Development of Damage Tolerance Methodology for Antenna Installations in Pressurized Aircraft

Development of Damage Tolerance Methodology for Antenna

Installations in Pressurized Aircraft

JENS FAGERBERG

KTH

SKOLAN FÖR TEKNIKVETENSKAP

Tolerance Methodology for Antenna Installations in

Pressurized Aircraft

JENS FAGERBERG

Master of Science in Aerospace Engineering Date: July 15, 2020

Supervisor: Douglas Jeleborg Examiner: Stefan Hallström School of Engineering Sciences

Host company: Bromma Air Maintenance AB

Swedish title: Framtagning av metod för skadetoleransberäkning av antenninstallationer i trycksatta flygplan

Abstract

Modifying an aircraft must be done in a safe way such that the safe operation of the aircraft is not violated. Compliance must be shown towards certification and airworthiness regulations in order to install a modification and allow for commercial flight. Certification is a time-consuming process where damage tolerance analysis is a major part.

The challenge for small and mid-sized companies is to simplify the dam- age tolerance methodology without diminishing the level of safety which is the top priority for aircraft operations. By utilizing proven methods and recom- mended theory with adequate conservatism, an mostly analysis-based method- ology was developed which includes stress analysis, finite element methods and crack growth analysis.

The resulting methodology provides the tools to estimate longitudinal and circumferential crack growth and the corresponding critical crack length that would cause a structural failure. This also enables the establishment of inspec- tions intervals which are required for continued airworthiness.

Sammanfattning

Modifikationer och installationer på flygplan måste utföras på ett sådant sätt att flygplanets driftsäkerhet ej äventyras. Luftvärdighetsdirektiv måste uppfyllas för att en modifiering skall kunna installeras och flygplanet tas i kommersiell drift. Denna certifieringsprocess är tidskrävande och skadetoleransberäkning- ar utgör en stor del av den.

Utmaningen för små och medelstora företag är att förenkla skadetolerans- beräkningar till en hanterbar nivå utan att minska på flygsäkerheten då den är av högsta prioritet. Via användning av beprövade metoder och rekommenderad teori tillsammans med adekvat konservatism framtogs en metodologi huvud- sakligen baserad på analytiska beräkningar för spricktillväxt och lastanalys.

Den framtagna metodologin estimerar spricktillväxt i longitudinell och ra- diell riktning samt respektive kritiska spricklängd som bedöms kunna orsaka kritisk strukturell skada. Dessa beräkningar möjliggör även upprättandet av inspektionsintervall vilket är ett krav för bestående luftvärdighet.

1 Introduction 2

1.1 Antenna Installation Characteristics . . . 3

2 Theory 4 2.1 Modelling of Aircraft Loads . . . 4

2.1.1 Load Factors . . . 4

2.1.2 Fuselage Loads . . . 7

2.2 Material Data . . . 10

2.2.1 Design Allowables . . . 10

2.2.2 Fracture Path Directions . . . 10

2.3 Model Preparation . . . 11

2.3.1 Geometry Repairing . . . 12

2.3.2 Geometry Defeaturing . . . 14

2.4 FE Modelling . . . 14

2.4.1 Elements . . . 15

2.4.2 Mesh Quality . . . 15

2.5 Damage Tolerance . . . 18

2.5.1 Fatigue Crack Growth Stress . . . 18

2.5.2 Residual Strength Stress . . . 19

2.5.3 Rivet Calculations . . . 19

2.5.4 Structural Failure Conditions . . . 22

2.5.5 Fatigue Crack Growth . . . 25

2.5.6 Initial Crack Conditions . . . 28

3 Method Description 29 3.1 Aircraft Data . . . 29

3.2 Installation Data . . . 30

3.3 Material Data . . . 31

3.4 Aircraft Stresses . . . 31

v

3.5 Rivet Calculations . . . 32

3.6 Crack Growth Analysis . . . 33

3.6.1 Net Section Yield . . . 34

3.6.2 Crack Growth Calculations . . . 34

3.7 Inspection . . . 36

3.7.1 Inspection Method . . . 36

3.7.2 Inspection Interval . . . 38

4 Discussion and Conclusion 39 4.1 Validity and Applicability . . . 39

4.2 Limitations . . . 39

4.3 Future Work . . . 40

Bibliography 41

A Compatibility Equations 44

List of Acronyms

Acronym Full Meaning

ACO Aircraft Certification Office

AMC Acceptable Means of Compliance

CAD Computer Aided Design

CAE Computer Aided Engineering

CS Certification Specification

DTA Damage Tolerance Analysis

EAS Equivalent Airspeed

EASA European Union Aviation Safety Agency ENAC Ecole Nationale de l’Aviation Civile

FAA Federal Aviation Administration

FAR Federal Aviation Regulation

FEA Finite Element Analysis

MMPDS Metallic Materials Properties Development and Standardization

MSD Multi-Site Damage

MTOW Maximum Take-Off Weight

NDT Non Destructive Testing

STC Supplemental Type Certificate

STCH Supplemental Type Certificate Holder

TC Type Certificate

TCH Type Certificate Holder

Table 1: List of Acronyms

Introduction

When performing modifications to an aircraft, regulatory authorities such as EASA and FAA require that the design organisation can show compliance to current legislation stated in CS and FAR. An STC, valid for a modification to a specific aircraft type, can only be issued once the design organisation can show compliance to relevant CS/FAR paragraphs.

An aircraft is subjected to cyclical loading as it goes through different phases of flight. Cyclical inertial and pressurization loads give rise to fatigue which degrades material properties and initiate crack growth. The purpose of damage tolerance analysis is to analyse where these cracks occur, at which rate they propagate and to establish inspection intervals and repair procedures.

Historically, a fail-safe and/or safe-life design philosophy was used prior to damage tolerance [1]. Fail-safe design required structural components to be redundant such that catastrophic failure wouldn’t occur after fatigue fail- ure in a single principal structural element. This approach didn’t however in- clude necessary engineering evaluation of crack growth and residual strength to specify inspection methods, thresholds and frequencies to detect damage prior to failure [2]. Safe-life design on the other hand assumed that no initial flaws were present in the material and through laboratory testing one could de- termine a number of cycles or service hours in which failure wouldn’t occur.

This method proved to be highly unconservative as flaws could occur at both manufacturing and maintenance stages.

The development of fatigue analysis have been driven by major accidents, such as the 1950s De Havilland Comet accidents [3] and the Aloha Boeing 737 accident in 1988 [4]. As a result, damage tolerance analysis has evolved from past experiences and methods into considering initial flaws, fracture me- chanics, crack growth, multiple site damage etc to establish inspection and

2

maintenance intervals.

This thesis will focus on antenna installations to pressurized aircraft and the main goal is to break down the DTA process into a handbook which can be used as guidance when developing a stress analysis report to be used in certification of an installation or modification.

