FML full scale aeronautic panel under multiaxial fatigue: Experimental test and DBEM Simulation

This paper concerns the numerical and experimental characterization of the static and fatigue strength of a flat stiffened panel, designed as a Fibre Metal Laminate (FML) and made of aluminium alloy and Fibre Glass FRP. The panel is full scale and was tested under both static and fatigue bi-axial loads, applied by means of an in house designed and built multiaxial fatigue machine. The strain gauge outcomes from a preliminary static test are compared with the corresponding numerical results, getting a satisfactory correlation. A crack propagation in the FML is simulated by a two dimensional original approach based on the Dual Boundary Element Method (DBEM). To overcome the lack of experimental information on the size of delamination area an “inverse” procedure is applied: the delamination introduced in the DBEM model is calibrated in such a way to minimise the numerical and experimental growth rate differences.This approach aims at providing a general purpose evaluation tool for a better understanding of the fatigue resistance of FML panels, providing a deeper insight into the role of fibre stiffness and of delamination extension on the Stress Intensity Factors. The experimental test was realized in the context of a European research project (DIALFAST).     

Crack propagation rate and failure life in biaxial low cycle fatigue at elevated temperatures

This paper describes the crack propagation rate and the failure life in the biaxial low cycle fatigue test for a type 304 stainless steel at elevated temperatures. Macro crack propagation rates were observed for the tubular specimen in the push-pull and the reversed torsion tests. The crack propagation rate in both the tests was discussed in connection with the crack opening displacement in experiments and FEM analyses. The new equivalent stress derived from the FEM analysis was proposed so as to correlate the biaxial crack propagation rate. The equivalent stress well correlated not only the crack propagation rate but also the biaxial low cycle fatigue failure data.     

Vibroacoustic performance of fiber metal laminates with delamination

In the present work, the numerical assessment of vibroacoustic (VA) performance of fiber metal laminates (FML) with mid-plane center delamination is presented. A fluid structure interaction study has been done using finite element method (FEM). Experimental validation is performed on an aluminium (AL) panel for verifying the correctness of finite element (FE) idealization procedure to simulate the fluid-structure interaction. Delamination is introduced in the FE model of FML panel and VA analysis is subsequently carried out. Sound transmission loss (STL) is computed on the panel with center delamination and without delamination. The overall sound pressure level (OASPL) shows that the presence of delamination (40% in total area) in FML has not changed the total energy of the transmitted sound when compared to aluminium and composites. However, in the narrow frequency bands (150–200 Hz, 200–250 Hz), the sound transmission nature has been significantly affected due to local delamination modes participating in the fluid-structure interaction process.     

DBEM and FEM analysis on non-linear multiple crack propagation in an aeronautic doubler-skin assembly

The performance of a riveted patch repair, applied on a cracked panel, is simulated by using both a commercially available boundary element code (BEASY) and a finite element code (ANSYS). A two-dimensional stress analysis on a single-sided repaired configuration is performed by both methodologies; consequently, the occurrence of out-of-plane bending and its effect on the through-thickness stress intensity factor (SIF) variation is neglected. The connection between the two layers (patch and panel) is realised by 32 rivets, with through-cracks initiated on the most loaded holes. Special elements are used to model the crack: discontinuous elements in the dual boundary element method (DBEM) approach or quarter point elements in the finite element method (FEM) approach. Different loading configurations are considered depending on the presence of a biaxial or uniaxial remote load and the non-linear hole/rivet contact is simulated by gap elements. The most stressed skin holes are highlighted, and the effect of a through crack from such holes is analysed in terms of SIFs and stress redistribution. The accuracy in SIFs assessment by DBEM and FEM and the respective computational and pre-processing efforts are determined. Such a two-dimensional analysis allows us a straightforward pre-processing phase, and very short run times are needed. A peculiar arrangement of the pin configuration in the DBEM analysis allows us to take into account the real in-plane plate stiffness and the transversal pin stiffness, even in a 2D analysis (this is straightforward by using FEM).     

Coupled FEM–DBEM approach on multiple crack growth in cryogenic magnet system of nuclear fusion experiment ‘Wendelstein 7‐X’

At the Max Planck Institute for plasma physics in Greifswald, Germany, the world's largest nuclear fusion experiment of modular stellarator type Wendelstein 7‐X has started plasma operation. The hot hydrogen plasma is confined in a plasma vessel by an electromagnetic field generated by 50 non‐planar and 20 planar superconducting coils. The superconducting coils are encased in cast stainless steel housings. The coils are bolted onto a central support ring and welded together by so called lateral support elements (LSEs). In this paper, a procedure, based on a global–local finite element method (FEM)–dual boundary element method (DBEM) approach, is developed to simulate the propagation of multiple cracks detected in LSEs and undergoing a fatigue load spectrum. The global stress analysis on the superconducting coils is performed by FEM whereas the sub‐modelling approach is adopted to solve the crack propagation in the DBEM environment. The boundary conditions applied on the DBEM submodel are the displacements calculated by the FEM global analysis, in correspondence of the cut surfaces (there are no body forces nor external loads applied on the submodel volume). Two cracks are simultaneously introduced, and a linear elastic fracture mechanics analysis is performed. Results in terms of cracks growth rates and evolving crack shapes are provided, and the residual life of the component is forecast.     

