12 fatigue of metals

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12 fatigue of metals

  1. 1. Chapter 12 Fatigue of metalsSubjects of interest • Objectives / Introduction • Stress cycles • The S-N curve • Cyclic stress-strain curve • Low cycle fatigue • Structural features of fatigue • Fatigue crack propagation • Factors influencing fatigue properties • Design for fatigue Suranaree University of Technology Tapany Udomphol May-Aug 2007
  2. 2. Objectives • This chapter provides fundamental aspects of fatigue in metals and the significance of fatigue failure. • Different approaches for the assessment of fatigue properties, i.e., fatigue S-N curve and fatigue crack growth resistance will be introduced. • Discussion will be made on factors influencing fatigue properties of metals, for example, mean stress, stress concentration, temperature • Finally design against fatigue failure will be highlighted.Suranaree University of Technology Tapany Udomphol May-Aug 2007
  3. 3. Introduction Fatigue failure in a bolt www.corrosionlab.comFatigue initiation Beach mark Suranaree University of Technology Tapany Udomphol May-Aug 2007
  4. 4. Introduction www.btinternet.comFatigue failure occurs at the outer rimof the wheel Fatigue fracture area in a shaft caused by corroded inside area Suranaree University of Technology Tapany Udomphol May-Aug 2007
  5. 5. Introduction Fatigue failures are widely studies because it accounts for 90% of all service failures due to mechanical causes. Characteristics mmd.sdsmt.edu• Fatigue failures occur when metal issubjected to a repetitive or fluctuating Failure of crankshaft journalstress and will fail at a stress much lowerthan its tensile strength.• Fatigue failures occur without any plasticdeformation (no warning).• Fatigue surface appears as a smoothregion, showing beach mark or origin offatigue crack. www.capcis.co.uk Fatigue failure of a bolt Suranaree University of Technology Tapany Udomphol May-Aug 2007
  6. 6. Factors causing fatigue failureBasic factors 1) A maximum tensile stress of sufficiently high value. 2) A large amount of variation or fluctuation in the applied stress. 3) A sufficiently large number of cycles of the applied stress.Additional factors • Stress concentration • Residual stress • Corrosion • Combined stress • Temperature • Overload • Metallurgical structure Suranaree University of Technology Tapany Udomphol May-Aug 2007
  7. 7. Stress cycles Different types of fluctuating stress σmax = - σmin(a) Completely reversed cycle of (b) Repeated stress cyclestress (sinusoidal) Tensile stress + Compressive stress - (c ) Irregular or random stress cycle Suranaree University of Technology Tapany Udomphol May-Aug 2007
  8. 8. Stress cycles Maximum stress, σmax Nomenclature of stress parameter in fatigue loading Minimum stress, σmin Stress range+ ∆σ or σ r = σ max − σ min Eq.1 σa ∆σ Alternating stress ∆σ σ max − σ min σa = = Eq.2 σmax 2 2 σm Mean stress σmin σ max + σ min σm = Eq.3 2_ cycles Stress ratio Amplitude ratio σ min σ a 1− R R= A= = Fatigue stress cycle σ max σ m 1+ R Eq.5 Suranaree University of Technology Tapany Udomphol Eq.4 May-Aug 2007
  9. 9. The S-N curve• Engineering fatigue data isnormally represented by means ofS-N curve, a plot of stress Sagainst the number of cycle, N.• Stress can be σa, σmax, σmin• σm , R or A should be mentioned. Typical fatigue curves • S-N curve is concerned chiefly with fatigue failure at high numbers of cycles (N > 105 cycles) high cycle fatigue (HCF). • N < 104 or 105 cycles low cycle fatigue (LCF). • N increases with decreasing stress level. • Fatigue limit or endurance limit is normally defined at 107 or 108 cycles. Below this limit, the material presumably can endure an infinite number of cycle before failure. • Nonferrous metal, i.e., aluminium, do not have fatigue limit fatigue strength is defined at ~ 108 cycles. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  10. 10. Basquin equation • The S-N curve in the high-cycle region is sometimes described by the Basquin equation Nσ ap = C Eq.6 Where σa is the stress amplitude p and C are empirical constants LCFHCF High cycle (low strain) fatigue Stress levelLCF Low cycle (high strain) fatigue HCF Log Nf Suranaree University of Technology Tapany Udomphol May-Aug 2007
