alloy. The enhancement in fatigue life that results from an improved surface finish has enabled that proportion of life expended during the initiation phase to be determined. It is further shown that the observed effect of mean stress and surface finish on the fatigue limit may be quantified with a change to the threshold of stress intensity for crack growth. A number of tests were conducted with two-step changes to the amplitude of the pressure cycle. In this instance, nonlinear, stress dependent, cumulative damage rules are shown to offer no advantage over Miner's rule in the prediction of fatigue life.     

Fatigue Resistance of an Anodized and Hardanodized 6082 Aluminum Alloy Depending on the Coating Thickness in the High Cycle Regime

In this study, the high cycle fatigue behavior of an anodized 6082 aluminum alloy is investigated. Main focus is on the most relevant influencing factors for crack initiation and propagation under cyclic loading and damage mechanisms considering coating type, thickness, and residual stresses. The bare substrate is compared to anodized and hardanodized specimens with three coating thicknesses, for each coating type, in the range from 20 to 70 μm. Coating hardness and microstructure as well as residual stresses are analyzed. Fatigue and fracture behavior under alternating tension–compression loading is determined. Dependent on the coating thickness, the fatigue strength is reduced by 8%–50% after anodizing and by 50%–62% after hardanodizing. As the coating thickness is equal to the initial crack length from a fracture mechanical point of view, stress intensities at the crack tips are higher for thicker coatings respectively longer initial crack lengths. Therefore, propagation of fatigue-induced cracks from the coating into the substrate is promoted for a higher coating thickness resulting in premature failure. A significant correlation between the coating thickness and tensile residual stresses induced by both coatings in the subjacent substrate is not found and residual stress influence on the overall fatigue strength is only minor.     

Tools and methods for addressing the durability of rolling stock

Railway rollingstock is subjected to an arduous regime of load and vibration. This implies a likelihood of encountering fatigue cracking within rollingstock structures and components at some stage in the asset life cycle. Whilst there is an abundance of tools aimed at preventing the occurrence of fatigue cracking at the design stage–typically adopting the so called ‘safe life’ design philosophy–tools to assess the growth and tolerance of cracks once initiated are less routinely applied in the rail industry than in other industries such as aerospace and power generation. Fatigue life prediction of rollingstock components is exceptionally difficult and computationally intensive as calculations need to be made at each stage of the life of a component/structure. This is done to compute the stress intensity factors for each crack configuration so as to calculate the amount of crack growth, update the crack geometry, and then re-compute the stress intensity factors for this new geometry. To meet this challenge, this paper will discuss the issues associated with fatigue crack growth within rollingstock and provide an overview of the tools available to assess the defect tolerance of rollingstock structures and manage the key considerations to safely ensure the integrity of assets, whilst maintaining asset availability/productivity.This study consists of the following areas of analysis. In the first stage, a 3D finite element model to evaluate the stress of rollingstock structure (with no cracking) is performed. The second stage of the (sequential) analysis is carried out for stress intensity factor of cracks in the rollingstock under service condition by using a semi-analytical solution technique that involves the use of an analytical solution combined with a numerical algorithm to assess fracture strength. In the third stage, the Hartman–Schijve approach is used to modelling crack growth. As the crack is not modelled explicitly a coarser mesh can be used thereby improving analysis time. This method is ideal for use on fatigue life prediction of rollingstock structures.     

Influence of foreign object damage on fatigue crack growth of gas turbine aerofoils under complex loading conditions

Foreign object damage (FOD) has been identified as one of the main life limiting factors for aeroengine blades, with the leading edge of aerofoils particularly susceptible. In this work, a generic edge ‘aerofoil’ geometry was utilized in a study of early fatigue crack growth behaviour due to FOD under low cycle fatigue (LCF), high cycle fatigue (HCF) and combined LCF and HCF loading conditions. Residual stresses due to FOD were analyzed using the finite element method. The longitudinal residual stress component along the crack path was introduced as a nodal temperature distribution, and used in the correction of the stress intensity factor range. The crack growth was monitored using a nanodirect current potential drop (DCPD) system and crack growth rates were correlated with the corrected stress intensity factor considering the residual stresses. The results were discussed with regard to the role of residual stresses in the characterization of fatigue crack growth. Small crack growth behaviour in FODed specimens was revealed only after the residual stresses were taken into account in the calculation of the stress intensity factor, a feature common to LCF, HCF and combined LCF + HCF loading conditions.     

Fracture toughness of laminated steels

Lamination occurs spontaneously in the transverse direction in many commercially available steel plates, if the transverse stresses are sufficiently high. Previous investigations have indicated that lamination is often accompanied by an improvement in the fracture toughness of the plate material. In the vicinity of the crack tip, the stress concentration is so large that the bond between adjacent layers will break before crack propagation sets in. If these layers are sufficiently thin, a state of plane stress is approached near the crack tip. In the present study, the influence of layer thickness and bond strength on the fracture toughness is investigated. It is shown that lamination does improve the toughness, if certain conditions in these variables are fulfilled. This offers a possibility to build up structures with high yield stress and high fracture toughness at the same time, since the permissible defect size to prevent unstable crack growth need not be uncomfortably small.     

Damage tolerance approach for analyzing a helicopter main rotor blade

In this article, damage tolerance approach is used for life estimation of the main rotor blade of a helicopter under random loading. At first, fatigue crack growth properties and threshold stress intensity range of the spar is obtained based on ASTM E647 test method. Then, crack growth analysis is done using Zencrack software. In order to calculate the length of the smallest growing cracks and their fatigue crack growth life, no crack growth and slow crack growth approaches were used. A comprehensive investigation was carried out on the effect of initial crack length on growth or no growth of cracks.     

Debonding of a Weak Interface in Front of a Through-Thickness Crack

A through thickness crack traversing a laminate and approaching an interface weakened by the presence of a small debonding defect is analysed in the case when the defect is fully embedded in the K-field of the main crack. Plane approximation estimates of critical interfacial strength for crack deflection are compared with 3D calculations using integral equation and weight function formulations.     

Evolution of subsurface radial cracks in bi-material structures undergoing indentation loading

Mathematical modelling is used to study the evolution of damage caused by indentation loading on curved bilayers consisting of brittle shells filled with polymer support material. Such loads are pertinent to all-ceramic crown structures on tooth dentin in occlusal function. The aim is to develop tools to assist in the design of such structures to ensure both high damage resistance and high damage tolerance. Specifically, the initiation and propagation of a radial crack emanating from the interface is studied using the boundary element method (BEM) in three dimensions. The system that is analysed consists of a spherical indenter and both flat and convex bi-material samples. A semi-circular intrinsic flaw/crack is assumed to lie on the axis of indentation at the interface of the two materials, in the coating. Upon application of an indentation load, the mode I stress intensity factor distribution along the crack front is determined and the crack front is propagated using a small increment. By repeating this process, the critical load for propagation of the crack is obtained as a function of crack size. The results compare well with experimental crack propagation studies in bi-materials, as well as observed damage in porcelain crowns that have been used to repair teeth. The convex models show that radial cracks can exist in the brittle coating, without leading to catastrophic failure, up to a critical crack length. An increase in the applied load, causing the crack to grow beyond this length, causes the coating to fail in an unstable way. The results show that there is an optimum combination of design parameters for maximising the damage resistance. It is shown that larger convex radii of curvature lead to higher damage tolerance.