Mechanical Failure a topic in material science engineering mechanical engineering in second year.pdf
- 1. Unit-IV Mechanical Failure • The design of a component or structure often calls upon the engineer to minimize the possibility of failure. • Thus, it is important to understand the mechanics of the various failure modes—fracture, fatigue, and creep
- 2. • The failure of engineering materials is almost always an undesirable event for several reasons; these include putting human lives in jeopardy, causing economic losses, and interfering with the availability of products and services. • Even though the causes of failure and the behavior of materials may be known, prevention of failures is difficult to guarantee. • The usual causes are improper materials selection and processing and inadequate design of the component or its misuse. Also, damage can occur to structural parts during service, • Regular inspection and repair or replacement are critical to safe design. • It is the responsibility of the engineer to anticipate and plan for possible failure • and, in the event that failure does occur, to assess its cause and then take appropriate preventive measures against future incidents.
- 3. • Simple fracture is the separation of a body into two or more pieces in response to an imposed stress that is static (i.e., constant or slowly changing with time) and at temperatures that are low relative to the melting temperature of the material. • Fracture can also occur from – fatigue (when cyclic stresses are imposed) – creep (time-dependent deformation, normally at elevated temperatures); FUNDAMENTALS of MECHANICAL FAILURE
- 4. • For metals, two fracture modes are possible: ductile and brittle. • Classification is based on the ability of a material to experience plastic deformation. • Ductile metals typically exhibit substantial plastic deformation with high energy absorption before fracture. • However, there is normally little or no plastic deformation with low energy absorption accompanying a brittle fracture.
- 5. • Ductile and brittle are relative terms; whether a particular fracture is one mode or the other depends on the situation. • Ductility may be quantified in terms of percent elongation and percent reduction in area. • Furthermore, ductility is a function of temperature of the material, the strain rate, and the stress state.
- 6. Fracture Any fracture process involves two steps, inresponse to an imposed stress 1. Crack formation 2. Crack propagation The mode of fracture is highly dependent on the mechanism of crack propagation. • Ductile fracture is characterized by extensive plastic deformation in the vicinity of an advancing crack. – The process proceeds relatively slowly as the crack length is extended. – Such a crack is often said to be stable—that is, it resists any further extension unless there is an increase in the applied stress. – In addition, there typically is evidence of appreciable gross deformation at the fracture surfaces (e.g., twisting and tearing). • For brittle fracture, cracks may spread extremely rapidly, with very little accompanying plastic deformation. – Such cracks may be said to be unstable, and crack propagation, once started, continues spontaneously without an increase in magnitude of the applied stress.
- 7. Ductile fracture is almost always preferred to brittle fracture for two reasons: • First, brittle fracture occurs suddenly and catastrophically without any warning; this is a consequence of the spontaneous and rapid crack propagation. By contrast, in ductile fracture, the presence of plastic deformation gives warning that failure is imminent, allowing preventive measures to be taken. • Second, more strain energy is required to induce ductile fracture inasmuch as these materials are generally tougher. Under the action of an applied tensile stress, many metal alloys are ductile, whereas ceramics are typically brittle, and polymers may exhibit a range of behaviors.
- 8. Brittle vs. Ductile Fracture A. Very ductile, soft metals (e.g. Pb, Au) at room temperature, other metals, polymers, glasses at high temperature. B. Moderately ductile fracture, typical for ductile metals C. Brittle fracture, cold metals, ceramics. A B C
- 9. Ductile Fracture (Dislocation Mediated) Crack grows 90 degree to applied stress 45 degree -Maximum shear stress Cup-and-cone fracture (a) Necking (b) Formation of microvoids (c) Coalescence of microvoids to form a crack (d) Crack propagation by shear deformation (e) Fracture
- 10. Brittle Fracture (Limited Dislocation Mobility) • No appreciable plastic deformation • Crack propagation is very fast • Crack propagates nearly perpendicular to the direction of the applied stress • Crack often propagates by cleavage – breaking of atomic bonds along specific crystallographic planes (cleavage planes).
- 11. Brittle Fracture A. Transgranular fracture: • Fracture cracks pass through grains. • Fracture surface have faceted texture because of different orientation of cleavage planes in grains. B. Intergranular fracture: • Fracture crack propagation is along grain boundaries • (grain boundaries are weakened or embrittled by impurities segregation etc.)
- 12. 12 Crack Propagation Cracks having sharp tips propagate easier than cracks having blunt tips • A plastic material deforms at a crack tip, which “blunts” the crack. deformed region brittle Energy balance on the crack • Elastic strain energy- • Energy stored in material as it is elastically deformed • This energy is released when the crack propagates • creation of new surfaces requires energy ductile
- 13. Stress Concentration • The measured fracture strengths for most materials are significantly lower than those predicted by theoretical calculations based on atomic bonding energies. • This discrepancy is explained by the presence of microscopic flaws or cracks that always exist under normal conditions at the surface and within the interior of a body of material. • These flaws are a detriment to the fracture strength because an applied stress may be amplified or concentrated at the tip, the magnitude of this amplification depending on crack orientation and geometry.
- 14. • This phenomenon is demonstrated in Figure—a stress profile across a cross section containing an internal crack. • As indicated by this profile, the magnitude of this localized stress decreases with distance away from the crack tip. • At positions far removed, the stress is just the nominal stress 𝜎0, or the applied load divided by the specimen cross-sectional area (perpendicular to this load). • Because of their ability to amplify an applied stress in their locale, these flaws are sometimes called stress raisers. If it is assumed that a crack is similar to an elliptical hole through a plate and is oriented perpendicular to the applied stress, the maximum stress, 𝜎m, occurs at the crack tip and may be approximated by where 𝜎0 is the magnitude of the nominal applied tensile stress, 𝜌t is the radius of curvature of the crack tip (Figure a), and a represents the length of a surface crack, or half of the length of an internal crack.
- 15. The ratio 𝜎m/𝜎0 is denoted the stress concentration factor Kt: Stress amplification may occur at macroscopic internal discontinuities (e.g., voids or inclusions), sharp corners, scratches, and notches. The effect of a stress raiser is more significant in brittle than in ductile materials. For a ductile metal, plastic deformation takes place when the maximum stress exceeds the yield strength. This leads to a more uniform distribution of stress in the vicinity of the stress raiser and to the development of a maximum stress concentration factor less than the theoretical value. Such yielding and stress redistribution do not occur to any appreciable extent around flaws and discontinuities in brittle materials; therefore, essentially the theoretical stress concentration results.
- 16. Critical Stress for crack propagation
- 19. Fracture Toughness Using fracture mechanical principles, an expression has been developed that relates this critical stress for crack propagation (𝜎c) and crack length (a) as In this expression Kc is the fracture toughness, a property that is a measure of a material’s resistance to brittle fracture when a crack is present.
- 20. Tensile Test
- 22. Elastic Region: •This is the region where stress is proportional to strain Tensile Test
- 23. Yielding Region: •Upper yield point is where when there is no application of any additional force the material will elongate. Tensile Test
- 24. Lower yield point : •This is the point where yielding will end . Tensile Test
- 25. Proportionality region: •This is the region where stress is proportional to strain. Tensile Test
- 26. Ultimate Tensile Strength: •The maximum loading occurs in this region. Tensile Test
- 27. Necking: •Fracture of material occurs by reduction of area. Tensile Test
- 28. FATIGUE
- 29. Fatigue • Fatigue is a form of failure that occurs in structures subjected to dynamic and fluctuating stresses (e.g., bridges, aircraft, machine components). • Under these circumstances, it is possible for failure to occur at a stress level considerably lower than the tensile or yield strength for a static load. • The term fatigue is used because this type of failure normally occurs after a lengthy period of repeated stress or strain cycling. . • Fatigue is important inasmuch as it is the single largest cause of failure in metals, estimated to be involved in approximately 90% of all metallic failures; polymers and ceramics (except for glasses) are also susceptible to this type of failure. • Furthermore, fatigue is catastrophic and insidious, occurring very suddenly and without warning.
