About Fatigue Algorithms

Brown-Miller

The Brown-Miller algorithm is a strain-based critical plane multiaxial fatigue algorithm based on the strain-life curve defined by the equation:

\frac{Δ γ}{2} + \frac{Δ ε_{n}}{2} = 1.65 \frac{σ_{f}^{'}}{E} {(2 N_{f})}^{b} + 1.75 ε_{f}^{'} {(2 N_{f})}^{c} .

If only the stress field from an elastic FEA is used to drive the fatigue analysis, a multiaxial elastic-plastic (Neuber) correction based on the Ramberg-Osgood cyclic plasticity equation is used to calculate elastic-plastic stresses and strains from the (pseudo-elastic) stresses. If an elastic-plastic FEA is used to drive the fatigue analysis, the algorithm uses the stresses plus either the sum of the elastic and plastic strains or the total mechanical strains from the FEA. For more information, see Section 15, "Fatigue analysis of elastic-plastic FEA results," in the fe-safe USER GUIDE.

Candidate planes are perpendicular to the surface and at 45 degrees to the surface, and are spaced 10 degrees apart about the surface normal.

For each candidate plane, the fatigue life is calculated as follows:

The history of the projected shear strains, normal strains, and normal stresses on the plane are computed.
Fatigue cycles are extracted and fatigue damage for each cycle is computed.
The fatigue damage is accumulated per Miner's rule, and the fatigue life is calculated.

The fatigue life reported is the shortest of the lives calculated for all candidate planes.

For finite life analysis, Morrow, User-defined, or no mean stress correction may be selected. See Section 14.9 of the fe-safe USER GUIDE for a definition of the user-defined MSC. For the Morrow mean stress correction, the strain-life equation is modified to:

\frac{Δ γ}{2} + \frac{Δ ε_{n}}{2} = 1.65 \frac{(σ_{f}^{'} - σ_{n, m})}{E} {(2 N_{f})}^{b} + 1.75 ε_{f}^{'} {(2 N_{f})}^{c}

For infinite life analysis, Goodman, Gerber, or a User-defined mean stress correction may be selected.

The Brown-Miller algorithm is the default fatigue algorithm for most ductile materials in the DS-ElasticFatigue.3dxml material briefcase. See the Fatigue Theory Reference Manual, Section 7, for the background to this algorithm.

Normal Strain

The Normal Strain algorithm is a strain-based critical plane multiaxial fatigue algorithm based on the strain-life curve defined by the equation:

\frac{Δ ε_{n}}{2} = \frac{σ_{f}^{'}}{E} {(2 N_{f})}^{b} + ε_{f}^{'} {(2 N_{f})}^{c}

If only the stress field from an elastic FEA is used to drive the fatigue analysis, a multiaxial elastic-plastic (Neuber) correction based on the Ramberg-Osgood cyclic plasticity equation is used to calculate elastic-plastic stresses and strains from the (psuedoelastic) stresses. If an elastic-plastic FEA is used to drive the fatigue analysis, the algorithm uses the stresses plus either the sum of the elastic and plastic strains or the total mechanical strains from the FEA. For more information, see Section 15 of the fe-safe USER GUIDE.

Candidate planes are perpendicular to the surface and are spaced 10 degrees apart about the surface normal.

For each candidate plane, the fatigue life is calculated as follows:

The history of the projected normal strains and normal stresses on the plane are computed.
Fatigue cycles are extracted and fatigue damage for each cycle is computed.
The fatigue damage is accumulated per Miner's rule, and the fatigue life is calculated.

The fatigue life reported is the shortest of the lives calculated for all candidate planes.

