Safety Factor

Safety factor is calculated based on the endurance limit or target stress (at target life) against the stress amplitude from the working stress history.

HyperLife calculates this ratio via two criteria:
  • Mean Stress = Constant
  • Stress Ratio = Constant

The safety factor (SF) based on the mean stress correction applied is given by the following equations.

Mean Stress = Constant
  1. Goodman or Soderberg

    When SN curve is of the Stress Ratio R = -1

    SF=sσa=seσa0

    se = Target stress amplitude against the target life from the modified SN curve

    σa0 = Stress amplitude after mean stress correction



    Figure 1.
    When SN curve is of the Stress Ratio R != -1


    Figure 2.

    σa = Stress Amplitude

    σm = Mean Stress

    Se−R = Endurance limit obtained from SN curve with R ratio

    Se−m = Mean Stress corresponding to Se−R

    If R > −1 , se=Se−R1−sm−RUTS

    sm−R=Se−R. 1+R1−R

    If R < −1 , Se=Se−R

    If σm> 0 , sa=σa1−σmUTS

    If σm≤0 , sa=σa

    SF= SeSa

  2. Gerber

    SF=sσa=seσa0



    Figure 3.
    When SN curve is of the Stress Ratio R != -1


    Figure 4.
    Sa=σa⋅(1−(σmUTS)2)
    Se=Se−R⋅(1−(sm−RUTS)2)
    sm−R=Se−R. 1+R1−R
    SF= SeSa
  3. Gerber2
    1. σm>0:  SF=sσa=seσa0
    2. σm≤0:  SF=sσa

    When SN curve is of the Stress Ratio R != -1

    If R > −1

    Se=Se−R⋅(1−(sm−RUTS)2)
    sm−R=Se−R. 1+R1−R

    If R < −1 , Se=Se−R

    If σm> 0 , Sa=σa(1−(σmUTS)2)

