Brown-Miller approach

With the Brown-Miller approach, the durability solver first decides the critical (maximum shear strain) plane using the three principal axes on the element face.

The solver calculates the maximum shear cycle in the constant shear direction on the critical plane. For each identified maximum shear strain cycle, a constant strain biaxial ratio rε is used to determine the corresponding normal strain cycle that is normal to the maximum shear direction NOTE.

Using this approach, the life criterion can be written as:

where:

• is the shear strain amplitude on maximum shear plane.

• rε is the strain biaxial ratio. See Strain biaxial ratio for more information.

• 2Nf is the number of reversals to failure.

• E is the modulus of elasticity.

• σ'f is the fatigue strength coefficient material property.

• b is the fatigue strength exponent material property.

• ε'f is the fatigue ductility coefficient material property.

• c is the fatigue ductility exponent material property.

• νe is the Poisson's ratio.

• νp is the plastic Poisson's ratio that is set to 0.5.

See Critical plane approach for more information.

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Biaxial fatigue evaluation on element free faces

Von Mises effective amplitude approach

Stress biaxial ratio

Strain biaxial ratio

Biaxial fatigue evaluation for beam elements

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Dowling, N. E., “Mechanical Behavior of Materials”, Prentice-Hall, 1993, p. 670.

Tipton, S.M., and Fash, J.W., “Multiaxial Fatigue Life Predictions for the SAE Specimen Using Strain-based Approach”, in Multiaxial Fatigue: Analysis & Experiments, SAE AE-14, 1989, pp. 67-80.

Brown, M.W., and Miller, K.J. “High Temperature Low-cycle Biaxial Fatigue of Two Steels”, Fatigue of Engineering Materials and Structure, Volume 1, 1979. pp. 217-225.

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