Investigation of the role of bulkhead and crack stopper strap in the fail-safe design of a wide bodied transport aircraft

Investigation of the role of bulkhead and crack stopper strap in the fail-safe design of a wide bodied transport aircraft

Chapter -1

INTRODUCTION1.1 Introduction to aircraft structure

Aircraft are vehicles which are able to fly by being supported by the air, or in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines. An aircraft is a complex structure, but a very efficient man-made flying machine.

Aircrafts are generally built-up from the basic components of wings, fuselage, tail units and control surfaces. Each component has one or more specific functions and must be designed to ensure that it can carry out these functions safely. Any small failure of any of these components may lead to a catastrophic disaster causing huge destruction of lives and property. When designing an aircraft, its all about ending the optimal proportion of the weight of the vehicle and payload. It needs to be strong and stiff enough to withstand the exceptional circumstances in which it has to operate. Durability is an important factor. Also, if a part fails, it doesnt necessarily result in failure of the whole aircraft. It is still possible for the aircraft to glide over to a safe landing place only if the aerodynamic shape is retained-structural integrity is achieved.The basic functions of an aircrafts structure are to transmit and resist the applied loads; to provide an aerodynamic shape and to protect passengers, payload systems, etc., from the environmental conditions encountered in flight. These requirements, in most aircraft, result in thin shell structures where the outer surface or skin of the shell is usually supported by longitudinal stiffening members and transverse frames to enable it to resist bending, compressive and torsional loads without buckling. Such structures are known as semi-monocoque, while thin shells which rely entirely on their skins for their capacity to resist loads are referred to as monocoque.

The load-bearing members of these main sections, those subjected to major forces, are called the airframe. The airframe is what remains if all equipment and systems are stripped away. In most modern aircrafts, the skin plays an important role in carrying loads. Sheet metals can usually only support tension. But if the sheet is folded, it suddenly does have the ability to carry compressive loads. Stieners are used for that. A section of skin, combined with stieners, called stringers, is termed a thin-walled structure.

The airframe of an aircraft is its mechanical structure, which is typically considered to exclude the propulsion system. Airframe design is a field of engineering that combines aerodynamics, materials technology and manufacturing methods to achieve balances of performance, reliability and cost.1.1.1 Major aircraft components

Fig.1.1Airplane parts and its functionFuselage:The main body structure is the fuselage to which all other components are attached. The fuselage contains the cockpit or flight deck, passenger compartment and cargo compartment. While wings produce most of the lift, the fuselage also produces a little lift. A bulky fuselage can also produce a lot of drag. For this reason, a fuselage is streamlined to decrease the drag. We usually think of a streamlined car as being sleek and compact - it does not present a bulky obstacle to the oncoming wind. A streamlined fuselage has the same attributes. It has a sharp or rounded nose with sleek, tapered body so that the air can flow smoothly around it.

Fig 1.2 Fuselage

Unlike the wing, which is subjected to large distributed air loads, the fuselage is subjected to relatively small air loads. The primary loads on the fuselage include large concentrated forces from wing reactions, landing gear reactions and pay loads. For airplanes carrying passengers, the fuselage must also withstand internal pressures. Because of internal pressures, the fuselage often has an efficient circular cross-section. The fuselage structure is a semi-monocoque construction consisting of a thin shell stiffened by longitudinal axial elements (stringers and Longerons) supported by many traverse frames are rings (Bulkheads) along the length. The fuselage skin carries the shear stresses produced by torques and transverse forces. It also bears the hoop stresses produced by internal pressures. The stringers carry bending moments and axial forces. They also stabilize the thin fuselage skin.

Fuselage frames often take the form of a ring. They are used to maintain the shape of the fuselage and to shorten the span of the stringers between supports in order to increase the buckling strength of the stinger. The loads on the frames are usually small and self equilibrated. Consequently their constructions are light. To distribute large concentrated forces such as those from the wing structure, heavy bulkheads are needed. A transverse partition or a closed frame in a structure separating one portion from another is called a Bulkhead. Also used to designate solid, webbed or trussed members to dissipate concentrated loads into monocoque or semi-monocoque structure especially a fuselage. Members approximately parallel to the longitudinal axis of a beam or semi-monocoque structure are called longitudinal stiffeners. They are designed to stiffen the skin and assist in resisting shear and bending loads. A stiffener is a member used to reinforce thin sheets. Sometimes they are called stringers.Stringers are longitudinal members in the fuselage to support the skin and to hold the frames in position. It is used to carry direct load in the direction of its length.Longerons are main structural members of the fuselage. It is generally used when there is a big cut-out to be provided. Ex: cockpit.Wings:

The wings are airfoils attached to each side of the fuselage and are the main lifting surfaces that support the airplane in flight. Wings vary in design depending upon the aircraft type and its purpose. Most airplanes are designed so that the outer tips of the wings are higher than where the wings are attached to the fuselage. This upward angle is called the dihedral and helps keep the airplane from rolling unexpectedly during flight. Wings also carry the fuel for the airplane.The wing is a framework made up of spars, ribs, skin and (possibly) stringers. This is the main lifting surface.

Fig.1.3 wing and its components

The Empennage:The empennage is most commonly referred to as the tail of the aircraft. It consists of two primary structures, the vertical stabilizer and the horizontal stabilizer. Both of these stabilizers help the aircraft maintain a straight path through the air as it flies. Both are also stationary (fixed) to the aircraft. In essence they act like the feathers on an arrow. Vertical Stabilizer - This stabilizer is as its name suggest. It is the vertical "fin" you see on an aircraft. The vertical stabilizer is home to another control surface of the aircraft: the rudder. The rudder looks just like the vertical stabilizer but is hinged on the trailing edge of the stabilizer and can deflect to the left or right. This control surface yaws the aircraft.

Horizontal Stabilizer - The horizontal stabilizer is home to the control surface known as the elevator. The elevator is attached to the horizontal stabilizer in much the same way the rudder is to the vertical stabilizer. The elevators pitch the aircraft. More specifically, they point the nose of the aircraft either up or down in the desired direction.

Fig 1.4 Empennage

Some aircraft have "trim tabs". Most have a trim tab only on the elevator, but some have them on the rudder and ailerons. They relieve the pressure a pilot must exert on the control yoke to maintain the aircraft orientation he/she desires. It is common for pilots to trim an aircraft for steady, level flight so that their hands are free to do other things.

Landing gear:

The landing gear is the principle support of the airplane when parked, taxiing, taking off, or when landing. The most common type of landing gear consists of wheels, but airplanes can also be equipped with floats for water operations, or skis for landing on snow.

Fig.1.5 landing gear

Control surfaces:

As aircraft move in three dimensions we need various control devices to control it. Fix-wing aircrafts have control surfaces for each one of these dimensions. Usually these are placed in the extremes of the aircraft (tail and wings) to get the maximum strength and response using small moving parts thanks to the lever concept. Following are the various Control Surfaces The Flaps on the wings control the drag and lift on the structure

The Rudder is used to change pitch (side-to-side) movement.

The Elevator is used to change pitch (up-down) movement.

The Aileron is uses to change lift, drag and roll. The Slats are used to change lift.

Following are the various Control Surfaces:

The Flaps on the wings control the drag and lift on the structure

The Rudder is used to change pitch (side-to-side) movement.

The Elevator is used to change pitch (up-down) movement.

The Aileron is uses to change lift, drag and roll. The Slats are used to change life.

1.2Aircraft Materials1.2.1Metallic Materials

The most common metals used in aircraft construction are aluminum, magnesium, titanium, steel, and their alloys. Traditional metallic materials used in aircraft structures are Aluminum, Titanium and steel alloys. In the past three decades applications of advanced fibre composites have rapidly gained momentum. To date, some modern military jet fighters already contain composite materials up to 50% of their structural weight. Selection of aircraft materials depends on any considerations, which can in general be categorized as cost and structural performance. Cost includes initial material cost, manufacturing cost and maintenance cost. The key material properties that are pertinent to maintenance cost and structural performance are

Density (weight)

Stiffness (youngs modulus)

Strength (ultimate and yield strengths)

Durability (fatigue)

Damage tolerance (fracture toughness and crack growth)

Corrosion

Seldom is a single material able to deliver all desired properties in all components of the aircraft structure. A combination of various materials is often necessary. Table 1.1 lists the basic mechanical properties of some metallic aircraft structural materials.Table 1.1 Material properties of metals at room temperature of aircraftstructure[18]

MaterialProperties

E

GPa(msi)

t

MPa(ksi)y

MPa(ksi)

g/cm3

Aluminum2024-T3

7075-T672(10.5)

71(10.3)0.33

0.33449(65)

538(78)324(47)

490(71)2.78(0.10)

2.78(0.10)

Titanium

Ti-6Al-4V110(16)0.31925(138)869(126)4.46(0.16)

Steel

AISI4340

300M200(29)

200(29)0.32

0.321790(260)

1860(270)1483(212)

1520(220)7.8(0.28)

7.8(0.28)

t = Tensile ultimate strengthy = Tensile Yield strength

Alloys:

An alloy is composed of two or more metals. The metal present in the alloy in the largest amount is called the base metal. All other metals added to the base metal are called alloying elements. Adding the alloying elements may result in a change in the properties of the base metal. For example, pure aluminum is relatively soft and weak. However, adding small amounts or copper, manganese, and magnesium will increase aluminum's strength many times. Heat treatment can increase or decrease an alloy's strength and hardness. Alloys are important to the aircraft industry. They provide materials with properties that pure metals do not possess.

Aluminum alloy:

Aluminum alloys are widely used in modern aircraft construction. Aluminum alloys are valuable because they have a high strength-to-weight ratio. Aluminum alloys are corrosion resistant and comparatively easy to fabricate. The outstanding characteristic of aluminum is its lightweight.

Among the aluminum alloys, the 2024 and 7075 alloys are perhaps the most used. The 2024 alloys (2024-T3,T42) have excellent fracture toughness and slow crack growth rate as well as good fatigue life. The code number following T for each aluminum alloy indicates the heat treatment process. The 7075 alloys (7075-T6, T6510) have higher strength than the 2024 but lower fracture toughness. The 2024-T3 is used in the fuselage and lower wing skins, which are prone to fatigue due to applications of cyclic tensile stresses. For the upper wing skins, which are subjected to compressive stresses, fatigue is less of a problem, and 7075-T6 is used. The recently developed Aluminum Lithium alloys offer improved properties over conventional aluminum alloys. They are about 10% stiffer and 10% lighter and have superior fatigue performance.Titanium alloy:

Titanium is a lightweight, strong, corrosion resistant metal. Recent developments make titanium ideal for applications where aluminum alloys are too weak and stainless steel is too heavy. Additionally, titanium is unaffected by long exposure to seawater and marine atmosphere.

Titanium alloy such as Ti-6Al-4V (the number indicates the weight percentage of the alloying element) with a density of 4.5 g/cm3 is lighter than steel (7.8 g/cm3) but heavier than aluminum (2.7 g/cm3). Its ultimate and yield stresses are almost double those of aluminum 7075-T6. Its corrosion resistance in general is superior to both steel and aluminum alloys. While aluminum is usually not for applications above 350o F, titanium, on the other hand, can be used continuously up to 1000 o F.

Titanium is difficult to machine, and thus the cost of machining titanium parts is high. Near net shape forming is an economic way to manufacture titanium parts. Despite its high cost, titanium has found increasing use in military aircraft. For instance, the F-15 contains 26% (structural weight) titanium.Steel Alloys:Among the three metallic materials, steel alloys have highest densities, and are used only where high strength, high yield stress are critical. Examples include landing gear units and highly loaded fittings. The high strength steel alloy 300 m is commonly used for landing gear components. Besides being heavy, steel alloys are generally poor in corrosion resistance. Components made of these alloys must be plated for corrosion. These steels contain small percentages of carbon, nickel, chromium, vanadium, and molybdenum. High-tensile steels will stand stress of 50 to 150 tons per square inch without failing. Such steels are made into tubes, rods, and wires. Another type of steel used extensively is stainless steel. Stainless steel resists corrosion and is particularly valuable for use in or near water.1.2.2 Non Metallic Materials

In addition to metals, various types of plastic materials are found in aircraft construction. Some of these plastics include transparent plastic, reinforced plastic, composite, and carbon-fiber materials.Transparent Plastic:

Transparent plastic is used in canopies, windshields, and other transparent enclosures. You need to handle transparent plastic surfaces carefully because they are relatively soft and scratch easily. At approximately 225F, transparent plastic becomes soft and pliable.

Reinforced Plastic:

Reinforced plastic is used in the construction of radomes, wingtips, stabilizer tips, antenna covers, and flight controls. Reinforced plastic has a high strength-to-weight ratio and is resistant to mildew and rot. Because it is easy to fabricate, it is equally suitable

for other parts of the aircraft. Reinforced plastic is a sandwich-type material. It is made up of two outer facings and a center layer. The facings are made up of several layers of glass

cloth, bonded together with a liquid resin. The core material (center layer) consists of a honeycomb structure made of glass cloth. Reinforced plastic is fabricated into a variety of cell sizes.Fiber-reinforced composites:

Materials made in to fibre forms can achieve significantly better mechanical properties than their bulk counterparts. A notable example is glass fiber v/s bulk glass. The tensile strength of glass fibre can be 2 orders of magnitude higher than that of bulk glass. . Listed in table 1.2 are the mechanical properties of some high performance man made fibers.Table 1.2: Mechanical Properties of Fibres[18]

MaterialProperties

E

GPa(msi)t MPa(ksi)

in g/cm3

E-glass77 (11)2.5 (350)2.54

S-glass85 (12)3.5 (500)2.48

Silicon carbide (nicalon)190 (27)2.8 (400)2.55

Carbon (Hercules AS4)240 (51)3.6 (510)1.80

Carbon (Hercules HMS)360 (35)2.2 (310)1.80

Carbon (Toray T300)240 (35)3.5 ()5001.80

Boron385 (55)3.5 (500)2.65

Kevlar-49(Aramid)130 (18)2.8 (400)1.45

Kevlar-2965(9.5)2.8 (400)1.45

Fibres alone are not suitable for structural applications. To utilize the superior properties of fibres, they are embedded in a matrix material that holds the fibers together to form a solid body capable of carrying complex loads. Matrix materials that are currently used for forming composites include 3 major categories: polymers, metals, and ceramics. The resulting composites are usually referred to as polymer matrix composites (PMC), metal matrix composites (MMC), and ceramic matrix composites (CMC). Table 1.3 presents properties of a list of composites. Its matrix material often determines the range of service temperature of a composite. Polymer matrix composites are usually for lower temperature ( 1500 o F) environments such as jet engines.Table 1.3 Longitudinal mechanical properties of fiber composite

MaterialTypeProperties

E in GPa(msi)t in MPa(ksi) in g/cm3

Carbon-EpoxyT300/5208IM6/3501-6

AS4/3501-6140 (20)177 (25.7)

140 (20)1.5 (210)2.86 (414)

2.1 (300)1.551.55

1.55

Boran-AluminumB/A12024210 (30)1.5 (210)2.65

Glass-EpoxyS2 Glass-Epoxy43 (6.2)1.7 (245)1.8

Aramid EpoxyKev 49-Epoxy70 (10)1.4 (200)1.4

Fibre composites are stiff, strong, and light and are thus most suitable for aircraft structures. They are often used in the form of laminates that consists of a number of unidirectional lamina with different fibre orientations to provide multidirectional load capability. Composite laminates have excellent fatigues life, damage tolerance, and corrosion resistance. Laminate constructions offer the possibility of tailoring fiber orientations to achieve optimal structural performance of the composite structure.1.3 Damage ToleranceIn todays structural design, fatigue and damage tolerance analysis have become most important and challenging task for the designers because of failure of structure due to different type of damages. Some of these damages have caused a loss of entire structure i.e. whole aircraft itself.

Damage toleranceis a property of a structure relating to its ability to sustain defects safely until repair can be affected. The approach to engineering design to account for damage tolerance is based on the assumption that flaws can exist in any structure and such flaws propagate with usage. This approach is commonly used inaerospace engineeringto manage the extension of cracks in structure through the application of the principles offracture mechanics. In aerospace engineering, structure is considered to be damage tolerant if a maintenance program has been implemented that will result in the detection and repair of accidental damage, corrosion and fatigue cracking before such damage reduces the residual strength of the structure below an acceptable limit.Two major approaches were developed in the past, namely, the safe-life and the fail-safe design concepts. The safe-life approach correlating the time to failure of the specimen with the applied loads characteristics to predict the time to failure of real components using Minors rule approach. The other is fail-safe concept, in which linear elastic fracture mechanics approach (LEFM) are used to predict the crack stability, crack growth and hence the minimal time between the two inspections to avoid a crack reaching critical size. The later concept called the damage tolerance, whose function is to asses the effect of cracks in the structure. The analysis of damage tolerance behavior plays an important role in the structural integrity program.Damage tolerant design methods were developed that assume the structure contains initial cracks. The initial crack usually based on the inspection limits. There are two general approaches, with variations, that may be followed to guarantee that the structure does not fail in service, they are;

Slow Crack Growth: The slow crack growth design criteria select component material and sets stress levels so that the assumed preexistent crack will not grow to failure during service and are the normal approach for single load path structure. For increased safety, the allowed service life usually obtained by dividing the total crack growth period by a factor of 2. The component would have to be inspected at this time before continued operation would be permitted.Fail-Safe Design: This design concept assumes the possibility of multiple load paths and/or crack arrest features in the structure so that a single component failure does not lead to immediate loss of the entire structure. The load carried by the broken member is immediately picked up by adjacent structure and total fracture is avoided. It is essential;

However, that the original failure be detected and promptly repaired, because the extra load they carry will shorten the fatigue lives of the remaining components.1.4 Introduction to tear strap

As a result of the investigations into the accidents in the 1950s, aircraft manufacturers began to incorporate into their fuselage designs features which would increase the ability of the aircraft to sustain damage caused by fatigue cracking; i.e., a damage tolerant design philosophy. A reinforced doubler on the inside of the fuselage skin, termed tear strap, crack stopper strap, or fail-safe strap, is commonly employed. Tear straps are simply strips of material attached circumferentially to the skin of the fuselage which capitalize on the advantage of flapping. A tear strap locally reduces the hoop stress thus causing the bulge stress to become greater than the hoop stress for an axial crack length that is less than the axial crack length for flapping the un-stiffened cylinder. Properly designed tear straps are able to induce flapping and contain the damage

between two tear straps.