    If σm≤0 , sa=σa

    SF= SeSa

  4. FKM
    SF=s'
    1. σ m < − s e 1 − m 2                   s ' e = − m ,   ( σ m + s e 1 − m 2 ) + s e 1 − m 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaHdp WCdaWgaaWcbaGaamyBaaqabaGccqGH8aapdaWcaaqaaiabgkHiTiaa dohadaWgaaWcbaGaamyzaaqabaaakeaacaaIXaGaeyOeI0IaamyBam aaBaaaleaacaaIYaaabeaaaaaakeaacaaMc8UaaGPaVlaaykW7caaM c8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caWGZbGaai4jamaaBa aaleaacaWGLbaabeaakiabg2da9iabgkHiTiaad2gacaGGSaGaaGPa VpaabmaabaGaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaOGaey4kaSYaaS aaaeaacaWGZbWaaSbaaSqaaiaadwgaaeqaaaGcbaGaaGymaiabgkHi Tiaad2gadaWgaaWcbaGaaGOmaaqabaaaaaGccaGLOaGaayzkaaGaey 4kaSYaaSaaaeaacaWGZbWaaSbaaSqaaiaadwgaaeqaaaGcbaGaaGym aiabgkHiTiaad2gadaWgaaWcbaGaaGOmaaqabaaaaaaaaa@67E9@
    2. − s e 1 − m 2 ≤ σ m < s e 1 + m 2                                     s ' e = − m 2 σ m + s e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaWcaa qaaiabgkHiTiaadohadaWgaaWcbaGaamyzaaqabaaakeaacaaIXaGa eyOeI0IaamyBamaaBaaaleaacaaIYaaabeaaaaGccqGHKjYOcqaHdp WCdaWgaaWcbaGaamyBaaqabaGccqGH8aapdaWcaaqaaiaadohadaWg aaWcbaGaamyzaaqabaaakeaacaaIXaGaey4kaSIaamyBamaaBaaale aacaaIYaaabeaaaaaakeaacaaMc8UaaGPaVlaaykW7caaMc8UaaGPa VlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8 UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caWGZbGaai4jamaaBaaa leaacaWGLbaabeaakiabg2da9iabgkHiTiaad2gadaWgaaWcbaGaaG OmaaqabaGccqaHdpWCdaWgaaWcbaGaamyBaaqabaGccqGHRaWkcaWG ZbWaaSbaaSqaaiaadwgaaeqaaaaaaa@7026@
    3. s e 1 + m 2 ≤ σ m < 3 ( 1 + m 3 ) 1 + 3 m 3   ·   s e 1 + m 2                                     s ' e = − m 3 ( σ m − s e 1 + m 2 ) + s e 1 + m 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaWcaa qaaiaadohadaWgaaWcbaGaamyzaaqabaaakeaacaaIXaGaey4kaSIa amyBamaaBaaaleaacaaIYaaabeaaaaGccqGHKjYOcqaHdpWCdaWgaa WcbaGaamyBaaqabaGccqGH8aapdaWcaaqaaiaaiodacaGGOaGaaGym aiabgUcaRiaad2gadaWgaaWcbaGaaG4maaqabaGccaGGPaaabaGaaG ymaiabgUcaRiaaiodacaWGTbWaaSbaaSqaaiaaiodaaeqaaaaakiaa ykW7cqWIpM+zcaaMc8+aaSaaaeaacaWGZbWaaSbaaSqaaiaadwgaae qaaaGcbaGaaGymaiabgUcaRiaad2gadaWgaaWcbaGaaGOmaaqabaaa aaGcbaGaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVl aaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8Ua aGPaVlaaykW7caaMc8Uaam4CaiaacEcadaWgaaWcbaGaamyzaaqaba GccqGH9aqpcqGHsislcaWGTbWaaSbaaSqaaiaaiodaaeqaaOWaaeWa aeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccqGHsisldaWcaaqaai aadohadaWgaaWcbaGaamyzaaqabaaakeaacaaIXaGaey4kaSIaamyB amaaBaaaleaacaaIYaaabeaaaaaakiaawIcacaGLPaaacqGHRaWkda WcaaqaaiaadohadaWgaaWcbaGaamyzaaqabaaakeaacaaIXaGaey4k aSIaamyBamaaBaaaleaacaaIYaaabeaaaaaaaaa@8A4C@
    4. 3 ( 1 + m 3 ) 1 + 3 m 3   ·   s e 1 + m 2 ≤ σ m                                     s ' e = − m 4 ( σ m − 3 ( 1 + m 3 ) 1 + 3 m 3   ·   s e 1 + m 2 ) + 1 3 ( 3 ( 1 + m 2 ) 1 + 3 m 3   ·   s e 1 + m 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaWcaa qaaiaaiodacaGGOaGaaGymaiabgUcaRiaad2gadaWgaaWcbaGaaG4m aaqabaGccaGGPaaabaGaaGymaiabgUcaRiaaiodacaWGTbWaaSbaaS qaaiaaiodaaeqaaaaakiaaykW7cqWIpM+zcaaMc8+aaSaaaeaacaWG ZbWaaSbaaSqaaiaadwgaaeqaaaGcbaGaaGymaiabgUcaRiaad2gada WgaaWcbaGaaGOmaaqabaaaaOGaeyizImQaeq4Wdm3aaSbaaSqaaiaa d2gaaeqaaaGcbaGaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8 UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7 caaMc8UaaGPaVlaaykW7caaMc8Uaam4CaiaacEcadaWgaaWcbaGaam yzaaqabaGccqGH9aqpcqGHsislcaWGTbWaaSbaaSqaaiaaisdaaeqa aOWaaeWaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccqGHsislda WcaaqaaiaaiodacaGGOaGaaGymaiabgUcaRiaad2gadaWgaaWcbaGa aG4maaqabaGccaGGPaaabaGaaGymaiabgUcaRiaaiodacaWGTbWaaS baaSqaaiaaiodaaeqaaaaakiaaykW7cqWIpM+zcaaMc8+aaSaaaeaa caWGZbWaaSbaaSqaaiaadwgaaeqaaaGcbaGaaGymaiabgUcaRiaad2 gadaWgaaWcbaGaaGOmaaqabaaaaaGccaGLOaGaayzkaaGaey4kaSYa aSaaaeaacaaIXaaabaGaaG4maaaadaqadaqaamaalaaabaGaaG4mai aacIcacaaIXaGaey4kaSIaamyBamaaBaaaleaacaaIYaaabeaakiaa cMcaaeaacaaIXaGaey4kaSIaaG4maiaad2gadaWgaaWcbaGaaG4maa qabaaaaOGaaGPaVlabl+y6NjaaykW7daWcaaqaaiaadohadaWgaaWc baGaamyzaaqabaaakeaacaaIXaGaey4kaSIaamyBamaaBaaaleaaca aIYaaabeaaaaaakiaawIcacaGLPaaaaaaa@A594@