1.1 Antenna Installation Characteristics

A typical installation of an antenna, as demonstrated in Fig. 1.1, consists of two major parts, the first being the antenna and the second being a doubler which is needed to reinforce the skin after drilling holes for fasteners and feed- through. The doubler should extend to the nearby frames and stringers to allow for adequate load transfer and rigidity.

Figure 1.1: Typical Antenna Installation

The skin and doubler are drilled with holes for fasteners which facilitate load transfer, antenna mounting holes and a cable feed-through hole.

Theory

The purpose of certification is to ensure safety of production, operation and maintenance of the aircraft. In order to receive a TC or STC, the applying or- ganisation has to show compliance to current regulations, such as CS-23 which is the main focus in this thesis. This is a complex and time-consuming process as the applicant has to justify methods and assumptions based on experience or similar work performed by companies or research institutes.

Therefore, the methods presented and used in this thesis will be based on currently used practices and methods proposed by acknowledged companies and research institutes. Developing new methods for this purpose is heavily time-consuming and requires long experience and extensive knowledge within the subject in order to attain acceptance from EASA and FAA.

2.1 Modelling of Aircraft Loads

Aircrafts are exposed to a variety of loads during the phases of a flight. The characteristics vary dependent on the mission profile which include parameters such as airspeed, altitude, aircraft weight and pressurization. In the scope of fuselage installations, pressurization and inertial loads dominates this spec- trum and will be focused upon [5]. The latter give rise to fuselage bend- ing loads and occur at different amplitudes which depend upon inertial factor caused by gusts and maneuvers.

2.1.1 Load Factors

For certification, numerous load factors will appear during the analysis.

4

Ultimate Load Factor

The ultimate load factor, denoted jultin this report, should be applied to limit loads to obtain ultimate loads. CS 23.303 [6] states this factor as 1.5. Limit loads are the maximum loads expected in service and the aircraft has to sustain these loads without detrimental, permanent deformation.

Maneuver Load Factor

When evaluating residual strength, it is necessary to consider inertial effects which arise when performing aircraft maneuvers. In the context of fuselage in- stallations, these give rise to fuselage bending which, for a positive maneuver, cause tension on the top side and compression on the bottom side. Maneuver load factors, n^z, can be found in the operational limits section of the aircraft manual and is given as both a positive (n^z+) and a negative limit (n^z−).

Gust Load Factors

Except for maneuvers, inertial effects occur when the aircraft flies through wind gusts. The amplitude of this factor ng is dependent upon gust allevia- tion factor kg, aeroplane mass ratio µg, gust velocity Ude, wing loading ^W_S

, equivalent airspeed VEAS and air density at sea level ρ0 as shown in Eq. 2.1.

The equations below are given in CS 23.341 [6].

n_g = 1 ± k_gρ₀U_deV_EAS

2 ^W_S
(2.1)

The aeroplane mass ratio in pitch, µg, is given in Eq. 2.2 where g is the gravitational acceleration, C is mean geometric chord, ρ is density at consid- ered altitude and Cnis the aeroplane normal force coefficient per radian.

µg = 2 ^W_S

ρCC_ng (2.2)

The gust alleviation factor is derived from the equations of motion for an airplane in an isolated gust and accounts for the instantaneous lift assumption and is adapted for the "1-minus-cosine" gust shape [7]. It is dependent upon µ_g and calculated as in Eq. 2.3.

k_g = 0.88µ_g

5.3 + µ_g (2.3)

The above equations are dependent on TCH information. This information is typically not available to the third party organisation which perform the in- stallation and acquiring it might be expensive. Therefore, it is common within the industry that maximum maneuver load factor is used considering present conservatism in the typical loads analysis [8]. However, if the information is available, calculating the gust factor is beneficial.

Fatigue Inertia Load Factor

For evaluation of crack growth, it is possible to use a "once-per-flight-equivalent cycle" to represent the cyclic characteristics of the load spectrum during flight, illustrated simply in Fig. 2.1. In practice, a single load factor is used to repre- sent the multiple load factors encountered in flight.

Figure 2.1: Equivalent Load Cycle

The Chicago ACO method [9] recommends this load factor to be nf at = 1.3. However, a more recent method based on gust exceedance probability suggested that n^{f at}= 1.8 is more adequate [10]. Important note to this factor is that it is only applied to circumferential cracks as fuselage bending give rise to mode 1 crack propagation in this direction.

Fatigue Scatter Factor

The scatter factor is a life reduction factor used to address possibly inherent uncertainties in the fatigue analysis. When TCH data isn’t available there is none or little information regarding material testing data and stress analysis data performed by the TCH. Therefore, a scatter factor of jsc = 8 is recom- mended for an STCH [8].

Residual Strength Load Factor

For a metallic airframe structure CS 23.573(b)(2) states that, for pressurized cabins, the residual strength has to withstand jres = 1.1 times the differential pressure combined with external aerodynamic forces during 1g-flight.

2.1.2 Fuselage Loads

The main loads driving crack propagation for fuselage-mounted antennas are pressurization loads and fuselage bending loads. There are mainly two meth- ods commonly referenced by design and regulatory organizations, the Chicago ACO method [9] and the ENAC method [10] which is a less conservative ap- proach to the first one. However, the ENAC method takes into consideration where the antenna is installed rather than the location where bending stress are at maximum.

Pressurization

Cabin pressurization will cause the fuselage skin to expand and the arisen stress is carried by the skin, frames and stringers. A conservative approach to analysing this structure is to neglect the effects of frames and stringers hence assuming the skin stress to be higher than in reality. The fuselage will also be assumed to be cylindrical, which in most cases is true but e.g. Beechcraft B300 has a non-conventional shape.

The maximum pressurization load, P^max, for a specific aircraft can be found in the operational limits section of the aircraft manual. In addition to this, a 0.5 psi contribution from external aerodynamic (Pa) pressure should be considered [9].

∆P = P_max+ P_a (2.4)

The circumferential stress is calculated in Eq. 2.5 and the longitudinal stress in Eq. 2.6. Where R is the fuselage radius and t^sis the skin thickness.

σ_p,c = ∆P R

t_s (2.5)

σ_p,l= ∆P R

2t_s (2.6)

Fuselage Bending

Inertial forces experienced during level flight, aircraft maneuvers and gust oc- currences will cause the fuselage to bend around the center of mass. In the most common case, positive maneuver, this will result in tension on the top- part of the fuselage and compression on the bottom part.

The two referenced methods [9][10] propose different modelling of the fuselage bending loads. Chicago ACO propose to assume that the aircraft manufacturer has designed the aircraft with zero static margin at ultimate load.

Eqs. 2.7 and 2.8 shows how the 1-g maximum bending load at center of gravity is obtained according to this method.