These tear straps are made up of aluminum alloy and are placed between the bulkhead and skin and they run below the bulkhead as shown in the fig1.6. It appears that the dimensions of the tear straps were, and even are to this day, determined largely by experiment.

Fig 1.6 Frame with crack stopper Fig 1.7 Frame without crack stopper1.5 Types of Crack in Fuselage

The Fuselage structure basically consists of skin panels connected to directly to frames and stringers. For circumferential and longitudinal splice Cabin pressure results in radial growth of skin and this radial growth is resisted by frames and stringers giving local bending along fastener lines. Fuselage skin panels are curved and these panels are biaxial tension loading due to cabin pressure. Two types of damage most frequently associated with the structural integrity of the fuselage structure are longitudinal cracks under hoop stresses induced by cabin pressurization and circumferential cracks under stresses from vertical bending of the fuselage.Circumferential crack

Fig 1.8 Typical fuselage circumferential splice at frame with circumferential crack

Longitudinal Crack Fig1.9 Typical fuselage longitudinal splice at stringer with longitudinal crack1.6Historical Perspective A critical survey of aircraft structure shows that most of the failure in aircraft structure design is mainly due to cracking problem. The figure 1.8 shows a survey of service cracking problem in Air Force Aircraft. The distribution shows that majority of incidents were in fuselage and wing. The major of these incidences were fatigue initiated, with corrosion fatigue second, followed by stress corrosion. The majority of the failures were due to poor quality where crack initiated at hole. Material flaw, defects and scratches were second followed by poor design details.

a) Distribution and magnitude of Service cracking problem

b) Cracking failure incidences

c) Cracking and failure origin

Fig 1.10(a, b, c) Survey of service cracking problem in air force aircraft

Fig 1.10 shows the different sources of damages in an aircraft structure. These damages are due to poor design details, corrosion pits and scratches, material flaws, defects and scratches, poor quality holes etc.Chapter-2

LITERATURE REVIEW

Aircraft structure is the most obvious example where functional requirements demand light weight and, therefore, high operating stresses. An efficient structural component must have three primary attributes; namely, the ability to perform its intended function, adequate service life, and the capability of being produced at reasonable cost. Attention is now focused on propagation of crack. The review summarizes the previous effort on the Damage tolerance assessment of stiffened structures.

Erdogan et al [1] studied on fatigue and fracture of cylindrical shells containing a circumferential crack, here the cylindrical shells containing a circumferential crack subjected to axial tension and stress from the vertical bending of fuselage are considered. and Longitudinal crack growth occurs mainly due to hoop stresses developed due to internal pressurization, He concluded that the longerons does not play much role in arresting longitudinal cracks in the fuselage structures. But Bulkheads are more effective in arresting longitudinal cracks.

H. Vlieger [2] proposed a method that relates the crack resistance of a stiffened panel to that of an un-stiffened sheet. Vlieger takes full account of sheet-stringer interaction in the cracked region. Vlieger bring into account the stiffener failure criterion , crack arrest criterion and a brief about residual strength theory. The more important is, the analytical approach to obtained the residual strength of the stiffened sheet using two important factor i.e. crack tip reduction factor (C) and stiffener load concentration (L). He also gives the analytical method (Displacement compatibility method) to calculate C and L and comparisons of the same were done with the results obtained from the finite element analysis. The assumptions that were taken into account while building up a finite element model are as follow: The rivet hole through which crack is emanating was neglected.

The Z- stiffeners are replaced by two flat strip of same cross-sectional area as of stiffener on both side of the panel there by neglecting the eccentricity effect.

H. Vlieger [3] studied the effect of crack elements in a built-up structure. He characterized that crack built-up structures has the ability to transfer load from the cracked to the intact element, thus reliving the most critical part of the structure. The interaction of intact and cracked element will be essential for residual strength and crack propagation behavior of the built-up structures as a whole. He also studied the fatigue crack propagation behavior in built-up skin-stringer riveted structure. The experimental side of the research consisted of set of crack propagation tests on panels with and without stiffeners under an axial constant amplitude pulsating load. The results were obtained by considering riveted joint to be rigid sheet is flexible and sheet and rivet are flexible.. Finally he concluded that stiffeners are less loaded than in case of rigid joints because of joint flexibility Thomas P. Rich et al [4] derived general equation for the prediction of structural failure of two dimensional cracked components in which the geometrical features of the component affect the stress intensity factor of the crack. The general equation is used to construct a new fracture diagram for a uniformly stressed sheet containing a crack which is constrained by two stiffening elements fastened to the sheet. By the use of an example it is shown that the shape of the fracture diagram, and hence the fracture behavior of the panel, depends on the spacing of the stiffening elements, rivet locations and the relative stiffness of the cracked sheet and the stiffeners. it is shown that there are stiffened panel diagrams which indicate that failure can occur at fracture toughness levels significantly higher than would be apparent from an un-stiffened panel of similar material.

Pir M. Toor [5] focuses its attention on designing a fail-safe fuselage structure. Two types of damage most frequently associated with the structural integrity of the fuselage are longitudinal cracks under high hoop stresses induced by cabin pressurization and circumferential cracks under stresses from vertical bending of the fuselage. The analysis of these types of cracks is complex, first due to the complex structural configuration (i.e. frames, skin longeron and crack stopper straps) and secondly due to the influence of the curvature of the shell. Describes a various analytical and empirical approaches used in evaluating the damage tolerance capability of the fuselage structure are critically evaluated and compared. A model which accounts for the influence of frames, straps and curvature is developed. This model is then used in an example problem having typical military cargo aircraft fuselage structural elements. The Air Force damage tolerance requirements are discussed in detail.

Pir M. Toor [6] focuses its attention on designing a fail-safe fuselage structure considering circumferential cracks under stresses from vertical bending of the fuselage. The analysis of these types of cracks is complex, first due to the complex structural configuration (i.e. frames, skin Longerons and crack stopper straps) and secondly due to the influence of the curvature of the shell. And he found that Longeron (stringers) are more effective in arresting circumferential cracks.Federal Aviation Administration technical center[7] propose Damage tolerance handbook Vol-1 and Vol-2, which explain fracture mechanics, fatigue crack propagation and damage tolerance evaluation and requirement. It also deals with all the structural failure of liberty ship i.e. 1943 to the Dan-Aircraft horizontal stabilizer failure in Zambia in 1976, which was the main reason to change the older design approach to current damage tolerance approach.

T. Swift (1994) [8] addresses some of these issues outlined as follows. The importance of the two-bay crack design criterion needs restating. The threshold for detailed inspection of fatigue critical elements needs close examination, especially for elements that do not have crack-arrest capability. The effects of multisite damage on residual strength and discrete source damage capability need to be addressed, especially for aircraft operating beyond half their test life. The current trend to eliminate fuselage crack stoppers should be reconsidered very carefully. J. Schijve [9] summarized the failure scenarios for a lead crack and more small MSD cracks as discussed by Broek and Swift are, including recent results of a relevant test series by Broek. It shows that small MSD cracks can significantly reduce the load for unstable crack extension. Prevention of catastrophic consequences requires crack arresting capability of the structure. Related aspects of the problem are discussed with reference to failure criteria for ligament failure, the MSD problem for existing and new aircraft, and different options for crack stopper bands. He proposed that by using Tear straps we can achieve fail safe design. A fuselage without crack-stopper bands is attractive for obvious production reasons. This can only be justified if the stress level is sufficiently low, or if the material has a high fatigue resistance.T. Swift [10] describes the approaches i.e. direct finite element method, Finite element energy release rate method and displacement compatibility method to meet damage tolerance requirement. He also described the role that stiffeners play in reduction the crack tip stress intensity factor to a level which can arrest crack after rapid propagation.E.F. Rybicki and M.F. Kanninen [11] presented an efficient technique for evaluating stress intensity factors. The method, based on the crack closure integral, can be used with a constant strain finite element stress analysis and a coarse grid. The technique also permits evaluation of both Mode I and Mode II stress intensity factors from the results of a single analysis. Example computations are performed for a double cantilever beam test specimen, a finite width strip with a central crack, and a pin loaded circular hole with radial cracks. Close agreement between numerical results given by this approach and reference solutions were found in all cases.

