Chapter 18: Fracture processes of aerospace materials – Introduction to Aerospace Materials

18

Fracture processes of aerospace materials

18.1 Introduction

Sudden fracture of structural materials was one of the most common causes of accidents in early aircraft. Materials for early aircraft were selected for maximum strength and minimum weight, and their fracture resistance was not an overriding consideration. Furthermore, the capability of materials to resist cracking and sudden failure was not well understood in the design and construction of these early aircraft. Many of the materials used in the earliest aircraft, particularly wood, were prone to sudden fracture which gave the pilot no opportunity to avoid crashing (Figure 18.1). The serious injuries and fatalities during the first decades of powered flight forced engineers to consider fracture as a critical factor in the safe design of aircraft structures and, later, jet engine components.

18.1 Fracture of materials caused many accidents in early aircraft.

Damage tolerance and fracture resistance became key considerations in the selection of aircraft materials following the de Havilland Comet jet airliner accidents in the early 1950s. From this period, fracture toughness became a critical property in the selection of materials for modern aircraft, and it is considered just as important as other material properties such as stiffness and strength. Aerospace engineers do not select a material based solely on its strength qualities, but also consider the ability of a material to withstand damage below a critical size (e.g. corrosion and fatigue cracks in metals or delamination cracks in composites) without catastrophic failure.

Fracture is a failure process that involves the initiation and growth of a crack, which can cause the material to break at a stress below its ultimate strength in the crack-free condition. In practice, there is no such thing as a defect-free material or a crack-free aircraft structure. Cracks and crack-like flaws (e.g. voids, corrosion damage) are present in many aircraft components. These cracks are produced during processing of the aerospace material and manufacture of the aircraft. Defects in metal alloys include gas holes, shrinkage, brittle inclusions and stress cracks formed during casting, quenching, heat treatment and shape forming (e.g. rolling, extrusion). Defects in metal components also occur during assembly as a result of poor machining quality or incorrect drilling of fastener holes. Defects in aircraft composite materials include delamination cracks, skin-core interfacial cracks, voids and dry spots. The aircraft industry uses manufacturing practices with stringent procedures to minimise defects in metals and composites, but it is still virtually impossible to produce a defect-free material. However, the defects are often microscopic in size and few in number and, therefore, do not normally pose an immediate problem to the structural integrity of the aircraft component.

In addition to defects created during manufacturing and processing of the material being the cause of cracking, cracks can also initiate at regions of high stress within the material. Regions of high stress occur when there is an abrupt change in the shape of the material, and this is often called a stress raiser. Examples of stress raisers are fastener holes, the corners of windows and doors, and the root of turbine blades. Careful design and materials selection can reduce the stress build-up in such regions, but it cannot be completely avoided. Stress raisers are a common cause for the formation of cracks within materials which are otherwise free of defects.

Cracks may grow by overstressing, fatigue cycling or corrosion damage during the operation of an aircraft, possibly leading to catastrophic damage. For example, Fig. 18.2 shows severe damage to a Boeing 737 fuselage owing to cracking caused by the combined effects of fatigue and corrosion. Cracks can also occur because of poor design, incorrect materials selection, and damage during normal flight operations from bird impacts, lightning strikes, large hail impact or other adverse events. Components are thoroughly inspected for cracks after fabrication and throughout the service life of an aircraft. Inspection and maintenance costs represent a high percentage (20% or more) of the direct operating costs for commercial airliners. The cost is also high for maintaining airframe and engine components of military aircraft against cracks. To minimise the cost, there is a need for more damage tolerant structural materials which resist crack growth under normal flight conditions, and which therefore require less maintenance.

18.2 Fuselage damage to an Aloha Airlines B737 aircraft.

Because cracks and flaws cannot be completely avoided, the important thing is to ensure they remain harmless and do not grow to be large enough so that the material fails at below the design ultimate load. The aerospace industry uses the so-called ‘ damage tolerance design’ philosophy to ensure the safety of aircraft structures containing cracks. Damage tolerance is the ability of structures to withstand the design load and maintain their function in the presence of cracks and other types of damage. The goal of this requirement is to ensure the continued safe operation of an aircraft over a specified period of time. Safe operation must be possible until the crack is detected during routine maintenance or, if undetected, for some multiple of the design life of the structure such as two times or four times (depending on the component and aircraft type).