F_tu = 1.5 ∆P R

2t + n_zσ_1g,max



(2.7)

σ_1g,max = 1 n_z

 F_tu

1.5 − ∆P R 2t



(2.8) ENAC [10] propose that the fuselage can be modelled as a beam. The bending stress amplitude then depends on where the antenna is installed and where the center of gravity is located. Center of gravity location can be as- sumed to coincide with the aircraft main spar, as it will vary slightly depending on payload and fuel conditions.

M_{b,f wd} = W_fgx²_inst

2L (2.9)

Mb,af t= Wfg(L − xinst)²

2L (2.10)

In Eqs. 2.9 and 2.10, xinstis the longitudinal fuselage coordinate of where the antenna is installed, as illustrated in Fig. 2.2. g is the graviational accel- eration. The distributed weight Wf is calculated by dividing MTOW with the fuselage length, which in this case is defined by the distance between forward and aft bulkheads.

W_f = M T OW

L (2.11)

As mentioned, stringer and frames are neglected and will not contribute to bending stiffness. The 1-g bending stress can then be calculated as in Eq.

2.12 where Z is the vertical distance from fuselage center. Ixx is the second moment of inertia for a thin-walled tube and can be found in most handbooks [11].

σ_1g = MbZ

I_xx = MbZ

πR³t (2.12)

Figure 2.2: Fuselage Bending Model

A comparison between the two methods can be seen in Fig. 2.3 where the Chicago ACO clearly yields higher bending stresses than the ENAC method.

The comparison is done with data for a Beechcraft King Air 300.

Figure 2.3: Bending Stress Comparison

2.2 Material Data

Obtaining material data from a reliable source is crucial within the aerospace industry as poor data accuracy can threaten analysis results and flight safety.

Therefore, it is regulated by both EASA (CS 23.613) and FAA (FAR 23.613).

Recommendations of reliable sources can be found in the corresponding AMC.

Metallic Materials Properties Development and Standardization (MMPDS- 01) is easily accessible and accepted by both authorities but other sources such as Handbuch Strukturberechnung, ISH ESDU Metallic Materials Data Hand- book and ASM Handbooks are also used and accepted within the industry.

2.2.1 Design Allowables

Material properties are given in A-, B- and S-basis. S-basis are statistically calculated values and therefore, according to CS 23.613(a), not valid for us- age in design. A- and B-basis properties are experimentally derived and shall be used. A-basis corresponds to the value which at least 99% of the test pop- ulation exceeds with 95% confidence and B-basis is the value where at least 90% of the test population exceeds with 95% confidence.

According to CS 23.613(b) [6], A-basis values must be used for structures where loads are transferred through a single structural member while B-basis can be used for redundant structures with multiple load-carrying members.

The methods for establishing these values are described in MMPDS-01 [12].

2.2.2 Fracture Path Directions

There are several methods when producing materials used in an airplane. For Aluminium 2024, which is commonly used in aerospace structures, extrusion and rolling are frequent methods for producing plates and parts. These meth- ods affect grain alignment within the material and as a result, fracture tough- ness can vary with grain direction.

The directions which material properties are given in is illustrated in Fig.

2.4. There are six principal fracture path directions; L-T, L-S, T-L, T-S, S-L and S-T. T is the abbreviation for transverse direction, L for longitudinal and S for short transverse. The first letter denotes grain direction normal to the crack plane while the second denote grain direction parallel to the crack plane.

Information regarding plate assembly and rolling/extrusion direction is rarely known and because of the relatively small differences, it is convenient

Figure 2.4: Fracture Path Directions. Source: MMPDS [12]

to conservatively use the smaller values provided in MMPDS or equivalent source.

2.3 Model Preparation

FEA will be used to validate stress levels, locations of high stress concen- trations and possible impact of stress-field of nearby antenna locations. In many cases, parts will be designed and analysed in different software suites.

SolidWorks, NX, Cathia are examples of CAE/CAD programs while Abaqus, Nastran and ANSYS Workbench are commonly used FEA software. Input er- rors and program compatibility can be error sources which require repairing actions or defeaturing before performing the analysis.

As all geometries and load cases are unique, this process might be time- consuming and require an experienced engineer. There are guidelines and recommendations but no explicit answers to how the geometry should be pre- processed and what it looks like, so it is up to the engineer responsible to perform this judgment upon what is being tested.

Due to limitations in the ANSYS Student Licence and the thesis time- frame, a small part of the frame, rather than a full fuselage sub-model, is used to demonstrate the techniques described in this section.

2.3.1 Geometry Repairing

The process of geometry repair is crucial when preparing the model for mesh- ing. Corrupt geometry, small or missing faces, inexact edges or non-connected parts will affect the mesh quality and in turn analysis results. There are plenty of tools which detect these irregularities and, in some cases, repair them.

In this project, ANSYS SpaceClaim was used and the tools described in this section are therefore named as they are in the software. The corresponding tools are available in other CAD/preprocessor softwares as well but might be named and structured differently.

Solidifying

The first step in this process is to check whether the model is solidified. In SpaceClaim, a model which isn’t a solid will appear transparent and be cate- gorised as a surface or volume in the structure tree. Three tools are available for solidifying; Stitch, Gaps and Missing Faces.

Stitch tool combines faces that has edges within a user-defined distance such that a larger, common surface is created. However, edges are still pre- served which can be important for sub-dividing a solid into mesh zones.

Gaps tool will remove gaps between faces which share an endpoint or that is paired but yet have a gap between them. The maximum distance and an- gle between edges are user-defined. A possible source for this error is lower tolerances in the upstream CAD process.

Missing faces tool differ from gaps in the sense that edges does not have to be paired. This tool is more intuitive as it identifies holes in the structure and creates a new face (patch) or extends an adjacent face to fill the hole (fill).

Fix and Adjust

When the model is solidified, further actions can be performed to improve geometry modifiability and final preparations for analysis.

Split Edges is helpful to ensure that edges are not divided into unneces- sary segments. This segmentation can, during meshing, cause unsatisfactory zoning of the part.

Merge Faces allows for the creation of larger areas from several small.

Faces are meshed individually and elements can not span across edges. Small faces should therefore be merged into larger ones for uniform mesh generation.

In Fig. 2.5, elements marked red obtain a high aspect ratio due to a small face being present.

Figure 2.5: Mesh with Small Faces

Small Faces detects, below a user-defined threshold, these faces which can be e.g. merged. Not all faces are supposed to be fixed by merging but might require geometry alteration.

Geometry Decomposition

As a last step before meshing, geometry can be split into several parts which can be meshed individually. Figure 2.6 demonstrates how a frame geometry can be broken down for increased mesh control. The light-blue colored flange has no fastener holes and can be meshed with lower element density compared to the rest of the structure. The other flanges require a finer mesh, especially around the fastener holes which are areas of interest when, for example, inves- tigating crack growth. When splitting the geometry, shared topology has to be activated such that nodes and elements align between each sub-part.

