Issue 38

T. Morishita et alii, Frattura ed Integrità Strutturale, 38 (2016) 289-295; DOI: 10.3221/IGF-ESIS.38.39 293 where Δε eq is the maximum principal strain range under non-proportional loading which can be calculated by ε and γ. α and f NP are the material constant and the non-proportional factor; respectively. The former is the parameter related to the additional hardening due to non-proportional loading and the latter is the parameter expressing the intensity of non- proportional loading. The value of α is the ratio to fit N f in the circle loading test to that in the push-pull loading test at the same Δε eq . In this study; the value of α for SS400 is put α = 0.59. f NP is defined as s t L f d)( 2 C I R 1 path ax Im NP        e e (3) where ε I ( t ) is the maximum absolute value of principle strain at time t and ε Imax is the maximum value of ε I ( t ) in a cycle. e 1 and e R are unit vectors for ε Imax and ε I ( t ); d s the infinitesimal trajectory of the strain path. L path is the whole strain path length during a cycle and “×” denotes vector product. The integral measures the rotation of the maximum principal strain direction and the integration of strain amplitude after the rotation. Therefore; f NP totally evaluates the severity of non- proportional loading in a cycle. Fig. 5 (a) shows failure life correlated by Δε NP . A relative good correlation can be seen in the LCF region but the failure life in the high cycle fatigue region tends to be underestimated. Fig. 5 (b) is a comparison of the failure life in evaluation N f eva and experiment N f exp ; where N f eva is evaluated from the life curve in the push-pull loading test and the following equation NP f f eq f BN AN       1 6.0 12.0 (4) Fig. 5 (b) also shows conservative estimation of failure life in the high cycle fatigue region. In the figure; data which did not reach to failure are omitted. The cause of the underestimation of N f eva in high cycle fatigue region is considered from that Eq. (4) does not take into account the effect of non-proportional loading on life being weak under elastic deformation. Actually; additional hardening becomes smaller in the lower stress and strain levels. In order to modify non- proportional strain range; the effect of non-proportionality depending on strain level is discussed in next section. Factor of 2 Method of universal slope curve 10 3 10 4 10 5 10 6 10 7 0.1 0.5 1 Number of cycles to failure N f , cycles Non proportional strain range  NP , % 2.0 1.0 Push-pull Rev.torsion Circle Non-proportional strain range  NP , % 10 2 10 3 10 4 10 5 10 6 10 7 10 2 10 3 10 4 10 5 10 6 10 7 Failure life in experiment N f exp , cycles Failure life in evaluation N f eva , cycles Push-pull Rev.torsion Circle exp f eva f N N  Factor of 2 Push-pull Rev.torsion Circle (a) Correlation of N f with Δε NP (b) Comparison of N f eva and N f exp Figure 5: Evaluation of failure life by non-proportional strain range. Modified Non-proportional Strain Range Fig. 6 shows correlations of N f with elastic and plastic strain ranges (Δε e eq and Δε p eq ). Δε e eq in the circle loading test is defined as Δε e eq = AN f 0.12 based on elastic part of universal slope curve [16] and Δε p eq is defined as Δε p eq =Δε eq  Δε e eq ; where Δε eq is the strain range obtained by test results. In Fig. 6; the bold lines show the relationships of Δε e eq  N f and