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DESIGNING AGAINST FATIGUE Fatigue failure account for about 80 % of part failure in engineering Occurs subjected to fluctuating loads

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designing against fatigue
  • Fatigue failure account for about 80 % of part failure in engineering
    • Occurs subjected to fluctuating loads
  • Generally, fatigue fractures occurs as a result of crack which usually start at some discontinuity in the material, or at other stress concentration location, and then gradually grow under repeated application of load.
  • As the crack grows, the stress on the load-bearing cross-section increase until it reaches a high enough level to cause catastrophic fracture of the part.
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  • Fracture surface which usually exhibits smooth areas which correspond to the gradual crack growth stage, and rough areas, which correspond to the catastrophic fracture stage.
  • The smooth parts of the fracture surface usually exhibit beach marks which occurs as a result of changes in the magnitude of the fluctuating fatigue load.
  • Fatigue behavior of materials is usually described by means of the S-N diagram which gives the number of cycles to failure, N as a function of the max applied alternating stress, Sa.
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  • Types of fatigue loading
    • Alternating stress
      • Alternating tension – compression
      • Stress ratio, R = min / max = -1
    • Fluctuating stress
      • Positive R value
      • Greater tensile stress than compressive stress
      • max = m + a
      • max = m - a
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  • Many types of test are used to determine the fatigue life of material
    • Small scale fatigue test – rotating beam test
      • Which a specimen subjected to alternating compression and tension stresses of equal magnitude while being rotate
    • Data from this result are plotted in the form of S-N curves
      • Which the stress S to cause failure is plotted against number of cycles N
    • Figure (a) – S-N curves for carbon steel

(b) - S-N curves aluminum alloy

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  • In the majority cases, the reported fatigue strength or endurance limits of the materials are based on the test of carefully prepared small samples under laboratory condition.
  • Such values cannot be directly used for design purposes because the behavior of a component or structure under fatigue loading does depend not only on the fatigue or endurance limit of the material used in making it, but also an several other factors including :
    • Size and shape of the component or structure
    • Type of loading and state of stress
    • Stress concentration
    • Surface finish
    • Operating temperature
    • Service environment
    • Method of fabrication
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  • Endurance-limit modifying factors

Se = kakbkckdkekfkgkhSe’

Where Se = endurance limit of component

Se’ = endurance limit experimental

ka = surface finish factor (machined parts have different finish)

kb = size factor (larger parts greater probability of finding defects)

kc = reliability / statistical scatter factor (accounts for random variation)

kd = operating T factor (accounts for diff. in working T & room T)

ke = loading factor (differences in loading types)

kf = stress concentration factor

kg = service environment factor (action of hostile environment)

kh = manufacturing processes factor (influence of fabrication parameters)