The fracture behaviour of aerospace materials is examined in this chapter and chapter 19. This chapter deals with the fracture mechanics and fracture mechanisms of materials whereas chapter 19 deals with their fracture toughness properties. This chapter examines the types of fracture processes that occur in metals and fibre–polymer composites used in aerospace structures. The fracture mechanisms of other materials such as polymers and ceramics are briefly mentioned, but are not considered in detail because they are not used in large quantities in aircraft structures. The fracture mechanics of brittle and ductile materials are described in this chapter, including models for predicting the failure strength and critical crack size. The fracture toughness properties of the various types of aircraft materials used in the aircraft structures and engines are discussed in the next chapter, including methods to improve the fracture strength of metals and fibre–polymer composites.

18.2 Fracture processes of aerospace materials

18.2.1 Modes of fracture

There are two types of fracture: brittle fracture and ductile fracture. Brittle fracture involves crack growth with little or no ductile deformation of the material around the crack tip. This is an undesirable mode of fracture because brittle cracking can lead to complete failure of the material very rapidly when a critical load is reached. Ductile fracture, in contrast, involves plastic deformation of the material at the crack tip. This often results in a stable and predictable mode of fracture in which crack growth can only occur under an increasing applied load; when the load is reduced the crack stops growing. As a result, ductile fracture is the preferred failure mode for damage-tolerant materials. Whether brittle or ductile fracture occurs, the mode of fracture depends on many factors, including the stress level, type of loading (static, cyclic, strain rate), presence of pre-existing cracks or defects, material properties, environment and temperature.

Aerospace structural metals including aluminium, magnesium, titanium, high strength steel and nickel-based superalloys usually fail by ductile fracture processes which involve a certain amount of ductility. In contrast, crack growth in fibre–polymer composites and ceramic aerospace materials (such as heat shields) occurs with less ductility and therefore is a more brittle fracture process. This chapter considers the mechanisms of ductile and brittle fracture of aerospace metals and the brittle fracture of fibre–polymer composites.

18.2.2 Ductile fracture processes

Crack tip stress and plastic zone

Ductile fracture is the most common failure mode in aerospace metal alloys and polymers (including structural adhesives). A ductile crack in a metal usually starts at an existing flaw, such as a brittle inclusion within a grain, a precipitate at a grain boundary, or a void. The stress condition ahead of a crack in a ductile material loaded in tension is shown schematically in Fig. 18.3. The stress ahead of the crack is not distributed evenly. Instead, the stress in the region immediately ahead of the crack tip is much higher than the nominal (applied) stress. Figure 18.3 shows that the closer one approaches the crack tip, the higher the local stress becomes until, at some distance ry from the crack the stress reaches the yield strength σy of the material. The material over a distance between the crack tip (r = 0) and ry is plastically deformed, and this region is called the plastic zone.

18.3 Stress field ahead of the main crack front in a ductile material, showing the plastic zone (shaded).

The size of the plastic zone is dependent on the yield strength of the material, the applied stress level, and the load conditions (e.g. tension, shear). The plastic zone can range in size from a few tens of micrometres in high-strength metals to many millimetres in soft plastics. The material outside the plastic zone is not stressed above the yield strength and, therefore, does not plastically deform. Owing to the formation of the plastic zone, which absorbs energy and thereby resists crack growth, the stress needed to initiate a crack in ductile materials is lower than the stress needed to grow the crack. In other words, it is easier to form a crack than to get the crack to grow and, therefore, the applied stress needed to cause crack growth increases with the length. This behaviour provides ductile materials with an intrinsic amount of damage tolerance because, as the crack becomes larger, it also becomes more difficult to grow to the critical size necessary to cause complete failure.

Ductile crack-growth mechanisms

Crack growth in ductile metals can occur in several ways, depending on the type of material and the applied stress conditions (Fig. 18.4). In some cases, complex dislocation interactions occur in the plastic zone that lead to the formation of microscopic cracks. This process involves the formation and movement of large numbers of dislocations within the plastic zone. The dislocations become entangled into a high density from which tiny cracks develop ahead of the main crack front. The cracks link up with the main crack to advance the fracture process. Another important fracture process is the formation, growth and coalescence of micrometre-sized voids in the plastic zone. The voids often develop at fractured inclusion particles or particle-matrix interfaces, and then grow in size under increasing local stress. The growing voids eventually link up with the main crack, with the ligaments between voids behaving like miniature tensile test specimens, promoting crack growth by ductile tearing. The fracture surface of a ductile material is often characterised by a dimpled texture, as shown in Fig. 18.5.

18.4 Schematic representations of the ductile fracture process involving crack development from (a) local regions of high dislocation density, and (b) particles in the metal.

18.5 Dimpled fracture surface of a ductile metal caused by fine-scale plastic yielding and tearing.

Transgranular and intergranular fracture

After the crack has initiated in a metal it grows through the grains, which is called transgranular fracture, or along the grain boundaries, known as intergranular fracture, or by a combination of transgranular and intergranular fracture (Fig. 18.6). Intergranular fracture often occurs in metals that contain a high concentration of brittle particles at the grain boundaries. These particles provide a pathway for crack growth and thereby lower the fracture toughness and damage tolerance of the material. Structural alloys requiring high fracture resistance must be processed and heat treated under conditions that suppress the formation of brittle particles at grain boundaries. Regardless of whether crack growth occurs via transgranular fracture, intergranular fracture or a combination of the two, the crack grows under an increasing applied load until it reaches a critical size where the remaining uncracked section of the material can no longer support the applied stress at which point complete fracture occurs.

18.6 (a) Transgranular fracture through the grains and (b) intergranular fracture along the grain boundaries.

18.2.3 Brittle fracture of materials

Brittle fracture describes the failure of a material that involves little or no plastic deformation at the crack tip. There is always some plastic deformation around the crack tip in many materials, but, in more extreme cases of brittle fracture, the size of the plastic zone is extremely small and has no significant influence on the fracture process. In the absence of the plastic zone, the force needed to grow the crack decreases with its length. In other words, once the critical load for brittle crack growth is reached, the crack grows quickly through the material.

Brittle fracture occurs in two stages: (i) initiation of the crack and (ii) rapid propagation of the crack leading to complete fracture. A brittle crack often starts at a pre-existing defect, such as a void or inclusion. A crack can also initiate in a defect-free material in a region of high stress concentration, such as at the edge of a drilled hole or notch. The stress needed to initiate a brittle crack is higher than the stress needed to grow the crack. It is this behaviour that distinguishes brittle fracture from ductile fracture, in which the stress to initiate a crack is lower than the stress to grow a crack.

Brittle fracture involves the sudden failure of the material by rapid crack growth immediately after crack initiation. This behaviour is called fast fracture. The crack speed approaches the speed of sound for the material, which for aluminium and titanium is about 5 km s−1 and for steel is 4.5 km s−1. Once the crack has started to grow there is virtually no chance of stopping it before the material completely breaks.

Fully brittle fracture involves the rupture of interatomic bonds ahead of the crack, as illustrated in Fig. 18.7. This produces a fracture surface that can be close to atomically flat, called the cleavage fracture. A cleavage crack grows between the atomic planes along a specific crystallographic direction that has the lowest atomic bond strength. In some instances, however, the crack may follow the grain boundaries (i.e. intergranular fracture) that are weakened by brittle inclusions or intermetallic precipitates.

18.7 Schematic of the brittle fracture process involving breaking of interatomic bonds.

Brittle fracture is the worse type of failure for aircraft materials because it is fast and catastrophic, with no visible signs of damage or prior warning that the material will break. Brittle fracture can normally be identified by smoothness of the failed surface. When the fracture surface is smooth and perpendicular to the applied stress then this is a strong indication that the fracture has a strong brittle component, as shown in Fig. 18.8.

18.8 Metal fracture surface with smooth appearance that is a characteristic of brittle (cleavage) failure.

Brittle fracture occurs most often in metals with high strength and low ductility. A high-strength, low-plasticity metal that is prone to brittle fracture generally has a yield strength of σy > E/150, which for steels is above 1400 MPa. The steels used in highly loaded aircraft structures, such as 4340 steel and maraging steels used in landing gear, have a yield strength exceeding 1400 MPa. However, the steels are heat-treated and processed to provide sufficient ductility to limit brittle fracture. A metal that is unlikely to fail by brittle fracture has σy < E/300, and failure occurs by ductile fracture. Structural aerospace materials such as high-strength aluminium and titanium alloys as well as the engine materials such as nickel superalloys all fail by ductile fracture.

Section 18.9 at the end of the chapter presents a case study of the role of fracture in the space shuttle Columbia disaster.

18.2.4 Fracture of fibre–polymer composite materials

Fracture of fibre–polymer composites involves a multiplicity of failure modes that are different from the ductile and brittle processes described for metals. Most composites show no significant sign of plastic deformation before failure and, therefore, their fracture behaviour is often described as being brittle. However, the brittle fracture of composites does not occur in the same way as brittle metals. The operative fracture modes are dependent on the microstructure of the composite, with the volume fraction, strength, toughness and dimensions of the fibres; the volume fraction, strength and ductility of the polymer matrix; and the fibre–matrix interface all influencing the fracture process. The failure modes are also dependent on the loading direction because of the anisotropic microstructure of composite materials.

The two basic modes of fracture for composite laminates are in-plane fracture and interlaminar fracture and they are illustrated in Fig. 18.9. Inplane fracture involves crack growth in the direction normal to the fibres whereas interlaminar fracture involves cracking parallel to the fibre ply layers. The in-plane fracture process is more resistant to crack extension than the process of interlaminar fracture. For example, the amount of energy required for crack growth in the in-plane direction of a carbon–epoxy composite is anywhere from 20 to 1000 times greater than in the interlaminar direction. For this reason, composite aircraft structures must be designed such that their damage tolerance is achieved by in-plane fracture resistance.

18.9 Schematic representations of (a) in-plane and (b) interlaminar fracture of composite laminates.

An interesting feature of carbon–epoxy and other composite materials is that their in-plane fracture toughness is much higher than the toughness of the fibres and polymer resin on their own. The high in-plane fracture toughness is the result of crack growth being resisted by various failure processes that occur near the crack tip and along the crack wake. In-plane fracture involves crack extension by plastic deformation and rupture of the polymer matrix and failure of the fibres. Fibres do not always break at the crack tip, but can fail a distance away at a pre-existing flaw in the fibre where the strength is low. As the two faces of the crack separate the broken fibres detach from the polymer matrix and pull out. The pull out of fibres can extend many millimetres behind the crack front. As the crack grows, its tip is often deflected along the fibre direction (i.e. 90° to the crack direction) as it follows weak interfaces between the fibres and matrix. This produces splitting cracks that can grow many millimetres from the main crack path. The main crack is repeatedly deflected at the fibre/matrix interfaces into splitting cracks thus resisting crack extension.

The damage processes involved in in-plane fracture absorb different amounts of energy which resist the crack growth process. Figure 18.9 gives the approximate amount of energy absorbed by the fracture processes in carbon–epoxy composite. Fracture and pull-out of the fibres absorb the greatest amount of energy and thereby provide the greater resistance against in-plane fracture whereas the failure of the polymer matrix and fibre–matrix splitting results in less resistance.

The interlaminar fracture process involves cracking in the fibre direction, usually between the ply layers which is called delamination fracture. The crack grows through the polymer-rich regions between the plies without the rupture, debonding and pull-out of the fibres experienced with in-plane fracture. The amount of energy needed for delamination crack growth is relatively low, and therefore interlaminar fracture occurs much more easily than in-plane fracture. Interlaminar fracture resulting in delamination cracking is a major problem with composite structures used in aircraft. Bird strike and other impact events can cause extensive delamination damage in aircraft structural composites because of their low interlaminar fracture resistance.

Section 18.10 at the end of the chapter presents a case study of the fracture of an aircraft composite radome.

18.3 Stress concentration effects in materials

18.3.1 Geometric stress concentration factor

Cracks often initiate and grow from sites of high stress in a material owing to a change in the shape (geometry) of the component. The change in geometry is called a ‘ stress concentration’ or ‘ stress raiser’, and is often the cause for cracking in aircraft components (Fig. 18.10). Common stress raisers in aircraft structures are corners, holes, fillets and notches. As examples, spars and ribs in the wings and fuselage contain cut-outs and notches to reduce the structural weight, and skin panels and many internal parts contain drilled holes for rivets, bolts and screws. Small stress raisers also reside within the material, such as micrometre-sized gas holes in metals or voids in composites.

18.10 Crack growth from a machined notch which acts as a stress raiser under load.

The study of fracture must consider a parameter known as the geometric stress concentration factor (also called the theoretical stress concentration factor). This factor defines the magnitude of the local stress at the stress raiser compared with the applied stress. When stress is measured at the edge of a stress raiser it is not at the same level as the nominal (or applied) stress, but is much higher. This is because the stress that would normally be supported by the material where the stress raiser occurs is concentrated at its edge. Thus, a stress concentration occurs at the edge of a stress raiser. Cracks in aircraft materials are most likely to develop in regions where there is high stress concentration. Therefore, knowledge of geometric stress concentrations is essential to understand the initiation of cracks which lead to fracture.

Figure 18.11 shows the stress distribution across the load-bearing section (between points xx′) of an infinitely wide plate containing a circular hole. A constant stress is applied to the ends of the plate σapp. The stress in the plate is greatest at the hole edge and drops off rapidly with distance away from the hole. The higher stress at the hole edge is described by the geometric stress concentration factor Kt which is the ratio of the maximum stress at the hole σmax to the applied stress σapp:

18.11 Stress distribution in a plate containing a stress raiser in the form of a circular hole.

[18.1]

The geometric stress concentration factor for a noncircular (elliptical) hole can be calculated using:

[18.2]

where a and b are the half-width and half-height of the hole.