    Figure 5.
  5. No Mean Stress Correction

    S F = s e σ a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaadA eacqGH9aqpdaWcaaqaaiaadohadaWgaaWcbaGaamyzaaqabaaakeaa cqaHdpWCdaWgaaWcbaGaamyyaaqabaaaaaaa@3D9C@

Stress Ratio = Constant
  1. Goodman

    When SN curve is of the Stress Ratio R = -1

    S F = O B O A = 1 ( σ a s e + σ m U T S ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaadA eacqGH9aqpdaWcaaqaaiaad+eacaWGcbaabaGaam4taiaadgeaaaGa eyypa0ZaaSaaaeaacaaIXaaabaWaaeWaaeaadaWcaaqaaiabeo8aZn aaBaaaleaacaWGHbaabeaaaOqaaiaadohadaWgaaWcbaGaamyzaaqa baaaaOGaey4kaSYaaSaaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqaba aakeaacaWGvbGaamivaiaadofaaaaacaGLOaGaayzkaaaaaaaa@4AAD@



    Figure 6.

    When SN curve is of the Stress Ratio R != -1

    If R   >   − 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGsbGaaeiiaiabg6da+iaabccacqGHsislcaaIXaaaaa@3AE0@ , s e = S e − R 1 − s m − R U T S MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Ca8aadaWgaaWcbaWdbiaadwgaa8aabeaak8qacqGH9aqpdaWc aaWdaeaapeGaam4ua8aadaWgaaWcbaWdbiaadwgacqGHsislcaWGsb aapaqabaaakeaapeGaaGymaiabgkHiTmaalaaapaqaa8qacaWGZbWd amaaBaaaleaapeGaamyBaiabgkHiTiaadkfaa8aabeaaaOqaa8qaca WGvbGaamivaiaadofaaaaaaaaa@4612@

    s m − R = S e − R .   1 + R 1 − R MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Ca8aadaWgaaWcbaWdbiaad2gacqGHsislcaWGsbaapaqabaGc peGaeyypa0Jaam4ua8aadaWgaaWcbaWdbiaadwgacqGHsislcaWGsb aapaqabaGcpeGaaiOlaiaacckadaWcaaWdaeaapeGaaGymaiabgUca Riaadkfaa8aabaWdbiaaigdacqGHsislcaWGsbaaaaaa@4642@

    If R   <   − 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOuaiaabccacqGH8aapcaqGGaGaeyOeI0IaaGymaaaa@3AD1@ , s e = S e − R MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Ca8aadaWgaaWcbaWdbiaadwgaa8aabeaak8qacqGH9aqpcaWG tbWdamaaBaaaleaapeGaamyzaiabgkHiTiaadkfaa8aabeaaaaa@3D45@

