Residual strength prediction for aircraft panels with Multiple Site Damage,using the “EPFEAM” for stable crack growth analysis

In this paper, a new analytical method for solving stable crack propagation problems in a ductile panel with a row of cracks, is presented. The main purpose of the present study is to estimate the maximum load carrying capacity of such panels accurately. The so called Elastic Plastic Finite Element Alternating Method (Pyo et al. (1994) was extended to account for the propagating cracks. The crack propagation algorithm utilizes the analytic crack solution to release the stresses ahead the crack tip. The T _inf ^sup* integral is employed as the crack extension criterion. This integral parameter accounts for the near tip stress-strain singularity and its critical values for crack propagation can be extracted from the P-a curve of single cracked specimen case. The present method can be applied to the problems of the fuselage skin of aging airplanes, in which a row of cracks develop (MSD; Multiple Site Damage) from rivet holes. The load carrying capacity of such damaged structure reduces by a considerable amount. In order to predict the behavior near the critical load, one must account for plastic deformation, if the material is ductile. Furthermore, the maximum load carried by the structure is often reached after some amount of crack propagation. In this paper, a series of analyses have been conducted and their results compare with the available experimental data.     

Fracture analysis of multi-site cracking in fuselage lap joints

A two-dimensional plane stress elastic fracture mechanics analysis of a cracked lap joint fastened by rigid pins is presented and results are applied to the problem of multi-site damage (MSD) in riveted lap joints of aircraft fuselage skins. Two problems are addressed, the problem of equal length MSD cracks and the problem of alternating length MSD cracks. For the problem of equal length cracks, two models of rivet/skin interactions are studied and the role of residual stresses due to the riveting process is explored. Stress intensity factors are obtained as a function of normalized crack length. Also, the load distribution among rivet rows and the compliance change of the joint due to MSD cracking are obtained. For the problem of alternating length cracks, attention is focussed on how load is distributed between columns of rivets and how this load shedding can alter crack tip stress intensity factors. The equal and alternating length crack analyses reveal no clear-cut mechanism to explain the relative uniformity of fatigue cracks emerging from lap joint rivet holes in actual aircraft and in mechanical lap joint tests.     

Fatigue growth of multiple-cracks near a row of fastener-holes in a fuselage lap-joint

The fatigue growth of multiple cracks, of arbitrary lengths, emanating from a row of fastener holes in a bonded, riveted, lap joint in a pressurized aircraft fuselage is studied. The effects of residual stresses due to a rivet misfit, and of plastic deformation near the hole, are included. A Schwartz-Neumann alternating method which uses the analytical solution for a row of multiple colinear cracks in an infinite sheet (the crack-faces being subject to arbitrary tractions), is developed to analyze this MSD problem on a personal computer. It is found that for a range of crack lengths, a phenomena wherein the shorter cracks may grow faster than longer cracks may exist.     

Analysis of cracks in aging aircraft structures,with and without composite-patch repairs

In this paper, the problems of composite-patch repair of (i) center and edge-cracked panels loaded in the far-field; and (ii) cracks emanating from pin-loaded fastener holes, are examined in thorough detail. The effects of various non-dimensional design parameters on the reduction in the stress-intensity factors near the crack-tip are determined, and are presented in the form of design charts. Both analytical and numerical methods are employed in this study. In the analytical method, the cracked metallic plate was considered to be infinitely large, and the composite patch was modeled as a long orthotropic strip of finite height (in the direction perpendicular to the crack axis). Next, by using the Finite Element Alternating Method (FEAM), a more general analysis capability that can treat arbitrary shapes of the cracked metallic sheet, as well as of the composite patches, is developed. This general FEAM is applied to: (i) composite patch repairs of cracks emanating from loaded fastener holes (the MSD problem); (ii) composite patch repairs of semi-elliptical surface flaws in thick plates; and (iii) composite patch repairs of quarter-elliptical surface flaws emanating from fastener holes. Problem (i) is two-dimensional in nature while problems (ii) and (iii) are fully three-dimensional. In all these cases, the effects of various design parameters on the crack-tip (front) stress-intensity factors are fully discussed.     

