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# History of Bueckner’s principle?

I am hoping someone has some historical knowledge of some

interesting mechanics, or just an interest to discuss it. A superposition principle is widely used to solve crack problems, with illustrations like these:

http://ars.sciencedirect.com/content/image/1-s2.0-S0142112308002211-gr1.jpg

http://ars.els-cdn.com/content/image/1-s2.0-S0142112399000778-gr2.gif

Bueckner proved this principle in 1958 [1] but never published a figure

similar to those we see. He did explain it in text, such as “….. Any [elastic]

crack or notch problem can be reduced to one where the external load appears in

the form of tractions distributed over the faces of the crack.[2]” The first drawing similar to

the modern ones that I could find that was attributed to Bueckner was by

Barenblatt in 1962 [3]. Paul Paris’ landmark 1961 paper

on fatigue crack growth [node/7705]

shows a similar figure that he credits to some report he wrote at Boeing in

1957 [4]

Anybody have any more history of this principle? I would not

be surprised if it was used well before Bueckner proved it. Any earlier

published figures that show the principle? Does anyone have Paris’ 1957 report?

[1] Bueckner, H., 1958, "The propagation of cracks and the energy of elastic

deformation," Transactions of the American Society of Mechanical

Engineers, 80, pp. 1225-1230.

[2] Bueckner, H. F., 1973, "Field singularities and related integral

representations," Mechanics of Fracture G. C. Sih, ed., pp. 239-314.

[3] Barenblatt, G. I., 1962, "The Mathematical Theory of Equilibrium Cracks in

Brittle Fracture," Advances in Applied Mechanics, H. L. Dryden, T. v.

Kármán, G. Kuerti, F. H. v. d. Dungen, and L. Howarth, eds., Elsevier, pp.

55-129.

[4] P. C. *Paris*,

"*The Mechanics of Fracture Propagation and Solutions* to Fracture

Arrestor Problems," Document No. D2- 2195, Boeing Co., 1957.

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## Comments

## Obscure Paul Paris reference

Looks like I'm not getting any takers.

Anybody have that reference 4: P. C.

Paris, "The Mechanics of Fracture Propagation and Solutionsto FractureArrestor Problems," Document No. D2- 2195, Boeing Co., 1957.? I would love to get a copy.

Michael B. Prime, Los Alamos, New Mexico

http://public.lanl.gov/prime/

## Mike, How are things

Mike,

How are things at Los Alamos?

I don't have much insight into the history. If you read Paris contribution in [1], he says this method was a novel application of Castigliano's Theorem. It may be useful to look for applications of Castigliano's Theorem to notches, inclusions, etc. that predate the Bueckner and Paris publications, or maybe the references from Eshelby's inclusion work.

It might also be useful to discuss this with Fred Smith - he was at Boeing after his PhD work. That was some time after the Paris publication, but I'm sure Fred was well aware of the work. His email is on his CSU webpage.

[1]Fracture Research in Retrospect: An Anniversary Volume in Honour of G.R. Irwin's 90th Birthday, pp 227-236

Jobie

## Thanks

Hey Jobie!

Thanks for the good ideas. I will contact Fred. I am on travel this week, so next week.

Things are fine in Los Alamos. How about at Ansys?

Michael B. Prime, Los Alamos, New Mexico

http://public.lanl.gov/prime/