    If σ m >   0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdm3damaaBaaaleaapeGaamyBaaWdaeqaaOWaaSbaaSqaa8qa cqGH+aGpcaqGGaGaaGimaaWdaeqaaaaa@3BD1@ , S F = 1 σ a S e + σ m U T S MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4uaiaadAeacqGH9aqpdaWcaaWdaeaapeGaaGymaaWdaeaapeWa aSaaa8aabaWdbiabeo8aZ9aadaWgaaWcbaWdbiaadggaa8aabeaaaO qaa8qacaWGtbWdamaaBaaaleaapeGaamyzaaWdaeqaaaaak8qacqGH RaWkdaWcaaWdaeaapeGaeq4Wdm3damaaBaaaleaapeGaamyBaaWdae qaaaGcbaWdbiaadwfacaWGubGaam4uaaaaaaaaaa@4602@

    If σ m ≤ 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdm3damaaBaaaleaapeGaamyBaaWdaeqaaOWaaSbaaSqaa8qa cqGHKjYOcaaIWaaapaqabaaaaa@3BDB@ , S F =   S e σ a MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4uaiaadAeacqGH9aqpcaGGGcWaaSaaa8aabaWdbiaadofapaWa aSbaaSqaa8qacaWGLbaapaqabaaakeaapeGaeq4Wdm3damaaBaaale aapeGaamyyaaWdaeqaaaaaaaa@3F3E@

  2. Gerber

    When SN curve is of the Stress Ratio R = -1

    1. If   σ m = 0 :                                 S F = s e σ a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaqGjb GaaeOzaiaaykW7cqaHdpWCdaWgaaWcbaGaamyBaaqabaGccqGH9aqp caaIWaGaaiOoaaqaaiaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaG PaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaM c8UaaGPaVlaaykW7caWGtbGaamOraiabg2da9maalaaabaGaam4Cam aaBaaaleaacaWGLbaabeaaaOqaaiabeo8aZnaaBaaaleaacaWGHbaa beaaaaaaaaa@5EFC@
    2. If   σ m ≠ 0 :                                 S F = 1 2 ( U T S σ m ) 2   ·   σ a s e [ − 1 + 1 + ( 2 s e σ m U T S   ⋅   σ a ) 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaqGjb GaaeOzaiaaykW7cqaHdpWCdaWgaaWcbaGaamyBaaqabaGccqGHGjsU caaIWaGaaiOoaaqaaiaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaG PaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaM c8UaaGPaVlaaykW7caWGtbGaamOraiabg2da9maalaaabaGaaGymaa qaaiaaikdaaaWaaeWaaeaadaWcaaqaaiaadwfacaWGubGaam4uaaqa aiabeo8aZnaaBaaaleaacaWGTbaabeaaaaaakiaawIcacaGLPaaada ahaaWcbeqaaiaaikdaaaGccaaMc8UaeS4JPFMaaGPaVpaalaaabaGa eq4Wdm3aaSbaaSqaaiaadggaaeqaaaGcbaGaam4CamaaBaaaleaaca WGLbaabeaaaaGcdaWadaqaaiabgkHiTiaaigdacqGHRaWkdaGcaaqa aiaaigdacqGHRaWkdaqadaqaamaalaaabaGaaGOmaiaadohadaWgaa WcbaGaamyzaaqabaGccqaHdpWCdaWgaaWcbaGaamyBaaqabaaakeaa caWGvbGaamivaiaadofacaaMc8UaeyyXICTaaGPaVlabeo8aZnaaBa aaleaacaWGHbaabeaaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiaa ikdaaaaabeaaaOGaay5waiaaw2faaaaaaa@8814@