  11. 11. Construction of S-N curve • The construction of S-N curve normally requires ~ 8-12 specimens by first testing at a high level of stress ~ 2/3 of the tensile strength of the material. • The test is then carried out at lower levels of stress until runout. www.statisticalengineering.com• The data obtained is normallyscattered at the same stress levelby using several specimens.• This requires statistic approachto define the fatigue limit. S-N fatigue curve Suranaree University of Technology Tapany Udomphol May-Aug 2007
  12. 12. Statistical nature of fatigue• Because the S-N fatigue data isnormally scattered, it should betherefore represented on aprobability basis.• Considerable number ofspecimens are used to obtainstatistical parameters.• At σ1, 1% of specimens would beexpected to fail at N1 cycles. Fatigue data on a probability basis• 50% of specimens would be Note: The S-N fatigue data is moreexpected to fail at N2 cycles. scattered at lower stress levels. Each specimen has its own fatigue limit. • For engineering purposes, it is sufficiently accurate to assume a logarithmic normal distribution of fatigue life in the region of the probability of failure of P = 0.10 to P = 0.90. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  13. 13. Effect of mean stress, stress range and stress intensity (notch) on S-N fatigue curve σm1 σloc σm4 > σm3 > σm2> σm1 Kt = σm2 σapp R = 0.3 σm3σa σmax σa σm4 R=0 Kt = 1 R = -0.3 R = -1.0 Kt = 1.5 Log Nf Log Nf Log Nf Mean stress Stress range Stress intensity Fatigue strength Fatigue strength Fatigue strength Suranaree University of Technology Tapany Udomphol May-Aug 2007
  14. 14. Goodman diagram Goodman diagram • Goodman diagram shows the variation of the limiting range of stress (σmax - σmin) on mean stress. • As the mean stress becomes more tensile the allowable range of stress is reduced. • At tensile strength, σu , the stress range is zero.Suranaree University of Technology Tapany Udomphol May-Aug 2007
  15. 15. Haig-Solderberg diagram• In Haig-Solderberg diagram isa plot of alternating stress σa andmean stress σm.• The Goodman relationship maybe expressed by  σ  x  σ a = σ e 1 −  m     Eq.7   σu     Haig-Solderberg diagramWhere x = 1 for the Goodman line, x = 2 for the Gerber parabola, σe = the fatigue limit for completely reversed loading. • If the design is based on the yield strength σo, (based on Solderberg line), then the σu is replaced by σo in this equation. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  16. 16. Master diagram for establishing influenceof mean stress in fatigue Ex: at σmax = 400 MPa, σmin = 0, a fatigue limit of the notched specimen is less than 106 cycles. For the unnotched specimen is below the fatigue limit.Suranaree University of Technology Tapany Udomphol May-Aug 2007
  17. 17. Example: A 4340 steel bar is subjected to a fluctuating axial load that varies from a maximum of 330 kN tension to a minimum of 110 kN compression. The mechanical properties of the steel are: σu = 1090 MPa, σo = 1010 MPa, σe = 510 MPa Determine the bar diameter to give infinite fatigue life based on a safety factor of 2.5.Cylindrical cross section of the bar = A, the variation of stress will be 0.330 0.110σ max = MPa, σ min = − MPa A A σ + σ min 0.330 / A + (−0.110 / A) 0.110σ mean = max = = MPa 2 2 A σ − σ min 0.330 / A − (−0.110 / A) 0.220  σ σ a = max = = MPa σ a = σ e 1 − m , σ e = 510 = 204 MPa 2 2 A  σ  2.5  u  0.220 / A 0.110 / AUsing the conservative Goodman line = 1− 204 1090and Eq.7. A = 1179 mm 2 4A D= = 38.7 mm π Suranaree University of Technology Tapany Udomphol May-Aug 2007
