Applet to calculate crack growth in either a finite plate with a centre crack or a finite plate with an elliptical surface crack subject to cyclic tensile stress.

 

Notes: h/B should be greater than 1.5.
From the shape of the sigmoidal crack growth curve, see notes, it can be seen that for small ranges of stress intensity factors (stage 1, Crack Formation) those below the threshold stress intensity factor range, dKth, the crack growth rate is zero and the equations used in the computation do not apply. For this reason the dK value for the first increment should be checked against published dKth values.

For crack growth calculations: Best explained by an example.
Enter the input values in the appropriate units in the white fields opposite the green labels. A value for 'c' is not needed for the centre cracked plate computation.
The value of 'C' entered should be for calculating crack growth rates in m/load cycle. To convert 'C' values between the common units, see the applet in Section 3.5 of the page on 'Failure Under Cyclic Loading - Fatigue and Fracture - Crack Growth Rates'.
To calculate the number of load cycles necessary to grow a crack of length a = 4mm to a length of 20mm using intervals of 1mm, enter a value of 4.5mm in the top input field, enter 1mm in the next to bottom input field (increment) and 16 in the botton input field (Number of increments). For intervals of 2mm, values of 5,2 and 8 should entered in these fields.

Click on whichever yellow button is appropriate.

In the results area on the right, the column Fs/(Q)0.5 is the combination of factors that when multiplied by the stress (based on the gross area) and (3.14159 x crack length)0.5 gives the stress intensity factor. The stress intensity factor range is shown in the dK column.
The 'Inc Cycles' column shows the number of cycles needed to grow the crack through the crack growth increment. The cumulative total of load cycles is shown in the right hand column.

The size of the plastic zone in plane stress is computed as: (stress intensity factor/yield stress)2/3.14159.

Notes for elliptical surface crack:
The equations used for this applet were based on (empirical) equations in ref. [1] which draws together results from finite element and boundary element analysis by several researchers. The equations cover a/t ratios of 0 to 1, and c/B values less than 0.5
a/c ratios from zero to less than or equal to 1 can be used, but if starting with 'c' greater than 'a', the computation assumes that once 'a' = 'c', then 'c' increases as 'a' does, remaining equal to 'a', as this tends to be the equilibrium shape as the crack grows.

To determine the stress intensity factor for a specific crack size and stress: Enter values for the first 7 inputs, then the same value for the maximum applied stress and the stress range fields. Values for 'C' and 'm' must be entered. In the last two boxes enter 1. Click the appropriate yellow button. The value in the dK column in the right hand results panel will be the stress intensity factor.

References
1. 'Stress-Intensity Factor Equations for Cracks in Three-Dimensional Finite Bodies', by J C Newman, Jr. and I S Raju, NASA Langley Research Centre, Hampton, Virginia, 23665.


David Grieve, 10th March 2013