    When SN curve is of the Stress Ratio R != -1

    S e = S e − R 1 − S m − R U T S 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaGqadabaaaaaaa aapeGaa83ua8aadaWgaaWcbaWdbiaa=vgaa8aabeaak8qacqGH9aqp caWFtbWdamaaBaaaleaapeGaa8xzaiabgkHiTiaa=jfaa8aabeaak8 qadaqadaWdaeaapeGaaGymaiabgkHiTmaabmaapaqaa8qadaWcaaWd aeaapeGaa83ua8aadaWgaaWcbaWdbiaa=1gacqGHsislcaWFsbaapa qabaaakeaapeGaa8xvaiaa=rfacaWFtbaaaaGaayjkaiaawMcaa8aa daahaaWcbeqaa8qacaaIYaaaaaGccaGLOaGaayzkaaaaaa@49E5@
    s m − R = S e − R .   1 + R 1 − R MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Ca8aadaWgaaWcbaWdbiaad2gacqGHsislcaWGsbaapaqabaGc peGaeyypa0Jaam4ua8aadaWgaaWcbaWdbiaadwgacqGHsislcaWGsb aapaqabaGcpeGaaiOlaiaacckadaWcaaWdaeaapeGaaGymaiabgUca Riaadkfaa8aabaWdbiaaigdacqGHsislcaWGsbaaaaaa@4642@

    If σ m ≠ 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdm3damaaBaaaleaapeGaamyBaaWdaeqaaOWaaSbaaSqaa8qa cqGHGjsUcaaIWaaapaqabaaaaa@3BED@ , S F = 1 2 U T S σ m 2 ⋅ σ e S e ⋅ − 1 + 1 + 2 σ m S e U T S σ a 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaGqadabaaaaaaa aapeGaa83uaiaa=zeacqGH9aqpdaWcaaWdaeaapeGaaGymaaWdaeaa peGaaGOmaaaadaqadaWdaeaapeWaaSaaa8aabaWdbiaa=vfacaWFub Gaa83uaaWdaeaapeGaa83Wd8aadaWgaaWcbaWdbiaa=1gaa8aabeaa aaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaikdaaaGccq GHflY1daWcaaWdaeaapeGaa83Wd8aadaWgaaWcbaWdbiaa=vgaa8aa beaaaOqaa8qacaWFtbWdamaaBaaaleaapeGaa8xzaaWdaeqaaaaak8 qacqGHflY1daqadaWdaeaapeGaeyOeI0IaaGymaiabgUcaRmaakaaa paqaa8qacaaIXaGaey4kaSYaaeWaa8aabaWdbmaalaaapaqaa8qaca aIYaGaa83Wd8aadaWgaaWcbaWdbiaa=1gaa8aabeaak8qacaWFtbWd amaaBaaaleaapeGaa8xzaaWdaeqaaaGcbaWdbiaa=vfacaWFubGaa8 3uaiaa=n8apaWaaSbaaSqaa8qacaWFHbaapaqabaaaaaGcpeGaayjk aiaawMcaa8aadaahaaWcbeqaa8qacaaIYaaaaaqabaaakiaawIcaca GLPaaaaaa@5FD3@

    If σ m = 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdm3damaaBaaaleaapeGaamyBaaWdaeqaaOWaaSbaaSqaa8qa cqGH9aqpcaaIWaaapaqabaaaaa@3B2C@ , S F =   S e σ a MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4uaiaadAeacqGH9aqpcaGGGcWaaSaaa8aabaWdbiaadofapaWa aSbaaSqaa8qacaWGLbaapaqabaaakeaapeGaeq4Wdm3damaaBaaale aapeGaamyyaaWdaeqaaaaaaaa@3F3E@

