Issue 38

T. Inoue et alii, Frattura ed Integrità Strutturale, 38 (2016) 259-265; DOI: 10.3221/IGF-ESIS.38.35 264 -1 -0.5 0 0.5 1 0 1 2 3 4 5 6 7 8 Normalized stress Time (sec.)  xy ： Measured stress ： Reproduced stress  y  x Figure 5 : Comparison between reproduced and measured stresses. Fatigue testing results under non-proportional loading conditions We made a comparison between measured fatigue lives and predicted fatigue lives under random non-proportional loading conditions. The fatigue tests were conducted by applying one random waveform for 240 seconds repeatedly. To execute the non- proportional test, the waveform having different amplitude and phase was generated in each axis. For predicting fatigue lives, two types of stresses,  cr (Eq. (5)) calculated by critical plane method [5] and  ma (Eq. (6)) in consideration of the non-proportional level calculated by amplitude and direction of principal stress, were used.               cr xy cr cr t x t y t x t y t 1 1 cos(2 ) sin(2 ) 2 2              (5)       ma ma t cr t f 1       (6) where  cr is the angle between the direction perpendicular to the critical plane and x axis, and  is the material constant expressing the influence of non-proportional loading. f ma is the parameter expressing the intensity of non-proportional loading and described as:       T I t I t ma T I t dt f dt 2 ( ) ( ) 0 2 ( ) 0 sin 2        (7) where  I ( t ) is the maximum absolute value of principal stress at time t , and  I ( t ) is the direction of  I ( t ) . Each stress is calculated by numerical results using the FE model shown in Fig. 4. Predicted fatigue lives were calculated using stress cycle counting, i.e. Rainflow method, and linear cumulative damage rule based on the modified Miner’s rule. It was found that predicted fatigue lives with  cr were over a factor of 10 against measured fatigue lives as shown in Fig. 6. On the other hand, predicted fatigue lives with  ma were within a factor of 3 against measured fatigue lives. It can be noticed that the errors of predicted fatigue lives using  ma are caused by the relationship between maximum principal stress and minimum principal stress. The minimum principal stress in condition A (the most conservative as shown in Fig. 6) has the opposite sign as the maximum principal stress. On the other hand, the minimum principal stress in condition B (the most non-conservative as shown in Fig. 6) has the same sign. When the maximum principal stress is tensile, the compressive minimum principal stress has a promoting effect on fatigue crack initiation and propagation. On the other hand, the tensile minimum principal stress has a suppressing effect. The stress states in condition B can only be reproduced in the advanced testing machine; therefore, the advanced testing machine is effective in developing the method for high-accuracy prediction of fatigue life in consideration of the minimum principal stress effect.