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 FATIGUE LIFE PREDICTION

Table of Contents

1. Description

2. Limit State Function

3. Random Variables

4. Analysis

5. Reference

Description:

The fatigue life may be computed using the following formula: 

 where:

Nf = cycles to failure

a_i = initial crack size

Ds= cyclic load (ksi)

c= Paris constant

K_IC = fracture toughness (failure occurs when K_I ³ K_IC)

m= exponent in Paris Law = 3

Limit-State Function: 

Random Variables:

X₁ = Load      = Ds: (ksi) ~ Lognormal(m=100.0, s=10.0)

X₂ = Crackl    = a_i : (inch) ~ Lognormal(m=0.01, s=0.005)

X₃ = ParisC    = c: ~ Lognormal(m=1.2E-10, s=1.2E-11)

X₄ = FractT    = K_IC : ksi(in)^0.5 ~ Normal(m=60.0, s=6.0)

Analysis:

Anal1:  Perform Inverse Probability Analysis to identify the level of Nf  in Eq. 1 such that Pf = .001.

Anal2:  Perform Probability Analysis for Nf (x)£ Nf (x^*), where x^* is the MPP obtained from Anal1 to verify the result of Anal1.

Anal3: Compute the CDF of the cycles to failure (Nf) using different input methods from the Pf=0.000001~0.999999.

Anal4: Plot Nf as a function of b.

  Plot of Beta Vs. Nf (Eq. 1)

Reference:

Millwater, Wu, Cardinal, “Probabilistic Structural Analysis of Fatigue and Fracture.” Proceedings of the 35th Structures, Structural Dynamics, and Materials Conference. AIAA/ASME/ASCE/AHS/ASC, AIAA-94-1507, April 18-20, 1994.

Last Updated 02/08/10

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