Boundary element analysis of fatigue crack propagation micromechanisms in austempered ductile iron

The Dual Boundary Element Method (DBEM) is used in this work to model the micro mechanics of fatigue crack propagation in austempered ductile iron (ADI). Emphasis is put in devising accurate procedures for the evaluation of the interaction effects between very close crack–microcrack arrays. Fracture parameters are computed via the so-called one-point displacement formula using special crack-tip elements. Crack propagation is modelled using an incremental crack extension analysis; with crack extensions calculated using a propagation law that accounts for the near-threshold regime. Obtained results are in agreement with experimental observations, providing evidence to fracture mechanics models proposed in the literature.     

Numerical simulation study of fatigue crack growth behavior of cracked aluminum panels repaired with a FRP composite patch using combined BEM/FEM

A combined boundary element method and finite element method (BEM/FEM) is employed to investigate the fatigue crack growth behavior of cracked aluminum panels repaired with an adhesively bonded fiber-reinforced polymer (FRP) composite patch. Numerical simulation of crack growth process of a cracked aluminum panel repaired with a FRP composite patch under uniaxial cyclic loading has been carried out. The curve of crack length on unpatched side of the cracked panel versus the number of cyclic loading is determined by the numerical simulation, and it agrees well with experimental data. Furthermore, the crack front profiles of the cracked panel during fatigue crack growth and the distributions of stress intensity factors along crack fronts are also numerically simulated.     

Comparison of crack growth simulation by DBEM and FEM for SEN-specimens undergoing torsion or bending loading

The 3D fatigue crack growth behaviour in 3PB-specimens or in cantilever beam specimens under, respectively, bending or torsion loading, with inclined planes for the initial crack, is investigated by the dual boundary element method (DBEM). Mixed mode conditions along the crack edge are characterized: stress intensity factors (SIFs) are determined using the J-integral method, and the crack growth direction is computed by the minimum strain energy density criterion. The evolving crack shape (spatially twisted or twisted and warped crack faces), computed by the DBEM model, is successfully compared with experimental findings and FEM results.     

玻璃纤维-Al 混杂复合层板的疲劳裂缝扩展行为

本文研究了一种新型结构复合材料玻璃纤维-Al 混杂复合层板(Glass Aluminum Laminates,GLALL)在不同外载荷作用下的疲劳裂缝扩展行为,以及疲劳破坏规律。试验发现,由于未断高强度纤维对裂缝的桥接作用降低了裂缝尖端的有效应力场强度因子,GLALL 的疲劳裂缝扩展速率远低于单一Al 合金。伴随 Al 合金层内疲劳裂缝的扩展,GLALL 疲劳裂缝附近区域会产生脱层破坏,脱层区宽度随外加载荷增大而增大。脱层区宽度越小,纤维对疲劳裂缝的桥接作用越强。     

An experimental study on fatigue characteristics of CFRP-steel hybrid laminates

This paper aims to investigate the fatigue characteristics of hybrid laminates consisting of wave carbon fiber reinforced polymer (CFRP) sheets and a thin stainless steel plate under the tension–tension loading. Different loading options (e.g. same stress and same force), layers of CFRP sheets, and lay-ups of laminates (single and double sides) were considered. A series of experimental tests were performed to determine the effectiveness of the CFRP bonding on prolonging fatigue crack initiation life, preventing fatigue crack propagation and extending fatigue life of the hybrid laminates. Three distinct failure modes, classified as delamination, delamination bending and fiber breakage, were observed in the tests. It is shown that the loading conditions and CFRP thickness are the critical parameters affecting the failure modes and fatigue resistance. The crack initiation life and fatigue life of fiber-metal laminates (FMLs) increase by factors ranging from 1.06 to 1.96 and 1.17 to 2.07, respectively, relative to monolithic steel plates under the same force condition; whereas decrease by factors ranging from 0.63 to 0.89 and 0.28 to 0.61 under the same stress condition. Moreover, the double-side bonded FMLs show better fatigue properties and more stable crack propagation than single-side counterpart with the same thickness of CFRP.     