- 30. Fatigue • Fatigue failure is brittle-like in nature even in normally ductile metals in that there is very little, if any, gross plastic deformation associated with failure. • The process occurs by the initiation and propagation of cracks, and typically the fracture surface is perpendicular to the direction of an applied tensile stress.
- 31. CYCLIC STRESSES
- 32. • The applied stress may be axial (tension–compression), flexural (bending), or torsional (twisting) in nature. • In general, three different fluctuating stress–time modes are possible. • One is represented schematically by a regular and sinusoidal time dependence in Figure a, where the amplitude is symmetrical about a mean zero stress level, for example, alternating from a maximum tensile stress (𝜎max) to a minimum compressive stress (𝜎min) of equal magnitude; this is referred to as a reversed stress cycle. • Another type, termed a repeated stress cycle, is illustrated in Figure b; the maxima and minima are asymmetrical relative to the zero stress level. • Finally, the stress level may vary randomly in amplitude and frequency, as exemplified in Figure c.
- 33. Also indicated in Figure 8.18b are several parameters used to characterize the fluctuating stress cycle. The stress amplitude alternates about a mean stress
- 34. Fatigue Test • As with other mechanical characteristics, the fatigue properties of materials can be determined from laboratory tests. • A test apparatus should be designed to duplicate as nearly as possible the service stress conditions (stress level, time frequency, stress pattern, etc.). • The most common type of test conducted in a laboratory setting employs a rotating–bending beam: alternating tension and compression stresses of equal magnitude are imposed on the specimen as it is simultaneously bent and rotated. • In this case, the stress cycle is reversed—that is, R = −1.
- 35. Fatigue Test Schematic diagrams of the apparatus and test specimen commonly used for this type of fatigue testing are shown in Figures 8.19a and 8.19b, respectively. From Figure 8.19a, during rotation, the lower surface of the specimen is subjected to a tensile (i.e., positive) stress, whereas the upper surface experiences compression (i.e., negative) stress. Furthermore, anticipated in-service conditions may call for conducting simulated laboratory fatigue tests that use either uniaxial tension–compression or torsional stress cycling instead of rotating–bending.
- 36. Fatigue Test • A series of tests is commenced by subjecting a specimen to stress cycling at a relatively large maximum stress (𝜎max), usually on the order of two-thirds of the static tensile strength; number of cycles to failure is counted and recorded. • This procedure is repeated on other specimens at progressively decreasing maximum stress levels. • Data are plotted as stress S versus the logarithm of the number N of cycles to failure for each of the specimens. • The S parameter is normally taken as either maximum stress (𝜎max) or stress amplitude (𝜎a).
- 37. • Two distinct types of S–N behavior are observed and are represented schematically in Figure . • As these plots indicate, the higher the magnitude of the stress, the smaller the number of cycles the material is capable of sustaining before failure. • For some ferrous (iron-base) and titanium alloys, the S–N curve (Fig. a) becomes horizontal at higher N values; there is a limiting stress level, called the fatigue limit (also sometimes called the endurance limit), below which fatigue failure will not occur. • This fatigue limit represents the largest value of fluctuating stress that will not cause failure for essentially an infinite number of cycles. • For many steels, fatigue limits range between 35% and 60% of the tensile strength.
- 38. • Most nonferrous alloys (e.g., aluminum, copper) do not have a fatigue limit, in that the S–N curve continues its downward trend at increasingly greater N values (Figure b). • Thus, fatigue ultimately occurs regardless of the magnitude of the stress. • For these materials, the fatigue response is specified as fatigue strength, which is defined as the stress level at which failure will occur for some specified number of cycles (e.g., 107cycles). • The determination of fatigue strength is also demonstrated in Figure b. • Another important parameter that characterizes a material’s fatigue behavior is fatigue life Nf. • It is the number of cycles to cause failure at a specified stress level, as taken from the S–N plot (Figure b). b
- 39. The fatigue behaviors represented in Figures a and b may be classified into two domains. • One is associated with relatively high loads that produce not only elastic strain but also some plastic strain during each cycle. • Consequently, fatigue lives are relatively short; this domain is termed as low-cycle fatigue and occurs at less than about 104 to105 cycles. • For lower stress levels wherein deformations are totally elastic, longer lives result. This is called high-cycle fatigue because relatively large numbers of cycles are required to produce fatigue failure. • High-cycle fatigue is associated with fatigue lives greater than about 104 to105 cycles.