For finite life analysis, Morrow, Walker, Smith-Watson-Topper, User-defined, or no mean stress correction may be selected. See Section 14.9 of the fe-safe USER GUIDE for a definition of the user-defined MSC. For the Smith-Watson-Topper mean stress correction, the strain-life equation is modified to:

\frac{Δ ε_{n}}{2} σ_{n, \max} = \frac{{(σ_{f}^{'})}^{2}}{E} {(2 N_{f})}^{2 b} + σ_{f}^{'} ε_{f}^{'} {(2 N_{f})}^{b + c}

For the Morrow mean stress correction, the strain-life equation is modified to:

\frac{Δ ε_{n}}{2} = \frac{(σ_{f}^{'} - σ_{n, m})}{E} {(2 N_{f})}^{b} + ε_{f}^{'} {(2 N_{f})}^{c}

For infinite life analysis, Goodman, Gerber, or a User-defined mean stress correction may be selected.

Cast Iron

The Cast Iron fatigue algorithm is similar to the Normal Strain method, but with the following differences tailored to cast irons:

If the fatigue analysis is driven by pseudo-elastic stresses only, the plasticity correction applied is more complex because the cyclic stress strain response is modified to capture the effects of internal and surface graphite and crack closure. These effects make cast irons stiffer in compression than in tension and hence make the stress-strain hysteresis loops nonsymetrical.
Fatigue damage accumulation is nonlinear; that is, it is not as simple as Miner's rule.

For finite life analysis, Smith-Watson-Topper or a user-defined mean stress correction may be selected.

Maximum Shear Strain

The Maximum Shear Strain algorithm is a strain-based critical plane multiaxial fatigue algorithm based on the strain-life curve defined by the equation:

\frac{Δ γ}{2} = 1.3 \frac{σ_{f}^{'}}{E} {(2 N_{f})}^{b} + 1.5 ε_{f}^{'} {(2 N_{f})}^{c}

If only the stress field from an elastic FEA is used to drive the fatigue analysis, a multiaxial elastic-plastic (Neuber) correction based on the Ramberg-Osgood cyclic plasticity equation is used to calculate elastic-plastic stresses and strains from the (psuedoelastic) stresses. If an elastic-plastic FEA is used to drive the fatigue analysis, the algorithm uses the stresses plus either the sum of the elastic and plastic strains or the total mechanical strains from the FEA. For more information, see Section 15 of the fe-safe USER GUIDE.

Candidate planes are 45 degrees to the surface and spaced 10 degrees apart about the surface normal.

For each candidate plane, the fatigue life is calculated as follows:

The history of the projected shear strains and normal stresses on the plane are computed.
Fatigue cycles are extracted, and fatigue damage for each cycle is computed.
The fatigue damage accumulates per Miner's rule, and the fatigue life is calculated.

The fatigue life reported is the shortest of the lives calculated for all candidate planes.

For finite life analysis, Morrow, user-defined, or no mean stress correction may be selected. See Section 14.9 of the fe-safe USER GUIDE for a definition of the user-defined MSC. With the Morrow mean stress correction, the strain-life equation is modified to:

\frac{Δ γ}{2} = 1.3 \frac{(σ_{f}^{'} - σ_{n, m})}{E} {(2 N_{f})}^{b} + 1.5 ε_{f}^{'} {(2 N_{f})}^{c}

Normal Stress

The Normal Stress algorithm is a stress-based critical plane multiaxial fatigue algorithm based on the stress-life curve defined by the equation:

\frac{Δ σ_{n}}{2} = {σ_{f}^{'} (2 N_{f})}^{b}

The stress-life curve is often defined by S-N data pairs.

Only the stress field from the FEA is used to drive the fatigue analysis, whether the FEA is elastic or elastic-plastic. For more information, see Section 15 of the fe-safe USER GUIDE.

Candidate planes are perpendicular to the surface and are spaced 10° apart about the surface normal.

For each candidate plane, the fatigue life is calculated as follows:

The history of the projected normal stresses on the plane is computed.
Fatigue cycles are extracted and fatigue damage for each cycle is computed.
The fatigue damage is accumulated per Miner's rule, and the fatigue life is calculated.

The fatigue life reported is the shortest of the lives calculated for all candidate planes.

For finite life analysis, Goodman, Gerber, Walker, Morrow, Smith-Watson-Topper, R-ratio S-N curves, user-defined, or no mean stress correction may be selected. See Section 14.9 of the fe-safe USER GUIDE for a definition of the user-defined MSC.