These tools, along with others that are provided in ANSYS SpaceClaim, are powerful and should be utilized to identify problem areas. However, in- specting the geometry before and after usage is required to assess the solution.

Some tools can damage the geometry further and require manual solutions.

When the geometry is repaired and prepared for meshing, the Check Geome- try function should preferably not yield any error messages.

Figure 2.6: Frame Decomposition

2.3.2 Geometry Defeaturing

Depending on the analysis type, features might be removed or simplified from the model to reduce complexity and the amount of elements needed for dis- cretisation. These features might be far away from the region of interest or simply not contribute to load distribution in a load case and can be excluded to improve computational efficiency. Smaller details such as drilled holes, rounds and various small details might also be removed or replaced to reduce mesh complexity.

Defeaturing can be performed either by directly modifying the geometry prior to meshing or, for smaller details, during the meshing. This can be con- trolled in ANSYS Mechanical and all details which is smaller than the set threshold will be ignored during meshing.

In the case of antenna installations, small details such as fastener joints, drill holes and cable feedthroughs are of importance for damage tolerance analysis as cracks can occur in these regions and no defeaturing is conducted in this particular study.

2.4 FE Modelling

With the increased computational power available at a consumer-level, FEA has become widely used as a tool for structural analysis. For certification pro- cesses, it is an important tool to verify analytical calculations and identify locations of high stress concentrations which are regions of interest in damage tolerance analysis.

There are multiple topics to pay attention to when performing a FE anal- ysis. Input data, geometry, boundary conditions and governing assumptions might result in non-satisfactory results and therefore caution must be taken when building the model and performing the analysis.

Even if several FEA software packages offer design capabilities, it is most common to import geometries from an external CAD program and prepro- cess it for meshing and element selection. For this project, SolidWorks CAD- models was preprocessed in ANSYS SpaceClaim and then meshed and anal- ysed in Workbench.

2.4.1 Elements

Selection of element types depends on geometry, analysis type and require- ments of the solution. A typical fuselage structure consists of fuselage skin, stringers and frames which all are suitable to be modelled with different ele- ments. These parts can be assembled with adhesives, bolts, rivets etc which are modelled with special elements.

Elements are available in several dimensions applicable for different struc- tural members. A 1D-element is suitable for e.g. bars and beams, 2D-element plates and shells and 3D-elements can be used for bulky parts but also for the previously mentioned parts. The reason to not use 3D-elements at all loca- tions is computational time. Most small and mid-sized companies do not have access to high computational power and even if they did, running simulations is expensive and thus it is desirable to minimize computational time.

2.4.2 Mesh Quality

Analysis and results quality are heavily dependent upon, amongst other pa- rameters, mesh quality. Verifying mesh quality is not necessarily trivial, but the purpose of the mesh is; accurately represent the system being analysed and generate accurate results [13]. Studying the mesh both visually and mathemat- ically is essential in establishing confidence for the final solution.

Models are representations of real systems and to generate a valid approxi- mation, the model geometry should correspond to the original system. Visual inspection of the mesh should be performed to ensure that geometrical details such as rounds, holes, cutouts etc are properly represented when the mesh is generated. In Fig. 2.7, it can be visually detected that the hole is not correctly represented in the model due to a coarse mesh.

While visual inspections allows for verification that the correct geometry is

(a) Coarse Mesh (b) Fine Mesh

Figure 2.7: Mesh Influence on Hole Representation

modelled, mathematical metrics are needed to control how the amount of ele- ments and their shape affect the solution accuracy. Several metrics is available by default in ANSYS Mechanical and will be discussed below.

Mesh Convergence

A method for verifying adequate mesh size is to perform a convergence check.

This is performed by refining the mesh and evaluating the results (stress, de- formation, crack growth etc) until convergence occurs. When convergence is obtained, the coarsest mesh setting which still produce convergent results can be chosen to minimize computational time.

Elemental Results Difference

By default, ANSYS displays averaged values when inspecting contour results such as stress and strain. When averaging, results are calculated for each el- ement and then averaged at a common node. By changing display option to Elemental Difference it is possible to find areas where adjacent elements have large differences and where mesh refinement is needed.

Element Quality

This metric provides a value between 0 and 1 which indicate the quality of the element shape. There are two governing equations for this metric, Eq. 2.13

for 2D-elements and Eq. 2.14 for 3D-elements [14].

Q_EQ,2D = C

 A_el P(Led)²



(2.13)

Q_EQ,3D = C Vel

p[P(Led)²]³

!

(2.14) In Eqs. 2.13 and 2.14, C is a constant dependent on element type, A^el is the element area, V^el element volume and L^ed edge length. Error limits suit- able for linear, modal, stress and thermal problems are pre-defined in ANSYS Mechnical and proven to be effective [14].

3D elements < 5 · 10⁻⁶ 2D elements < 0.01 1D elements < 0.75 Skewness

This metric mesaures how close to equilateral (triangular elements) or equian- gular (quadrilateral elements) are. A less skewed element has higher solution accuracy.

Skewness Quality

1 Degenerate

0.9 - 1 Bad

0.75 - 0.9 Poor 0.5 - 0.75 Fair 0.25 - 0.5 Good

0 - 0.25 Excellent

0 Perfect

Table 2.4.2 lists how skewness values should be interpreted and the pre- ferred range is between 0.5 and 0 [14].

There are an infinite amount ways to generate a mesh and evaluating the quality of it. The above mentioned metrics are a few where numerical thresh- olds are provided by the ANSYS manual. Qualitative mesh is important es- pecially in locations of result evaluation and mesh improvement should be fo- cused to those areas. Low-quality elements far from these regions will rarely affect the numerical results.

2.5 Damage Tolerance

Estimating where cracks occur and how they propagate are crucial in order to verify design safety and to establish an inspection program based on the mod- ifications that are being done to the aircraft. Both crack growth and residual strength analysis needs to be performed. Critical locations for crack growth in antenna installations are the outer rivet rows and the cable feed-through [15].

Multi-Site-Damage (MSD) is the result of simultaneous crack-initiation and growth in a rivet row. If these individual cracks grow large enough in a similar manner, they can consolidate into one, much larger crack and cause critical failure in the structure as illustrated in Figure 2.8. The crack growth calculations presented later in this paper will consider multi-site damage with multiple cracks growing simultaneously as this is a standardized approach for antenna installations. The initial conditions for this approach is described in Section 2.5.6.

Figure 2.8: Multi-Site-Damage Crack Formation

2.5.1 Fatigue Crack Growth Stress

The stress used for crack growth calculations are representative for the nominal stress experienced each flight. Eq. 2.15 is the circumferential stress and Eq.

2.16 is the longitudinal stress.

σ_{f at,c} = ∆P R

t_s (2.15)

As discussed in Section 2.1.1, a once-per-flight-equivalent load factor is used for calculations considering circumferential cracks together with pressuriza- tion and bending stresses.