  18. 18. Cyclic stress-strain curve • Cyclic strain controlled fatigue occurs when the strain amplitude is held constant during cycling. • Found in thermal cycling where a component expands and contracts in response to fluctuations in the operating temperature or in reversed bending between fixed displacements. • During the initial loading, the stress-strain curve is O-A-B. • Yielding begins on unloading in compression at a lower stress C due to the Bauschinger effect. • A hysteresis loop develops in reloading with its dimensions of width, ∆ε and height ∆σ. • The total strain range ∆ε consists of the elastic strain component plus the plastic strain component.Stress strain loop for ∆ε = ∆ε e + ∆ε p Eq.8constant strain cyclingSuranaree University of Technology Tapany Udomphol May-Aug 2007
  19. 19. Cyclic hardening and cyclic softening • Cyclic hardening would lead to a decreasing peak strain with increasing cycles. (n>0.15) • Cyclic softening would lead to a continually increasing strain range and early fracture. (n<0.15)Suranaree University of Technology Tapany Udomphol May-Aug 2007
  20. 20. Comparison of monotonic and cyclic stress-strain curves of cyclic hardened materials • The cycle stress-strain curve may be described by a power curve as follows ∆σ = K (∆ε p ) n Eq.9 Where n’ is the cyclic strain-hardening exponent K’ is the cyclic strength coefficient Since strain amplitude ∆ε ∆ε e ∆ε p = + 2 2 2 1 nMonotonic and cyclic stress-strain curves ∆ε ∆σ 1  ∆σ  = +   2 2E 2  K  For metals n’ varies between 0.10 -0.20. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  21. 21. Low cycle fatigue• Low cycle fatigue (LCF) (high strain) is concerned about fatiguefailure at relatively high stress and low numbers of cycles to failure.• Ex: in the nuclear pressure vessels, steam turbines and powermachinery. Usually concerned with cyclic strain rather than cyclicstress.• LCF data is normally present as a • On the log scale, this relationplot of strain range ∆εp against N. can be best described by ∆ε p = ε f (2 N ) c Eq.10 2 Where ∆εp/2 = plastic strain amplitude ε’f = fatigue ductility coefficient 2N = number of strain reversals to failure. Low-cycle fatigue curve (∆εp vs. N). c = fatigue ductility exponent varies between -0.5 to -0.7.Suranaree University of Technology Tapany Udomphol May-Aug 2007
  22. 22. Example: For the cyclic stress-strain curve, σB =75 MPa and εB = 0.000645. If εf = 0.30 and E = 22x104 MPa.Determine (a) ∆εe and ∆εp ∆σ 2(75) ∆ε e = = = 6.818 × 10 − 4 E 22 × 10 4 ∆ε p = ∆ε − ∆ε e = (2 × 0.000645) − 0.0006818 = 6.082 × 10 − 4 (b) The number of cycles to failure. ∆ε pFrom the Coffin-Manson relation = ε f (2 N ) c 2 If c = -0.6 and ef ~ e’f 6.082 × 10 − 4 = 0.30(2 N ) −0.6 2 N = 49,000 cycles Suranaree University of Technology Tapany Udomphol May-Aug 2007
  23. 23. Strain-life equation• For the high-cycle (low strain) fatigue (HCF) regime, where thenominal strains are elastic, Basquin’s equation can bereformulated to give ∆ε e σa = E = σ f (2 N ) b 2 Eq.11 ∆ε ∆ε e ∆ε p = + 2 2 2 ∆ε σ f = (2 N ) b + ε f (2 N ) c 2 E Where σa = alternate stress amplitude ∆εe/2 = elastic strain amplitude E = Young’s modulus σ ’f = fatigue strength coefficient defined by the stress intercept at 2N=1. 2N = number of load reversals to failure (N = number of cycles to failure) b = fatigue strength exponent, which varies between – 0.05 and -0.12 for most metals. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  24. 24. Fatigue strain-life curve Ductile materials High cyclic strain condition Strong materials Low cyclic strain condition The fatigue life value at which this transition occurs is 1 (b −c )  ε f E  2Nt =   Eq.12 σ   f The fatigue strain-life curve • tends toward the plastic curve at large total strain amplitudes • tends toward the elastic curve at small total strain amplitudes. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  25. 25. Structural features of fatigueThe fatigue process can be divided into the following processes; 1) Crack initiation: the early development of fatigue damage (can be removed by a suitable thermal anneal). 2) Slip band crack growth: the deepening of the initial crack on plane of high shear stress (stage I crack growth) 3) Crack growth on planes of high tensile stress: growth of well-defined crack in direction normal to maximum tensile stress 4) Ultimate ductile failure: occurs when the crack reaches sufficient length so that the remaining cross section cannot support the applied load.Suranaree University of Technology Tapany Udomphol May-Aug 2007