For an isotropic material containing a circular hole (a = b), Kt is 3.0, which means the maximum stress at the hole edge is three times greater than the applied stress. The stress concentration factor is greater than three when the stress raiser has an elliptical shape (i.e. a > b) elongated across the plate width.

The end radius of a hole (ρ) is determined from:

[18.3]

By combining the two previous equations, the maximum stress at the hole edge is:

[18.4]

In most cases a > > p, and so the approximation is:

[18.5]

where the term is the geometric stress concentration factor Kt.

The calculation of the stress concentration factor given in equation [18.2] and that for maximum stress given in equation [18.4] are only valid for a plate of infinite width. In reality, of course, components have a finite size and can have shapes other than a flat plate. In these instances, the stress-concentration factor is dependent on the sizes and shapes of both the stress raiser and component.

Calculating the stress concentration factor for components having a complex shape can be time-consuming and often requires finite-element analysis or advanced analytical methods. To avoid detailed calculations, engineering textbooks and aircraft design manuals give the theoretical stress concentrations for components with a wide range of shapes, often presented as a stress concentration plot. For example, Figure 18.12 shows the effects of notch shape (a/b) and part geometry on the stress concentration factor for three simple cases: a plate with a circular hole, a plate with a double notch, and a T-section.

18.12 Stress concentration factor plots for three geometries: (a) axial loading of a flat plate with a circular hole, (b) axial loading of a notched bar, (c) axial loading of a T-section.

The stress concentration factor is only valid for elastic stress conditions; that is for brittle materials at any stress level and ductile materials at any stress below the yield strength. In a brittle material, a crack develops at the edge of a stress raiser when the local stress reaches the failure stress of the material. Once the crack has initiated, it grows rapidly (fast fracture) through the remaining material causing complete fracture. Ductile materials plastically deform at the edge of a stress raiser when the local stress exceeds the yield strength. The ability of a ductile material to plastically deform at a stress raiser avoids sudden fracture.

18.3.2 Stress concentration factors for anisotropic (composite) materials

The stress concentration factor for isotropic materials, such as metals and plastics, is determined using the procedure described in 18.3.1. The situation is somewhat different with anisotropic materials, such as fibre–polymer composites, because the stress concentration factor is dependent on the elastic modulus in different directions. The stress concentration factor Kt for an anisotropic material containing a circular hole is given by:

[18.6]

where Ex and Ey are the Young’s moduli in the loading and transverse directions, vxy is the Poisson’s ratio in the x–y plane, and Gxy is the in-plane shear modulus. When there is a high degree of anisotropy, such as when all of the fibres in a polymer composite are aligned in the load direction (i.e. Ex > > Ey), then the stress concentration factor is very high at the hole edge. For example, the geometric stress concentration for a unidirectional carbon–epoxy panel containing a circular hole is about 6.6, whereas for an isotropic material it is only 3.0. Therefore, considerable care must be exercised when using anisotropic materials in aircraft components containing stress raisers such as fasteners holes, windows and cut-outs.

One approach to reducing the stress concentration factor is increasing the percentage of ± 45° and other off-axis plies in the composite. This increases the shear modulus Gxy and brings the ratio of Ex/Ey closer to unity. Table 18.1 shows the effect of reducing the number of axial (0°) plies and increasing the number of ± 45° plies on the stress concentration factor for a circular hole in a composite panel. A composite with all ± 45° plies has the lowest stress concentration factor of 2, but it also has the lowest strength because of the absence of 0° plies. The best compromise is a laminate that has a sufficient number of 0° plies to carry the load, but also ± 45° plies to reduce the stress concentration factor. The two fibre lay-up patterns most often used in carbon–epoxy composites, quasi-isotropic [0/± 45/90] and cross-ply [0/90], have stress concentration factors of about 3 and 3.5, respectively.

Table 18.1

Stress concentration factors for a 24-ply carbon–epoxy panel containing a circular hole

18.4 Fracture mechanics

18.4.1 Introduction to fracture mechanics

Fracture mechanics is the mechanical analysis of materials containing one or more cracks to predict the conditions when failure is likely to occur. It is an important topic for many reasons, and is used to:

• design aircraft structures and select materials with high resistance against cracking;

• calculate the residual strength of aircraft structures containing cracks;

• determine whether a crack is benign and does not affect the strength of an aircraft structure or whether the crack may lead to complete failure and therefore the structure must be repaired or replaced before failure occurs;

• determine the cause of structural failures in aircraft accident investigations; and

• minimise the need for expensive structural tests on large aircraft components to assess their damage tolerance and residual strength.