Residual strength of unstiffened aluminum panels with multiple site damage

This study investigated the residual strength of unstiffened aluminum panels with widths of 381 mm and 229 mm containing multiple site damage (MSD). The MSD usually occurs at rivet holes, or other stress concentration locations within an aircraft structure. This study simulated rivet holes with MSD, by using holes of constant diameter with small cracks, evenly spaced across the midspan of specimens. The panels were prepared by either fatiguing MSD damage at rivet holes or simulating fatigue damage by saw cuts at each hole. Each specimen was subjected to a monotonically increasing tensile load until failure occurred across the midspan of the gauge section. Five different failure criteria which do not model the stable crack extension were evaluated to predict the residual strength (failure load) for each specimen geometry. These criteria provided a wide range of residual strength predictions for wide and narrow panels with MSD. A failure criterion which involved the plastic zone (yielding) of the lead and MSD cracks gave the most accurate prediction of failure load for panels with MSD damage. The width of the specimens did not affect, in general, the trends in the prediction of failure loads from the five failure criteria.     

A theoretical and computational framework for studying creep crack growth

In this study, crack growth under steady state creep conditions is analysed. A theoretical framework is introduced in which the constitutive behaviour of the bulk material is described by power-law creep. A new class of damage zone models is proposed to model the fracture process ahead of a crack tip, such that the constitutive relation is described by a traction-separation rate law. In particular, simple critical displacement, empirical Kachanov type damage and micromechanical based interface models are used. Using the path independency property of the \(C^*\)-integral and dimensional analysis, analytical models are developed for pure mode-I steady-state crack growth in a double cantilever beam specimen (DCB) subjected to constant pure bending moment. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models. The theoretical framework gives the fundamental form of the model and only a single quantity \(\hat{C}_k\) needs to be determined from the Finite Element analysis in terms of a dimensionless quantity \(\phi _0\), which is the ratio of geometric and material length scales. Further, the validity of the framework is examined by investigating the crack growth response in the limits of small and large \(\phi _0\), for which analytical expression can be obtained. We also demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments.     

Fracture and safety analysis of nuclear pressure vessels

An evaluation of the safety factors of nuclear reactor pressure vessels for pressurized water reactors to resist fracture is an important feature in ensuring nuclear reactor safety. The safety analysis has to demonstrate that there is no danger of failure at all. By means of brittle and ductile fracture mechanics the safety factors against critical stress, critical crack size and critical stress intensity factor will be shown. The linear, elastic and plastic stress distributions for plane stress and plane strain conditions are derived for the different modes of fracture. A critical analysis of crack growth and of stress corrosion cracking extends the use of fracture mechanics. A comparison between stress intensity factors obtained by analytical computation and by the Finite Element Method for the case of emergency core cooling is shown.Some technical applications as the estimation of critical crack sizes, the evaluation of operating performance and undercladding cracks are briefly discussed.     

Effect of fiber damage on the overall electrical conductivity of bare carbon fiber strand

The simple method developed by Kachanov (1985) for multiple interacting cracks in homogenous medium is extended to predict complex stress intensity factor for multiple split type interface cracks. Calculations are implemented for two equal cracks and infinite row of periodic cracks at the interface between two dissimilar isotropic materials. Results for infinite row of cracks are compared against the exact analytical solution provided by Sih (1973). The approximate method leads to the results very close the exact solution for crack density up to 0.90 (relative error is less than 3.8% for real part of stress intensity factor) and material dissimilarity does not have a major influence on the error. For crack densities higher than 0.90, the influence of material dissimilarity is more evident and the error increases as material dissimilarity increases. The promising match between the approximate and exact method proves the capability of the approximate method for solving other interacting interface crack problems, such as multiple penny-shaped interface cracks, in which the solution is not obtained in the literature yet.     