  26. 26. Initiation of fatigue crack and slip band crack growth (stage I)• Fatigue cracks are normally initiated at a free surface. Slip linesare formed during the first few thousand cycles of stress.• Back and forth fine slip movements of fatigue could build up notchesor ridges at the surface. act as stress raiser initiate crack. Extrusion Intrusion • In stage I, the fatigue crack tends to propagate initially along slip planes (extrusion and intrusion of persistent ix slip bands) and later take the direction atr dm PSB PSB de ely me normal to the maximum tensile stress un lativ for Re (stage II). • The crack propagation rate in stage I Model for fatigue initiation by is generally very low on the order of extrusions and intrusions caused by cyclic slip during nm/cycles giving featureless fatigue loading. surface. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  27. 27. Stable crack growth (stage II) Crack closed Crack opening Crack at maximum load Crack closing Fatigue striations Crack closed• The fracture surface of stage II crack Plastic blunting model of fatigue striationpropagation frequently shows a pattern of • Crack tip blunting occursripples or fatigue striations. during tensile load at 45o and• Each striation is produced by a single crack grows longer by plasticstress cycle and represents the shearing.successive position of an advancing crack • Compression load reverses thefront normal to the greatest tensile stress. slip direction in the end zones crushing the crack surface to form a resharpened crack tip. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  28. 28. Fatigue crack propagation Stage I Non-propagating fatigue crack (~0.25nm/cycle) Fatigue crack Stage II Stable fatigue crack propagation- widely study propagation Stage III Unstable fatigue crack propagation failure • For design against fatigue failure, fracture mechanics is utilised to monitor the fatigue crack growth rate in the stage II Paris regime. da = A(∆K ) m Crack length, aEq.13 dN Monolithic • Where the fatigue crack growth rate da/dN varies with stress intensity factor range ∆K, which is a function of stress range ∆σ and crack length a. ao ∆K = K max − K min Number of cycles to failureEq.14 ∆K = σ max πa − σ min πa FCG curve A log scale plot gives Paris exponent m as the slope Suranaree University of Technology Tapany Udomphol May-Aug 2007
  29. 29. Fatigue crack propagation Stage I Non-propagating fatigue crack (~0.25nm/cycle)Fatigue crackpropagation Stage II Stable fatigue crack propagation- widely study Stage III Unstable fatigue crack propagation failure Non continuum Continuum behaviour Static mode of behaviour (striations) or transition behaviour Fatigue crack growth rate da/dN (log scale) from non continuum (cleavage, Large influence of behaviour with intergranular and • microstructure Small to large influence of dimples) • mean stress • microstructure, Large influence of • environment depending on the • microstructure material • mean stress • thickness Large influence of • certain combination of Little influence of environment, mean stress • environment and frequency Non propagating Unstable crack growth fatigue cracks m 1 da = a(∆K ) m dN for linear portion ∆Kth Stage I Stage II Stage III Fatigue crack Stress intensity factor range, ∆K (log scale) growth behaviour Suranaree University of Technology Tapany Udomphol May-Aug 2007