σ_{f at,l} = ∆P R

2t_s + j_{f at}σ_1g (2.16)

2.5.2 Residual Strength Stress

According to CS 23.573(b)(1)(2), there are two load conditions which the air- craft must withstand even after some damage has occurred to the structure [6]. The first condition is 110% of pressurization loads combined with aero- dynamic suction which is included in ∆P as shown in Eq. 2.4.

σres,c= jres

∆P R

t_s = 1.1∆P R

t_s (2.17)

The second condition is pressurization loads combined in combination with the maximum inertial load factor.

σ_res,l = ∆P R

2t_s + n_z,maxσ_1g (2.18)

Condition 1 will affect longitudinal cracks since inertia effects are negligi- ble while condition 2 will affect circumferential cracks where fuselage bending is significant.

2.5.3 Rivet Calculations

Rivets are used to join the antenna doubler with the fuselage skin and transfer loads to the structure. Enough rivets must be used to ensure that each individ- ual rivet load is less than the maximum allowable load. The load distribution amongst rivets has the characteristics demonstrated in Figure 2.9 and due to symmetry, less rivets must be included in the analysis.

Calculating rivet loads in each row is performed by displacement compati- bility analysis [16]. For longitudinal and circumferential directions separately, fastener rows perpendicular to the load direction are split into idealized strips according to Fig. 2.10. There are as many strips as there are rivets and hence the strip width is calculated as Eq.2.19.

w_strip = w_d

n_r (2.19)

Figure 2.9: Rivet Load Distribution

The load in the skin is calculated as in Eq. 2.20 where the doubler width w_d is used. The skin section being analyzed has equal size to the doubler footprint regardless if the fuselage pocket is wider and hence wskin = w_dfor rivet calculations.

F_skin = σ_{f at}w_dt_s (2.20) The load applied on the strip is equal to, as calculated in section 2.1.2, the total circumferential or longitudinal load on the section divided by the amount of rivets. In Fig. 2.10, there are 6 rivets in the horizontal row and the applied load FS on each strip is therefore one sixth of the circumferential or longitudinal load.

Fs = F_skin

n_r (2.21)

The fastener flexibility Cf, strip flexibility Cs and doubler flexibility Cd

is calculated as Eqs. 2.22-2.24 where κ, λ and m are constants dependent on rivet type and if it undergoes single or double shear [17].

Figure 2.10: Idealized Strip in Doubler Fastener Type κ λ

Solid Rivet 2.2 2/5 Hi-Lok, Hi-Lite, Lockbolt 3.0 2/3

Table 2.1: Values of κ and λ

Cf = κ m

 t_s+ t_d 2D_r

λ 1

E_st_s + 1

mE_st_d + 1

2E_ft_s + 1 2mE_ft_d



(2.22)

C_s= p_r

E_sw_stript_s (2.23)

C_d= p_r

Edwstriptd (2.24)

Flexibilities are used to calculate displacements of fasteners, doubler and skin. Comptability between the displacements must be fulfilled as well as

Single Shear m = 1 Double Shear m = 2 Table 2.2: Values of m-constant

equilibrium between loads in the idealized strip and the fasteners. The config- uration is shown in Figure 2.11 and the corresponding compatibility equations is presented in Appendix A.

Figure 2.11: Doubler and Skin Configuration

With equilibrium, compatibility and force-displacement equations, a solv- able linear system can be obtained in the form of Ku = F where u is a vector with unknows, F a vector with externally applied forces and K a connectivity matrix between unknown variables. The unknowns are then calculated in e.g.

MATLAB according to Eq. 2.25.

u = K⁻¹F (2.25)

Maximum shear force for specific sheet and rivet combinations can be found in e.g. MMPDS-01 [12] and should be compared to the largest of the fastener loads which is located at the first row. Bearing stress at this location should also be verified lower than maximum allowable in both doubler and skin.

σ_br,s = F_{f 1}

D_rt_s (2.26)

σbr,d = F_{f 1}

D_rt_d (2.27)

2.5.4 Structural Failure Conditions

Critical failure will happen when the first of two different conditions occur, either when the critical fracture toughness is exceeded or when the net section stress surpasses the yield stress [18].

Net Section Yield

When a crack grows, the remaining section which is able to carry a load is reduced in size. Stress, being a function of area, will then increase over this section. At a certain point, stress levels in the reduced section will exceed the ultimate yield strength of the material.

Figure 2.12: Net Section Stress

For both longitudinal and circumferential cracks, critical length has to be investigated for the identified crack growth paths. It can be calculated by equi- librium of applied external force and net sectional force as illustrated in Fig.

2.12 where two cracks are present on each side of the antenna feed-through hole.

σ_resw_p = σ_ns(w_p− 2a_c,ns− D_{f t}) (2.28) Yield occurs when σ^ns ≥ Fty and therefore we can replace σ^ns in 2.28 with F^ty when solving for the critical crack length.

ac,ns = 1 2

 wp



1 −σ_res F_ty



− Df t



(2.29) The critical crack length for net section yield is given in Eq. 2.29 where D_{f t}is the diameter of the feedthrough hole, σresthe required residual strength stress and wp pocket width. Eq. 2.29 is also applicable for the rivet holes where D^{f t}is replaced with the rivet hole diameter.

Critical Fracture Toughness

When the stress intensity factor at a crack tip exceeds the critical fracture toughness of a specimen, the crack will become unstable, grow rapidly and possibly cause a fracture. The critical fracture toughness, K^c, is constant for plane strain conditions above a certain material thickness. However, as the fuselage skin consists of thin sheets, the valid condition is plane stress where K_cis not truly a material constant anymore.

By utilizing the Feddersen concept it is possible to establish the critical stress level for a fracture by linking elastic and plastic fracture concepts [19].

The critical stress for a centrally cracked plate (σCCT) with crack length 2a =

w

3 is calculated and used to calculate the apparent fracture toughness Kcofor the real plate. The initial fracture toughness for a centrally cracked plate KCCT

must be derived from experiments and can be interpolated from handbooks [20].

The idealized elastic stress and crack length relationship for a centrally cracked specimen is represented by the dashed line in Fig. 2.13. However, the crack will undergo both elastic and plastic instability before causing a fracture.

Test have shown that, at crack length extremities and during plastic instability, stress and crack length have a linear relationship and can be represented by the solid-line tangents to establish a curve of fracture behavior which is divided into three regions.

In the first region, for crack lengths 0 ≤ 2a ≤ _2π⁹

KCCT

FT Y

2

, critical stress is given by Eq. 2.30. The stress in this region is bounded by F^tyand ²₃F_ty.

σ_{CCT ,1} = F_ty 1 − 2π 27

 F_ty KCCT

2!

(2.30)

Stress in region 2 is given by Eq. 2.31 for crack lengths _2π⁹

KCCT

FT Y

2

≤ 2a ≤ ^w₃^p.