Residual strength analysis using CTOA criteria for fuselage structures containing multiple site damage

An extensive experimental program was conducted by the Boeing Company under the funding of the Federal Aviation Administration (FAA), National Aeronautics and Space Administration (NASA), and the United States Air Force Research Laboratory (USAF/RL) to investigate the effects of multiple-site damage (MSD) on the residual strength of typical fuselage splice joints. The experimental results were used to validate the analytical prediction using various methodologies, including STAGS (a generalized shell finite element code) with the crack-tip-opening angle and T^* fracture criteria.The test specimens consisted of large flat panels, curved panels, and an aft pressure bulkhead. The flat panel specimens included three types of longitudinal splice joints and one type of circumferential splice joint. For each type, one panel contained only a lead crack and the other two panels contained MSD 1.3 and 2.5 mm in size, respectively, at the fastener holes ahead of the lead crack. The curved panels were tested under simulated loads of combined cabin pressure and fuselage down bending. Two skin splice types were tested. For each splice type, one panel contained a lead crack only and the other had a lead crack with various sizes of MSD. A section of an aft fuselage containing a large lead crack and MSD in the pressure dome was also tested to demonstrate the capabilities of the methodologies in analyzing actual aircraft structures. This paper presents the analytical approaches and the comparison of predictions with the experimental results in terms of crack linkup stress and residual strength.     

Fracture due to damage from projectile impact

In the usual application, the methods of fracture mechanics are used to determine growth rates and critical load levels for sharp-tipped flaws such as fatigue cracks. By way of contrast to this classic application, another way of introducing fracture producing flaws is to expose a structure to impacts from penetrating projectiles. This paper presents recent test data and analytical techniques for predicting the fracture response of tensile panels impacted by small caliber bullets. Panels of 7075-T6, 2024-T81 and 6A1-4V were tested in thicknesses ranging from 0.032 to 0.375 in. A bracketing technique was used to establish threshold values of prestress for catastrophic fracture. For comparison, a number of impact damaged panels were statically tested for residual tensile strength. These results are compared with the impact fracture threshold values and with strength predictions using the plane-stress stress intensity factor for center-notched panels.     

侧边边界条件对复合材料加筋板轴压载荷下屈曲和后屈曲性能的影响

为研究侧边边界条件对复合材料加筋板压缩稳定性能的影响,首先采用有限元软件对压缩载荷作用下的复合材料加筋板进行建模数值计算,得到加筋板在侧边简支和自由2种边界条件下的屈曲载荷和形式,然后采用工程计算方法对加筋板轴压承载能力进行了估算,参考计算结果,分别对侧边有支持和侧边自由2组加筋板进行轴向压缩试验,分析侧边边界条件对试验件的屈曲形式、屈曲载荷以及后屈曲破坏过程的影响。试验结果表明：侧边支持条件会影响加筋板的屈曲形式和破坏形式。对于侧边有支持的试验件,屈曲后整体变形较小,筋条的压缩断裂是主要的破坏形式;而侧边自由的试验件屈曲后会逐渐出现整体弯曲变形,变形引起的筋条脱粘和弯曲断裂则是主要的破坏形式,且筋条脱粘会显著降低结构的承载能力。有限元计算结果与试验结果较吻合,验证了有限元模型的合理性。采用工程计算方法对侧边有支持的加筋板承载能力进行估算具有较好的精度。     

MULTIPLE-SITE DAMAGE IN AIRCRAFT FUSELAGE STRUCTURES

Abstract— Since the Aloha accident the multiple site damage (MSD) problem of riveted lap joints in aircraft fuselages has drawn much attention. The failure scenarios for a lead crack and more small MSD cracks as discussed by Broek and Swift are summarized, including recent results of a relevant test series by Broek. It shows that small MSD cracks can significantly reduce the load for unstable crack extension. Prevention of catastrophic consequences requires crack arresting capability of the structure. Related aspects of the problem are discussed with reference to failure criteria for ligament failure, the MSD problem for existing and new aircraft, and different options for crack stopper bands.     

