R. Citarella

Three-Dimensional BEM and FEM Submodelling in a Cracked FML Full Scale Aeronautic Panel

This paper concerns the numerical characterization of the fatigue strength of a flat stiffened panel, designed as a fiber metal laminate (FML) and made of Aluminum alloy and Fiber Glass FRP. The panel is full scale and was tested (in a previous work) under fatigue biaxial loads, applied by means of a multi-axial fatigue machine: an initial through the thickness notch was created in the panel and the aforementioned biaxial fatigue load applied, causing a crack initiation and propagation in the Aluminum layers. Moreover, (still in a previous work), the fatigue test was simulated by the Dual Boundary Element Method (DBEM) in a bidimensional approach. Now, in order to validate the assumptions made in the aforementioned DBEM approach and concerning the delamination area size and the fiber integrity during crack propagation, three-dimensional BEM and FEM submodelling analyses are realized. Due to the lack of experimental data on the delamination area size (normally increasing as the crack propagates), such area is calculated by iterative three-dimensional BEM or FEM analyses, considering the inter-laminar stresses and a delamination criterion. Such three-dimensional analyses, but in particular the FEM proposed model, can also provide insights into the fiber rupture problem. These DBEM-BEM or DBEM-FEM approaches 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 fiber stiffness and of delamination extension on the stress intensity factors.

Numerical-experimental crack growth analysis in AA2024-T3 FSWed butt joints

This paper deals with a numerical and experimental investigation on the influence of residual stresses on fatigue crack growth in AA2024-T3 friction stir welded butt joints. The computational approach is based on the sequential usage of the Finite Element Method (FEM) and the Dual Boundary Element Method (DBEM). Linear elastic FE simulations are performed to evaluate the process induced residual stresses, by means of the contour method. The computed stress field is transferred to a DBEM environment and superimposed to the stress field produced by a remote fatigue traction load applied on a friction stir welded cracked specimen; the crack propagation is then simulated according to a two-parameter growth model. Numerical results have been compared with experimental data showing good agreement and evidencing the predictive capability of the proposed method. The obtained results highlight the influence of the residual stress distribution on crack growth.

Thermo-mechanical crack propagation in aircraft engine vane by coupled FEM-DBEM approach

New generation jet engines are subject to severe reduced fuel consumption requirements. This usually leads to thin components in which damage issues such as thermo-mechanical fatigue, creep and crack propagation can be quite important. The combination of mechanical and thermal stresses usually leads to mixed-mode loading. Consequently, a suitable crack propagation tool must be able to predict mixed-mode crack propagation of arbitrarily curved cracks in three-dimensional space. To tackle this problem a procedure has been developed based on a combined FEM (finite element method) - DBEM (dual boundary element method) approach. Starting from a three-dimensional FEM mesh for the uncracked structure a subdomain is identified, in which crack initiation and propagation are simulated by DBEM. Such a subdomain is extracted from the FEM domain and imported, together with its boundary conditions (calculated by a previous thermal-stress FEM analysis), in a DBEM environment, where a linear elastic multiple crack growth analysis is performed. Once the crack propagation direction is determined a new crack increment can be calculated and, for the new crack front, the procedure can be repeated until failure. The proposed procedure also allows the consideration of the spectrum effects and creep effects: both conditions determine residual stresses that the crack will encounters during its propagation. The procedure has been tested on a gas turbine vane, getting sound results, and can be made fully automatic, thanks to in house made routines needed to facilitate the data exchange between the two adopted codes.

DBEM crack propagation in friction stir welded aluminum joints

This paper deals with the simulation of multiple crack propagation in friction stir welded butt joints and the aim is to assess the influence of process induced residual stresses on the fatigue behavior of the assembly. The distribution of the process induced residual stresses is mapped by means of the contour method; then, the computed residual stress field is superimposed, in the DBEM environment, to the stress field due to a remote fatigue traction load and the crack growth is simulated.A two-parameters crack growth law is used for the crack propagation rate assessment. The Stress Intensity Factors are evaluated by the J-integral technique. Computational results have been compared with experimental data, provided by constant amplitude crack propagation tests on welded samples, showing the subdivision of the overall fatigue life in the two periods of crack initiation and crack propagation.