Amy L. Cowan [12] developed a finite element model of a fracture test specimen is using the STAGS computer code (Structural Analysis of General Shells). The test specimen was an internally pressurized, aluminum cylindrical shell reinforced with two externally bonded aluminum tear straps around its circumference. The shell contained an initial, axial through-crack centered between the straps. The crack propagated slowly in the axial direction as the pressure increased above a certain value until a maximum pressure was attained, and then the crack propagated dynamically. The tear straps sufficiently toughened the shell such that the dynamic crack path bifurcated near the edges of the straps. The bifurcated crack branches ran circumferentially, parallel to the straps causing the shell wall to flap open. A parametric study is then conducted to determine the influence of tear strap thickness and width on the location of crack bifurcation. From a limited parametric study, it is found that varying the thickness of a tear strap has a larger effect on the behavior of a crack than varying the width of a tear strap.Andrzej Leski [13] studied the implementation of virtual crack closure technique in engineering FE calculation. Equations for three-dimensional brick elements are given. Algorithms of applying the VCCT are presented and precisely explained. General conditions and limitations for using the VCCT with commercial software are provided. An example of implementing the VCCT in the MSC. Patran follows. The presented example consists of two PATRAN-dedicated procedures. In this way a useful tool for fracture mechanics calculations has been created. He concluded that The virtual crack closure technique is a convenient tool for stress intensity factor investigation. The main advantage of the VCCT is that it does not require a special mesh arrangement around the crack front. The major limitation of the VCCT is that it can only be applied to linear elastic fracture mechanics problems. The VCCT can be easily implemented in any commercial FE software.Jaap Schijve [14] proposed new concepts related to structural design, material selection, production techniques, inspection procedures and load spectra. Extensive research efforts have been spent. Our understanding of fatigue damage problems increased significantly. Simultaneously our tools to tackle problems have been developed to a high potential efficiency. And still, there are problems. The present paper is a personal impression of evaluating experience, design aspects, predictions and experiments associated with damage tolerance of aircraft structures.X Zhang et al [15] investigated on the effectiveness of crack growth retarders bonded to integral metallic structures. The study was performed by both numerical modeling and experimental tests. It focuses on aluminum alloy panels reinforced by bonded straps made of carbon-epoxy, glass-epoxy composite materials or a titanium alloy. The goal was to develop a fail-safe design for integrally stiffened skin-stringer panels applicable to aircraft wing structures. The modeling strategy and finite element models are presented and discussed. The requirements that the models should meet are also discussed. The study has focused on establishing the extent of crack retarder benefits, in terms of fatigue crack growth life improvement, by numerical simulation and experimental tests of various crack retarders. The results of predicted fatigue crack growth retardation have been validated by tests of laboratory samples. This study concludes that by bonding discrete straps to an integral structure, the fatigue crack growth life can be significantly improved.Chapter-3FORMULATION OF PROBLEM3.1The problemStiffened panels are the most generic structural elements in an airframe. Currently large transport airplanes are being developed with Large damage tolerance capability as a design goal. An important concept in the design of the pressurized fuselage of large transport aircraft is the provision of crack stopper straps to arrest the fast fracturing of a crack. 3.1.1 Objective of the present workIn this project the role of the crack stopper strap in the fail-safe design of the fuselage is investigated. As a first approximation a stiffened flat panel with a center longitudinal crack is considered. The strength of this cracked panel is investigated as a function of crack length in the absence of crack stopper straps. Crack stopper straps is then introduced at the locations of stiffeners perpendicular to the crack line and strength of the cracked flat panel is investigated as a function of crack length in the presence of crack stopper straps.

The thickness of the crack stopper straps will be varied in the parametric study.

The failure criteria that is used in this study are

1. The skin crack will have a fast fracture when the maximum stress intensity factor becomes equal to the fracture toughness of the skin material at that thickness

2. There is no rivet failure

3. There is no failure of the stiffener normal to the crack line

A Finite element analysis approach is followed in this investigation. Industry relevant data is used in this investigation .Geometrical dimensions representative of actual aircraft in service is considered. The material is taken as 2024-T3 sheet aluminum alloy.

A panel strength diagram is derived from the stress analysis of this cracked stiffened panel. This diagram illustrates the strength of the skin and the stiffener as function of crack length3.2 MATERIAL PROPERTIESThe material considered for the structure is Aluminum Alloy 2024-T351, with the following properties.1. Youngs Modulus, E = 70,000 N/mm22. Poison's Ratio, = 0.3

3. Ultimate Tensile Strength, u = 420 N/mm2

4. Yield Stress, y = 350 N/mm2 The following table shows the composition of the material considered.Table 3.1 Showing composition of the material [18]

CompositionWt. %CompositionWt. %

Al90.7-94.7Mn0.3-0.9

Crmax. 0.1Simax. 0.5

Cu3.8-4.9Timax. 0.15

Femax. 0.5Znmax. 0.25

Mg5.2-5.8Othersmax. 0.15

Chapter-4

FINITE ELEMENT ANALYSIS

4.1Introduction to FEA approachThe finite element method (FEM) is a numerical technique for solving problems which are described by partial differential equations or can be formulated as functional minimization. A domain of interest is represented as an assembly of finite elements. Approximating functions in finite elements are determined in terms of nodal values of a physical field which is sought. A continuous physical problem is transformed into a discretized finite element problem with unknown nodal values. For a linear problem, a system of linear algebraic equations should be solved. Values inside finite elements can be recovered using nodal values.

Two features of the FEM are worth to be mentioned:

1) Piece-wise approximation of physical fields on finite elements provides good precision even with simple approximating functions (increasing the number of elements we can achieve any precision).

2) Locality of approximation leads to sparse equation systems for a discretized problem. This helps to solve problems with very large number of nodal unknowns.4.1.1How the FEM works

To summarize in general terms how the finite element method works we list main steps of the finite element solution procedure below.

1. Discretize the continuum. The first step is to divide a solution region into finite elements. The finite element mesh is typically generated by a preprocessor program, which is MSC Patran in our case. The description of mesh consists of several arrays, main of which are nodal coordinates and element connectivity.

2. Select interpolation functions. Interpolation functions are used to interpolate the field variables over the element. Often, polynomials are selected as interpolation functions. The degree of the polynomial depends on the number of nodes assigned to the element.

3. Find the element properties. The matrix equation for the finite element should be established which relates the nodal values of the unknown function to other parameters. For this task different approaches can be used; the most convenient are: the variational approach and the Galerkin method.

4. Assemble the element equations. To find the global equation system for the whole solution region, we must assemble all the element equations. In other words we must combine local element equations for all elements used for discretization. Before solution, boundary conditions (which are not accounted in element equations) should be imposed.

5. Solve the global equation system. The finite element global equation system is typically sparse and symmetric. Direct and iterative methods can be used for solution. The nodal values of the sought function are produced as a result of the solution.

6. Compute additional results. In many cases, we need to calculate additional parameters. For example, in mechanical problems strains and stresses are of interest in addition to displacements, which are obtained after solution of the global equation system. So, these values of displacements can be used to find other parameters.In fact, Finite element modeling (FEM) is a powerful computer tool for determining stresses and deflections in a given structure which is too complex for classical analysis. Material properties such as Youngs modulus (E) and Poissons ratio () are entered along with boundary conditions such as displacements (u QUOTE ), applied loads (P), etc.The FEM method has these characteristics:

Solving arrays of large matrix equations

Fundamentally simple concepts involving basic stiffness and deflection equations

The first step is the construction of a structural model that breaks a structure into simple shapes or elements located in space by a common coordinate grid system The coordinate points, or nodes, are locations in the model where output data are provided

Essentially, FEM geometrically divides a structure into small elements with easily defined stress and deflection characteristics

The method appears complex because a model of an airframe structure can have thousands of elements or members, each with its own set of equation. Because of the very large number of equations and corresponding data involved, the finite-element method is only possible when performed by computer. With FEM, modeling is critical because it establishes the structural locations where stresses are evaluated, thus:

If a component is modeled inadequately, the resulting computer analysis could be quite misleading in its predictions in areas of maximum stress, deflection etc.

Modeling inadequacies include the incorrect placement of elements and attempting to define a structure with an insufficient number of elements

Such errors can be avoided by anticipating areas of maximum strain, but doing so requires engineering experience

In most cases, the finer the grid, the more accurate the results.

However, the computer capacity, time required and cost of analysis increases with the numbers of elements used in the model.

The efficiency can be increased by concentrating elements in the interested areas of high stress while minimizing the number of elements in low stress areas

It is not uncommon to develop FEM for prototype design for which experimental data can be obtained. Strain gauging is probably the most common method of obtaining experimental data in structural tests. Once FEM results and experimental data have been correlated, design modifications can be made, and these subsequent changes are often tested through FEM before being implemented on the actual prototype.

