BIZOMAT MAKEOS · Strength
Fatigue Safety Factor (Goodman)
Is this fluctuating stress safe for infinite life by the Goodman, Soderberg and Gerber criteria?
Fatigue safety factors for combined alternating and mean stress by modified Goodman, Soderberg and Gerber, plus first-cycle yield, against a required factor.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Alternating stress amplitude σa | MPa | Half the stress range, including the fatigue stress concentration factor Kf. |
| Mean stress σm | MPa | Average of maximum and minimum stress (tension positive), including Kf where your method requires it. |
| Corrected endurance limit Se | MPa | Endurance limit corrected for surface, size, load, temperature and reliability, from test data or your design method. |
| Ultimate tensile strength | MPa | Ultimate tensile strength from the material certificate. |
| Yield strength | MPa | Minimum yield strength from the material certificate or specification, not a typical value. |
| Required safety factor | Factor of safety required by your design code, customer specification or company standard. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Alternating stress amplitude σa
- What it is
- The alternating stress amplitude: half the difference between the maximum and minimum stress in each load cycle.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher amplitude lowers every fatigue safety factor.
- Get it right
- Enter half the range, not the full range, and include the fatigue stress concentration factor Kf.
What this means: Mean stress σm
- What it is
- The mean stress: the average of the maximum and minimum stress in each load cycle. Tension is positive.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts -100000 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- When the mean stress is zero or compressive, the tool uses the alternating stress alone for fatigue.
What this means: Corrected endurance limit Se
- What it is
- The endurance limit of the part, corrected for surface finish, size, load type, temperature and reliability: the alternating stress it can take indefinitely with no mean stress.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 220 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the corrected value for the actual part, not the plain test-specimen value; the result depends strongly on it.
What this means: Ultimate tensile strength
- What it is
- The ultimate tensile strength of the material, the highest stress it reaches in a tensile test, from the material certificate. It is used by the Goodman and Gerber lines.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the certified or specified minimum, not a typical value.
What this means: Yield strength
- What it is
- The minimum yield strength of the material, from the material certificate or specification. It is used for the Soderberg line and the first-cycle yield check.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the specified minimum, not a typical value.
What this means: Required safety factor
- What it is
- The minimum fatigue safety factor the part must achieve, from your design code, customer specification or company standard. It is compared with the lower of the Goodman and yield factors.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- This is a requirement you set; the tool only compares the calculated factor with it.
Method and formulas
- Goodman: n = 1 ÷ (σa ÷ Se + σm ÷ Su). Soderberg: n = 1 ÷ (σa ÷ Se + σm ÷ Sy).
- Gerber: n = ½(Su ÷ σm)²(σa ÷ Se)[−1 + √(1 + (2σm Se ÷ (Su σa))²)].
- Compressive mean stress: n = Se ÷ σa. Yield (Langer): n = Sy ÷ (σa + |σm|).
- Example: σa 100 and σm 80 MPa with Se 220 and Su 600 MPa give a Goodman factor of 1.701.
Limitations
- Infinite-life (endurance) criteria for steels; materials without an endurance limit need a life-based method.
- The accuracy depends on the corrected endurance limit, which is the user’s responsibility.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check shafts, springs and brackets under cyclic load
- Compare mean-stress criteria
- Screen a design before testing
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Goodman, Soderberg and Gerber safety factors
- First-cycle yield safety factor
- Governing factor
Interpreting the result
- Goodman is the usual design criterion; Gerber fits test data better; Soderberg is the most conservative.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 200–211, 280. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Mean stress: Goodman, Soderberg and Gerber
In Metal Fatigue by the Numbers
What it covers: Why a tensile mean stress lowers the alternating stress a part can take, how the Goodman, Soderberg and Gerber lines and the yield line work, and how to choose between them.
Method explained here · BIZOMAT original book
Drift, moisture, overload and fatigue
In Strain Gauges and Load Cells by the Numbers
What it covers: How to keep a weighing system honest between calibrations: daily checks on an EWMA chart, insulation and bridge tests, overload and welding damage, and a fatigue check of the cell.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.