σCCT ,2 = K_CCT

√πa (2.31)

For region 3, stress is given by Eq. 2.32 and the crack length is bounded by ^w₃^p and wp.

σ_{CCT ,3} = 3K_CCT 2

r 6 πw

 1 −2a

w



(2.32)

When the critical stress is calculated, apparent fracture toughness can be calculated according to Eq. 2.34 where the real crack length a and shape func- tion f^CCT is inserted. This is the threshold value where the crack will become unstable and grow rapidly.

f_CCT(a, w_p) = s

sec

 π a

w_p



(2.33) K_co= σ_CCT√

πaf_CCT(a, w_p) (2.34)

Figure 2.13: Critical Stress Curve

2.5.5 Fatigue Crack Growth

In a structure which is subjected to variable loading over a high number of cycles fatigue crack growth will occur even at nominal stress-levels. This anomaly undergoes two phases, crack initiation and crack growth. For this analysis, crack growth will be focused upon as the crack is already present in the component.

To calculate crack growth per cycle, the Paris-Erdogan law with the mod- ification proposed by Walker [21] will be used as it takes stress ratio Rσ into consideration.

da

dN = C ((1 − R_σ)^q∆K)ⁿ (2.35) Where C, q and n are material properties defined by curve fitting experi- mental data and a is the crack length. ∆K is the difference between maximum and minimum stress intensity factors. However, the load cycle span between 0 and the calculated once-per-cycle equivalent load and therefore ∆K = Ktot.

Due to stress intensity factors being part of linear elastic fracture mechan- ics, it is possible to apply superposition to calculate a total stress intensity factor as there will be contribution from both tensile (Kt) and bearing (Kb) stresses for the rivet rows. There is no fastener present in the antenna feed- through hole and therefore only tensile stresses are present in that case.

K_tot,i= K_t,i+ K_b,i (2.36)

K_t,i = σ_{f at}f_t,i(a)√

πa (2.37)

K_b,i = σ_bf_b,i(a)√

πa (2.38)

In Eqs. 2.37 and 2.38, ft,i(a) and fb,i(a) are required correction factors as the equations are valid only for infinite width plates in tensile loading. The index i denotes if the equation considers one or two through-cracks emanat- ing from the hole. The assumptions behind one or two cracks is explained in Section 2.5.6.

f_{f w} = s

sec πD 2W_p



(2.39) The finite strip width correction, expressed in Eq. 2.39 is valid for a cen- trally located through-crack subjected to tensile loading [22]. However, the case of interest is one or two cracks originating from a fastener or antenna feed-through hole and therefore more correction factors are needed.

f_bc= F₁

F₂+ ^2a_D + F₃ (2.40)

The Bowie correction factor (Eq. 2.40) is valid for both one and two through-cracks in mode 1 loading which originate radially from a internal hole [23]. The constants F!, F2 and F3can be found in Table 2.3.

The final correction factors for both one and two through-cracks emerging from a central hole in a finite width strip subjected to tensile loading are cal- culated as shown in Eqs. 2.41 and 2.42. The last expression in each equation are corrections as proposed by Newman [24].

One Crack Two Cracks F₁ 0.8733 0.6865 F₂ 0.3245 0.2772 F₃ 0.6762 0.9439

Table 2.3: Constants for Bowie Correction Factor

ft,1(a) = fbc,1ff w

s

sec π 2

D + a W_p− a



(2.41)

f_t,2(a) = f_bc,2f_{f w} s

sec π 2

D + 2a Wp



(2.42) The correction factor for one and two through-cracks from pin-loaded holes is shown in Eqs. 2.43 and 2.44 . They have been re-expressed in terms of hole diameter D compared to Ref. [20].

fb,1 = ft,1

D 2W_p + 1

π

 D

D + a

 r D

D + 2a

!

(2.43)

f_b,2 = f_t,2

 D

2Wp

+ 1 π

 D

D + 2a



(2.44) With the stress intensity factors known it is possible to perform the crack- growth analysis. The value of interest is the amount of cycles until critical crack length is reached. By re-arranging Eq. 2.35 and integrating from initial crack length to critical crack length, this value is obtained.

N_cr = Z acr

ainit

1

C ((1 − R)^qK_tot,i)ⁿda (2.45)

2.5.6 Initial Crack Conditions

For this analysis, a conservative approach of two, equal-sized and symmetri- cally growing initial cracks will be used for both rivet and antenna holes. The recommendations are to let the crack sizes to be 1.3mm for the central hole and 0.26mm for the adjacent holes as demonstrated in Figure 2.14 [5][8][9].

Figure 2.14: Initial Crack Sizes and Locations

The symmetric growth is used due to the lack of solutions for apparent fracture toughness. The current solution is relying on the crack to be centered in the specimen, which would not be the case of unsymmetrical growth of two cracks of different initial size.

Method Description

The theory needed to perform a Damage Tolerance Analysis has been provided in Chapter 2 and in this chapter, the workflow of the methodology will be described.

3.1 Aircraft Data

The first step in the loads analysis is to obtain the required aircraft data. Inputs needed for calculations are listed in Table 3.1. MTOW, maneuver limits and maximum cabin pressurization are most of the times found in the pilots oper- ating handbook while the construction-specific data has to be acquired from maintenance manuals, inspection, aircraft TC-holder etc.

Parameter Notation Unit Maximum Takeoff Weight MTOW Kg

Fuselage Length L m

Fuselage Radius R m

Maneuver Limits n_z -

Maximum Cabin Pressurization P_max Pa

Skin Thickness t_s mm

Installation Location x_inst m Table 3.1: Required Aircraft Data

The installation location will decide the magnitude of bending stresses ac- cording to Fig. 2.2 and also whether the fuselage bending gives rise to com- pression or tension. In Eq. 2.12 there is a dependency on vertical distance Z

29

which is shown in Fig. 3.1 and for locations that are not on the top or bottom of the fuselage, it has to be calculated according to Eq. 3.1.

Z = Rsinθ (3.1)

Figure 3.1: Vertical Distance on Fuselage

3.2 Installation Data

In order to perform both rivet calculations and for the crack growth analysis, geometrical input data which is required is listed in Table 3.2.

Parameter Notation Unit

Doubler Width wd mm

Doubler Length l_d mm

Doubler Thickness t_d mm

Rivet Diameter Dr mm

Feed-through Diameter D_{f t} mm

Rivet Pitch p_r mm

Pocket Length L_p mm

Pocket Width W_p mm

Table 3.2: Required Geometrical Data

3.3 Material Data

The required material data, which should be obtained according to Section 2.2, is listed in Table 3.3. Note that several values might be needed if skin and doubler are of different materials or if different fasteners are used.