FEM is useful in design work, such as structural repair or modification, where a structural beef-up or change is contemplated. A FEM baseline model can be made for an existing structure for which stress and deflection data are known. A comparison is made between FEM results and known experimental data to calibrate the FEM results. Proposed design modifications can then be evaluated to the baseline modeling knowing that the new FEM results will have the same accuracy and requires the same calibration as the baseline case. 4.1.2The different stages of FEA

The software used for the analysis of the Landing gear lug attachment joint in an airframe is MSC Patran & MSC Nastran. The stages involved in FEM are shown in the figure below,

Fig 4.1: Different stages of Finite Element Analysis

4.2Software description

Softwares used in the present work are

Geometric modeling CATIA V5 Finite element modeling MSC PATRAN Finite element solver MSC NASTRAN4.2.1 CATIA V5

CATIA V5 is mechanical design software, addressing advanced process centric design requirement of the mechanical industry. This tool makes it possible for mechanical designers to quickly sketch ideas, experiment with features and dimensions, and produce models and detailed drawings. The following commands are commonly used in geometric

modeling. One can create geometrical drawing using 2D sketched geometry only, without

reference to existing models or assemblies.

This sketched geometry can be controlled by relations (collinear, parallel, tangent, and so on), as well as parametric dimensions. Extrude, using this option one can extrude base features and other features using 2D sketch. Revolve command can creates a feature that adds or removes material by revolving one or more profiles around a centerline. Pattern command can create a linear pattern, a circular pattern, a curve driven pattern, or use sketch points or table coordinates to create the pattern. Mirror, command copies the selected features or all features, mirroring them about the selected plane or face. Circular pattern command used to creates multiple instances of one or more features, which we can space uniformly around an axis.

Fillet and Chamfer command can be used to create fillet all edges of a face, selected sets of faces, selected edges, or edge loops and beveled feature on selected edges or a vertex. Cut, option is used to trim features and 3Dmodel with respect to a defined plane. In the present work geometric models was created by using all these commands.

4.2.2MSC PATRANDeveloping a finite element model manually is a time consuming, tedious and error prone activity making sense of the large stake of finite element computer output is also a considerable challenge.

A finite element pre and post processors (such as MSC/PATRAN) is a graphic based software package primarily designed to aid in the development of Finite Element Model (Pre processing) and to aid the display and interpretation of analysis results (Post processing). MSC/ PATRAN software is a mechanical computer aided engineering tool created for design engineers.Utilizing integrated automatic technologies MSC/PATRAN enables design engineers to build and modify solid models of computer parts and predicts their behavior through design optimization. In addition preprocessing software helps the analyst modify the model if the result shows that changes and subsequent reanalysis are required.

Some pre processors able to import geometric data from solid modeling or computer aided design manufacturing (CAD/CAM) software to be used as a basis for the finite element model. Components of MSC PATRAN Pre-Processor: Preprocessing involves the preparation of data such as nodal co- ordinates, connectivity boundary conditions, loading and material information. The pre processor takes minimum input for the user, creates the finite element mesh and other data required for analysis.

Solver/processor: The processing stage involves stiffness generation, modification and solution of equations resulting in the evaluation of nodal variables.

Post Processing: The post processing stage deals with the presentation of results. Typically the Deformed configurations, mode shape, displayed at this stage. Graphical post- Processing of results helps to receive the physical consequences of the analysis.Basic steps in MSC PATRANRepresent a continuous structure as a collection ofgrid points connected by discrete elements

Formulate Element Stiffness Matrices from element properties

geometry and material properties

Assemble all element stiffness matrices in to global stiffness

Apply Boundary Condition to constraint modelApply loads to the model (forces, moments, pressure etc)

Solve the matrix equation {F} = [K] {Q}

Calculate Element StressesFig 4.2 Basic steps in MSC/PATRAN linear static structural analysis4.2.3 MSC NASTRAN

The finite element method [FEM] has a seminal impact on the field of analysis and design. This technique has allowed thing solution of a new class of problem that is practically difficult, costly or was not possible in the past. The acceptance of FEM in the industry however did not enjoy wide popularity until the acceptance of general purpose programs finite element programs. R.J.Melosh developed the first note worthy general purpose finite element program SAMIS (Structural Analysis and Matrix Inerpretive System) in 1996.NASTRAN is the acronym of NASA structural analysis that is one of the popular general finite element programs of today. In 1965n NASA decided to support development of large capacity, general purpose FEM based structural analysis program, because the capabilities of number of existing FEA programs met NASAs Science Corporation, MACNEAL- SCHWNDLER and NASTRAN. Then MSC established MARTIN MARIETTA CORPORATION developed MSC/NASTRAN and released it into the market in 1972.Today a potential user of MSC/ NASTRAN (Version 70) has many useful features and capabilities. The potential users of MSC/NASTRAN include a majority of automobile manufacture, most of Aerospace firms, Universities, Research labs and many other industries.

MSC/NASTRAN library contains more than 50 types of elements which include one, two and three dimensional elements, Scalar elements, mass elements and heat transfer elements. Several new elements exists including constraint elements, shell elements (QUAD4 & TRIA 3), curved shell elements (QUAD8 & TRIA 60), Solid elements (CROD, CBAR & TRAPRG) and a linear strain triangular element (TRIAX6), CROD element, CBEND element, QUAD element, CTRIA3 element, CQUAD8 element, CTRIA6 shear plane element, two dimensional Crack tip element (CRAC2D), CHEXA, CTETRA, CTRIAHEX6, element, CRAC3A elements, composite element (PCOMP).

Features of MSC NASTRANMSC/NASTRAN package has many special features including

Linear static analysis. Static analysis with geometric and material non-linearity. Transient analysis with geometric and material non-linearity. Normal mode sand buckling analysis. Direct and model vibration analysis (including response spectrum analysis) Linear static and vibration analysis. Linear and Non-linear steady state transfer. Transient Heat Transfer Aero elasticity Multilevel super element Design sensitivity and optimization AcousticsLinear static analysis Multi load case and load case combination Equivalent stress concentration Internal shear and edge effects in compositesMaterial properties Isotropic or orthographic Temperature dependent Directional tensile, compressive and shear failure stress for compositeLoading Point force, momentum on nodes or range of nodes in local or global coordinate

System

Pressure load

Linear, angular acceleration, angular velocities

Temperature distribution can be obtained directly from Heat Transfer

Analysis

Thermal loading

Specified DisplacementKinematics constraints Specified Nodal Displacement Coupled Displacement Multiple constrainsOutput Displacement and stress at elements and nodes Reaction forces Element strain energy and internal forces Sorted result summaries Stress and strains at element centric Gauss point stress Principal stresses and directions Von-mises, maximum and octahedral shear stressChapter-5

GEOMETRIC AND FINITE ELEMENT MODELING OF STIFFENED PANEL

5.1Introduction to stiffened panel

Stiffened panels are the most generic structural elements in an airframe. The fuselage is a cylindrical shell as shown in Fig5.1, made up of stiffened panel but for the analysis, small part of fuselage is taken, which is rectangular stiffened panel as shown in the Fig 5.2 and relevant loads and boundary conditions are applied and analyzed. The stiffened panel consists of

Skin

Bulkhead

Crack stopper strap (tear strap)

Longerons (stringer)and

Fasteners (rivets).

The geometric dimensions of the stiffened panel are discussed in session 5.2, which is modeled by using CATIA V5 software and analyzed by using FEA tool MSC NASTRAN, MSC PATRAN. The material will be taken as 2024-T3 sheet aluminum alloy. 5.1 Fuselage part 5.2 Detailed view of fuselage part

(Stiffened panel)

5.2Geometric configuration of the stiffened panel

Geometric modeling is carried out by using CATIA V5 software .Skin

Fig 5.3 Detailed view of skin

The above fig 5.3 shows the skin dimensions. Skin has the thickness of 1.5 mm. The skin houses rest of the components like Bulkheads, Longerons, Tear strap, which are assembled by riveting process, From fig5.3, it is clear that the rivets which are in rows holds the skin with longeron and the rivets which are in columns holds the tear strap and bulkhead, distance between the rows is 150mm and distance between the columns is 300mm, diameter of the rivet used is 5mm pitch of the rivet is 25mm.The fig 5.4 shows the CAD model of the skin with rivet holes.

Fig 5.4 CAD Model of skin

Crack stopper strap

Crack stopper straps are also known as tear straps, these tear straps runs in circumferential direction below the bulkhead which are fastened with skin by using rivets of 5mm diameter with 25mm pitch. Below fig5.5 shows the geometric dimensions of the tear strap whose thickness varies from 1.2mm to 2mm.

Fig 5.5 Geometric dimensions of tear strap (crack stopper strap)

The fig5.6 shows the CAD model of the tear strap. There are five tear straps which are spaced 300mm from each other and 150mm from the edge of the skin.