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ka = Surface finish factor

  • The surface finish factor, ka, is introduced to account for the fact that most machine elements and structures are not manufactured with the same high-quality finish that is normally given tolaboratory fatigue test specimens.
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  • kb = Size factor
    • Large engineering parts have lower fatigue strength than smaller test specimen
      • Greater is the probability of finding metallurgical flaws that can cause crack initiation
  • Following values can be taken as rough guidelines :
    • kb = 1.0 for component diameters less than 10 mm
    • kb = 0.9 for diameters in the range 10 to 50 mm
    • kb = 1 – [( D – 0.03)/15], where D is diameter expressed in inches, for sizes 50 to 225 mm.
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  • kc = Reliability factor
  • Accounts for random variation in fatigue strength.
  • Published data on endurance limit, represent 50 % survival fatigue test.
    • Since most design require higher reliability, the published data must be reduced by the factor of kc
    • The following value can be taken as guidelines
      • kc = 0.900 for 90% reliability
      • kc = 0.814 for 99 % reliability
      • kc = 0.752 for 99.9 % reliability
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  • kd = Operating temperature factor
  • Accounts for the difference between the test temperature and operating temperature of the component
  • For carbon and alloy steels, fatigue strength not affected by operating temperature – 45 to 4500C kd = 1
  • At higher operating temperature
  • kd = 1 – 5800( T – 450 ) for T between 450 and 550oC, or
  • kd = 1 – 3200( T – 840 ) for T between 840 and 1020oF
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  • ke = Loading factor
  • Accounts for the difference in loading between lab. test and service.
    • During service – vibration, transient overload, shock
    • From experience show that repeated overstressing can reduce the fatigue life
  • Different type of loading, give different stress distribution
    • ke = 1 for application involving bending
    • ke = 0.9 for axial loading
    • ke = 0.58 for torsional loading
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  • kf = Stress concentration factor
  • Accounts for the stress concentration which may arise when change in cross-section
  • kf = endurance limit of notch-free part
  • endurance limit of notched part
  • Low strength, ductile steels are less sensitive to notched than high-strength steels
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  • kg = Service environment factor
  • Accounts for the reduced fatigue strength due to the action of a hostile environment.
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  • kh = Manufacturing process factor
  • Accounts for the influence of fabrication parameter
    • Heat treatment, cold working, residual stresses and protective coating on the fatigue material.
  • kh difficult to quantify, but important to included.
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  • Endurance limit/Fatigue strength
  • The endurance limit, or fatigue strength, of a given material can usually be related to its tensile strength, as shown in table 2.2.
  • The endurance ratio, defined as (endurance limit/ tensile strength), can be used to predict fatigue behavior in the absence of endurance limits results.
  • From the table shows, endurance ratio of most ferrous alloys varies between 0.4 and 0.6
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  • Other fatigue-design criteria
    • Safe-life or finite-life
    • Design is based on the assumption that the component is free from flaws, but stress level in certain areas is higher than the endurance limit of the material
    • Means that fatigue-crack initiation is inevitable and the life of the component is estimated on the number of stress cycles which are necessary to initiate crack
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  • Fail-safe design
    • Crack that form in service will be detected and repaired before they can lead to failure.
    • Employed material adapted with high fracture toughness, crack stopping features and reliable NDT program to detect crack.
  • Damage-tolerant design
    • Is an extension of fail-safe criteria and assume that flaws exist in the component before they put in service.
    • Fracture mechanics techniques are used to determine whether such crack will grow large enough to cause failure before they are detected during periodic inspection.
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  • Selection of materials for fatigue resistance
  • In many application, the behavior of a component in service is influence by several other factor besides the properties of the material used in its manufacture.
  • This is particularly true for the cases where the component or structure is subjected to fatigue loading.
  • The fatigue resistance can be greatly influenced by the service environment, surface condition of the part, method of fabrication and design details.
  • In some cases, the role of the material in achieving satisfactory fatigue life is secondary to the above parameters, as long as the material is free from major flaws
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  • Steel and cast iron
  • Steel are widely used as structural materials for fatigue application as they offer high fatigue strength and good processability at relatively low cost.
  • The optimum steel structure for fatigue is tempered martensite, since it provide max homogeneity
  • Steel with high hardenability give high strength with relatively mild quenching and hence, low residual stresses, which is desire in fatigue applications.
  • Normalized structure, with their finer structure give better fatigue resistance than coarse pearlite structure obtained by annealing.
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  • Nonferrous alloys
  • Unlike ferrous alloy, the nonferrous alloys, with the exception of titanium, do not normally have endurance limit.
  • Aluminum alloys usually combine corrosion resistance, light weight, and reasonable fatigue resistance
  • Fine grained inclusion-free alloys are most suited for fatigue applications.
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  • Plastics
  • The viscoelasticity of plastics makes their fatigue behavior more complex than that of metals.
  • Fatigue behavior of plastics is affected by the type of loading, small changes in temperature and environment and method of fabrication
  • Because of their low thermal conductivity, hysteretic heating can build up in plastics causing them to fail in thermal fatigue or to function at reduces stiffness level.
  • The amount of heat generated increases with increasing stress and test frequency.
    • This means that failure of plastics in fatigue may not necessarily mean fracture
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  • Composite materials
  • The failure modes of reinforced materials in fatigue are complex and can be affected by the fabrication process when difference in shrinkage between fibers and matrix induce internal stresses.
  • However from practical experiences, some fiber reinforced plastics are known to perform better in fatigue than some metal, refer table 2.2.
  • The advantage of fiber-reinforced plastics is even more apparent when compared on a per weight basics.
  • As with static strength, fiber orientation affects the fatigue strength of fiber reinforced composite
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  • In unidirectional composites, the fatigue strength is significantly lower in directions other than the fiber orientation.
  • Reinforcing with continuous unidirectional fibers is more effective than reinforcing with short random fibers.