  30. 30. Fatigue crack growth propagation in stage II regime Stage II fatigue crack growth propagation has been widely investigated in order to determine the fatigue crack growth life from the representing stable fatigue crack growth rate. da m = A(∆K ) m 1e-1 dN da/dN R = Pmin/Pmax = 0.1 Frequency = 0.25 Hz 1e-2 The fatigue crack growth TIMET bar III m = 2.02 life Nf (stage II) can be da/dN, mm/cycle BuRTi EBW01 m = 9.05 1e-3 determined by BuRTi EBW02 m = 2.35 Nf Ti679-BuRTi-TI679 TIG01 m = 6.84 1e-4Nf = ∫ dN 0 Ti679-BuRTi-Ti679 TIG02 m = 10.18 1e-5 a −( m / 2 ) +1 − ai−( m / 2 ) +1 fNf = Eq.15 (−(m / 2) + 1) Aσ π m r m/2 α m 1e-6 1 10 100where m≠2 ∆K, MPa.m 1/2 α is the crack geometry factor Fatigue crack growth in base metal and welded materials Suranaree University of Technology Tapany Udomphol May-Aug 2007
  31. 31. Example: A mild steel plate is subjected to constant amplitude uniaxialfatigue loads to produce stresses varying from σmax = 180 MPa toσmin = -40 MPa. The static properties of the steel are σo = 500 MPa,σu = 600 MPa, E = 207 MPa, and Kc = 100 MPa.m1/2. If the plate containsan initial through thickness edge crack of 0.5 mm, how many fatiguecycles will be required to break the plate? For through thickness edge crack, α = 1.12, and for ferritic-pearlitic steels, A = 6.9 x 10-12 MPam1/2 and m = 3.0. σr = (180-0), since compressive stress are ignored, and neglect the influence of mean stress on the crack growth. 2 2 1  Kc  1  100  ai = 0.0005 m, a f =   =   = 0.078 m π  σ maxα    π  180 × 1.12 From Eq.15 a − ( m / 2 ) +1 − ai− ( m / 2 ) +1 f Nf = (−(m / 2) + 1) Aσ rmπ m / 2α m (0.078) −(3 / 2 ) +1 − (0.0005) −( 3 / 2 ) +1 Nf = −12 = 261,000 cycles (−(3 / 2) + 1)(6.9 × 10 )(180) (π ) (1.12) 3 3/ 2 3 Suranaree University of Technology Tapany Udomphol May-Aug 2007
  32. 32. P/2 P/2 S-N curve fracture surfaces• S-N curve test involves crack initiation and crack 20 mmpropagation to failure. overall fatigue life. 40 mm• Fatigue testing normally uses plain specimens of Crackdifferent specimen surface conditions, i.e., polished, length aground, machined, etc. under tension or bending.• Crack initiation might be due to inclusions, second Cornerphases, porosity, defects. crack Porosity Fractured carbides Fatigue crack initiation Fatigue crack from porosity initiation from inclusion/particle. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  33. 33. Crack growth direction FCG fracture surfaces • Fatigue crack growth (FCG) test involves only crack propagation stage but excludes crack initiation stage. • Specimen has an initial short or small crack and this Fatigue striation crack will propagate under cyclic loading. (a) Crack growth direction Fatigue crack growth rate da/dN (log scale) Brittle facet (slip) + fatigue striation Brittle facetsStage I (b) Non propagating Unstable crack growth Fatigue fatigue cracks m striation 1 da = a(∆K ) m dN (c) for linear portion Stage II ∆Kth Stage I Stage II Stage III Brittle facets (cleavage) + Stress intensity factor range, ∆K (log scale) microvoids Stage III Suranaree University of Technology Tapany Udomphol May-Aug 2007
  34. 34. Factors influencing fatigue properties • Stress concentration • Size effect • Surface effects • Combined stresses • Cumulative fatigue damage and sequence effects • Metallurgical variables • Corrosion • Temperature Suranaree University of Technology Tapany Udomphol May-Aug 2007
  35. 35. Effect of stress concentration on fatigue Stress raiser Fatigue strength Should avoid stress raisers from machining and fabrication processes. • The effect of stress raiser or notch on fatigue strength can be determined by comparing the S-N curve of notched and unnotched specimens. (based on the net section of specimen). • The notch sensitivity factor q in fatigue is determined from K f −1 q= Eq.16 K −1 tWhereKt is theoretical stress-concentration factor, depending on elasticity of crack tipKf is fatigue notch factor, ratio of fatigue strength of notched and unnotched specimens. S-N curve of notched and unnotched specimens Suranaree University of Technology Tapany Udomphol May-Aug 2007