Fig 5.6 CAD model of the Tear strap

Bulkhead

Bulkhead is also known as frame. Bulkhead is a stiffening member in circumferential direction in the fuselage structure. There are five bulkheads in this stiffened panel. All the dimensions of the bulkheads are shown in fig5.7 and fig 5.8.CAD model is shown is shown in fig 5.9.

Fig5.7 Cross sectional view (Bottom view) of the bulkhead

Fig5.8 Front, side and bottom view of the Bulkhead with dimensions

Fig5.9 CAD Model of the Bulkhead

Longeron (stringer)

Longerons are also known as stringers which run in longitudinal direction in the fuselage structure. There are six longerons in the panel, which are 150mm apart from each other. The fig5.10 shows geometric dimensions and fig 5.11 shows the CAD model Fig5.10 Geometric dimensions of the Longeron

Fig 5.11 CAD Model of the Longeron

Fig5.12 CAD Model of the stiffened panel

Fig 5.13 Front, side and bottom view of stiffened panel

All the components of the stiffened panel are assembled together by riveting with the rivet pitch 25mm and diameter of the rivet is 5mm, Fig 5.14 show the positions of the tear strap bulkhead and longeron on the skin.

Fig 5.14 lose up view of stiffened panel 5.3Finite element model of the stiffened panel

Finite element meshing is carried out for all the components of the stiffened panel such that there is a node present at the point where riveting is to be done and fine meshing is done at the critical sections where stresses are expected to be more.

The following figures show the details about the finite element mesh generated on each part of the structure using MSC PATRAN.

skin:The fig5.15 shows the finite element mesh on skin. The skin houses rest of the components like bulkheads, longerons, tear strap. The mesh was carefully generated such that there is a node present at the point where riveting is to be done. The fig5.16 shows the rivets that are placed on the skin to hold the frames, tear strap and longeron together.

Fig 5.15 Finite element Mesh on skin

Fig 5.16, Close up view of mesh on the skin with beam elements as rivets

Riveting is carried out by selecting the node on the skin and the corresponding node on the other component and created a beam element between them. So, the riveting process is completed in this manner. It is shown in the fig 5.16Tear strap:

The tear straps are also known as crack stopper straps. In model there are five tear straps, whose Finite element meshing is shown in fig 5.17Fig 5.17 Finite element mesh on Tear strap

In the Finite element meshing of tear strap nodes are placed at calculated distance so that the riveting could be carried out in a proper way. The tear straps are placed on the skin and the rivet nodes are aligned so that the riveting could be carried out once the rest of the components are ready. These tear straps are placed in between the skin and bulkhead and runs below the bulkhead in the circumferential direction and perpendicular to the longitudinal crack. The close up view of the meshed tear strap is shown in fig 5.18

Fig 5.18 Close up view of finite element mesh on tear strap

Longeron (Stringers)

The Longeron is also known as stringer, in our case, it is of Z cross-section, and it runs from tip to tip of the fuselage in the longitudinal direction. The Finite element mesh for stringer shown in fig5.19

Fig 5.19 Finite element mesh on Longeron

These stringers are placed on top of the Skin and Tear strap, and then riveted into its position. The tear strap runs under the stringer and enough space is provided for this purpose by bending the longeron at calculated distances as shown in fig 5.20

Fig 5.20 Close-up view of Finite element mesh on stringer with bulged region

The stringer is bulged at specific locations so that the tear strap is placed below it and more specifically so that there wont be any discontinuity in the longeron, which run from one tip to the other in longitudinal direction. The fig 5.20 shows clearly the bulged region in the longeron under which tear strap passes.

In this analysis as a first approximation a stiffened flat panel with a center crack will be considered. The strength of this cracked panel will be investigated as a function of crack length in the absence of crack stopper straps. Crack stopper straps will then be introduced at the locations of stiffeners perpendicular to the crack line. So for the stiffened panel without tear strap there will not be any bulged region in the longeron which is shown in figure 5.21.

Fig 5.21 Close-up view of finite element mesh on stringer without bulged region

For the longeron meshing is done such that the nodes are present at point where the rivets are applied. Now the longeron is placed on top of the Skin and the tear strap and then the beam element representing a rivet is connected between the riveting nodes.In practical shop floor, the tear strap is place in its location and clamped in. And then the stringers are placed on top of it and hammered using a mallet so that the required bulge is obtained without spending much on the machining processes.

Bulkhead (Frame)Bulkhead is also known as Frame. In our case it has Z cross-section. The bulkheads are place on top of the tear strap and riveted onto the skin. These bulkheads run in circumferential direction. There are stringer cut-out (mouse holes) provided in the bulkhead so that the stringers run continuously from one end to the other in longitudinal direction.

Fig 5.22Finite element mesh on Bulkhead

The fig 5.22 shows the meshing for the bulkhead. The meshing is maintained such that there is a node present at the point where a rivet is used to fasten the bulkhead onto the skin.

As seen in fig5.23, the meshing near the stringer cut-out (mouse hole) is very fine so that the stress variation around the mouse hole could be obtained accurately. Tria elements are used for the sake of continuity from fine-meshed region to the coarse mesh. First, stringer cut-out on the segment is drawn and projected to certain distance and meshed between the two drawing using Mesh with two curves process in the software. As the loading is done along the direction of the frame, the stress concentration is predicted to be maximum around the stringer cut-out (mouse hole).Hence getting fine mesh around the stringer cut-out increases accuracy of results.

Fig 5.23 Close-up view of bulkhead with stringer cut-out (mouse hole)

The meshing for the bulkhead is maintained such that there is a node present at the point where a rivet is used to fasten the bulkhead onto the Skin.

Fastening (riveting)

The rivets are used as the fasteners in the assembly of the component of the fuselage structure such as skin, tear strap, longeron and bulkhead. The meshing on these structural components is carefully generated such that there is a node present at the point where riveting is to be carried out. The riveting process is completed by creating beam element between the nodes by selecting the node on the skin and the corresponding node on the other component. The pitch of the rivet is 25mm. Diameter of the rivet is 5mm.

The fig5.24 shows the beam elements which are indicated in red color connects all the components of the stiffened panel and acts as the rivets.

Fig 5.24 Rivets used to assemble all components of stiffened panel

Fig 5.25 Complete finite element mesh on stiffened panel

From the fig 5.25 it can be seen that the longeron is bulged at the region where the tear strap run below longeron.

Fig 5.26 Close up view of stiffened panel with tear strap

.

Fig 5.27 Close up view of stiffened panel without tear strap

From the fig 5.27 it can be seen that there are no bulged region it the longeron since there are no tear straps

5.4 Quality criteria for elements

Once after meshing and before proceeding further, we check for elements so that no elements fail during the application of the load. The elements which failed under the specific condition was checked and modified so that all the elements fell under the pre-defined standards and hence we ended up with a mesh where none of the elements failed.

The elements were checked for the following criteria:

Fig 5.28 Quality criteria for elements

Aspect ratio: It is the ratio of the largest to its adjacent side. Aspect ratio should be less than 5 and much less in region of higher stress distribution. Element with unit aspect ratio yields the best results.Skew: Skew in trias is calculated by finding the minimum angle between the vector from each node to the opposing mid-side and the vector between the two adjacent midsides at each node of the element. Ninety degrees minus the minimum angle found is reported as the skew.Warp: The amount by which an element or element face (In case of solid elements) deviates from being planar.

Mesh was checked for any duplicate nodes and elements. Mesh optimization was effectively implemented to check the convergence of the results by iteratively increasing the mesh density5.4.1Finite element model summary

Stiffened panel with tear strap Total number of Grid points=38124 Total number of Beam elements=668

Total number of Quad elements=32700 Total number of Tria elements=2880Stiffened panel without tear strap

Total number of Grid points= 35265 Total number of Beam elements= 499 Total number of Quad elements= 30300 Total number of Tria elements= 2520Chapter-6STRESS ANALYSIS OF THE STIFFENED PANEL

At the higher altitudes atmospheric pressure will be less. As an Aircraft fly at higher altitudes, fuselage (passenger cabin) will be pressurized for the passenger comfort. Then pressure inside the fuselage will be more than the outside atmospheric pressure.

For the analysis internal pressurization of the cabin is taken as the load case.6.1 Aircraft cabin pressurization

Aircraft are flown at high altitudes for two reasons. First, an aircraft flown at high altitude consumes less fuel for a given airspeed than it does for the same speed at a lower altitude because the aircraft is more efficient at a high altitude. Second, bad weather and turbulence may be avoided by flying in relatively smooth air above the storms. Many modern aircraft are being designed to operate at high altitudes, taking advantage of that environment. In order to fly at higher altitudes, the aircraft must be pressurized. It is important for pilots who fly these aircraft to be familiar with the basic operating principles.

