Issue 41

T. Morishita et alii, Frattura ed Integrità Strutturale, 41 (2017) 45-53; DOI: 10.3221/IGF-ESIS.41.07 49   Imin Imax Imean 5.0 S S S   (10) As mentioned above, the reference axis (S I 1 ) is the direction of maximum principal stress or strain. In the model, it is also possible to use Tresca and von Mises stress or strain as S . By utilizing the IS-method, even complex non-proportional multiaxial cyclic loading can be replaced by simple waveform, similar to uniaxial loading case. Figure 3 : Definition of principal range and mean principal values. Strain Parameter for Life Evaluation In order to evaluate the fatigue life of non-proportional multiaxial loading, Itoh et al . have proposed life evaluation equation,  NP , taking into account material dependence and strain paths [1-5].   I NP NP 1     f (11) In the equation,  I is the principal strain range stated previously as  S I and  is a material parameter expressing the amount of additional hardening by non-proportional loading, which is defined as the ratio of stress amplitudes between circular loading and push-pull loading. f NP is the non-proportional factor which expresses the severity of non-proportional loading and is defined as,          C R 1 I path Imax NP d 2 s t L f e e (12) where, e 1 and e R are the unit vectors of S I ( t 0 ) (  I ( t 0 )) and S I ( t ) (  I ( t )), respectively as shown in Fig. 3. L path is the full length of loading path, C is the integration of strain paths, d s is the increase in the strain path, '  ' shows the cross product. f NP totally evaluates the severity of non-proportional loading in a cycle. Therefore, the maximum non-proportionality ( f NP =1) occurred in circular straining and the minimum non-proportionality ( f NP =0) in proportional loading. Evaluation for Random Loading When loading for life evaluation is random loading, appropriate counting method is required. Some counting methods are already proposed, e.g. peak counting, the level crossing counting, the range-pair counting and the rain-flow counting. However, the method for adapting cycle counting method to multiaxial random loading is not established. Since multiaxial random loading can be converted to equivalent uniaxial loading by using IS-method, the counting methods for uniaxial random loading can be used as they are. Fig. 4 shows loading waveform and non-proportionality before and after using cycle counting method. In the figure, the rain-flow method is used and the equivalent strain (  I ( t )cos  ( t )) is divided into 2 cycles: O-A-BC’-D-E and B-C-C’. Accordingly, non-proportionality (  I ( t )| e 1  e R |) is split at B and C’. Using strain range and non-proportional factor in each cycle, the strain range for evaluation of failure life under non-proportional loading is calculated by Eq (11). Applicability of this method for life evaluation under non-proportional loading will be discussed further in the future based on the test results. S I 1  ( t )  ( t ) S I ( t ) S I ( t 0 ) S I 2 S I 3 Δ S I 0.5Δ S I S I mean S I max S I min S I max e 1 e 2 e 3 e R