2015-08-13
303
Durability of structures is connected with degradation processes such as fatigue, creep and others. "Stress - Number ofциклы на неудачу» (S-N) диаграмма описывает усталость металлов. Усталость прочности s-1 соответствует горизонтальный сегмент кривой. Если нет горизонтального сегмента, значение можно предположить при N = 106 или N = 107. На высоких напряжений усталость жизни и его дисперсия малы. При низком давлении функция плотности вероятности не симметрично и его дисперсия больше.
Initiation and growth of fatigue cracks occur under cyclic loading. The figure shows an experimental diagram "fatigue crack growth rate vs stress intensity factor" for two butt-welds made from different steels. The smaller the fatigue crack growth rate, the better. The smaller the fatigue crack growth rate at small values of stress intensity factor, A, the longer the fatigue macrocrack growth is in the initial stage.
The dispersion increases with time for fatigue cracks. Short cracks have no significant increase, but the longer cracks grow faster. Theoretical distributions for fatigue crack go from zero to infinity. This means that the theoretical reliability measure cannot be equal to 1.0.
A fatigue crack grows in a structural element from initial size ao to its critical size ac. The reliability is approximately equal to 1 for a small crack. The fatigue crack reaches its critical size at failure and the reliability decrease. When the means coincide, the reliability is equal to 0.5.
Airplane fuselages are periodically inspected for fatigue crack identification. Probability of crack detection depends on the method of nondestructive testing (NDT) and the inspection interval. Probability of crack detection is approximately equal to 1 for short intervals and decreases as the intervals increase. The ultrasonic NDT is the most effective technique.
The figure shows the dependence of maximum stress on the number of cycles sustained by an element of a pressure vessel. The engineers can suppose service at different stress, for example:
1000 MPa - 100 cycles
500 MPa - 500 cycles
100 MPa - 50000 cycles
The element fails if the sum damage parameter exceeds 1.
In our case:
w = 100/200 + 500/1000 + 50000/100000 = 0.5 + 0.5 + 0.5 = 1.5 > 1.0
The element fails.
