# Fit a Curve by Estimating UTS

An empirical formula can be used to estimate SN/EN data from ultimate tensile strength (UTS) and Young's modulus (E).

1. From the Assign Material dialog, click the My Material tab and select your created material.
2. Select Estimate from UTS as the input method.
3. Click to view the model description.
4. Enter a value for UTS and Elastic modulus.
5. Click Estimate.

## SN Properties

* 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:

Once b1 is known, SRI1 is calculated by:

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

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

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

## EN Properties

** Source: Anton Baumel and T. Seeger, Materials Data for Cyclic Loading, Elsevier, 1990
$Sf/{{\sigma }^{\prime }}_{f}$
Fatigue strength coefficient.
$b$
Fatigue strength exponent.
$c$
Fatigue ductility exponent.
$Ef/{{\epsilon }^{\prime }}_{f}$
Fatigue ductility coefficient.
$Np/{n}^{\prime }$
Cyclic strain-hardening exponent.
$Kp/{K}^{\prime }$
Cyclic strength coefficient.
${N}_{c}$
Reversal limit of endurance. One cycle contains two reversals.
$S{E}_{e}$
Standard Error of Log(elastic strain).
$S{E}_{p}$
Standard Error of Log(plastic strain).