  36. 36. Size effect on fatigue Due toFatigue properties Experimental scale ≠ Industrial scale size effect• Fatigue property is better in the small sized specimens.• Problem: the machine cannot accommodate large specimens.• Larger specimens increases surface area subjected to cyclic load, higher possibility to find defects on surface. decrease the stress gradient and increases the volume of material which is highly stressed. Explain: It is usually impossible to duplicate the same stress concentration and stress gradient in a small-sized laboratory specimens. Solution: Use statistic approaches, i.e., Weibull statistics. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  37. 37. Surface effects on fatigue • Fatigue properties are very sensitive to surface conditions, • Fatigue initiation normally starts at the surface since the maximum stress is at the surface.The factors which affect the surface of a fatigue specimen canbe roughly divided into three categories; • Surface roughness • Changes in surface properties • Surface residual stress Suranaree University of Technology Tapany Udomphol May-Aug 2007
  38. 38. Surface roughness• Different surface finishes produced by different machining processescan appreciably affect fatigue performance.• Polished surface (very fine scratches), normally known as ‘par bar’which is used in laboratory, gives the best fatigue strength. Reduction factor for fatigue limit of steel due to various surface treatments Suranaree University of Technology Tapany Udomphol May-Aug 2007
  39. 39. Changes in surface properties• Changes in surface properties due to Change in fatiguesurface treatments strength/properties.Treatments which reduces fatigue performance Decarburization Ex: decarburization of surface of heat-treated steels. Soft coating Ex: Soft aluminium coating on an age-hardenable Al alloy. Electroplating Might reduces fatigue strength due to changes in residual stress, adhesion, porosity, hardness.Treatments which improves fatigue performance Carburizing • Forming harder and stronger surface Nitriding introducing compressive residual stress. Flame hardening • The strengthening effect depends on the diameter of the part and the depth of the Induction hardening surface hardening. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  40. 40. Surface residual stress• Residual stresses arise when plasticdeformation is not uniform throughout theentire cross section of the part being deformed. Loading Unloading Part undergone Compressive plastically deformed in residual stress tension Part undergone Tensile residual plastically deformed in stress compression Superposition of applied and residual stresses (a) Shows the elastic stress distribution in a beam with no residual stress. (b) Typical residual stress distribution produced by shot peening where the high compressive stress is balanced by the tensile stress underneath. (c) The stress distribution due to the algebraic summation of the external bending stress and the residual stress. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  41. 41. Commercial methods introducingfavourable compressive stress • Surface rolling - Compressive stress is introduced in between the rollers during sheet rolling. • Shot peening Sheet rolling - Projecting fine steel or cast-iron shot against the surface at high velocity. • Polishing - Reducing surface scratches • Thermal stress - Quenching or surface treatments introduce volume change giving compressive stress.Suranaree University of Technology Tapany Udomphol May-Aug 2007