Many analytical methods are available to calculate the fracture strength of materials containing cracks, and almost all are based on the principles of linear elastic fracture mechanics (LEFM). LEFM can be simply described as the analysis of materials containing one or more cracks that fail by brittle fracture. It is assumed in LEFM that failure occurs under elastic conditions, and plastic flow at the crack tip is not significant. LEFM can be applied to brittle materials such as ceramics and high-strength, low-plasticity metals. LEFM is the basis for determination of the critical flaw size or critical stress to cause failure and the prediction of fatigue life for isotropic materials.

LEFM is not accurate for ductile materials where a large plastic zone at the crack tip affects the fracture process. The fracture mechanics analysis of ductile materials is performed using elastoplastic fracture mechanics (EPFM).

18.4.2 Linear elastic fracture mechanics

The simplest LEFM model for calculating the fracture strength of a brittle material containing a crack is the Griffith failure criterion. The model is based on work performed during World War 1 by A. A. Griffith on the fracture strength of glass. Griffith considered an apparent contradiction in the breaking strength of glass plate. The tensile stress needed to fracture bulk glass is around 100 MPa. However, the theoretical stress needed to break the atomic bonds (Si—O) in glass is about 10 000 MPa. Griffith made the important observation that the fracture load is not dependent on the load-bearing area of the material, but that cracks within the glass determine the strength.

Griffith showed experimentally that the fracture stress σf of glass is inversely related to the square root of the crack length a:

[18.7]

where C is a constant. The importance of equation [18.7] is that the fracture stress of a brittle material with a known crack size can be calculated. Alternatively, equation [18.7] can be used to calculate the maximum crack size that causes a brittle material to break under a known operating stress. Equation [18.7] can be applied to predict the failure strength and damage tolerance for any brittle isotropic material.

In the simple case shown in Fig. 18.13, the brittle material contains a through-thickness crack of length 2a lying normal to an applied tensile stress. The fracture stress σf of the material is related to the half-crack length a by:

18.13 Through-thickness crack of length 2a in an infinitely wide plate under tension.

[18.8]

where E is the Young’s modulus of the material, and γe is the elastic surface energy density needed to form a new crack surface in a brittle material, and has the units J m−2. Because two new opposing surfaces are produced during crack growth the surface energy term is 2γe. Equation [18.8] is the same equation as [18.7], where the constant C equals .

18.4.3 Ductile fracture mechanics analysis

Linear elastic fracture mechanics is accurate for calculating the fracture stress of brittle materials in which the stress field at the crack tip is elastic. However, LEFM does not consider plastic flow at the crack tip that occurs in ductile materials. The metals used in aircraft are ductile, and therefore LEFM cannot be used to calculate the fracture strength. With some modification, however, LEFM can be used to calculate the fracture stress of ductile metals. Two scientists named Orowan and Irwin modified LEFM to account for plastic flow at the crack tip. Orowan adapted the Griffith model for ductile materials by including a term to account for the extra work of fracture that occurs in the plastic zone. This is the basis of elastoplastic fracture mechanics.

In mathematical terms, when the work of fracture for both elastic γe and plastic γp crack growth is considered then the fracture stress is calculated using:

[18.9]

The plastic surface energy density γp for ductile metals is usually in the range 100–1000 J m−2, which is much higher than the energy density for brittle materials γe which is only about 1–20 J m−2. This is because the amount of energy needed to plastically deform the material at the crack tip and then extend the crack by the joining of microvoids and tiny cracks is orders of magnitude higher than the energy needed for elastic deformation. Because the energy needed to grow a crack through the plastic zone is much greater (γp > > γe), the elastic fracture energy term can be ignored in plastic fracture analysis. Therefore, the fracture stress for a ductile material containing a small crack can be approximated using:

[18.10]

It is not easy to measure or calculate γp and, therefore, it is difficult to determine the fracture stress of a ductile material using equation [18.10]. To avoid the problem, Irwin showed that when the plastic zone size is very small compared with the size of the metal component, then the fracture stress can be determined by:

[18.11]

where Gc is the critical strain energy release rate or potential energy release rate of the material, G = 2(γe + γp). Gc is one measure of the fracture toughness of a material, and has the units J m−2.

Equation [18.11] shows that increasing the fracture toughness Gc increases the fracture stress σf of a material containing a crack. chapter 19 describes the fracture toughness properties of materials, and how Gc can be increase to improve the fracture strength.