  3. Gerber2
    1. If  σ m ≤ 0 :                       S F = s e σ a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaqGjb GaaeOzaiaabccacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccqGHKjYO caaIWaGaaiOoaaqaaiaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaG jbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8Uaam4uaiaadAeacqGH 9aqpdaWcaaqaaiaadohadaWgaaWcbaGaamyzaaqabaaakeaacqaHdp WCdaWgaaWcbaGaamyyaaqabaaaaaaaaa@5722@
    2. If   σ m ≥ 0 :                                 S F = 1 2 ( U T S σ m ) 2   ·   σ a s e [ − 1 + 1 + ( 2 s e σ m U T S   ⋅   σ a ) 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaqGjb GaaeOzaiaaykW7cqaHdpWCdaWgaaWcbaGaamyBaaqabaGccqGHLjYS caaIWaGaaiOoaaqaaiaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaG PaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaM c8UaaGPaVlaaykW7caWGtbGaamOraiabg2da9maalaaabaGaaGymaa qaaiaaikdaaaWaaeWaaeaadaWcaaqaaiaadwfacaWGubGaam4uaaqa aiabeo8aZnaaBaaaleaacaWGTbaabeaaaaaakiaawIcacaGLPaaada ahaaWcbeqaaiaaikdaaaGccaaMc8UaeS4JPFMaaGPaVpaalaaabaGa eq4Wdm3aaSbaaSqaaiaadggaaeqaaaGcbaGaam4CamaaBaaaleaaca WGLbaabeaaaaGcdaWadaqaaiabgkHiTiaaigdacqGHRaWkdaGcaaqa aiaaigdacqGHRaWkdaqadaqaamaalaaabaGaaGOmaiaadohadaWgaa WcbaGaamyzaaqabaGccqaHdpWCdaWgaaWcbaGaamyBaaqabaaakeaa caWGvbGaamivaiaadofacaaMc8UaeyyXICTaaGPaVlabeo8aZnaaBa aaleaacaWGHbaabeaaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiaa ikdaaaaabeaaaOGaay5waiaaw2faaaaaaa@8813@

    When SN curve is of the Stress Ratio R != -1

    If R   >   − 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaaCOuaiaabccacqGH+aGpcaqGGaGaeyOeI0IaaCymaaaa@3AD8@

    S e = S e − R ⋅ 1 − s m − R U T S 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaGqadabaaaaaaa aapeGaa83ua8aadaWgaaWcbaWdbiaa=vgaa8aabeaak8qacqGH9aqp caWGtbWdamaaBaaaleaapeGaamyzaiabgkHiTiaadkfaa8aabeaak8 qacqGHflY1daqadaWdaeaapeGaaGymaiabgkHiTmaabmaapaqaa8qa daWcaaWdaeaapeGaam4Ca8aadaWgaaWcbaWdbiaad2gacqGHsislca WGsbaapaqabaaakeaapeGaamyvaiaadsfacaWGtbaaaaGaayjkaiaa wMcaa8aadaahaaWcbeqaa8qacaaIYaaaaaGccaGLOaGaayzkaaaaaa@4C73@
    s m − R = S e − R .   1 + R 1 − R MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Ca8aadaWgaaWcbaWdbiaad2gacqGHsislcaWGsbaapaqabaGc peGaeyypa0Jaam4ua8aadaWgaaWcbaWdbiaadwgacqGHsislcaWGsb aapaqabaGcpeGaaiOlaiaacckadaWcaaWdaeaapeGaaGymaiabgUca Riaadkfaa8aabaWdbiaaigdacqGHsislcaWGsbaaaaaa@4642@

    If R   <   − 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaaCOuaiaabccacqGH8aapcaqGGaGaeyOeI0IaaCymaaaa@3AD4@ , S e = S e − R MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaGqadabaaaaaaa aapeGaa83ua8aadaWgaaWcbaWdbiaa=vgaa8aabeaak8qacqGH9aqp caWGtbWdamaaBaaaleaapeGaamyzaiabgkHiTiaadkfaa8aabeaaaa a@3D29@