- 40. • The process of fatigue failure is characterized by three distinct steps: • (1) crack initiation, in which a small crack forms at some point of high stress concentration; • (2) crack propagation, during which this crack advances incrementally with each stress cycle; • (3) final failure, which occurs very rapidly once the advancing crack has reached a critical size. • Cracks associated with fatigue failure almost always initiate (or nucleate) on the surface of a component at some point of stress concentration. • Crack nucleation sites include surface scratches, sharp fillets, keyways, threads, dents, and the like. • In addition, cyclic loading can produce microscopic surface discontinuities resulting from dislocation slip steps that may also act as stress raisers and therefore as crack initiation sites.
- 41. Maximum stress for rotating–bending test For a cylindrical bar of diameter do, maximum stress for rotating–bending tests may be determined using the following expression:
- 42. • The region of a fracture surface that formed during the crack propagation step may be characterized by two types of markings termed beachmarks and striations. • Both features indicate the position of the crack tip at some point in time and appear as concentric ridges that expand away from the crack initiation site(s), frequently in a circular or semicircular pattern.
- 43. Fatigue • Beachmarks (sometimes also called clamshell marks) are of macroscopic dimensions, and may be observed with the unaided eye. • These markings are found for components that experienced interruptions during the crack propagation stage—for example, a machine that operated only during normal workshift hours. • Each beachmark band represents a period of time over which crack growth a period of time over which crack growth occurred.
- 44. Fatigue • However, fatigue striations are microscopic in size and subject to observation with the electron microscope (either TEM or SEM). Figure 8.24 is an electron fractograph that shows this feature. • Each striation is thought to represent the advance distance of a crack front during a single load cycle. • Striation width depends on, and increases with, increasing stress range. • During the propagation of fatigue cracks and on a microscopic scale, there is very localized plastic deformation at crack tips, even though the maximum applied stress to which the object is exposed in each stress cycle lies below the yield strength of the metal. • This applied stress is amplified at crack tips to the degree that local stress levels exceed the yield strength. The geometry of fatigue striations is a manifestation of this plastic deformation.
- 47. CREEP
- 48. Creep • Materials are often placed in service at elevated temperatures and exposed to static mechanical stresses (e.g., turbine rotors in jet engines and steam generators that experience centrifugal stresses; high-pressure steam lines). Deformation under such circumstances is termed creep. • Defined as the time-dependent and permanent deformation of materials when subjected to a constant load or stress, creep is normally an undesirable phenomenon and is often the limiting factor in the lifetime of a part. • It is observed in all materials types; for metals, it becomes important only for temperatures greater than about 0.4Tm, where Tm is the absolute melting temperature. • Amorphous polymers, which include plastics and rubbers, are especially sensitive to creep deformation
- 49. Creep
- 50. Creep • Upon application of the load, there is an instantaneous deformation, as indicated in the figure, that is totally elastic. • The resulting creep curve consists of three regions, each of which has its own distinctive strain–time feature. • Primary or transient creep occurs first, typified by a continuously decreasing creep rate—that is, the slope of the curve decreases with time. • This suggests that the material is experiencing an increase in creep resistance or strain hardening— deformation becomes more difficult as the material is strained.
- 51. Creep • For secondary creep, sometimes termed steady- state creep, the rate is constant—that is, the plot becomes linear. • This is often the stage of creep that is of the longest duration. • The constancy of creep rate is explained on the basis of a balance between the competing processes of strain hardening and recovery, • Recovery being the process by which a material becomes softer and retains its ability to experience deformation.