  42. 42. Effect of combined stresses on fatigue Few data has been made on fatigue test with different combinations of types of stresses. • Ductile metals under combined bending and torsion fatigue follow a distortion-energy (von Mises). • Brittle materials follows the maximum principal stress theory (Tresca). Sines has proposed expressions forLow strain [(σ a1 − σ a 2 ) + (σ a 2 − σ a 3 ) + (σ a 3 − σ a1 ) 2 2 ] 2 1/ 2 + C 2 (m1 + m2 + m3 ) ≥ 2σ a Kf Eq.17High strain γ 2 1 3 [ ε q = oct = (ε 1 − ε 2 )2 + (ε 2 − ε 3 )2 + (ε 3 − ε 1 )2 ] 1/ 2 Eq.18 Note: Effects of residual stress and triaxial stress are included. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  43. 43. Cumulative fatigue damage and sequence effects on fatigue Practically, levels of stress are not held constant as in S-N tests, but can vary below or above the designed stress level.• Overstressing : The initial applied stress levelis higher than the fatigue limit for a short periodof time beyond failure, then cyclic stressingbelow the fatigue limit. This overstressing σ Overstressingreduces the fatigue limit. Cycle Stress level• Understressing : The initial applied stresslevel is lower than the fatigue limit for a periodof time, then cyclic stressing above the fatigue Fatigue limitlimit. This understressing increases the σfatigue limit (might be due to strain hardening Cycle Understressingon the surface. Log Nf Suranaree University of Technology Tapany Udomphol May-Aug 2007
  44. 44. Cumulative damage ruleThe percentage of fatigue life consumed by operation at one operatingstress level depends on the magnitude of subsequent stress levelsthe cumulative rule called Miner’s rule. j =k nj n1 n n + 2 + ... + k = 1 or N1 N 2 Nk ∑N j =1 Eq.19 j Where n1, n2,..nk = the number of cycles of operation at specific overstress levels. N1, N2,..Nk = the life (in cycles) at this same overstress level.Note: for notched specimen, the fatigue strength is reduced muchmore than it would be predicted from the Miner’s linear damage rule.This is due to the effect of residual stress produced at the notch byoverload stresses in the plastic region. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  45. 45. Example: A plain sided specimen is subjected to 1x107 cycles, at an applied stress range of 200 MPa. Estimate how many further cycles can be applied at a stress range of 500 MPa before failure is predicted to occur. Given informationApplied stress range (MPa) Number of cycles to failure 600 1x104 500 2x104 400 5x104 300 3x105 250 3x106 200 8x107 n1 n2 n + + ... + k = 1 From Miner’s rule N1 N 2 Nk 1×107 x Assumption: the total life of a part can be + =1 estimated by adding up the percentage of 8 ×10 7 2 ×10 4 life consumed by each overstress cycle. x 1 = 1− 2 × 10 4 8 Therefore, the specimen can further 7 x = × 2 ×10 4 = 1.75 × 10 4 cycles withstand the fatigue load at 500 MPa for 8 Suranaree University of Technology Tapany Udomphol May-Aug 2007
  46. 46. Effects of metallurgical variableson fatigue• Fatigue property is normally greatly improved by changing thedesigns or, reducing stress concentration, introducing compressivestress on the surface.• Few attempts have paid on improving metallurgical structure toimprove fatigue properties but it is still important.• Fatigue property is frequently correlated with tensile properties. Tensile strength Fatigue strength Fatigue ratio = Tensile strength Fatigue strength Note: for smooth and polished specimen. Ex: fatigue ratio ~ 0.5 for cast and wrought steels, ~ 0.35 for non-ferrous.Suranaree University of Technology Tapany Udomphol May-Aug 2007
  47. 47. Fatigue strength improvement by controlling metallurgical variablesBy increasing tensile strength • Grain boundary strengthening By strengthening • Fibre strengthening mechanisms • Second phase strengthening • Cold working Note: not for all cases and Stress level not proportionally. • Grain size has its greatest effect on fatigue life in the Fatigue limit low-stress, high cycle regime. Log Nf Suranaree University of Technology Tapany Udomphol May-Aug 2007
  48. 48. Fatigue strength improvement by controlling metallurgical variables By controlling microstructure• Promote homogeneous slip /plastic deformation throughthermomechanical processing reduces residual stress/ stressconcentration.• Heat treatments to give hardened surface but should avoid stressconcentration.• Avoid inclusions stress concentration fatigue strength• Interstitial atoms increase yield strength , if plus strain aging fatiguestrength Strain aging from interstitials Solid solution Pure metal Effect of interstitial atoms Suranaree University of Technology Tapany Udomphol May-Aug 2007