Fatigue simulation for titanium/CFRP hybrid laminates using cohesive elements

This paper presents a new numerical approach for predicting fatigue crack growth in fiber-metal laminate (FML). Cohesive elements are used to express the complicated damage consisting of transverse cracking, splitting, and interlaminar delamination. The damage growth in the cohesive elements due to cyclic loading is represented by the conventional damage-mechanics model. The simulation was applied to notched Ti/CFRP hybrid laminates of two stacking configurations. In both cases, the crack growth rate in the titanium layer and the delamination shape agreed well with experiments reported in the literature. Complementary analysis for crack extension in the metal sheet is performed out of consideration of the damage in internal FRP layers. The numerical results demonstrated that the underlying damage modes in the FRP layer must be taken into account to predict the fatigue crack growth at the metal layer in FMLs.     

斜纹编织碳纤维/环氧树脂复合材料II型分层性能及损伤演化表征

为研究编织复合材料在静载及疲劳载荷下的分层特性及损伤演化模式,对斜纹编织CF3052/3238A碳纤维/环氧树脂复合材料II型静开裂及疲劳开裂性能进行了测试。结果表明:斜纹编织CF3052/3238A碳纤维/环氧树脂复合材料裂纹扩展行为受纬向纤维影响存在周期性局部受阻现象,分层破坏模式除层间开裂外还存在纬向纤维脱粘;斜纹编织CF3052/3238A碳纤维/环氧树脂复合材料裂纹扩展速率符合Paris公式,不同加载控制模式下编织复合材料疲劳驱动力增长规律存在本质区别:恒幅疲劳载荷下斜纹编织复合材料疲劳驱动力呈抛物线型单调增长;而恒幅疲劳位移下复合材料疲劳驱动力随分层长度呈波峰型分布;采用基于载荷控制模式和位移控制模式下的疲劳驱动力模型,可对斜纹编织CF3052/3238A碳纤维/环氧树脂复合材料进行损伤演化表征,其表征效果良好,具有工程参考价值。      

Fatigue crack growth and delamination behaviours of advanced Al‐Li alloy laminate under single tensile overload

In this paper, fatigue crack growth and delamination behaviours of a new fibre metal laminate (FML) named as Al‐Li alloy laminate were tested under different single tensile overloads and compared with those of glass laminate aluminium reinforced epoxy. The results indicate that the crack growth rate of Al‐Li alloy laminate after overload applied can quickly get back to its original level when the crack grows outside of the overload plastic zone. The overload has no influence on the delamination shape and size of Al‐Li alloy laminate. These results are obviously different from those found in the present study for GLARE, in which the crack growth rate cannot recover after overload, even though the crack is far beyond the overload plastic zone. A kink nearby the location of overload applied was found in the obtained delamination shape. This study provides some new results for better understanding the damage tolerance mechanism of FMLs.     

Stress concentrations around bonded repairs

Ageing aircraft fuselages require safe and damage-tolerant repair techniques. Bonded fibre–metal laminates (FML) combine a small mismatch in coefficients of thermal expansion (CTE) with the cracked skin, excellent fatigue properties and high strength, and are therefore promising materials for bonded repairs. This paper focuses on local stress concentrations in the fuselage skin at the edge of a bonded FML repair, and presents analytical, FEM and experimental results of single and multiple repairs in close proximity. Repairs on both flat uniaxially loaded skins and curved biaxially loaded skins were considered. The main objective of this research is the validation of the crack patching design program CalcuRep. The model on which CalcuRep is based, the 'Rose model', was extended and used for the analytical prediction of skin stresses in the specimens. It appeared that, in order to prevent fatigue critical stresses in the skin next to the patch, one should carefully choose the patch material and geometry. Furthermore, in a specific repair configuration with multiple patches, a minimum separation is required to prevent high stress concentrations in the skin between the patches. It was confirmed that, in most cases, a biaxial stress field has a favourable effect on the stress in the skin along the patch edge, compared with the uniaxial situation. With both the FEM and the extended Rose model, the stresses in the skin next to the patch could be predicted with sufficient accuracy. It is the intention to implement the extended Rose model in a new version of CalcuRep.     

High performance estimations of delamination of graphite/epoxy laminates with electric resistance change method

Delamination of laminated composites is usually invisible or difficult to detect visually. Delamination causes low reliability for primary structures. Automatic systems for in-service delamination identifications are desired to improve low reliability. The present study employs an electric resistance change method for delamination detection. Since the method adopts reinforcement carbon fiber itself as sensors for delamination detection, this method does not reduce static or fatigue strength; also, the method is applicable to existing structures. Authors have found that the electric resistance change method with response surfaces is very effective experimentally and analytically. However, a large error of estimation remains for estimation of delamination location. In the present study, a new data processing procedure is proposed to improve performance of estimations of delamination location. The new method is applied to laminated composite beams. A delamination crack of a laminated composite beam is monitored with the new method using FEM analyses. As a result, the method reveals excellent performance of estimations of delamination location even for new data not used in regression equations.     