- 53. Creep • Finally, for tertiary creep, there is an acceleration of the rate and ultimate failure. • This failure is frequently termed rupture and results from microstructural and/or metallurgical changes • —for example, grain boundary separation, and the formation of internal cracks, cavities, and voids. • Also, for tensile loads, a neck may form at some point within the deformation region. • These all lead to a decrease in the effective cross- sectional area and an increase in strain rate.
- 54. Creep Test • A typical creep test consists of subjecting a specimen to a constant load or stress while maintaining the temperature constant; deformation or strain is measured and plotted as a function of elapsed time. • ASTM Standard E139, “Standard Test Methods for Conducting Creep, Creep- Rupture, and Stress-Rupture Tests of Metallic Materials.” • Most tests are the constant-load type, which yield information of an engineering nature; constant-stress tests are employed to provide a better understanding of the mechanisms of creep.
- 55. Creep Test • For metallic materials, most creep tests are conducted in uniaxial tension using a specimen having the same geometry as for tensile tests. • However, uniaxial compression tests are more appropriate for brittle materials; these provide a better measure of the intrinsic creep properties because there is no stress amplification and crack propagation, as with tensile loads. • Compressive test specimens are usually right cylinders or parallelepipeds having length-to-diameter ratios ranging from about 2 to 4. • For most materials, creep properties are virtually independent of loading direction.
- 56. Creep Test • Possibly the most important parameter from a creep test is the slope of the secondary portion of the creep curve (Δ𝜀/Δt in Figure 8.30); this is often called the minimum or steady-state creep rate • It is the engineering design parameter that is considered for long-life applications, such as a nuclear power plant component that is scheduled to operate for several decades, and when failure or too much strain is not an option. • However, for many relatively short-life creep situations (e.g., turbine blades in military aircraft and rocket motor nozzles), time to rupture, or the rupture lifetime tr, is the dominant design consideration; it is also indicated in Figure. • Of course, for its determination, creep tests must be conducted to the point of failure; these are termed creep rupture tests. • Thus, knowledge of these creep characteristics of a material allows the design engineer to ascertain its suitability for a specific application.
- 57. STRESS AND TEMPERATURE EFFECTS • Both temperature and the level of the applied stress influence the creep characteristics (Figure). • At a temperature substantially below 0.4Tm, and after the initial deformation, the strain is virtually independent of time. • With either increasing stress or temperature, the following will be noted: – (1) the instantaneous strain at the time of stress application increases, – (2) the steady-state creep rate increases, and – (3) the rupture lifetime decreases.
- 58. STRESS AND TEMPERATURE EFFECTS • Empirical relationships have been developed in which the steady-state creep rate as a function of stress and temperature is expressed. Its dependence on stress can be written where K1 and n are material constants. A plot of the logarithm of versus the logarithm of σ yields a straight line with slope of n; this is shown in Figure for an S-590 alloy at four temperatures. Clearly, one or two straight-line segments are drawn at each temperature. Now, when the influence of temperature is included, where K2 and Qc are constants; Qc is termed the activation energy for creep; also R is the gas constant, 8.31 J⋅mol/K.
- 60. DATA EXTRAPOLATION METHODS • The need often arises for engineering creep data that are impractical to collect from normal laboratory tests. • This is especially true for prolonged exposures (on the order of years). • One solution to this problem involves performing creep and/or creep rupture tests at temperatures in excess of those required, for shorter time periods, and at a comparable stress level, and then making a suitable extrapolation to the in-service condition. • A commonly used extrapolation procedure employs the Larson–Miller parameter, m, defined as where C is a constant (usually on the order of 20), for T in Kelvin and the rupture lifetime tr in hours. • The rupture lifetime of a given material measured at some specific stress level varies with temperature such that this parameter remains constant. • Alternatively, the data may be plotted as the logarithm of stress versus the Larson–Miller parameter, as shown in Figure.
