Probabilistic Stress-Life Analysis

If needed, please go to the Constant Amplitude section for a review of the general terms and terminology related to Stress-Life fatigue analysis.

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Description of Distribution Types

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Loading on structures frequently follows a Normal or LogNormal distribution. In a well controlled situation, such as may be encountered in a test track or in an electric motor, the coefficient of variation COV is typically 0.1. The COV increases to as much as 0.5 for uncontrolled customer usage. In the absence of any other information, a reasonable value of 0.2 or 0.3 may be assumed. If you enter a value of zero for either the normal or the uniform distribution types, you should enter the standard deviation for the scale parameter. This allows you to generate a distribution around zero.

				Distribution Type	Scale Parameter
Loading Units
Maximum	S_max or e_max =
Minimum	S_min or e_min =
OR
Alternating	S_a or e_a =
Mean	S_m or e_m =

Material

Material properties are the most common source of uncertainty in a fatigue life calculation. Fatigue is a weakest link process and fatigue cracks start from the most severe flaw in the material. There is considerable variability in fatigue lives often a factor of 2 - 10 in fatigue life. But because of the strong dependance of fatigue life on stress or strength, the COV of material properties is on the order of 0.1 - 0.2.

You may load a material from the database by selecting it and clicking on "Load Material", or browse the database by clicking the "Material Property Finder" button, or specify individual properties directly. Clicking "Material Property Estimator" will show the default properties that are computed from the input values.

For registered users, the Material Property Estimator will display a curve plot. Registered users may also save this material in their personal database by clicking the "Save Material" button.


Name
Type
Ultimate Strength	S_u =
Elastic Modulus	E =
Fatigue Limit	S_FL =
Fatigue Limit Cycles	N_FL =	Cycles
Intercept	S_f′ =
Slope	b =

Modifying Factors

The various modifying factors sometimes play an important role in calculating the fatigue life. A normal distribution is typically used with a coefficient of variation, COV, of 0.1 as a reasonable value.

				Distribution Type	Scale Parameter
Surface Factor	k_SF =	or

The type of loading, axial, bending, or torsion has an effect because of the stress gradient in bending and torsion.


Loading Factor	k_L =	or

Fatigue is controlled by the weakest link. Small parts have a larger fatigue strength than larger ones because there is a higher volume of highly stressed material. The size affect may be correlated to the volume of the material subjected to 95% of the maximum stress. It is computed from the diameter of the part. An effective diameter is used for non-circular sections. The effective part diameter may be visualized as modeling the stress gradient as a simple bending beam with the effective diameter.

Either specify k_size directly or enter the diameter.


Size Factor	k_size =
Diameter	d =

Stress Concentration Factor

The stress concentration factor, Kt, is subject to any uncertainties in the model used to obtain its value as well as any variability in the structure. A normal distribution is typically used with a coefficient of variation, between 0.05 and 0.3.

				Distribution Type	Scale Parameter
Stress Concentration Factor	K_t =

Either specify K_f directly or enter K_t and the radius.


Use K_f in analysis?
Fatigue Notch Factor	K_f =
Radius	r =

Probabilistic Stress-Life Analysis

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Material

Modifying Factors

Stress Concentration Factor

Calculate