Constant Amplitude Stress-Life Analysis

The stress-life method is typically used for long life situations (millions of cycles) where the stresses are elastic. This method is often referred to as infinite life design. It is based on the fatigue limit or endurance limit of the material. Material properties from polished specimens are modified for surface conditions and loading conditions being analyzed. Stress concentration factors are used to account for locally high stresses. An effective stress concentration in fatigue loading is computed. An estimate of the fatigue life is determined from the Goodman diagram. Fatigue lives are assumed to be infinite in the safe region and a factor of safety is computed. Outside the safe region an estimate of the fatigue life is determined. Many components do not require an infinite number of cycles to be a safe design, for example something loaded once a day for 20 years accumulates only 7300 cycles. Remember, the concept of safe and unsafe depends on the application not the number of cycles.

Enter as much data as you know. If it is not enough, you will be asked for more. Fields with a light blue/gray background represent the minimum required data to begin calculations. Other data may become necessary as calculation proceeds. Pressing the button provides help in the form of an equation or default information for a parameter.

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Loading

Loads can be entered as either the maximum and minimum values or as the alternating stress and mean stress. Remember that the alternating stress is only one half of the stress range.

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

The endurance limit (sometimes called fatigue limit) is determined from polished laboratory specimens. In the absence of test data, it can be estimated from the ultimate strength of the material. Aluminum does not have an endurance limit, instead a fatigue limit for 10⁷ cycles is used.

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 plot of the data. 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
For finite life design, the entire stress-life curve must be known. Stress life curves are characterized by a slope and an intercept.
Intercept	S_f′ =
Slope	b =

Modifying Factors

Many factors effect the the endurance limit of a mechanical part or structure. Modifications are made to the endurance limit found in laboratory specimens. Some of the more important ones are listed here; the surface finish factor, k_SF, the loading factor, k_L, and the size factor, k_size.

Fatigue usually starts at the surface so that the quality of the surface finish is very important. The surface finish becomes even more important as the strength of the material increases.

Either specify the modifying factor directly or choose a finish from the drop-down box. If you don't know, select None and a default value of 1 will be used.

Surface Factor

k_SF =

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

Loading Factor

k_L =

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

All mechanical components are structures contain some form of stress concentrators which can cause cracks to form. The theoretical stress concentration depends on geometry and relates the local maximum stress to the nominal or average stress through a stress concentration factor.

Stress Concentration Factor

K_t =

Small stress concentrations are less effective in fatigue than predicted by K_t. A fatigue notch factor (effective stress concentration in fatigue) is used to account for this effect. It is related to the size of the local stress gradient and material strength.

Either specify K_f directly or enter K_t and the radius.

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

Safety Factor

The safety factor represents how much you have underestimated the strength of the material in order to ensure a safe design with a life equal to the fatigue limit.

Two stresses, alternating and mean are needed to calculate fatigue lives. It is impossible to back calculate both stresses from a single safety factor. Some information about the mean must be specified. You must choose to set the mean, maximum, minimum, or stress ratio to some value.

If you wish to calculate a safety factor, leave this section blank and click the Calculate Life / Safety Factor button below. If you wish to calculate the stresses, you must specify the desired safety factor and provide some additional information about the mean stresses.

Safety Factor	n =
Mean Stress Definition	=