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Chinese Journal of Materials Research  2015, Vol. 29 Issue (9): 714-720    DOI: 10.11901/1005.3093.2014.651
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R-S-N Mathematical Model Based on TC18 by BW High Cycle Fatigue Test Data
Liang ZHU1,*(),Jing WANG1,Xiaohui LI1,Hongbo SUO2,Yiliang ZHANG1
1. College of Mechanical Engineering and Applied Electronics Technology Beijing University of Technology, Beijing 100022, China
2. Science and Technology on Power Beam Processing Lab Beijing Aeronautical Manufacturing Technology Research Institute, Beijing 100024, China
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Liang ZHU,Jing WANG,Xiaohui LI,Hongbo SUO,Yiliang ZHANG. R-S-N Mathematical Model Based on TC18 by BW High Cycle Fatigue Test Data. Chinese Journal of Materials Research, 2015, 29(9): 714-720.

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Abstract  

For the influence of stress ratio on fatigue life, fatigue tests of TC18 titanium alloy produced by build-up welding (TC18 by BW) samples were carried out under three stress ratios (R=0.5、R=0.06、R=-1), to draw three fatigue limits and 6 S-N curves of “stress amplitude life model ” and “ three-parameter model ”. Based on the integral relationship of the crack growth rate and fatigue life and considering both of mathematical models of fatigue life, a systematic investigation of the relationship between stress ratio (R) and fatigue life curve (S-N) was performed to build the fatigue life mathematical model (R-S-N). According to the modified formula proposed in this paper, the establishment of two R-S-N mathematical models, applicable for TC18 by BW materials. The results show that “stress amplitude” model can accurately predict moderate fatigue life, and “three-parameter fatigue” model is more suitable for the prediction of long-life area. The predictive value of two proposed R-S-N mathematical models are in better agreement with the experimental values, they can accurately predict the fatigue curve under any stress ratio in engineering.
Key words:  foundational discipline in materials science      stress ratio      fatigue life      fatigue limit      R-S-N mathematical models     
Received:  06 November 2014     
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Liang ZHU
Jing WANG
Xiaohui LI
Hongbo SUO
Yiliang ZHANG

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https://www.cjmr.org/EN/10.11901/1005.3093.2014.651     OR     https://www.cjmr.org/EN/Y2015/V29/I9/714

Fig.1  Size of the sample for fatigue testing
Rj Number of Valid Sample Pairing Number Fatigue Limit /MPa Standard Deviation / MPa Coefficient Variation Regulation Coefficient Variation
0.5 12 6 889.17 20.7 0.023 0.040
0.06 13 6 747.08 14.2 0.019 0.040
-1 14 7 529.29 9.76 0.018 0.048
Table 1  All the results of the fatigue limit
R Smax lgSmax Sa lgSa lgN n
0.5 990 2.9956 247.5 2.3936 5 6
962.5 2.9834 240.6 2.3813 5.19 7
935 2.9708 233.8 2.3688 6.09 5
907.5 2.9578 226.9 2.3558 6.51 4
0.06 880 2.9445 413.6 2.6166 5.33 6
852.5 2.9307 400.7 2.6028 5.66 4
825 2.9165 387.8 2.5886 5.94 4
-1 600 2.7782 600 2.7782 4.57 7
560 2.7482 560 2.7482 4.82 6
550 2.7404 550 2.7404 4.88 6
Table 2  Experimental data with the grouped method
R Equations of Sa-N curve Equations of Smax-N curve
0.5 S a 43.22 N = 10 108.35 ( S m a x - 889.17 ) 2.14 N = 10 9.32
0.06 S a 21.8 N = 10 62.37 ( S m a x - 747.08 ) 2.61 N = 10 10.89
-1 S a 8.24 N = 10 27.47 ( S m a x - 529.29 ) 0.6 N = 10 5.68
Table 3  Equations of Sa-N curve、(Smax-S0)-N curve with different stress ratio
Fig.2  Fatigue limit paired up and down figure with R=0.5, R=0.06, R=-1
Fig.3  Sa-N curves of three stress ratio
R Equations a b
0.5 S a 43.22 N = 10 108.35 108.35 43.22
0.06 S a 21.8 N = 10 62.37 62.37 21.8
-1 S a 8.24 N = 10 27.47 27.47 8.24
表4  Sa-N 曲线方程中的参数
R Equations a b
0.5 ( S m a x - 889.17 ) 2.14 N = 10 9.32 9.32 2.14
0.06 ( S m a x - 747.08 ) 2.61 N = 10 10.89 10.89 2.61
-1 ( S m a x - 529.29 ) 0.6 N = 10 5.68 5.68 0.6
表5  Smax-N 曲线方程中的参数
Predictive value/MPa Experimental value/MPa Relative Error/%
S ^ 50 0.5 842.73 889.17 5.22
S ^ 50 0.06 718.01 747.08 3.89
S ^ 50 - 1 529.29 529.29 0
Table 6  The fatigue limit with different stress ratio
Fig.4  Smax-N curves of three stress ratio
Fig.5  Sa-N curves of model and real (a), Fig.5 Smax-N curves of model and real (b)
Fig.6  Sa-N curves with different stress ratio (a), Smax-N curves with different stress ratio (b)
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