Parameter Notation Unit

Skin Modulus E_s Pa

Doubler Modulus E_d Pa

Fastener Modulus Ef Pa

Rivet Shear Allowables F_a,r Newton

Ultimate Stress F_tu Pa

Yield Stress Fty Pa

Ultimate Bearing Stress F_bru Pa Table 3.3: Required Material Data

As discussed in Section 2.5.4, fracture toughness Kcis normally a material parameter. However, for plane stress conditions, dependency of geometry is introduced. An apparent fracture toughness is considered and discussed in the section mentioned above.

3.4 Aircraft Stresses

Once the installation and aircraft characteristics are known, the initial stresses emerging from pressurization and fuselage bending can be calculated.

1. Calculate pressure difference ∆P . (Equation 2.4)

2. Calculate circumferential pressure stress σp,c. (Equation 2.5) 3. Calculate longitudinal pressure stress σ^p,l. (Equation 2.6) 4. Calculate distributed weight Wf. (Equation 2.11)

5. Calculate fuselage bending moment Mb. (Equation 2.9 or 2.10)

6. Calculate 1-g bending stress σ^1g using the ENAC model. (Equation 2.12)

7. Control that no other sources of stress concentrations in the vicinity of the antenna mounting point are present. Unforeseen interaction of these are one of the most common causes of fatigue failure.

Analysis for crack propagation and residual strength has different require- ments for stress magnitude and they are, according to Sections 2.5.1 and 2.5.2, calculated differently.

1. Calculate fatigue stresses σf at,cand σf at,l. (Equations 2.15 and 2.16) 2. Calculate residual strength stresses σres,cand σres,l. (Equations 2.17 and

2.18)

3.5 Rivet Calculations

To ensure that selected rivets are satisfactory in terms of strength, both shear force and bearing stress is calculated and verified against allowable values.

The initial task is to define geometrical parameters needed for the rivet analys- is. Also note that this analysis has to be performed twice. Once for the lon- gitudinal direction and once for the circumferential. Rivets attached to the fuselage stringers will be excluded in the analysis to reduce complexity. This will in turn provide conservative values due to the excluded stiffness of the stringer.

The example shown in Figure 2.10 demonstrates rivet loads in the circum- ferential direction. The strip width is therefore decided by the doubler width and the amount of longitudinal rivets. The rivet rows, also numbered in the figure, are taken in the circumferential direction to decide the load distribution amongst them, which has the characteristics shown in Figure 2.9 which also shows that only three rows must be considered due to symmetry. For longitu- dinal rivet loads, the same procedure is applied with corresponding loads and directions.

1. Calculate idealized strip width ws (Equation 2.19).

The strip width is equal to the distance between two adjacent fastener holes. This can vary throughout the installation.

2. Calculate applied force to the skin section F^skin. (Equation 2.20) The stress to be used are the fatigue crack growth stresses.

3. Calculate applied force to each strip Fs. (Equation 2.21)

4. Decide constants κ, m and λ. For an internal or external doubler, m = 1 while κ and λ depends on used fastener type.

5. Calculate skin, doubler and fastener flexibilities. (Equations 2.22 and 2.23, 2.24)

Equilibrium and compatibility equations may now be written according to Appendix A where the index n equals the amount of rivets nr, index 1 represent the fuselage skin and index 2 represents the doubler. These equations together with the force-displacement relationship shown in Eq. 3.2 forms a linear system of equations where each included rivet adds 6 unknowns.

u_i = C_iF_i (3.2)

The system of linear equations, described in Section 2.5.3 and Eq. 2.25, should be organized in the same way as shown in Appendix A but placing external forces on the right-hand side of the equality sig. For Eq. 3.2, both terms are moved to the same side such that the questions equals zero. The vector of unknowns should take on the form below.

Figure 3.2: Vector of Unknowns

When the linear system is solved, fastener loads F^{f i}can be obtained from u to lastly validate that maximum allowable bearing stress Fbru and fastener shear force Fa,ris not exceeded.

3.6 Crack Growth Analysis

The main goal of the crack growth analysis is to estimate growth rate and to verify safety and structural integrity over the life of the aircraft. This analy- sis requires careful considerations regarding crack growth paths, initial condi- tions, crack interaction and stress field characteristics.

Critical locations for crack growth are the feed-through hole and outer rivet rows [8][25] and hence the initial conditions and growth paths at these loca- tions must be considered. The cracks will grow either in the circumferential or the longitudinal directions and these instances will be analysed separately with symmetrical crack growth as described in 2.5.6 starting at centered holes.

3.6.1 Net Section Yield

Prior to crack growth calculations, critical crack lengths due to net section yielding can be decided. Critical crack lengths due to stress intensity factor is calculated in the crack growth algorithm. For each location and direction of interest, Eq. 2.29 results in the critical crack length. For this particular application, longitudinal and circumferential cracks must be analysed for both antenna feed-through hole and rivet holes.

3.6.2 Crack Growth Calculations

Prior to calculating crack growth, the geometry conditions must be decided and the corresponding parameters decided. The four different cases which must be calculated are:

1. Longitudinal cracks emanating from the antenna feed-through hole.

2. Circumferential cracks emanating from the antenna feed-through hole.

3. Longitudinal cracks emanating from a rivet hole.

4. Circumferential cracks emanating from a rivet hole.

For this example, longitudinal cracks at the antenna feed-through hole will be demonstrated while the others will be left out. The analysis should how- ever be performed in the same way with the correct stresses and geometrical parameters.

The geometrical properties to be decided are, with propagation path in mind, is the amount of holes the crack will encounter during growth. Fig.

3.3 shows the antenna feed-through hole of a doubler. There are two adjacent holes with different pitch and for simplicity and conservatism it will be as- sumed that a hole with pitch P¹will be present at the right side of the hole and another hole with pitch P2will be present at the left side such that symmetry is achieved according to Fig.3.4 . The conservatism in this assumption lies in the incremental crack growth whenever a hole is reached resulting in less cycles needed to reach critical length.

The crack growth then has to be iterated between each rivet hole and the crack length constantly verified not to exceed critical crack length due to net section yield or critical fracture toughness. The process differs somehow for the first crack and the upcoming ones due to simultaneous growth. For the first crack the growth calculations are described below.

Figure 3.3: Doubler Antenna Crack Growth

Figure 3.4: Doubler Rivet Symmetry

1. The initial crack length a0,0, according to Section 2.5.6, is 1.3 mm.

2. Decide crack length a^max,0when the next hole is reached which is equal to the hole pitch. (P1in Fig. 3.4)

3. Decide crack size increment with each iteration. This is governed by the desired resolution size nsteps which is chosen according to user prefer- ence.

da = amax,0− a0,0

n_steps

4. Calculate the crack growth according to the flowchart presented in Fig- ure 3.5. Note that the stress intensity factor Kt,2is the correction for two cracks. This is due to the central hole having one 1.3mm crack on each side. The stress σf at must be the stress which opens the crack. In the case of longitudinal crack propagation, this is the circumferential fatigue stress.

