ZAHORANSKÝ, R., STEIN, J.: Modelling a simple oscillatory system with friction under bi-axial base random excitation 117 BAKHSHANDEH, K., SARANJAM, B.: Orthotropy ratio effect on dynamic response of a cylinder tube under moving pressure 133 KLIMAN, V.: A probabilistic approach to fatigue life estimation under biaxial non-proportional random loading. Part I. Methodology 147 KLIMAN, V.: A probabilistic approach to fatigue life estimation under biaxial non-proportional random loading. Part II. Model experiment 168

RADÚZ ZAHORANSKÝ, JURAJ STEIN

KAMBIZ BAKHSHANDEH, BAHADOR SARANJAM

Part I. Methodology

VLADIMÍR KLIMAN

A new method of fatigue life distribution function prediction of the structure has been
proposed for the random non-proportional biaxial loading. The method is based

– on the probability approach to respect the non-proportionality between normal
(s) and
shear (t) stress under random biaxial loading, and

– on the probabilistic interpretation of the loading characteristics and cyclic material
properties in fatigue damage calculations.

The suggested methodology (Part I) of the structure fatigue life calculation takes into account
the directional nature of fatigue damage, enables to calculate the fatigue life distribution
function (FLDF) for an arbitrary plane and, on the base of comparison of fatigue life
distribution functions calculated for the individual planes, enables to establish a plane with the
maximum fatigue damage. The resulting FLDF (calculated for the most damaged plane and
representing the service fatigue life of the structure) respects the random nature of cyclic
materials properties, the random nature of the loading process and the random nature of the
relation between normal (s) and shear
(t) stress during the loading – non-proportionality in
loading. The proposed methodology of life calculation is demonstrated and discussed on the
concrete model example presented in Part II.

Part II. Model experiment

VLADIMÍR KLIMAN

Concrete procedure of fatigue-life distribution function estimation for biaxial
non-proportional random loading according to the method proposed in Part I is demonstrated on
the model example. Straining of a critical spot of the structure is simulated by two
independent random processes:
s_{x}(*t*) – time behaviour of normal stress, and
t_{z}(*t*) – time
behaviour of shear stress. Computed fatigue-life distribution function for combined loading
by the
s_{x}(*t*)
and
t_{z}(*t*)
processes, using the method proposed in Part I, has been compared with
the experiments and with the evaluation of the fatigue life for loading by the
s_{x}(*t*)
process only. Model experiment proved that the presented method of life estimation for biaxial non-proportional
random loading is simple to apply. Computed representative fatigue-life
distribution function enables to assess the fatigue reliability with probability interpretation.