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Fatigue Crack Propagation

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					Fatigue Crack Propagation
        Fatigue Crack Growth
• Once a crack is present in a material, it will
  tend to grow under the influence of cyclic
  loading.
• The crack may be initiated by fatigue, or
  may be pre-existing from manufacture, or
  may be caused by an impact, or similar
  event (e.g., a thermal shock.)
• The crack will grow to a critical length then
  fracture of the component will occur.
 Driving Force for Crack Growth
• The driving force for crack growth is the
  range in the stress intensity factor during
  cycling.
      K  f (a/W) a
         max   min for R  0
         max for R  0
          Cyclic Loading

                                              max   min
                                   mean 
                                                    2
                                   range   max     min
                                                   max   min
   Rotating Machinery              amplitude 
                                                        2
                                                    min
                                  StressRatio, R 
                                                    max




Airframes, Bridges, Tanks, etc,
  Crack Growth Rate, da/dN

                        1 < 2             1
Crack Length, a
                  ac1                          X
                                    2
                  ac2               X

                                     da/dN2
                                              da/dN1


                  ao


                              Cycles, N
                    log(da/dN)




          A
                  Threshold Region
                  Slow Growth
                             da
                             dN


                      m
                                            Paris Region


                                 A(K) m
                                            Stable Growth




log(K)
                                                            Paris Law




          Fast Fracture Region
          Rapid-unstable Growth
Crack Growth Rates and
Microstructural Features
Fractographic Evidence of Crack Growth




                                 fatigue
                                 striations




     10 mm
  Fatigue Striations in Al-alloy:
5 small cycles between overloads




                     Crack Growth
                     direction
Crack Growth Mechanisms


    No Load
                     Load reduced
              Slip


    Loaded           No Load




    Max Load
                     Loaded again
Model for
Crack Growth
        4       6
    2

1
            5       7
               Crack Propagation Life, Np
   Total fatigue life is the sum of the crack initiation life and the
   crack propagation (growth) life.

                        Nf  Ni  N p

For some components, where stress levels are high and/or the critical
crack size is small, the crack propagation life is neglected in design.
For other structures, including pressure vessels, ship structures,
transport aircraft, etc. the crack growth life may be a substantial
component of total life.
                            ac
                            da
                 Np           m
                      a o A(K)
            Limits of Integration
• The initial crack length, ao, is usually either
  found by inspection or a reasonable minimum
  size of crack is assumed for the analysis.

• The critical crack size is found from:
                                     2
               1       Kc       
           ac                  
                 f (a/W)  max 
                                
• Where max is the maximum stress.
  (it’s not the stress range)
 Procedure for Constant Amplitude
   Crack Growth life Calculation
• Obtain appropriate crack growth rate data
  for material, environment and stress ratio
• Determine starting crack size, ao
• Determine critical crack size, ac
• Determine K for starting crack size, ao. If
  K< Kth then crack will not grow
• If K> Kth then integrate to get crack
  growth life. (Can conservatively use Paris
  Law, if appropriate)
   General Paris Law Solution for Np
       ac
                      da
Np     A f (a/W)
       ao                     a )    m




 Special Case: m=3; f(a/W) constant=Y

            2           1    1 
Np                            
     A (  ) Y
       3/ 2   3  3
                        ao
                             ac 
                                 
           General Solution:
• A more general solution will include the
  actual growth rate data in the threshold and
  near-threshold region.
• If the starting crack size is relatively small,
  this will represent a major portion of growth
  life, so it may be un-economical to neglect it.
• The life in the fast fracture region is
  generally neglected. Use this data carefully.
Try it!
• A fatigue crack 1.5 mm long has been discovered in a
  main wing spar of a CC-130 Hercules undergoing
  structural tear down and inspection. Given the loading,
  material and geometry shown, estimate the number of
  flying hours to fracture, and comment on the results.

               7075-T73511 al alloy
               Kc (6mm) = 40 MPam
               Sy = 455 MPa
               A = 1.3x10-10 m/cycle
               m=3
               Y = 1.27 (assume constant)
S
                  Crack
              a




Section A-A Through Spar (inches)
                                        10
                Loading              R     0.133
                                        75
Stress (MPa)


               75




               10
                0
                                                     time

                          100 cycles=1 flying hour
 OK...                    ac
                                  da
                    Np  
                         a o A( Y a )
                                        m


 • ao = 1.5 mm, find ao

                2                2
     1  Kc    1  40 
 ac   YS     1.27( 75 )   0.0561m (56.1mm)
                              
       max 
                             

Stress Range,  = max-min = (75 - 10) MPa = 65 MPa
For m=3, Y constant:

                2      1     1 
 Np                            
      A3 / 2 (  )3 Y 3
                       ao
                             ac 
                    2              1       1   
 Np        10 3 / 2         3 
                                               
      1.3x10  ( 65 ) ( 1.27 )  0.0015
                        3
                                          0.0561
 106000 cycles
                  1hr
 106000 cycles           1060 flight  hrs
               100cycles
Crack Growth Curve




                           95000 cycles
      5 mm at half life!   at half length!
      a/ac =15%            N/Np =89%
 Comments & Observations
• There is a substantial period of crack
  growth for this component. The fatigue
  crack can be monitored, inspected, and the
  component can be replaced or repaired after
  500 more hours of operation.

• Half-life (factor of safety on life) is a safer
  criterion than length, because cracks grow
  too rapidly as they become longer.

				
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