10 4 10 5 10 6 10 7 10 8 10 9 spectrum cumulative frequency of applied loading stress SaD Sa ^ number of cycles N (log) k*: slope of the S-N-curve for variable. ampl. S-N-curve (constant amplitude) LiuZenner MinerOriginal MinerElemetary MinerModified stress amplitude S [MPa] a SaD 1 2 k: slope of the S-N-curve for constant amplitude m: slope of the crack growth S-N-curve for constant amplitude Sa ³ SD Sa < SD original: k* = k k* = ¥ elementary: k* = k k* = k modified by Haibach: k* = k k* = 2 k –1 modified by Liu/Zenner: k* = (k + m) / 2 k* = ¥ Figure 4: Lifetime Predictions Using Miner Modifications Current data analysis of variable amplitude tests has shown that components tend to fail at a mean value damage sum equal 0,3 for steel and 0,5 for aluminium [3, 4, 8, 11]. Therefore the relative Miner’s Rule is introduced. Based on variable amplitude tests of components a different damage sum can be used to calculate the failure of a component. The analysis of the Miner’ Rule and its modifications has proven that the modification by Liu/Zenner has the most accuracy. The different Miner’s Rule modifications lead to longer or shorter calculated lifetimes [7]. Lifetime Predictions for Variable Amplitude Loads in the High Cycle Regime In the high cycle regime the calculated lifetimes of variable amplitude tests differ magnificently for the different Miner’s Rule modifications. The calculated lifetimes can differ depending on the spectrum, the slope k of the S-N-curve and the components up to a factor of 200 in lifetime. The modification leading to the shortest calculated lifetime is the Miner Modification by Liu/Zenner. The modification leading to the longest calculated lifetime is the Miner original modification. Compared to the experimentally investigated lifetimes the Miner elementary modification tends to lead to a safe and conservative lifetime calculation, the Miner original modification tends to lead to an unsafe and progressive lifetime calculation. For the experimental test results it was observed that the experimental lifetimes are in the range of the calculated lifetimes of the Miner elementary and original modification. 10 4 10 5 10 6 10 7 10 8 10 9 spectrum cumulative frequency of applied loading stress SaD Sa ^ number of cycles N (log) S-N-curve (constant amplitude) LiuZenner MinerOriginal MinerElemetary MinerModified stress amplitude S [MPa] a HCF Figure 5: Difference in calculated lifetimes depending on Miner Modifications Lifetime Prediction using a Form Parameter c A method to describe a S-N-curve for variable amplitudes was published by [1]. The function describes any S-N-curve for variable amplitude tests in dependency of a single form parameter, eqn. ( 2 ). This function uses the point of the fatigue limit of the S-N-curve for constant amplitude loads as a reference point. The base point for the calculation is the limiting number of load cycles to the fatigue limit and the fatigue limit of the S-N-curve for constant amplitudes. The number of load cycles which can be applied to a component under variable amplitude loads of a spectrum with a maximum load Sˆ can be calculated by the use of the fatigue limit base point for constant amplitudes. The function for the finite life fatigue strength of constant
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