Common Mathematical Model of Fatigue Characteristics

Z. Maléř, S. Slavík, T. Marczi, M. Růžička


This paper presents a new common mathematical model which is able to describe fatigue characteristics in the whole necessary range by one equation only:
log N = A(R) + B(R) ∙ log Sa
where A(R) = AR2 + BR + C and B(R) = DR2 + AR + F.
This model was verified by five sets of fatigue data taken from the literature and by our own three additional original fatigue sets. The fatigue data usually described the region of N 104 to 3 x 106
and stress ratio of R = -2 to 0.5. In all these cases the proposed model described fatigue results with small scatter. Studying this model, following knowledge was obtained:
– the parameter ”stress ratio R” was a good physical characteristic
– the proposed model provided a good description of the eight collections of fatigue test results by one equation only
– the scatter of the results through the whole scope is only a little greater than that round the individual S/N curve
– using this model while testing may reduce the number of test samples and shorten the test time
– as the proposed model represents a common form of the S/N curve, it may be used for processing uniform objective fatigue life results, which may enable mutual comparison of fatigue characteristics.


fatigue characteristics; mathematical model; stress ratio R

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague