fatigue crack growth

Having glanced at the web site I can see that it might be useful to shed some light on fatigue crack growth and crack closure based concepts.

    In the early 70’s Elber [1] hypothesised that the R ratio effect seen in constant amplitude fatigue tests was due to plasticity related crack closure and he presented an empirical formulation to account for this effect. Following this work a number of people have proposed that, for crack growth under constant amplitude loading, the concept of an opening stress intensity factor and crack closure is based on sound fundamental mechanics concepts. This methodology uses a ΔKeffecive (=Kmax  - Kopen) versus da/dN curve that is (effectively) associated with constant amplitude load tests and is thought to coincide with the ΔK versus da/dN curve as measured at high R ratio (R > 0.7) tests. This approach thus rests on several assumptions, viz: that similitude is valid, that the  crack closure hypothesis is valid and that the mechanisms associated with constant amplitude testing also holds for the problem of interest. It is further implicitly assumed that the physical process responsible for R ratio effects, as evidenced in experimental data, is due to crack closure and furthermore to crack closure alone.     With this in mind can I recommend that you read references [2, 3].  The experimental data presented in these works reveal that the crack growth mechanisms under variable amplitude loading and those seen under constant amplitude loading differ.  

    These experimental results raise the question:

  If closure is seen under constant amplitude tests does it mean it will hold under variable amplitude loading where the mechanisms of crack growth differ?  

Next consider the question: Is crack closure universal?

    To address this question you need to read the paper by Forth, James, Johnston, and Newman [4]. Note that this is the same Newman who developed FASTRAN. This work reveals, and subsequently states, that crack closure does not apply to high strength aerospace steels. Reference [5] subsequently shows that crack closure does not apply to Mil Annealed Ti-6Al-4V.  Reference [6] reveals that there were minimal R ratio effects in a rail locomotive steel. Hence closure didn’t apply for that particular steel. If you read the paper by Frost and Dugdale [7] you will see that the mild steel specimens tested in [8] also had (essentially) no R ratio effect and hence exhibited no closure. Thus experimental data reveals there are a number of materials for which closure does not apply.  

     Consequently the answer to the questions is:  No, the crack closure hypothesis is not universal even when the tests are constant amplitude fatigue tests. This does not mean that closure does not occur for some materials, just that the hypothesis is not universal.

  Now read the presentation by Scott Forth at NASA [9].  Here NASA shows that the fatigue threshold ΔKth is a function of the test geometry, and as such is not unique. This means that the Region I crack growth law is a function of the test geometry. This, in turn, means that similitude does not hold in Region I. Indeed, for the D6ac steel considered in [8] and also in [4] Forth and Jones [9] have shown that crack growth in Regions I and II conforms to a non-similitude based growth law.  

Since for practical problems we are dominantly interested in Region I crack growth (any design that starts off with crack growth in Region II will have a very short life!) this means that similitude can’t be routinely assumed in Region I. This finding also applies to non-aerospace materials, see [10] which reveals that crack growth in rail steels and Grade I ductile iron follows a non-similitude crack growth law. Thus Elber’s, Newman’s, Paris’, etc growth laws, which are all based on the concept of similitude,  can’t be assumed to be valid in Region I. 

      This begs the question: What happens if we use closure based laws to predict the growth of short cracks under representative in-service load spectra? To answer this question read the paper by Jones et al [11]. This paper shows that using FASTRAN, a closure based program developed by Newman, the predictions are out by a factor of approximately 7. Furthermore the predicted life is not conservative, i.e. the closure based prediction is 7 times too big.  

    If we draw all of these experimental findings together we see that:

        ·         The crack growth mechanisms under variable amplitude loading and those seen under constant amplitude loading differ.  

(Thus the usefulness of constant amplitude da/dN versus ΔK data for addressing variable amplitude problems must be questioned.)

        ·         The experimental data reveals that crack closure is not universal.  

  ·         The assumption that the physical process responsible for R ratio effects is due to crack closure and furthermore to crack closure alone has not been universally established.

        ·         Crack growth laws that are based on the concept of similitude can’t be assumed to be valid in Region I.   

     So in summary, using similitude based laws to predict in-service growth of small cracks and hence the life of operational equipment should be avoided.

  REFERENCES

[1]                     Elber W., The significance of fatigue crack closure, Damage Tolerance of Aircraft Structures, ASTM STP-486; 1971: 230-242.

[2]                     White P., Barter SA., and Molent L., Observations of crack path changes under simple variable amplitude loading in AA7050-T7451, Int. Journal of Fatigue, 30, (2008) 1267–1278.

[3]                     Barter SA. and Wanhill R., Marker loads for quantitative fractography (QF) of fatigue in aerospace alloys, NLR-TR-2008-644, November 2008.

[4]                     Forth S.C., James M.A., Johnston W.M., and Newman, J.C. Jr., Anomalous fatigue crack growth phenomena in high-strength steel, Proceedings Int. Congress on Fracture, Italy, 2007.

[5]                     Jones R., Farahmand B. and Rodopoulos C., Fatigue crack growth discrepancies with stress ratio, Theoretical and Applied Fracture Mechanics, (2009), Volume 51, Issue 1, pp 1-10.

[6]                     Jones R., Pitt S. and Peng D, The Generalised Frost–Dugdale approach to modelling fatigue crack growth, Engineering Failure Analysis, Volume 15, (2008), pp 1130-1149.

[7]                     Frost N.E., Dugdale D.S., The propagation of fatigue cracks in test specimens, Journal Mechanics and Physics of Solids, 6, (1958), pp 92-110.

[8]                     Forth SC., The purpose of generating fatigue crack growth threshold data, NASA Johnson Space Center, available on line at http://ntrs.nasa.gov/

[9]                     Jones R. and Forth SC., Cracking in D6ac Steel, Proceedings International Conference on Fracture, Ottawa, 2009.

[10]                 Jones R, Chen B. and Pitt S., Similitude: cracking in steels, Theoretical and Applied Fracture Mechanics, Volume 48, Issue 2, (2007), pp 161-168. 

[11]                 Jones R., Molent L, and Pitt S., Crack growth from small flaws, International Journal of Fatigue, Volume 29, (2007), pp 1658-1667.

By: Rhys Jones and Susan Pitt