Linear Damage Accumulation

If it is assumed that cycles of stress level 5i are applied in a number ni N such that the initial crack grows from a to ai a without producing failure 

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Fig. 8.26 Nonlinear damage progression with linear damage accumulation characteristic of Stage II of fatigue...

Mechanistically, the formation of malonaldehyde and TBA-active DNA-bound material is not yet fully understood. While free malonaldehyde increases linearly with dose (G = 0.1 x 10 7 mol J 1 = 1.7% of OH), the efficiency of forming TBA-active DNA-bound material markedly decreases with increasing dose, that is when the integrity of the DNA is getting lost upon damage accumulation. At one stage, 02- seems to play a role, since the yield of total TBA-active material is G = 0.3 x 10"7 mol J-1 in N20/02-saturated and 0.2 x 10"7 mol J 1 in ( -saturated solution (at 100 Gy). As compared to N20/02, the OH yield is about half in 02-saturated solutions, but the 02 yield is markedly enhanced (Chap. 2.2). This could point to hydroperoxides as precursors of the TBA-active material, but details remain open. Yet, a G value of 0.2 x 10"7 mol J 1 (02-saturated) indicates that this type of lesion is not an unimportant one, about 7% of OH. 

If Eq. 1.10 is not valid, the assumption of damage accumulation according to Eq. 1.8 is also no longer valid. Equation 1.8 then shifts to a non-linear relation of the type... 

Fig. 8.17 Linear damage progression and accumulation according to the Palmgren-Miner rule...

Fig. 8.27 Damage evolution in Stage I and II of fatigue. In Stage I damage progression and accumulation is not linear and depends on stress amplitude. In Stage II damage progression is not linear, but accumulation is linear...

Fig. 23 Illustration of the nonlinearity of the accumulated damage and inadequacy of the linear approach for extrapolating crack propagation for future operating periods.

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