Non-linear MSD crack growth by DBEM for a riveted aeronautic reinforcement

Abstract A special specimen is created cutting a rectangular notched area from the surrounding of the upper left corner of a wide body aircraft door. Then a constant amplitude fatigue traction load is applied by a special servo-hydraulic machine, in order to induce a Multi Site Damage (MSD) scenario. The Dual Boundary Element method (DBEM), as implemented in a commercial code, is adopted for a three-dimensional MSD crack growth simulation of such multi-layer and multi-material component. To this aim, the cracked part of a pre-existing global two-dimensional model is extracted and “extruded” in order to generate a three-dimensional submodel, whose boundary conditions are imposed displacements, calculated by the two-dimensional model, along a virtual line corresponding to the submodel boundary. Non-linear contact conditions are applied between the mating plate surfaces in the area surrounding the cracks, in order to precisely model the plate interactions in the area of interest. The three-dimensional approach is aimed to improve, with respect to the two-dimensional approach, the correlation between numerical and experimental results (e.g. by an accurate assessment of the secondary bending effects). The obtained improvements on crack growth rates, in the initial part of the crack propagation, justify the increased computational effort that a three-dimensional non-linear approach involves. The proposed numerical procedure, based on DBEM, is successfully validated for the virtual testing of a complex aeronautic reinforcement.

Three-dimensional crack growth: Numerical evaluations and experimental tests

Abstract Experimental observations of three- and two-dimensional fatigue crack growth are compared to numerical predictions from the computer code BEASY. The two dimensional propagation occur in a Multiple Site Damage (MSD) scenario created on a pre-notched specimen, undergoing a traction fatigue load as defined by a general load spectrum. Experimental analyses on a fatigue machine were carried out in order to validate the numerical simulation and to provide the necessary material fatigue data for the aluminium plates. The numerical code adopted (BEASY) is based on Dual Boundary Element Method (DBEM). General modelling capabilities are allowed by this approach, with the allowance for general crack front shape and a fully automatic propagation process. By means of a non-linear regression analysis, applied on in house obtained experimental data, the material parameters for the NASGRO 2.0 crack propagation law were defined, capable to effectively keep into account the threshold effect and the unstable final propagation (the crack closure option was switched off). A satisfactory agreement between numerical and experimental crack growth rates was obtained, even starting from a complex MSD scenario, created by the presence of three holes in the plate. Moreover the load introduction to the specimen was monitored by strain gauge equipment. The numerical simulation include also the through the thickness propagation, corresponding to 3D part-through cracks; in this case some specimen were pre-notched by a corner crack on one of the holes and the 3D experimental crack propagation monitored.

Multiple Crack Propagation with Dual Boundary Element Method in Stiffened and Reinforced Full Scale Aeronautic Panels

In this work, the performance of a new methodology, based on the Dual Boundary Element Method (DBEM) and applied to reinforced cracked aeronautic panels, is assessed. Such procedure is mainly based on two-dimensional stress analyses, whereas the three-dimensional modelling, always implemented in conjunction with the sub-modelling approach, is limited to those situations in which the so-called secondary bending effects cannot be neglected. The connection between the different layers (patches and main panel) is realised by rivets: a peculiar original arrangement of the rivet configuration in the two-dimensional DBEM model allows to take into account the real in-plane panel stiffness and the transversal rivet stiffness, even with a two dimensional approach. Different in plane loading configurations are considered, depending on the presence of a biaxial or uniaxial remote load. The nonlinear hole/rivet contact, is simulated by gap elements when needed. The most stressed skin holes are highlighted, and the effect of through the thickness cracks, initiated from the aforementioned holes, is analysed in terms of stress redistribution, SIF evaluation and crack propagation. The two-dimensional approximation for such kind of problems is generally not detrimental to the accuracy level, due the low thickness of involved panels, and is particularly efficient for studying varying reinforcement configurations, where reduced run times and a lean pre-processing phase are prerequisites.The accuracy of the proposed approach is assessed by comparison with Finite Element Method (FEM) results and experimental tests available in literature.This approach aims at providing a general purpose prediction tool useful to improve the understanding of the fatigue resistance of aeronautic panels.KEYWORDSDBEM, full scale aeronautic panel, 2D/3D crack growth, MSD, doubler-skin assembly, damage tolerance

FEM simulation of a crack propagation in a round bar under combined tension and torsion fatigue loading

An edge crack propagation in a steel bar of circular cross-section undergoing multiaxial fatigue loads is simulated by Finite Element Method (FEM). The variation of crack growth behaviour is studied under axial and combined in phase axial+torsional fatigue loading. Results show that the cyclic Mode III loading superimposed on the cyclic Mode I leads to a fatigue life reduction. Numerical calculations are performed using the FEM software ZENCRACK to determine the crack path and fatigue life. The FEM numerical predictions have been compared against corresponding experimental and numerical data, available from literature, getting satisfactory consistency.

Coupled FEM-DBEM method to assess crack growth in magnet system of Wendelstein 7-X

The fivefold symmetric modular stellarator Wendelstein 7-X (W7-X) is currently under construction in Greifswald, Germany. The superconducting coils of the magnet system are bolted onto a central support ring and interconnected with five so-called lateral support elements (LSEs) per half module. After welding of the LSE hollow boxes to the coil cases, cracks were found in the vicinity of the welds that could potentially limit the allowed number N of electromagnetic (EM) load cycles of the machine. In response to the appearance of first cracks during assembly, the Stress Intensity Factors (SIFs) were calculated and corresponding crack growth rates of theoretical semi-circular cracks of measured sizes in potentially critical position and orientation were predicted using Paris’ law, whose parameters were calibrated in fatigue tests at cryogenic temperature. In this paper the Dual Boundary Element Method (DBEM) is applied in a coupled FEM-DBEM approach to analyze the propagation of multiple cracks with different shapes. For this purpose, the crack path is assessed with the Minimum Strain Energy density criterion and SIFs are calculated by the Jintegral approach. The Finite Element Method (FEM) is adopted to model, using the commercial codes Ansys or Abaqus;, the overall component whereas the submodel analysis, in the volume surrounding the cracked area, is performed by FEM (“FEM-FEM approach”) or alternatively by DBEM (“FEM-DBEM approach”). The “FEM-FEM approach” considers a FEM submodel, that is extracted from the FEM global model; the latter provide the boundary conditions for the submodel. Such approach is affected by some restrictions in the crack propagation phase, whereas, with the “FEM-DBEM approach”, the crack propagation simulation is straightforward. In this case the submodel is created in a DBEM environment with boundary conditions provided by the global FEM analysis; then the crack is introduced and a crack propagation analysis has been performed to evaluate the effects of the crack shape and of the presence of nearby cracks on the allowed number of EM load cycles.

Fem Sensitivity Analyses on the Stress Levels in a Human Mandible with a Varying ATM Modelling Complexity

In this work the structural behaviour of a mandible considering a unilateral occlusion is numerically analysed by means of the Finite Element Method (FEM). The mandible, considered as completely edentolous, is modelled together with its articular disks, whose material behaviour is assumed as elastic or hyper-elastic. The mandible model is obtained by computer tomography scans. The anisotropic and non homogeneous bone material behaviour is considered and the loads applied to the mandible are those related to the active muscle groups during unilateral occlusion. The results of FEM analysis are presented mainly in terms of stress distribution on the mandible. Because of uncertainty on the determination of the adopted parameters, a sensitivity analysis is provided, showing the way in which the variation of articular disc stiffness and temporomandibular joint friction coefficient has an impact on the mandible stress peak and occlusal force.