The critical strain energy release rate Gc is a material property that is proportional to the amount of plastic deformation that occurs at the tip of a growing crack. However, the fracture toughness of materials is more often defined by its critical stress intensity factor Kc which has the units of Pa m1/2. It is useful at this point to compare the critical stress intensity factor Kc and the geometric stress concentration factor Kt. The meaning of these two factors is easily confused, although they are different parameters used in fracture mechanics. Kc (similarly to Gc) is the fracture toughness of a material, and describes how easily a crack grows under an externally applied stress. This is different from the definition of Kt, which defines the magnification of the applied stress at the edge of a stress raiser. Kc is used more often than the Gc to define the fracture toughness of materials, although both are a direct measure of toughness and are related by the expression:

[18.12]

where α = 1 for plane stress and α = (1–v)2 for plane strain conditions for crack growth. Plane stress defines the condition where a two-dimensional stress state occurs in the plastic zone at the crack tip whereas plane strain involves a three-dimensional stress state. Plane stress is often dominant in thin materials and plane strain in thick materials. The effect of plane stress and plane strain conditions at the crack tip on the fracture toughness of materials is explained in chapter 19.

18.5 Application of fracture mechanics to aerospace materials

Fracture mechanics is indispensable for the design of damage-tolerant aircraft structures. The application of fracture mechanics in materials selection for new aircraft and the calculation of residual strength for existing aircraft components depend on three parameters:

• fracture toughness Kc of the material;

• critical crack length ac; and

• operating stress σ.

The equation relating these parameters is:

[18.13]

The parameter β is a geometry factor that depends on the crack location and the shape of the component. Table 18.2 shows equation [18.13] for three different cases of a single crack within a material. Values for β for a wide variety of crack conditions can be found in engineering handbooks.

Table 18.2

Stress intensity factors for various geometries

Equation 18.13 can be used in several important ways to design damage-tolerant aircraft structures. The engineer decides what is the most important about the design: certain material properties (e.g. E, σy), the design stress level (σ), or the critical crack length (ac) that must be tolerated for safe operation of the component. Equation [18.13] is then used to design the structure, including the selection of material, based on the main design requirement. For example, if a specific type of aluminium alloy is selected with a known toughness Kc for an aircraft component that is required to support a certain stress σ, then equation [18.13] can be used to calculate the critical crack length (ac) that can be tolerated without causing fracture. Alternatively, if a crack of a known size is detected within an aircraft component, the residual strength of the component can be calculated.

18.6 Summary

Structural materials used in the airframe and engine must be damage tolerant, which means that they retain their strength, fatigue life and other properties in the presence of cracks below a critical length. A key property that ensures high damage tolerance in materials is fracture toughness.

The initiation of cracks often occurs in metals at microstructural imperfections such as large and brittle particles and gas holes or in fibre–polymer composites at voids. These defects must be avoided by careful processing of the material, including the heat treatment of metals. Cracks also initiate at geometric stress raisers, such as fastener holes, sharp corners, and abrupt changes in section thickness or shape. Careful design can eliminate or minimise the concentration of stress at these sites.

The metals used in aircraft fail by ductile fracture processes, which involves plastic yielding of the material ahead of the main crack. Crack growth occurs along the grain boundaries (intergranular fracture) or through the grains (transgranular fracture) or a combination of both. Ductile metals can display brittle-like fracture properties when a high concentration of brittle particles occurs at the grain boundaries, which promotes intergranular fracture. Structural metals must be processed under conditions which eliminate or minimise the presence of brittle particles at grain boundaries.

Brittle fracture is an unstable failure process that occurs in fibre–polymer composite materials, metals with high strength and low ductility, and in some metal types at low temperature (i.e. below the ductile/brittle transition temperature). Aerospace metals used in structural and engine applications should not display brittle fracture properties to ensure sufficient damage tolerance.

Fracture mechanics, based on linear elastic and elastoplastic fracture, is used to calculate the damage tolerance of materials. Fracture mechanics is used to determine the fracture toughness, operating stress and maximum crack size of materials to avoid fracture.

18.7 Terminology

Brittle fracture: A fracture event that involves little or no plastic deformation of the material. Typically, brittle fracture occurs by fast crack growth with less expenditure of energy than for ductile fracture.

Cleavage fracture: Fracture event that involves cracking along specific planes in the crystal resulting in a smooth fracture surface.

Critical strain energy release rate: The fracture toughness of a material expressed in the units J m−2.

Critical stress intensity factor: The fracture toughness of a material expressed in the units Pa m1/2.

Delamination: Cracking between the ply layers in composite laminates.

