Page 290 - Aircraft Stuctures for Engineering Student

References 271

The curves represented by Eq. (8.71) may be divided into three regions. The first
corresponds to a very slow crack growth rate (< m/cycle) where the curves
approach a threshold value of stress intensity factor AK,, corresponding to
4 x lO-”m/cycle, i.e. no crack growth. In the second region (10-8-10-6m/cycle)
much of the crack life takes place and, for small ranges of AK, Eq. (8.71) may be
represented by
du
- C(AK)” (Refs 10, 12) (8.74)
=
dN
in which C and n depend on the material properties; over small ranges of da/dN and
AK, C and n remain approximately constant. The third region corresponds to crack
growth rates > m/cycle, where instability and final failure occur.
An attempt has been made to describe the complete set of curves by the relationship
da - C(AK)” (Ref. 13) (8.75)
dN- (1 - R)Kc - AK
in which K, is the fracture toughness of the material obtained from toughness tests.
Integration of Eqs (8.74) or (8.75) analytically or graphically gives an estimate of
the crack growth life of the structure, that is, the number of cycles required for a
crack to grow from an initial size to an unacceptable length, or the crack growth
rate or failure, whichever is the design criterion. Thus, for example, integration of
Eq. (8.74) gives, for an infinite width plate for which Q = 1.0

for n > 2. An analytical integration may only be carried out if n is an integer and Q is
in the form of a polynomial, otherwise graphical or numerical techniques must be
employed.

1 Zbrozek, J. K., Atmospheric gusts ~ present state of the art and further research, J. R~J.
Aero. Soc., Jan. 1965.
2 Cox, R. A,, A comparative study of aircraft gust analysis procedures, J. Roy. Aero. Soc..
Oct. 1970.
3 Bisplinghoff, R. L., Ashley, H. and Halfman, R. L., Aeroelasticity, Addison-Wesley
Publishing Co. Inc., Cambridge, Mass., 1955.
4 Babister, A. W., Aircraft Stability and Control, Pergamon Press, London. 1961.
5 Zbrozek, J. K., Gust Alleviation Factor, R. and M. No. 2970, May 1953.
6 Handbook of Aeronautics No. 1. Structural Principles and Datu, 4th edition, The Royal
Aeronautical Society, 1952.
7 ESDU Data Sheets, Fatigue, No. 80036.
8 Knott, J. F., Fundamentals of Fracture Mechanics, Butterworths, London, 1973.
9 McClintock, F. A. and Irwin, G. R., Plasticity aspects of fracture mechanics. In: Fructure
Toughness Testing and its Applications, American Society for Testing Materials, Phila-
delphia, USA, ASTM STP 381, April, 1965.
10 Paris, P. C. and Erdogan, F., A critical analysis of crack propagation laws, Trans. An?. Soc.
Mech. Engrs, 85, Series D, No. 4. Dec. 1963.