5. Given the critical crack length isn’t reached, calculate the growth ag for the initial ainit,1 = 0.26mm crack during the amount of cycles calcu-

lated in previous step. Note that Kt,2 is replaced by Kt,1 as this hole only has one initial crack.

Z ag

ainit,1

1

C ((1 − R)^qK_t,1(i))ⁿda − N_{f inal} = 0 6. Calculate an initial crack length a0, 1 for this phase.

a_0,1 = a_{f inal}+ a_g + D_r

7. Calculate the crack length for when the next hole is reached and continue as step 3 and 4 above.

a_max,1 = P₁+ D_r+ P₂

This process continues until the critical crack length or critical fracture toughness values are exceeded. As there are two directions and two locations (rivet rows and antenna hole), four different values of critical crack lengths and their corresponding cycle count are obtained. Naturally, the lowest number of cycles required to reach any critical crack length will be used to establish inspection intervals.

3.7 Inspection

Estimating the extent of the damage and inspecting it during the service life- time is equally important to verify that actual damage growth does not exceed (or diverge from) the estimations. Establishing inspection intervals alongside inspection technique is required by EASA and FAA to comply to continued airworthiness directives.

3.7.1 Inspection Method

During maintenance, the airframe is inspected with non-destructive testing (NDT) methods. NDT is used to detect flaws in the material without caus- ing further damage or even destroying the part, which is common to do when e.g. investigating material properties. There are many NDT methods available such as visual and optic testing, penetrant testing, eddy current testing and ul- trasonic testing to mention a few. The minimum detectable crack length differ amongst these and which method being used is dependent upon the workshop preference and competence.

Figure 3.5: Algorithm First Crack

Bromma Air Maintenance utilize eddy current testing which detects cracks or flaws by measuring conductivity in the material. This method yields imme- diate results and requires minimal preparation of the part but has a rather low penetration depth, something which can cause problems if e.g. the doubler is attached externally and skin cracks is to be inspected [26].

The minimum detectable crack size is dependent upon material and dis- tance from surface to the flaw. However, generally acceptable lengths are 1.6mm at fastener and 3.2mm away from fastener [27]. For conservative pur- poses the larger value will be chosen and adet = 3.2mm.

3.7.2 Inspection Interval

The maximum amount of cycles in between inspections is decided by a safety factor jinspwhich can be chosen according to conservatism in the analysis per- formed. The methodology used in this report is based upon proven theories widely used in the industry [2][5][8][9][10]. The safety factor recommenda- tions lies between 3-6 and maximum cycles between inspection is calculated according to Eq. 3.3. Further recommendations state that the inspection inter- val should not exceed half of the aircraft life [28].

N_insp,max= N_c− N_det

j_insp (3.3)

The amount of cycles for the crack to become detectable Ndet is calcu- lated from the obtained crack growth results by interpolating the results or by integration of Eq. 2.45.

Defining the final inspection interval should be done with consideration to the modified aircraft inspection and maintenance program. To reduce aircraft ground time, it is desirable to synchronize the aircraft inspection program with the newly modification inspection program.

Discussion and Conclusion

4.1 Validity and Applicability

The methodology is applicable to small antenna installations that do not span over several pockets on the fuselage. It is valid for demonstrating compliance according to CS-23, and possibly FAR-23 regulations. However, for CS-25 validity it must be verified. Validity for larger antennas is further discussed in Section 4.3.

The result is a proposed methodology based on recommended work and used standards within the industry. The importance of using these methods lies in the fact that they are proven to be accurate enough to ensure aircraft safety, which is the single most important concern for the industry.

4.2 Limitations

For this project, a standardized fatigue factor was utilized due to the lack of a more advanced load spectrum. The development of this spectrum is time con- suming and requires thorough knowledge of the aircraft mission profile. This is different for each individual aircraft, customer and target mission. However, the development of a load profile would allow for higher accuracy in terms of fatigue stress.

Due to the limited time-frame of a MSc. thesis report and the complexity of fracture mechanics, crack retardation, fuselage bulging, crack/hole interaction and secondary bending was left out. It has also been shown that these are not required in order for EASA or FAA to approve a STC.

39

4.3 Future Work

The methodology can be further improved for higher accuracy but also a wider field of applicability. Bromma Air Maintenance expressed a desire to perform such an analysis to a large antenna which span across several pockets in both circumferential and longitudinal direction. This would require modification of the analysis taking secondary bending and frame/stringer stiffness contri- butions into consideration.

The software AFGROW could be implemented for crack growth analysis which would reduce the time needed to manually create the algorithm but also provide more sophisticated crack-growth models, load spectrum creation and potentially provide a crack-growth material database. The FE software, in this methodology, is mainly used for validation of the analytical stress calculations and a means to check if the new modification influences the stress-field at installations. It can be used for crack-growth analysis as well but due to the cost and competence required, analytical solutions are often preferred.

[1] Russell Wanhill. “Fatigue Requirements for Aircraft Structures”. In:

Nov. 2017, pp. 331–352. isbn: 978-981-10-2142-8. doi: 10 . 1007 / 978-981-10-2143-5_16.

[2] T. Swift. “Repairs to Damage Tolerant Aircraft”. In: Structural Integrity of Aging Airplanes. Ed. by S. N. Atluri, S. G. Sampath, and Pin Tong.

Berlin, Heidelberg: Springer Berlin Heidelberg, 1991, pp. 433–483.

[3] P.A Withey. “Fatigue failure of the de Havilland comet I”. eng. In: En- gineering Failure Analysis 4.2 (1997), pp. 147–154. issn: 1350-6307.

[4] Federal Aviation Administration. Aloha Airlines 737 Accident Overview.

Accessed: February 27, 2020. url: https://lessonslearned.

faa.gov/ll_main.cfm?TabID=4&LLID=20&LLTypeID=2.

[5] Patrick Safarian. Damage Tolerance Evaluation of Antenna Installa- tions. University of Washington.

[6] European Union Aviation Safety Agency. CS-23 Amendment 4. url:

https://www.easa.europa.eu/sites/default/files/

dfu/CS-23%5C%20Amendment%5C%204.pdf.

[7] W. G Walker and K. G Pratt. A revised gust-load formula and a re- evaluation of v-g data taken on civil transport airplanes from 1933 to 1950. eng. 1954. url: http : / / hdl . handle . net / 2060 / 19930090988.

[8] E. García. Damage Tolerance for Antenna Installations. EASA STC Structural Substantiation Workshop, Cologne, September 17-18, 2014.

url: https : / / www . easa . europa . eu / newsroom - and - events / events / stc - structural - substantiation - workshop-antenna-installation-damage.

[9] Chicago Aircraft Certification Office. Damage Tolerance Analysis for Antenna Installations on Pressurized Transport Airplanes. Federal Avi- ation Administration.

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