For infinite life analysis, Goodman, Gerber, R-ratio S-N curves, or a user-defined mean stress correction may be selected.

von Mises

This option is a signed von Mises stress-based multiaxial fatigue algorithm based on the stress-life curve defined by the equation:

\frac{Δ σ_{v m}}{2} = {σ_{f}^{'} (2 N_{f})}^{b}

The stress-life curve is often defined by S-N data pairs.

Only the stress field from the FEA is used to drive the fatigue analysis, whether the FEA is elastic or elastic-plastic. For more information, see Section 15 of the fe-safe USER GUIDE.

Fatigue damage is accumulated per Miner's rule.

For finite life analysis, Goodman, Gerber, Walker, Morrow, Smith-Watson-Topper, R-ratio S-N curves, user-defined, or no mean stress correction may be selected. See Section 14.9 of the fe-safe USER GUIDE for a definition of the user-defined MSC.

For infinite life analysis, Goodman, Gerber, R-ratio S-N curves, or a user-defined mean stress correction may be selected.

Two methods are provided to allocate a sign to the von Mises stress before cycle counting is performed:

Use the sign of the hydrostatic stress (average of direct stress components or principals)
Use the sign of the principal stress with the largest magnitude.

The lack of a sign for the von Mises stress makes it unreliable to identify fatigue cycles correctly. Consider the following sequence of stress states (both almost pure shear), where a large shear (or torsional) stress reverses fully while a very small direct (axial) stress remains constant:


State #	Sxx	Txy
1	0.1	100.0
2	0.1	-100.0

In this case, both signed von Mises options fail to identify any fatigue cycles because the principal stress with the largest magnitude is +100.05 for both stress states and the sum of the direct stresses is +0.1 for both stress states.

Manson McKnight Octahedral

The Manson McKnight Octahedral fatigue algorithm is a stress-based multiaxial fatigue model based on the concept of a signed von Mises stress, but it uses a cycle counting method that is more reliable than the simple von Mises method. See section 14.7 of the fe-safe USER GUIDE for the details.

It is a partial implementation of the NASALife software described in the https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140010774.pdf (J. Z. Gyekensi, P. L. Murthy and S. K. Mital, "NASALIFE – Component Fatigue and Creep Life Prediction Program," National Aeronautics and Space Administration, Cleveland, 2005). The SIMULIA implementation is limited to the simplest Manson-McKnight algorithm, and it does not address creep at all.

Uniaxial Strain Life

The Uniaxial Strain Life algorithm is a strain-life method that is similar to the Normal Strain method, with the following differences:

Just two candidate critical planes are considered.
The stress history is searched for the stress sample with the largest principal stress magnitude to define a reference tensor.
The directions of the two principals of the reference tensor with the largest magnitudes define the normals to the two candidate planes.
The history of stress projected onto the normal to each candidate plane is computed.
The fatigue life is then computed as if the stress experienced uniaxial stress conditions; that is, all other stress components are treated as if they are zero. In the normal strain method, the plasticity correction still accounts for all six stress and strain components, but this is not the case in the uniaxial strain method.

If the stress history is purely uniaxial, then this method gives identical results to the Normal Strain method.

For finite life analysis, Morrow, Walker, Smith-Watson-Topper, or no mean stress correction may be selected.

Uniaxial Stress Life

The Uniaxial Stress Life fatigue algorithm is a stress-life method is similar to the Normal Stress method, with the following differences:

Just two candidate critical planes are considered.
The stress history is searched for the stress sample with the largest principal stress magnitude to define a reference tensor.
The directions of the two principals of the reference tensor with the largest magnitudes define the normals to the two candidate planes.
The history of stress projected onto the normal to each candidate plane is computed, fatigue cycles identified, and fatigue damage computed.

If the stress history is proportional, this method gives identical results to the Normal Stress method.

For finite life analysis, Goodman, Gerber, Walker, or no mean stress correction may be selected.