While trying to verify some AFGROW solutions for the Single Corner Crack at Hole in bending, I was comparing the Stress Intensity Factors (SIFs) that I compute in a separate Excel spreadsheeet (VBA). My VBA program computes the SIFs from the original Newman Raju curve fits in Chapter 9 of Computational Methods in the Mechanics of Fracture, 1986. I am using version 184.108.40.206 06/29/2006, which I think is last version before AFGROW got really big (since it didn’t include the Fawaz curve fits for corner crack(s) at a hole)—I am running AFGROW on an old computer which is severely RAM limited compared to 2010 computers.
There are actually 3 references given in the AFGROW help for this crack scenario and the bending load, The first one can be downloaded from the AFGROW site, http://afgrow.net/downloads/ddownload.aspx, the 2nd can be downloaded from a NASA website, and the third is unavailable.
1) Newman, J.C., and Raju, I.S., "Stress Intensity Factor Equations for Cracks in Three-Dimensional Bodies Subjected to Tension and Bending Loads," Chapter 9, Computational Methods in the Mechanics of Fracture, Elsevier Science Publishers B.V., 1986
2) Zhao, W., J. C. Newman, Jr., M. A. Sutton, X. R. Wu, and K. N. Shivakumar, "Analysis of Corner Cracks at Hole by a 3-D Weight Function Method with Stresses from Finite Element Method," NASA Technical Memorandum 110144, July 1995.
3) Zhao, W. and Newman, Jr., J. C., Electronic Communication, Unpublished NASA Langley Research Center Results, 24 February 1998.
I noticed substantial differences between what I was computing with my VBA (20% or more) and what AFGROW was computing, suggesting that whatever equations were in Ref. 2 and 3 were affecting my results:
My configuration was double (n=2) or single corner crack (n=1), so I show results for both:
VBA VBA AFGROW AFGROW
n SIFc SIFa SIFc SIFa
1 3.95091 3.6774 3.952 3.678
2 4.01409 3.73621 4.112 3.736
SIFc is the SIF for crack “c” and SIFa applies to crack “a.” VBA are my spreadsheet solutions. Geometry was 2 inches wide, thickness 0.25 inches, hole diameter 0.25 inches, and both crack dimensions are 0.05 inches. Bending stress is 10 ksi, no tension (BSR=1, TSR=0, no bearing). Interesting that all these SIFs are close except for the double corner crack, SIFc.
After double checking all of my equations, I contacted AFGROW support to try to resolve the differences. Turns out there is a 4th reference not mentioned in Help that summarizes the equations used to modify the bending SIFs from the Ref. 1 above that you can download from AFGROW’s site:
Modification of Stress Intensity Factor Equation for Corner Cracks From a Hole Under Remote Bending by Zhao and Newman.
Jim Harter gave me this document, which contains modifications to 3 sub-equations in the Newman Raju curve fits, coded those into my VBA; still had a difference. I went to another computer that had a more recent version of AFGROW, 220.127.116.11 07/26/2010, which gave me the following comparison:
VBA VBA 18.104.22.168 22.214.171.124
n SIFc SIFa SIFc SIFa
1 3.95091 3.6774 3.9509 3.6774
2 4.01409 3.73621 4.0141 3.7362
Turns out there is a small undocumented bug in this old version of AFGROW; mystery solved.