  49. 49. Effect of corrosion on fatigue • Fatigue corrosion occurs when material is subjected to cyclic stress in a corrosive condition.• Corrosive attack produces pittingon metal surface. Pits act as notches fatigue strength .• Chemical attack greatly acceleratesthe rate of fatigue crack propagation. Corrosion fatigue of brass Role of a corrosive environment on fatigue crack propagation Suranaree University of Technology Tapany Udomphol May-Aug 2007
  50. 50. Corrosion fatigue test Corrosion fatigue test can be carried out similar to fatigue test but in a controlled corrosive environment. • Since corrosion process is a time-dependent phenomenon, the higher the testing speed (frequency), the smaller the damage due to corrosion. • The action of the cyclic stress causes localised breakdown of the surface oxide film corrosion pits.Corrosion fatigue test www.mtec.or.th www.corrosion-doctors.org S-N curve in various condition Suranaree University of Technology Tapany Udomphol May-Aug 2007
  51. 51. Minimization of corrosion fatigue• Select corrosion-resistant materials for the desired application.Ex: stainless steel, bronze, would give better service than heat-treated steel.• Protection of the metal from contact with the corrosiveenvironment by protective metallic or non-metallic coatings.• Introducing compressive residual stresses by nitriding, shotpeening eliminating surface defects. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  52. 52. Effect of temperature on fatigueTemperature If testing temp < RT low temperature fatigue.(Increasing σTS) If testing temp > RT high temperature fatigue.Fatigue strength• In high temperature fatigue, there is a transition from fatigue failureto creep failure as the temperature increases (creep dominates athigh temperatures).• Coarse grained metal has higher fatigue strength – where creepdominates.• Fine grained metal has higher fatigue strength at low temperatures. Temp Fatigue failure Creep failure Transcrystalline Intercrystalline fatigue failure creep failure Suranaree University of Technology Tapany Udomphol May-Aug 2007
  53. 53. Thermal fatigueThermal fatigue occurs when metal is subjectedto high and low temperature, producingfluctuating cyclic thermal stress. Volume change Thermal fatigue failureThermal cycle • Normally occurs in high Cold Hot temperature equipment. • Low thermal conductivity and high thermal expansion properties are critical. • The thermal stress developed by a temperature change ∆T is σ = αE∆T Eq.19 Where α is linear thermal coefficient of expansion E is elastic modulus If failure occurs by one application of thermal stress, the condition is called thermal shock. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  54. 54. Stress level Design for fatigue Fatigue limitThere are several distinct philosophies Allowable stressconcerning for design for fatigue Log Nf1) Infinite-life design: Keeping the stress at some fraction of the fatigue limit of the material.2) Safe-life design: Based on the assumption that the material has flaws and has finite life. Safety factor is used to compensate for environmental effects, varieties in material production/manufacturing.3) Fail-safe design: The fatigue cracks will be detected and repaired before it actually causes failure. For aircraft industry.4) Damage tolerant design: Use fracture mechanics to determine whether the existing crack will grow large enough to cause failure. Suranaree University of Technology Tapany Udomphol May-Aug 2007
  55. 55. References • Dieter, G.E., Mechanical metallurgy, 1988, SI metric edition, McGraw-Hill, ISBN 0-07-100406-8. • Suresh, S., Fatigue of materials, 1998, 2nd edition, Cambridge university press, ISBN 0-521-57847-7. • Lecture note, MRes 2000, School of Metallurgy and Materials, Birmingham University, UKSuranaree University of Technology Tapany Udomphol May-Aug 2007

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