I try to model fatigue crack growth in aluminium 2024-T3 alloy.
I have plate specimens with finite width 'W' and a circular cut-out with an additional notch, as shown in Figure.
1. The number of fatigue cycles for crack initiation could be predicted by Stress Concentration Factor, but how to find a suitable equation for that complicated notch?
2. When calculating fatigue crack growth rate by Paris-Erdogan equation:
da/dN = C * (dK) ^m
the difference in Stress Intensity Factor (dK) in a specified fatigue cycle should be calculated for crack length caused by fatigue crack growth 'a_CG'? Or as a total crack length, taking into account also initial crack length ('a_CG' + 'a_ini') ?
You should keep some points in mind while performing fatigue crack growth.
1: Paris' equation is applicable for the stable crack growth region only, it is not applicable for the crack initiation from a notch. And SIFs for this geometry and loading can be found easily from a fracture simulation using software like ANSYS, ABACUS.
The notch given in the figure is called U-notch. And Notch Stress Intensity Factor (NSIF) is used to characterize the stress intensity around the notch. You read some available literature.
2: For Paris's law, only the crack increment (delta(a)) per cycle matters, not the full crack length a_ini+a_CG.
Only the crack growth from a current position to next position matters irrespective of reference crack length.
3: For your simulation, you assume the crack starting from the middle of the notch. Create a suitable small initial crack (eg. 1mm-2mm ) ahead of the notch. And calculate the SIFs for that configuration.
Shiv Sahaya Shukla than you for the answer.
Stress concentration factors can be used to predict crack initiation (only for short cracks, e.g. 1mm) since that short cracks are not crucial in the final result of the crack growth.
2. Yes, Paris law is applied to predict crack increment 'da', but in the equation, there is a deltaK 'dK'. However, the magnitude of 'dK' depends on the stresses as well as an actual crack length. And that is my question if, in the Paris equation, which relates da/dN with dK, the crack length should be the total crack or just length of a crack caused by the fatigue.
Konrad Dadej First thing stress concentration factors (SCF) and stress intensity factors (SIF) are different concepts. For the crack analysis we use SIFs. And for the threshold values for crack initiation we use SCF (NSIF).
For the initiation of the crack during fatigue loading we need stress concentrated zones defined by stress concentration factors. Which only tells about the fact that the probability of crack initiation is very high near the stress concentration zone, that is why we intentionally create a sharp notch in our specimens for the fatigue crack growth studies. The notch gives the advantage of fixing the crack initiation point before hand.
The Paris' law is applicable only in the stable crack growth regime II for the sigmoidal curve obtained from fatigue test.
And finally the dK calcualtion is not the difference between the SIFs values at different crack length. It is the difference of maximum SIF and minimum SIF for a particular loading cycle. Kmax-Kmin =(Pmax-Pmin)sqrt(pi*a)/(area under load). at a fixed crack length.
Shiv Sahaya Shukla
Yes I agree with you. Indeed, dK is a difference between K_max and K-min, which is dK = K_max - K_min. However, if you will look on your equation, the K_max is also dependent on the crack length because of the term (pi*a).
Therefore, calculating the K_max according to the Feddersen formula:
K_max = σ_max * sqrt(pi*a) * sqrt(sec((pi*a)/W))
where
σ_max = Pmax / (cross section area)
and a should be calculated as a = a_CG or a = a_CG + a_ini ?
Konrad Dadej
the total crack length under calculation will be a=a_cg+a_ini.
Whenever there is a crack ahead of the notch, the crack length will be the total length of separated region from the beginning. Notch will have some effect on the stress distribution, but that is always taken care by SIFs values.
Dear Konred,
Generally, for 2024-T3 most common aluminum copper heat treated alloy values have stress intensity factor in range of 36-40 MPa√m and △K= 10-11 MPa√m.(you can check with heat treatment materials ASM handbook). Use SENT specimens for the same.
Use appropriate formula for calculation. AFGROW developed code by NASA is used for simulation of fatigue crack growth with and without residual stress. Many models for fatigue crack growth are implemented so far. The effect of loading ratio and heat treatment (tempered situation) for aluminum alloy 2024 can be investigated. The effect of condition temper for aluminum alloy on fatigue crack growth rate can be presented using paris....miller and take the slope, use the equation da/dn to find your values. find f= kop/Kmax, use this value in da/dn calculation.
Refer this paper: file:///C:/Users/3020/Cookies/Desktop/Downloads/FatiguecrackgrowthofdifferentAluminiumalloys2024.pdf
Hope it is helpful to you.
Ashish
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