Fatigue Crack Growth - Paris Law This page is not supported in this days.
Fatigue Crack Growth - Paris Law
Fatigue damage often appears in the form of cracks.
If the crack reaches a critical length ,at which the "Stress Intensity Factor" of the "strain energy release rate" is equal to the critical value Kc or Gc,
then catastrophic failure would appear.
Failure damage can be appears in two parts:
1. Crack ignition part
2. The crack growth.

The fatigue life is composed of numbers of cycles of load application,
until the numbers of cycles until the "small" crack, and numbers of cycles 
until the crack  start to growth.

We are interested to find the crack growth pre cycle of load application, da/dN
under Mode I loading.
The crack growth (da/dN) is a function of  "Srtess Intensity Factor", Ki, 
or a range of stress intensity factor, dK:

da/dN=f(dK)

 * Constant Stress Amplitude

  Stress range:        dS = Smax-Smin
  Stress amplitude:  Sa = 0.5*dS
  Mean stress:         Sm = 0.5*(Smax+Smin)
  Stress Ratio:         R = Smin/Smax
  Fatigue life:           Nf - Number of cycles to failure.
 

  Smax = Sm + Sa
  Smin  = Sm - Sa
  dS      = Smax*(1-R)
  Sm     = 0.5*Smax*(1+R)
  

  Paris Law:   da/dN = C*dK^m

  And we defined:
                        dK = Kmax - Kmin

  SI Units:
                              K - [MPa * m^0.5]
                      da/dN - [m / cycle]

  US Units:
                              K - [ksi * in^0.5]
                      da/dN - [in / cycle]

The constants of some kind of steel:

  SI Units:
                  C - [ m / (cycle*MPam^0.5) ]
                  m - [ no unit ]
 
Marerial
R
C
m
2024-T3
1
1.6e-11
3.59
2024-T3
0.5
3.15e-11
3.59
 Martensitic Steel
0
1.36e-10
2.25
Austenitic Steel 
0
5.6e-12
3.25


  US Units:
                    C - [ in / (cycles*kpi*in^0.5) ]
                    m - [ no unit ]
 
Material
C
m
Martensitic Steel
0.66e-8
2.25
Austenitic Steel 
3.0e-10
3.25
Ferrite/Pearlite Steel 
3.6e-10
3.0

Actualy,I didn't find any demo software that can be download,
and work with.


My Work:
I made a few test on asphalt , and we don't work according the ASTM standarts and models,
because I can't make this models in asphalt.
Also, the results in asphalt, is not "beautiful" like in metals.

I put the results in Excel, and made a chart : da/dN vs. dK, 
and find the constant: Kic,c and m




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Email : dansc@nana.co.il