Page 312 - Shigley's Mechanical Engineering Design

bud29281_ch06_265-357.qxd 11/30/2009 4:23 pm Page 287 pinnacle s-171:Desktop Folder:Temp Work:Don't Delete (Jobs):MHDQ196/Budynas:

Fatigue Failure Resulting from Variable Loading 287
12
Marin identified factors that quantified the effects of surface condition, size, loading,
temperature, and miscellaneous items. The question of whether to adjust the endurance
limit by subtractive corrections or multiplicative corrections was resolved by an exten-
sive statistical analysis of a 4340 (electric furnace, aircraft quality) steel, in which a
correlation coefficient of 0.85 was found for the multiplicative form and 0.40 for the
additive form. A Marin equation is therefore written as

S e = k a k b k c k d k e k f S e (6–18)

where k a = surface condition modification factor
k b = size modification factor
k c = load modification factor
k d = temperature modification factor
k e = reliability factor 13
k f = miscellaneous-effects modification factor
S = rotary-beam test specimen endurance limit

e
S e = endurance limit at the critical location of a machine part in the
geometry and condition of use
When endurance tests of parts are not available, estimations are made by applying
Marin factors to the endurance limit.

Surface Factor k a
The surface of a rotating-beam specimen is highly polished, with a final polishing in the
axial direction to smooth out any circumferential scratches. The surface modification
factor depends on the quality of the finish of the actual part surface and on the tensile
strength of the part material. To find quantitative expressions for common finishes of
machine parts (ground, machined, or cold-drawn, hot-rolled, and as-forged), the coordi-
nates of data points were recaptured from a plot of endurance limit versus ultimate
14
tensile strength of data gathered by Lipson and Noll and reproduced by Horger. The
data can be represented by
k a = aS b ut (6–19)

where S ut is the minimum tensile strength and a and b are to be found in Table 6–2.

12 Joseph Marin, Mechanical Behavior of Engineering Materials, Prentice-Hall, Englewood Cliffs, N.J.,
1962, p. 224.
13 Complete stochastic analysis is presented in Sec. 6–17. Until that point the presentation here is one of a
deterministic nature. However, we must take care of the known scatter in the fatigue data. This means that
we will not carry out a true reliability analysis at this time but will attempt to answer the question: What is
the probability that a known (assumed) stress will exceed the strength of a randomly selected component
made from this material population?
14 C. J. Noll and C. Lipson, “Allowable Working Stresses,” Society for Experimental Stress Analysis, vol. 3,
no. 2, 1946, p. 29. Reproduced by O. J. Horger (ed.), Metals Engineering Design ASME Handbook,
McGraw-Hill, New York, 1953, p. 102.