The characteristics of an inclined crack in anisotropic paperboard under biaxial loading

In this paper, a fracture mechanics method was applied for the evaluation of crack behaviour in anisotropic paperboard subjected to biaxial uniform loading. The experiment was performed to determine the crack propagation angle and the fracture strength of paperboard under biaxial loading with the cruciform specimen optimized by FEM simulation. The effects of biaxial loads on the critical stress ratio and crack propagation angle for various inclination angles were investigated. The experimental results were compared with theoretical results, which were calculated by using the Normal Stress Ratio Criteria. The experimental results for crack propagation angle and critical stress show good agreement with theoretical results.     

Modeling of fatigue crack propagation using dual boundary element method and Gaussian Monte Carlo method

This paper studies the modeling of fatigue crack propagation on a multiple crack site of a finite plate using deterministic and probabilistic methods. Stress intensity factor has been calculated by the combined deterministic approach of the dual boundary element method (DBEM) and the probabilistic approach of the Gaussian Monte Carlo method. The Gaussian Monte Carlo method has been incorporated to simulate the random process of the fatigue crack propagation. A finite plate of aluminum alloy 2024-T3 with a thickness of 1.6 mm and 14 holes is analyzed and the fatigue life of the plate is predicted by following a linear elastic law of fracture mechanics. The results of fatigue life predicted by DBEM-Monte Carlo method are in good agreement with experimental ones. The same approach is also applied to two other engineering applications of a gear tooth and a bracket.     

Fatigue crack growth behavior of cracked aluminum plate repaired with composite patch

In this study, we investigated the fatigue crack growth behavior of cracked aluminum plate repaired with bonded composite patch especially in thick plate. Adhesively bonded composite patch repair technique has been successfully applied to military aircraft repair and expanded its application to commercial aircraft industry recently. Also this technique has been expanded its application to the repair of load bearing primary structure from secondary structure repair. Therefore, a through understanding of crack growth behavior of thick panel repaired with bonded composite patch is needed. We investigated the fatigue crack growth behavior of thick panel repaired with bonded composite patch using the stress intensity factor range (ΔK) and fatigue crack growth rate (da/dN). The stress intensity factor of patched crack was determined from experimental result by comparing the crack growth behavior of specimens with and without repair. Also, by considering the three-dimensional (3D) stress state of patch crack, 3D finite element analyses were performed to obtain the stress intensity factor of crack repaired by bonded composite patch. Two types of crack front modeling, i.e. uniform crack front model and skew crack front model, were used. The stress intensity factor calculated using FEM was compared with the experimentally determined values.     

A non-linear damage evolution model for mode II fatigue delamination onset and growth

A novel approach is proposed describing both the onset and growth of delaminations in fibre-reinforced laminates under pure mode II constant amplitude loading with the same damage evolution rule, unifying these two aspects of the material behaviour that are normally treated separately. A scalar damage variable is introduced to represent the fraction of overall fatigue endurance used up at ply interfaces as a function of the number of accumulated cycles. The damage rate equation is postulated in a generic power law format, which also includes the effect of the load stress-ratio. The material SN curves for pure mode II loading are obtained in closed form by a simple integration of the assumed damage evolution law. The material delamination propagation rate as a function of the energy release rate and the stress-ratio is similarly obtained combining the aforementioned damage evolution law with a regularized expression for the stress field at the crack tip. Two independent fatigue related parameters are sufficient for describing both the delamination onset and its growth. This modelling approach is validated by means of experimental fatigue delamination data for IM7/8552 carbon fibre/epoxy, demonstrating that the unified modelling strategy is able to describe both fatigue initiation and propagation and the associated effect of the stress-ratio.     

铁素体管线钢的分层裂纹及其对断裂的影响

通过对针状铁素体管线钢缺口根部三维应力状态的有限元分析和不同形式的断裂实验,研究了管线钢分层裂纹产生的条件及其对断裂性能的影响.结果表明裂纹或缺口根部的三维应力状态是产生分层裂纹的必要条件,材料的强度分布影响分层裂纹的形式和方向.分层裂纹均为主裂纹扩展前材料中的弱界面在垂直该弱界面的拉应力作用下产生的,其数量和方向受裂纹端部三维应力场和材料的强度分布状态控制.分层裂纹面上的应力为零,分层裂纹有一定的间距.在断裂过程中产生的分层裂纹使裂纹或缺口根部的构形发生改变,从而对裂尖的应力状态和材料的断裂性能产生巨大的影响.穿透裂纹体的分层裂纹使其有效厚度减小,表面裂纹体的分层裂纹与裂纹扩展方向垂直.在断裂过程中产生分层裂纹需要消耗更多的能量、降低裂端三维应力约束、有效厚度降低或裂尖钝化.这些因素均使断裂扩展更加困难,而使材料韧性得到提高.