Ductile/brittle fracture transition: Change in the failure mode of certain types of metals from ductile tearing to brittle (cleavage) fracture when cooled below the transition temperature.

Fast fracture: A fracture event in which the crack in the material grows rapidly (usually near the speed of sound of the material) and leads to catastrophic failure. Stress acting on a material when fast fracture occurs is less than the yield strength.

Fracture toughness: A generic term to describe the resistance of a material to crack extension.

In-plane fracture: Crack growth normal to the fibre direction in composite materials.

Intergranular cracking: Cracking along the grain boundaries, and not through the grains. Usually occurs when the phase in the grain boundary is weak and brittle.

Interlaminar fracture: Cracking between the ply layers along the fibre direction in composite materials. Also called delamination.

Linear elastic fracture mechanics: A method of fracture analysis that can determine the stress (or load) required to induce brittle fracture in a material or structure containing a crack-like flaw of known size and shape.

Plane strain: The stress condition in linear elastic fracture mechanics in which there is zero strain in a direction normal to both the axis of applied tensile stress and the direction of crack growth (that is, parallel to the crack front). Usually occurs in loading thick plate along a direction parallel to the plate surface.

Plane stress: The stress condition in linear elastic fracture mechanics in which the stress in the thickness direction is zero. Usually occurs in loading thin sheet along a direction parallel to the sheet surface.

Plastic zone: The region ahead of a crack tip where a ductile material is plastically deformed owing to the local stress field exceeding the yield strength.

Stress concentration factor: A parameter that defines the magnification of the applied stress at the crack tip, that includes the geometrical parameter. Ratio of the greatest stress in the region of a notch or other stress raiser to the nominal (applied) stress. It is a theoretical indication of the effect of stress concentrations on the fracture strength of materials.

Transgranular cracking: Cracking through the grains of the material.

18.8 Further reading and research

Dieter, G.E. Mechanical metallurgy. London: McGraw–Hill; 1988.

Dimatteo, N.D. ASM handbook, volume 19: fatigue and fracture. ASM International; 1996.

Gordon, J.E. The new science of strong solids or why you don’t fall through the floor. Penguin Science; 1991.

Hertzberg, R.W. Deformation and fracture mechanics of engineering materials. John Wiley & Sons; 1996.

Knott, J.F. Fundamentals of fracture mechanics. Wiley; 1973.

18.9 Case study fracture in the space shuttle Columbia disaster

One of the most high profile accidents involving fracture was the space shuttle Columbia disaster that occurred during re-entry into the Earth’s atmosphere on February 1, 2003. The seven crew members of flight STS-107 were killed when Columbia broke up while travelling at about Mach 18.5 at an altitude of 64 km. Following an exhaustive investigation it was concluded that the loss of Columbia was the result of damage sustained to the thermal protection system. The leading edges of the space shuttle wings are covered with a brittle reinforced carbon–carbon composite to provide thermal protection to the underlying aluminium structure. (chapter 16 provides details about the ceramic materials used in the thermal protection system).

During take-off a piece of foam insulation broke away from an external fuel tank. The foam, which was about the size of a small briefcase, smashed into the leading edge of the left-side wing of Columbia. The reinforced carbon–carbon composite, which is a brittle material with low fracture toughness, broke under the impact force. Tests performed as part of the accident investigation showed that the foam insulation could breach the thermal protection system, leaving a large hole that exposed the underlying aluminium structure (Fig. 18.14). The extremely high temperatures experienced during re-entry caused the exposed aluminium structure to melt which subsequently caused Columbia to break up. The reinforced carbon–carbon material has low resistance against fracture because no plastic deformation occurs during crack growth. This accident tragically highlights the risk involved in using brittle materials, even in accidental load cases such as the foam impact on Columbia.

18.14 Brittle fracture of reinforced carbon–carbon panel under a simulated test of the foam impact to Columbia. photograph supplied courtesy of NASA

18.10 Case study: fracture of aircraft composite radome

An example of the fracture of fibre–polymer composites was the sudden, catastrophic failure of the radome on an F-111C aircraft (Fig. 18.15). In April 2008, the aircraft operated by the Royal Australian Air Force was flying at more than 550 km h−1 at an altitude of 900 m when the fibreglass radome suddenly fractured as the result of a collision with a large bird (pelican). The low interlaminar fracture toughness of the radome material caused extensive delamination cracking and splintering. However, the high in-plane toughness of the composite stopped the radome from completely breaking away from the forward fuselage section.

18.15 Damage to an RAAF F-111C radome made of fibreglass composite. photograph supplied courtesy of the Australia Department of Defense