    If σ m >   0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdm3damaaBaaaleaapeGaamyBaaWdaeqaaOWaaSbaaSqaa8qa cqGH+aGpcaqGGaGaaGimaaWdaeqaaaaa@3BD1@ , S F = 1 2 U T S σ m 2 ⋅ σ a S e ⋅ − 1 + 1 + 2 σ m S e U T S σ a 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaGqadabaaaaaaa aapeGaa83uaiaa=zeacqGH9aqpdaWcaaWdaeaapeGaaGymaaWdaeaa peGaaGOmaaaadaqadaWdaeaapeWaaSaaa8aabaWdbiaa=vfacaWFub Gaa83uaaWdaeaapeGaa83Wd8aadaWgaaWcbaWdbiaa=1gaa8aabeaa aaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaikdaaaGccq GHflY1daWcaaWdaeaapeGaa83Wd8aadaWgaaWcbaWdbiaa=fgaa8aa beaaaOqaa8qacaWFtbWdamaaBaaaleaapeGaa8xzaaWdaeqaaaaak8 qacqGHflY1daqadaWdaeaapeGaeyOeI0IaaGymaiabgUcaRmaakaaa paqaa8qacaaIXaGaey4kaSYaaeWaa8aabaWdbmaalaaapaqaa8qaca aIYaGaa83Wd8aadaWgaaWcbaWdbiaa=1gaa8aabeaak8qacaWFtbWd amaaBaaaleaapeGaa8xzaaWdaeqaaaGcbaWdbiaa=vfacaWFubGaa8 3uaiaa=n8apaWaaSbaaSqaa8qacaWFHbaapaqabaaaaaGcpeGaayjk aiaawMcaa8aadaahaaWcbeqaa8qacaaIYaaaaaqabaaakiaawIcaca GLPaaaaaa@5FCF@

    If σ m ≤ 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdm3damaaBaaaleaapeGaamyBaaWdaeqaaOWaaSbaaSqaa8qa cqGHKjYOcaaIWaaapaqabaaaaa@3BDB@ , S F =   S e σ a MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4uaiaadAeacqGH9aqpcaGGGcWaaSaaa8aabaWdbiaadofapaWa aSbaaSqaa8qacaWGLbaapaqabaaakeaapeGaeq4Wdm3damaaBaaale aapeGaamyyaaWdaeqaaaaaaaa@3F3E@

  4. FKM

    S F = s e σ a 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaadA eacqGH9aqpdaWcaaqaaiaadohadaWgaaWcbaGaamyzaaqabaaakeaa cqaHdpWCdaWgaaWcbaGaamyyamaaBaaameaacaaIWaaabeaaaSqaba aaaaaa@3E8E@

    σ a 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadggadaWgaaadbaGaaGimaaqabaaaleqaaaaa@39BD@ = Corrected Stress Amplitude in Constant R mean stress correction

  5. No Mean Stress Correction

    S F = s e s a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaadA eacqGH9aqpdaWcaaqaaiaadohadaWgaaWcbaGaamyzaaqabaaakeaa caWGZbWaaSbaaSqaaiaadggaaeqaaaaaaaa@3CD1@

  6. Interpolate
    Safety Factor with Multi-Mean
    To calculate safety factor, HyperLife creates an internal Haigh diagram for the target life using multi-mean SN curve by finding stress amplitude-mean stress pairs at the target life. Using the internally created Haigh diagram, HyperLife calculates safety factor as described in section Safety Factor in Chapter Haigh diagram. The number of data points of the Haigh diagram is the number of curves. Thus the more number of curves, the better result. When Haigh diagram is not available in mean stress ranges, HyperLife extrapolates the Haigh diagram.


    Figure 7. Conversion of Multi-Mean Curve to Haigh Diagram
    Safety Factor with Multi-Ratio
    To calculate safety factor, HyperLife create an internal Haigh diagram for the target life using multi-mean SN curve by finding stress amplitude-mean stress pairs at the target life. The number of data points of the Haigh diagram is the number of curves. Thus, the more number of curves, the better result. When Haigh diagram is not available in mean stress ranges, HyperLife extrapolates the Haigh diagram.


    Figure 8. Conversion of Multi-Mean Curve to Haigh Diagram
    Safety Factor with Haigh
    Safety factor (SF) is calculated in the following manner in Figure 9.


    Figure 9.
    When target life is 100000:
    • Constant R : SF = OB/OA
    • Constant mean : SF = OD/OC
    If Haigh diagram for a target life is not defined, HyperLife creates Haigh diagram for the target life. In Figure 9, if target life is 10000, and Haigh diagram for N=10000 is not defined, HyperLife will created dashed curve to calculate Safety factor.