In a typical pressurization system, the cabin, flight compartment, and baggage compartments are incorporated into a sealed unit capable of containing air under a pressure higher than outside atmospheric pressure. On aircraft powered by turbine engines, bleed air from the engine compressor section is used to pressurize the cabin. Superchargers may be used on older model turbine-powered aircraft to pump air into the sealed fuselage. Piston-powered aircraft may use air supplied from each engine turbocharger through a sonic venturi (flow limiter). Air is released from the fuselage by a device called an outflow valve. By regulating the air exit, the outflow valve allows for a constant inflow of air to the pressurized area. [Fig 6.1]

Fig6.1 High performance airplane pressurization system.

A cabin pressurization system typically maintains a cabin pressure altitude of approximately 8,000 feet at the maximum designed cruising altitude of an aircraft. This prevents rapid changes of cabin altitude that may be uncomfortable or cause injury to passengers and crew. In addition, the pressurization system permits a reasonably fast exchange of air from the inside to the outside of the cabin. This is necessary to eliminate odors and to remove stale air. [Fig 6.2]

Pressurization of the aircraft cabin is an accepted method of protecting occupants against the effects of hypoxia. Within a pressurized cabin, occupants can be transported comfortablyand safely for long periods of time, particularly if the cabin altitude is maintained at 8,000 feet or below, where the use of oxygen equipment is not required. The flight crew in this type of aircraft must be aware of the danger of accidental loss of cabin pressure and be prepared to deal with such an emergency whenever it occurs.

Fig 6.2 Standard atmospheric pressure chart.

6.2 Loads and boundary conditions

A differential pressure of 13.5 psi (0.0931MPa) is considered for the current case. Due to this internal pressurization of fuselage (passenger cabin) the hoop stress will be developed in the fuselage structure. The tensile loads at the edge of the panel corresponding to pressurization will be considered for the linear static analysis of the panel.

Hoop stress is given by

hoop = ---(Eq6.1)

Where

Cabin pressure (p)=13.5 psi=0.0931MPa Radius of curvature of fuselage(r) = 1500 mm Thickness of skin (t) = 1.5mmAfter substitution of these values in (Eq6.1) we will get

hoop =9.49 Kg/mm2

=93.11 MPaWe know that hoop =

Above equation can be written as

P = hoop *A --- (Eq6.2)

1) Uniformly distributed tensile load is applied on either side of the stiffened panel in Y axial directionLoad on the skin

Here

Ps=Load on skin

hoop =9.491439 Kg/mm2

A=Cross sectional area of skin in mm2

i.e. Width *Thickness(1500*1.5)Substituting these values in the Eq6.2 we get

Ps=21355.73Kg Ps=2094499.78NUniformly distributed load on skin will be Ps =21355.73/1500 =14.24 Kg/mm

Load on Tear strap

Here

Pts=Load on skin

hoop =9.49 Kg/mm2

A=Cross sectional area of each Tear strap in mm2

i.e. Width *Thickness(46*1.2)Substituting these values in the Eq6.2 we get

Pts=523.93 Kg On each Tear strapPts=5139.75 NUniformly distributed load on Tear strap will be

Pts =523.93/46

=11.39Kg/mm

Load on BulkheadHere Pb =load on Bulkhead in Kg

hoop =9.49 Kg/mm2

A =Cross sectional area of each Bulkhead in mm2 i.e. (18.5+68.5+18)*1.5

Substituting the values in (Eq6.2) we get

Pb =1494.90Kg on each BH Pb =14664.98N on each BH

Uniformly distributed load on Bulkhead will be Pb = 1494.90/105 =14.24 Kg/mm on each BH2) All the edge nodes of stiffened panel are constrained in all five degree of freedom (i.e13456) except loading direction which is Y direction (i.e. 2). At the centre of the skin loading direction(Y direction) is constrained (if we consider centre crack then that crack region should not be constrained in Y direction). All the elements along the thickness direction is constrained to avoid the eccentricity due to stiffening members.

Fig.6.3 Loads and boundary conditions on skin

(a) (b)

Fig6.4 Loads and boundary conditions on Bulkhead (a) and Tear strap (b)

Fig6.5 Loads and boundary conditions on stiffened panel6.3Results obtained from the finite element analysis of the stiffened panel

Pre-processing and post-processing is carried out by using MSC Patran software and Solved by using MSC Nastran (solver) software. The response of the stiffened panel in terms of displacements and stresses due to loads and boundary conditions described in the previous sections are explained in the following sections.6.3.1Displacement contour of the stiffened panel

Fig 6.6 Displacement contour of the stiffened panel

The Fig 6.6 shows the displacement contour of stiffened panel. Displacement contour increases from fixed end to loading end and it is shown by different colors fringes where white color showing minimum magnitude of displacement while red color showing maximum magnitude of displacement. The panel is constrained in the loading direction at the mid section. One can observe a symmetrical displacement contours from the mid section in the above figure.

6.3.2Stress contour of the stiffened panelSkin

Fig 6.7 Stress contour for skin

Fig 6.7 shows the stress contour on the skin from global analysis results. It is clear that the maximum stress on skin is at the rivet location where the rivets are used to fasten the tear strap, bulkheads, longerons and skin. The magnitude of maximum tensile stress is 11kg/mm2 in the loading direction can be observed from the fig6.7. The maximum stress locations are the probable locations for crack initiation. Invariably these locations will be at rivet locations in the skin. Representation of layered structure is important in identifying critical stress locations, integral representation will miss lead as for as critical locations are concerned.Tear strap Fig 6.8 Stress counter for tear strap

Fig 6.8 shows the stress contour on the tear strap from global analysis results. It is clear that the maximum stress on tear strap is at the rivet location where the rivets are used to fasten tear strap, bulkhead and longeron on skin. The magnitude of maximum tensile stress is 11.3kg/mm2 in the loading direction can be observed from the fig 6.8. The maximum stress will be at rivet locations in the tear strap. Invariably these maximum stress locations are the probable locations for crack initiation. Longeron

Fig 6.9 Stress counter for Longeron

Fig 6.9 shows the stress contour on the longeron from global analysis results. It is clear that the maximum stress on longeron is at bulged region, where the rivets are used to fasten the tear strap, bulkhead and longeron on skin. The magnitude of maximum tensile stress is 1.36 kg/mm2in the loading direction can be observed from the fig6.9.Other then this bulged region the stresses are very less in the longeron because they are perpendicular to the loading direction in the stiffened panel (Fig 6.11), Stringers will not take any loads when they are perpendicular to loading direction, but just holds the skin in its position. Bulkhead

Fig 6.10 Stress counter for Bulkhead

Fig 6.10 shows the stress contour on the bulkhead from global analysis results. It is clear that the maximum stress on bulkhead is at stringer cut-out (mouse cut-out) and this maximum stress is uniform in all the stringer cut-outs. The magnitude of maximum tensile stress is 35.4 kg/mm2 in the loading direction can be observed from the fig 6.10, which is more than the stresses in all other components of the stiffened panel. In the bulkhead the maximum stress will be at the stringer cut-out (mouse hole) which is shown in fig 6.10 and the maximum stress locations are the probable locations for crack initiation. Invariably these locations will be at stringer cut-out locations in the bulkhead.

Fig 6.11 Stress counter stiffened panel without centre crack

Fig 6.11 shows the stress contour on the stiffened panel from global analysis results. It is clear that the maximum tensile stress on stiffened panel is at stringer cut-out (mouse cut-out) and this maximum tensile stress is uniform in all the stringer cut-outs.

From the stress analysis of the stiffened panel it can be observed that a crack will get initiated from the maximum stress location. There are three structural elements at the rivet location near the high stress location. Crack will either get initiated from the bulkhead at stringer cut out or from the nearby rivet location from the rivet hole. This eventually will lead to the failure of the bulkhead in the perpendicular direction to loading. Once the bulkhead is broken, simultaneously cracks will appear on the tear strap and the skin.

Chapter-7DAMAGE TOLERANCE EVALUATION OF THE STIFFENED PANEL7.1Virtual crack closure technique for determining stress intensity factor

There are different methods used in the numerical fracture mechanics to calculate stress intensity factors (SIF). The crack opening displacement (COD) method and the force method were popular in early applications of FE to fracture analysis. The virtual crack extension (VCE) lead to increased accuracy of stress intensity factor results. The virtual crack extension method requires only one complete analysis of a given structure to calculate SIF. The total energy release rate or J-integral is computed locally, based on a calculation that involves only elements affected by the virtual crack extension. Both the COD and VCE methods can be used to calculate SIF for all three fracture modes. However, additional complex numerical procedures have to be applied to get results. The equivalent domain integral method which can be applied to both linear and nonlinear problems renders mode separation possible.

