Issue 38

T. Morishita et alii, Frattura ed Integrità Strutturale, 38 (2016) 281-288; DOI: 10.3221/IGF-ESIS.38.38 285       C path C I R path max I NP d ,d)( | 2 1 s L s tS L S f e e | (3) where S I ( t ) is the maximum absolute value of principal strains at time t , S Imax is the maximum value of S I ( t ). e 1 and e R are unit vectors of S Imax and S I ( t ), d s the infinitesimal trajectory of the loading path. L path is the whole loading path length during a cycle and “  ” denotes vector product. Integrating the product of amplitude and principal direction change of stress and strain by path length in Eq. (3) is a suitable parameter for evaluation of the additional damage due to non- proportional loading. Detail descriptions of f NP and the life evaluations have been mentioned in reference [12] and are omitted here. f NP in the PP test (proportional loading) takes 0 and that in the CI (non-proportional loading) takes 1. Fig. 5 shows a correlation of the failure life by  NP . This figure shows that dark symbols for PP-FF and CI-FF tests are plotted beside the bold line and  NP can evaluate non-proportional loading tests at the high strain rate. Because of creep damage, the failure lives in lower strain rates are scattered even though almost of all data are correlated within the factor of 2 band. Therefore,  NP may need some modification which considers the effect of strain rate. 10 2 10 3 10 4 Factor of 2 PP-FF PP-SS PP-SS* PP-TH-3 PP-TH-10 PP-CH-3 PP-CH-10 1.0 2.0 Strain range  NP , % Failure life N f , cycles CI-FF CI-SS CI-SS* CI-TH-3 CI-TH-10 0.4 0.2 Figure 5 : Correlation of N f by non-proportional strain range. Creep Fatigue Damage under Proportional Loading Condition The evaluation method proposed by Coffin [14], which takes into account the strain rate under proportional loading, is employed for life evaluation. The equation is given by   C N v k   β f 1 P Δε (4) where  p and v are plastic strain and cyclic frequency. C ,  and k are material constants. From the experimental results in PP-FF and PP-SS tests, the material constants and a correlation of strain ranges in PP-FF and PP-SS tests can be calculated by Eq. (5).   β1 0 SS PP p FF PP p Δε           k v v (5)