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

Figure 1. Estimated SN Data from Empirical formulae*


* Source: Yung-Li Lee, Jwo. Pan, Richard B. Hathaway and Mark E. Barekey. Fatigue testing and analysis: Theory and practice, Elsevier, 2005.
S R I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaadk facaWGjbGaamymaaaa@3929@
Fatigue strength coefficient. It is the stress amplitude intercept of the SN curve at 1 cycle on a log-log scale.
b 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyaiaadg daaaa@3793@
The first fatigue strength exponent. The slope of the first segment of the SN curve in log-log scale.
N c 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtaiaado gacaWGXaaaaa@3867@
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).
b 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyaiaadk daaaa@3794@
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:

b 1   =   l o g 0.9 U T S     l o g F L   /   l o g 1000     l o g N c 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGIbGaaGymaiaabccacqGH9aqpcaqGGaWdamaabmaabaWdbiaa dYgacaWGVbGaam4za8aadaqadaqaa8qacaaIWaGaaiOlaiaaiMdaca WGvbGaamivaiaadofaa8aacaGLOaGaayzkaaWdbiaabccacqGHsisl caqGGaGaamiBaiaad+gacaWGNbWdamaabmaabaWdbiaadAeacaWGmb aapaGaayjkaiaawMcaaaGaayjkaiaawMcaa8qacaqGGaGaai4laiaa bccapaWaaeWaaeaapeGaamiBaiaad+gacaWGNbWdamaabmaabaWdbi aaigdacaaIWaGaaGimaiaaicdaa8aacaGLOaGaayzkaaWdbiaabcca cqGHsislcaqGGaGaamiBaiaad+gacaWGNbWdamaabmaabaWdbiaad6 eacaWGJbGaaGymaaWdaiaawIcacaGLPaaaaiaawIcacaGLPaaaaaa@61B5@

Once b1 is known, SRI1 is calculated by:

2 S 1000 = S R I 1 ( 1000 ) b 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaaIYaGaeyyXICTaam4uaiaaigdacaaIWaGaaGimaiaaicdacqGH 9aqpcaWGtbGaamOuaiaadMeacaaIXaGaeyyXICTaaiikaiaaigdaca aIWaGaaGimaiaaicdacaGGPaWaaWbaaSqabeaacaWGIbGaaGymaaaa aaa@4973@

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

SRI1=2S1000/( 1000 b1 ) MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGtbGaamOuaiaadMeacaaIXaGaeyypa0JaaGOmaiabgwSixlaa dofacaaIXaGaaGimaiaaicdacaaIWaGaai4laiaacIcacaaIXaGaaG imaiaaicdacaaIWaWaaWbaaSqabeaacaWGIbGaaGymaaaakiaacMca aaa@47E6@

Figure 2. One-segment SN curve in log-log scale (b2=0) (Nc1 is not defined or less conservative than FL)


Figure 3. One-Segment SN Curve in Log-Log Scale (b2=0) (FL is Not Defined or Less Conservative than Nc1)


Figure 4. Two-Segment SN Curve in Log-Log Scale


EN Properties

Figure 5. Estimated EN Data from UTS and E**


** Source: Anton Baumel and T. Seeger, Materials Data for Cyclic Loading, Elsevier, 1990
S f / σ f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaadA gacaGGVaGafq4WdmNbauaadaWgaaWcbaGaamOzaaqabaaaaa@3B52@
Fatigue strength coefficient.
b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyaaaa@36DD@
Fatigue strength exponent.
c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yaaaa@36DE@
Fatigue ductility exponent.
E f / ε f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyraiaadA gacaGGVaGafqyTduMbauaadaWgaaWcbaGaamOzaaqabaaaaa@3B28@
Fatigue ductility coefficient.
N p / n MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtaiaadc hacaGGVaGabmOBayaafaaaaa@3970@
Cyclic strain-hardening exponent.
K p / K MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saiaadc hacaGGVaGabm4sayaafaaaaa@394A@
Cyclic strength coefficient.
N c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaWGJbaabeaaaaa@37DD@
Reversal limit of endurance. One cycle contains two reversals.
S E e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaadw eadaWgaaWcbaGaamyzaaqabaaaaa@38AE@
Standard Error of Log(elastic strain).
S E p MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaadw eadaWgaaWcbaGaamiCaaqabaaaaa@38B9@
Standard Error of Log(plastic strain).
Figure 6. EN Curve in Log-Log Scale