Issue 38

T. Morishita et alii, Frattura ed Integrità Strutturale, 38 (2016) 289-295; DOI: 10.3221/IGF-ESIS.38.39

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





e e



 

f

s t

(3)

d)(

NP

I R 1





L

2

C

path ax Im

( t ) is the maximum absolute value of principle strain at time t and ε Imax

( t ) in a cycle. e 1

is the maximum value of ε I

where ε I and e R

are unit vectors for ε Imax 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 (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. and ε I ( t ); d s the infinitesimal trajectory of the strain path. L path NP f BN AN  6.0 f f eq      1 12.0

Factor of 2 Non proportional strain range  NP , % 2.0 1.0 Non-proportional strain range  NP , % 10 3 10 4 10 5 0.1 0.5 1

10 7

10 3 Failure life in evaluation N f eva , cycles Push-pull Rev.torsion Circle Factor of 2 Push-pull Rev.torsion Circle 10 4 10 5 10 6

Push-pull Rev.torsion Circle

Method of universal slope curve

eva

exp f N N 

f

10 2 10 3 10 4 10 5 10 6 10 7 10 2

10 6

10 7

exp , cycles

Number of cycles to failure N f

, cycles

Failure life in experiment N f

(a) Correlation of N f

(b) Comparison of N f eva

and N f exp

with Δε NP

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

 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

defined as Δε e 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

where Δε eq

293