# 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).

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

## SN Properties

- $$SRI1$$
- 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:

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

Once `b1` is known, `SRI1` is calculated by:

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

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

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

## EN Properties

- $$Sf/{{\sigma}^{\prime}}_{f}$$
- 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).