- 61. Environmental Effects • Under particular environmental conditions, some normally active metals and alloys lose their chemical reactivity and become extremely inert- This phenomenon is termed passivity, • It is displayed by chromium, iron, nickel, titanium, and many of their alloys. • It is believed that this passive behavior results from the formation of a highly adherent and very thin oxide film on the metal surface, which serves as a protective barrier to further corrosion. • Stainless steels are highly resistant to corrosion in a rather wide variety of atmospheres as a result of passivation. • They contain at least 11% chromium, which as a solid-solution alloying element in iron, minimizes the formation of rust; instead, a protective surface film forms in oxidizing atmospheres. • Stainless steels are susceptible to corrosion in some environments and therefore are not always “stainless.” • Aluminum is highly corrosion resistant in many environments because it also passivates. If damaged, the protective film normally re-forms very rapidly. • However, a change in the character of the environment (e.g., alteration in the concentration of the active corrosive species) may cause a passivated material to revert to an active state. • Subsequent damage to a preexisting passive film could result in a substantial increase in corrosion rate, by as much as 100,000 times.
- 62. Environmental Effects • The variables in the corrosion environment, which include fluid velocity, temperature, and composition, can have a decided influence on the corrosion properties of the materials that are in contact with it. • In most instances, increasing fluid velocity enhances the rate of corrosion due to erosive effects. • The rates of most chemical reactions rise with increasing temperature; this also holds for most corrosion situations. • Increasing the concentration of the corrosive species (e.g., H+ ions in acids) in many situations produces a more rapid rate of corrosion. • However, for materials capable of passivation, raising the corrosive content may result in an active-to-passive transition, with a considerable reduction in corrosion. • Cold working or plastically deforming ductile metals is used to increase their strength; however, a cold-worked metal is more susceptible to corrosion than the same material in an annealed state. • For example, deformation processes are used to shape the head and point of a nail; consequently, these positions are anodic with respect to the shank region. • Thus, differential cold working on a structure should be a consideration when a corrosive environment may be encountered during service.
- 63. Environmental factors affecting fatigue behavior of materials • Environmental factors may also affect the fatigue behavior of materials. • Two types of environment-assisted fatigue failure: – Thermal Fatigue – Corrosion Fatigue • Thermal fatigue is normally induced at elevated temperatures by fluctuating thermal stresses; mechanical stresses from an external source need not be present. • The origin of these thermal stresses is the restraint to the dimensional expansion and/or contraction that would normally occur in a structural member with variations in temperature. • The magnitude of a thermal stress developed by a temperature change ΔT depends on the coefficient of thermal expansion 𝛼l and the modulus of elasticity E according to • Thermal stresses do not arise if this mechanical restraint is absent. • Therefore, one obvious way to prevent this type of fatigue is to eliminate, or at least reduce, the restraint source, thus allowing unhindered dimensional changes with temperature variations, or to choose materials with appropriate physical properties.
- 64. Environmental factors affecting fatigue behavior of materials • Failure that occurs by the simultaneous action of a cyclic stress and chemical attack is termed corrosion fatigue. • Corrosive environments have a deleterious influence and produce shorter fatigue lives. • Even normal ambient atmosphere affects the fatigue behavior of some materials. • Small pits may form as a result of chemical reactions between the environment and the material, which may serve as points of stress concentration and therefore as crack nucleation sites. • In addition, the crack propagation rate is enhanced as a result of the corrosive environment. • The nature of the stress cycles influences the fatigue behavior; for example, lowering the load application frequency leads to longer periods during which the opened crack is in contact with the environment and to a reduction in the fatigue life.
- 65. Environmental factors affecting fatigue behavior of materials • Several approaches to corrosion fatigue prevention exist. • On one hand, we can take measures to reduce the rate of corrosion by some of the techniques like, apply protective surface coatings, select a more corrosion-resistant material, and reduce the corrosiveness of the environment. • It might be advisable to take actions to minimize the probability of normal fatigue failure, as outlined previously—for example, reduce the applied tensile stress level and impose residual compressive stresses on the surface of the member.