Fit a Curve by Estimating UTS

* Source: Yung-Li Lee, Jwo. Pan, Richard B. Hathaway and Mark E. Barekey. Fatigue testing and analysis: Theory and practice, Elsevier, 2005.

$SRI1$

Fatigue strength coefficient. It is the stress amplitude intercept of the SN curve at 1 cycle on a log-log scale.

$b1$

The first fatigue strength exponent. The slope of the first segment of the SN curve in log-log scale.

$Nc1$

In one-segment SN curves, this is the cycle limit of endurance (See Nc1 in Figure 2). In two-segment SN curves, this is the transition point (see Nc1 in Figure 4).

$b2$

The second fatigue strength exponent.

Empirically, the life of a metal is 1000 when the stress amplitude is approximately 90% of the UTS. (S1000 = 0.9UTS) when loading type is a bending load.

According to "Engineering Considerations of Stress, Strain, and Strength" by Juvinall RC, 1976, McGraw-Hill, fatigue limit (FL) can be estimated as follows:

• For steel that has pearlite microstructure, FL = 0.38UTS at Nc1 = 1E6
• For aluminum alloys whose UTS < 336MPa, FL = 0.4UTS at Nc1 = 5E8
• For Aluminum Alloys whose UTS >= 336MPa, FL = 130MPa at Nc1 = 5E8

With the above information, two points on the SN curve are known: (1000, S1000) and (Nc1, FL). Thus, slope can be calculated:

$b1=\left(log\left(0.9UTS\right)-log\left(FL\right)\right)/\left(log\left(1000\right)-log\left(Nc1\right)\right)$

Once b1 is known, SRI1 is calculated by:

$2\cdot S1000=SRI1\cdot {(1000)}^{b1}$

(The stress range 2*S1000 is used.) Therefore,

$SRI1=2\cdot S1000/({1000}^{b1})$