The VCCT, originally proposed in 1977 by Rybicki and Kanninen, is a very attractive SIF extraction technique because of its good accuracy, a relatively easy algorithm of application capability to calculate SIF for all three fracture modes. The VCCT has a significant advantage over other methods, it has not yet been implemented into most of the large commercial general-purpose finite element codes. This technique can be applied as a post processing routine in conjunction with general-purpose finite element codes. The VCCT is based on the energy balance. In this technique, SIF are obtained for three fracture modes from the equation. GI= --- (Eq7.1)Where GI= the energy release rate for mode I, KI = stress intensity factor for mode I in MPa ,

E =elastic modulus in MPa,

= Poisson ratio, = 1 for plane stress, = 1 2 for plane strain. The energy released in the process of crack expansion is equal to work required to close the crack to its original state as the crack extends by a small amount c.

W =

--- (Eq7.2)Where u = relative displacement, =stress, r = distance from the crack tip, c = change in virtual crack length. Therefore, the energy release rate is,

G =

--- (Eq7.3)Figure7.1 shows a FE model in the vicinity of a crack tip before the virtual crack closure, while Figure 7.2 shows the same finite elements after the closure. In the finite element (FE) calculations, changes in the crack length as it progresses are governed by size of finite element. Moreover, the interaction between the neighboring FE exists only in shared nodes. Therefore, the element edges do not transfer forces. Generally, work needed to close the crack stating from the state shown in fig.7.1 to reach the state shown in fig 7.2 is equal to

W=

--- (Eq7.4)

Fig7.1, 2D finite element model in the vicinity of a crack tip before the

virtual closure.

Fig7.2 Virtual crack closure in the FE model.

The detail calculation of the energy release rate is,

G=

--- (Eq7.5)Where

G=Strain energy release rate

F=Forces at the crack tip in kg or N

c=change in virtual crack length in mm

t= thickness of skin in mmThen the SIF is calculated by FEM method by substituting Eq7.5 in below Eq7.6

KI= --MPa --- (Eq7.6)

Where

KI= stress intensity factor (SIF)

E =youngs modulus

=7000Kg/mm2 =68670 Mpa G=Strain energy release rate Theoretically SIF value is calculated by

KI = * f ( ---MPa --- (Eq7.7)

And f ( = ---(Eq7.8)Where

= Crack length in mm

f ( =Correction factor

b=Width of the plate (1500mm)

From the stress analysis of the stiffened panel it can be observed that a crack will get initiated from the maximum stress location but there are other possibilities of crack initiation at different locations in the stiffened panel due to discrete source of damage. It may be due to bird hit, foreign object hit etc. Fine meshing is carried out near the crack to get accurate results which is shown in Fig 7.3 and Fig 7.4 .Other than the crack region coarse meshing is carried out. To get the mesh continuity from fine-mesh to coarse-mesh different quad and tria elements are used.

Fig 7.3 Fine element mesh at the centre of skin near the crack

Fig 7.4 Close up view of fine mesh at the centre of skin near the crack 7.2 Validation of FEM approach for stress intensity factor (SIF)

calculation

In thesis SIF (stress intensity factor) has been calculated by FEM (by using VCCT technique). SIF values are obtained analytically(FEM) by using Eq7.5 and Eq7.6 for un-stiffened panel having same dimension as skin in stiffened panel by applying boundary conditions which are discussed in session 6.2. SIF values are also obtained for stiffened panel using FEM. Consider crack length, 2a=50

1) SIF calculation by Theoretical method KI = * f ( --- (From Eq7.7)Where

=93.12 MPa

=25 mm

f (= 1.00208 which is calculated by using Eq7.8Substituting above values in Eq7.7 .SIF value will be

KI theoretical =26.1 MPa2) SIF calculation by Analytical method(FEM)Strain energy relies rate is calculated by Eq7.5 which is

G=Where

F=746.85N

u=0.03217 mm

c=0.78125 mm

t=1.5 mmSubstitute all values in Eq7.5 then

G=10.25 MPaNow Analytical SIF is calculated by Eq7.6 which is

KI fem=Where

E=7000kg/mm2=68670 MPaSubstituting G and E values in Eq7.6

KI fem=26.53 MPa

The above calculation is carried for different crack length considering fuselage internal pressurization of 13.5 psi (0.093111016MPa). Stress intensity factor values calculated by FEM (using VCCT technique) and stress intensity values calculated by theoretical method for un-stiffened panel is tabulatedTable 7.1 Comparison of analytical (FEM) SIF values with theoretical SIF value for un-stiffened panel

Crack length 2a in mmC.FSIF by Theoretical in MPamSIF by FEA(Analytical) in MPam

501.000126.126.53

1001.000536.9237.59

1501.001145.2546.13

2001.002152.3053.39

2501.003358.5459.85

3001.004864.2365.75

3501.006669.5071.25

4001.008774.4676.45

4501.011379.1681.39

5001.014083.6886.16

5501.017388.0490.78

6001.020892.2895.28

From the table7.1 and the fig 7.5 it is clear that SIF values obtained by using FEM (by using VCCT technique) for un-stiffened panel agrees with the SIF values calculated theoretically by Eq7.7.Therefor FEM (by using VCCT method) for finding SIF value is valid.

Fig7.5Comparison of Theoretical SIF value with analytical SIF value

Methodology of finding SIF values for un-stiffened panel using FEM was extended to get SIF values for stiffened panel. The fig 7.6 shows the displacement counter of un-stiffened panel. Orientation of crack is in longitudinal direction and crack widens due to loading in transverse direction. Where red fringes shows the maximum displacement which is at the centre of the panel.

Fig7.6 Displacement contour for un-stiffened panel with centre crack7.3Evaluation of the effect of tear strap (crack stopper strap) for crack arrest capability

As a result of the investigations into the accidents in the 1950s, aircraft manufacturers began to incorporate into their fuselage designs features which would increase the ability of the aircraft to sustain damage caused by fatigue cracking; i.e., a damage tolerant design philosophy. A reinforced doubler on the inside of the fuselage skin, termed tear strap, crack stopper strap, or fail-safe strap, is commonly employed.

Tear straps are simply strips of material attached circumferentially to the skin of the fuselage. These tear straps are made up of aluminum alloy .for the analysis aluminum 2024 T3 is considered.

Stress intensity factor (SIF) approach

For the evaluation of effect of tear strap (crack stopper strap) for crack arrest capability, as a first approximation a stiffened flat panel with a center longitudinal crack is considered. The SIF value of this cracked panel is investigated as a function of crack length in the absence of crack stopper straps. Crack stopper straps are then introduced at the locations of stiffeners perpendicular to the crack line. The SIF Values of the cracked flat panel is investigated as a function of crack length in the presence of crack stopper straps. In the parametric study the thickness is varied. The SIF values obtained for stiffened panel without tear strap and stiffened panel with tear strap are compared with the critical stress intensity factor KIc (Fracture toughness of the material)

If SIF (K) at the crack tip approaches or exceeds an upper limit of stress intensity factor (KIc), then the crack will zip through leading to catastrophic failure of the structure. The upper limit is known as critical stress intensity factor (Fracture toughness of the material) which is the material property and is usually denoted by KIc. The stress intensity factor is a parameter to measure severity of stress at the crack tip but critical stress intensity factor is the limit on SIF such that if SIF exceeds beyond the critical stress intensity factor, the crack will grow rapidly leading to the final failure. When the crack stress intensity factor due to remote loading reduces below the fracture toughness of the material then a crack will get arrested.Residual strength predictionThe residual strength is the remaining strength in the structure under given geometry and loading condition. The safety of modern aircraft is ensured based on the concept of operating durability. Residual strength is one of the main characteristics of survivability. The residual strength of stiffened panel with crack is an important design criterion in the aerospace industry to ensure the damage tolerance quality of the structure. The stiffening members like bulkheads which are perpendicular to the crack front will help in arresting the rapidly growing skin cracks.

The computational results obtained were used to determine the complete residual strength diagram of panel configuration considered.Residual strength equations1) For skin,

= --- (Eq7.8)Where, = Fracture toughness= 98.9 MPam

= Stress Intensity Factor

=93.12 MPa2) For bulkhead

= * --- (Eq7.9)Where

=420MPa=maximum stress in the bulkhead MPa=98.9 MPam

By using above Eq7.8 and Eq7.9 residual strength values are calculated for stiffened panel without considering tear strap, then stiffened panel with tear strap

Chapter-8RESULTS AND DISCUSSION

For the evaluation of crack arrest capability of bulkheads in the stiffened panel with and without the presence of tear strap is studied. This is discussed in the previous section6.3. This crack present in the stiffened panel is assumed to be caused due to the discrete sources of damage. It may be due to bird hit, foreign object hit etc. The internal pressurization of the cabin is considered to be 13.5 psi (Corresponding loads and boundary conditions are applied which are discussed in unit 6.2). The SIF value for different crack length is calculated by analytical(FEM) method by using Eq7.5 and Eq7.6(which is discussed in section 7.1) initially, for stiffened panel without tear strap and then considering the tear strap .In the parametric study thickness of the tear strap is v