Fracture analysis of strength undermatched Al‐Alloy welds in edge cracked tensile panels using FITNET procedure

This paper presents a methodology for the assessment of the remaining load carrying capacity of thin‐walled components under tension containing highly strength undermatched welds and edge cracks. The analysis is based on the strength mismatch option of the fracture module, part of the newly developed European fitness‐for‐service (FFS) procedure FITNET. The mismatch option of the FITNET fracture module allows weld features such as weld tensile properties and weld geometry to be taken into account in the fracture analysis of cracked welded components. The methodology described was verified for centre cracked Al‐alloy large tensile panels containing undermatched welds in Ref. [ 1 ] and hence the present work provides validation with experimental results of the single edge cracked (SEC) and double edge cracked (DEC) panels. The material used is an age‐hardening aluminium alloy 6013 in T6 temper condition used in welded airframe components. The welds in the form of butt joints were produced using the CO₂ laser beam welding process. The results show that by using the FITNET FFS methodology with an appropriate selection of the input parameters, safe acceptable predictions of the maximum load carrying capacity of the welded panels can be obtained. It should also be noted that one of the main difficulties that engineers encounter when applying mismatch analysis for first time is its apparent complexity. A step‐by‐step analysis is proposed here in order to provide guidance for this kind of assessments.     

FRACTURE MECHANICS ASSESSMENT OF PLANAR BRANCHED CRACKS IN AN EQUIBIAXIAL STRESS FIELD

Abstract A simplified fracture mechanics assessment is presented of branched planar cracks in an equibiaxial stress state. In linear-elastic fracture mechanics the stress intensity factors which characterize the load at the crack tips depend, for a given external load, only on the crack geometry. The stress intensity factors of a large number of branched cracks were evaluated using the Boundary Element method, and correlations between the stress intensity factors and the crack geometry were investigated. Formulae are presented which assign an individual effective crack length to each crack tip of a branched crack and hence allow approximate stress intensity factors to be determined for very complicated crack geometries. An algorithm is used for the stochastic simulation of an irregular crack pattern formation in thermal fatigue.     

A general weight function for inclined kinked edge cracks in a semi-plane

A general method for evaluating the Stress Intensity Factors (SIFs) of an inclined kinked edge crack in a semi-plane is presented. An analytical Weight Function (WF) with a matrix structure was derived by extending a method developed for an inclined edge crack. The effects of the principal geometrical parameters governing the problem were studied through a parametric Finite Element (FE) analysis, carried out for different reference loading conditions. The WF can be used to produce efficient and accurate evaluations of the SIFs for cracks with initial inclination angle in the range −60° to +60° and kinked angle in the range from −90° to +90°. The agreement between the results with those obtained by accurate FE solutions suggests that the proposed WF can be used as a general tool for evaluating the fracture mechanics parameters of an inclined kinked crack.     

压电复合材料中幂函数型曲线裂纹的反平面问题

通过构造新保角映射, 利用Stroh公式研究了远场受反平面剪应力和面内电载荷共同作用下无限大压电复合材料中幂函数型曲线裂纹的断裂行为。给出了电不可渗透边界条件下裂纹尖端场强度因子和机械应变能释放率的解析解。该解析解在幂函数的幂次为零时, 可退化为已有文献中无限大压电复合材料含直线裂纹的结果, 证明了其合理性。由解析解可知, 裂纹几何形状一定时, 电场分布将不受机械载荷的影响。最后, 通过数值算例讨论了幂函数的幂次、 系数及其在 x₁轴上的投影长度对机械应变能释放率的影响。结果表明, 当压电体仅受 x₂方向载荷作用时, 对于给定幂次与开口的曲线裂纹, 在 x₁轴上的投影长度存在一临界值使其最容易开裂; 而对于给定投影长度与幂次的曲线裂纹, 开口越大裂纹越容易扩展。