BIZOMAT MAKEOS · Strength
Fatigue Design Check (Corrected Endurance, Notch, Mean Stress, Life)
Will this notched part survive its fluctuating load indefinitely, and if not, how many cycles will it last?
Fatigue check of a notched part under a fluctuating stress: the endurance limit corrected by your surface, size, load, temperature and reliability factors, the fatigue notch factor from the stress concentration factor and notch radius (as the fatigue notch factor tool), alternating and mean stresses from the nominal maximum and minimum, safety factors by Goodman, Soderberg and Gerber with a first-cycle yield check (as the Goodman fatigue tool), and the finite life from the S-N line for the equivalent fully reversed stress (as the S-N fatigue life tool).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Material | ||
| Ultimate tensile strength | MPa | Ultimate tensile strength. |
| Yield strength | MPa | Yield strength. |
| Test-specimen endurance limit (0 = estimate as 0.5 Su, at most 700 MPa) | MPa | Rotating-beam endurance limit of polished specimens; 0 estimates it as half the tensile strength, capped at 700 MPa (steels). |
| Endurance correction factors | ||
| Surface factor | Surface factor for the finish (machined, ground, as-forged; your value). | |
| Size factor | Size factor for the section size. | |
| Load factor | Load factor (1 bending, about 0.85 axial, 0.59 torsion). | |
| Temperature factor | Temperature factor. | |
| Reliability factor | Reliability factor (1 for 50%, about 0.868 for 99%). | |
| Notch and load | ||
| Stress concentration factor | Theoretical stress concentration factor for the notch geometry and load type. | |
| Notch radius | mm | Notch root radius (for the notch sensitivity). |
| Nominal maximum stress | MPa | Largest nominal stress in the cycle (without the notch). |
| Nominal minimum stress | MPa | Smallest nominal stress in the cycle. |
| Safety factor required | Safety factor you require. | |
| Cycles required (if below infinite life) | cycles | Cycles the part must last if it cannot reach infinite life. |
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.
Material
What this means: Ultimate tensile strength
- What it is
- The ultimate tensile strength of the part material: the highest stress a tensile test specimen reaches before it breaks. It anchors the Goodman line, the notch sensitivity and the S-N line.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 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 strength of the material in its final heat-treated condition, from the certificate or data sheet.
What this means: Yield strength
- What it is
- The yield strength of the part material, the stress at which it starts to deform permanently. It is used for the yield safety factor and the Soderberg line.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 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.
- Effect on the result
- The yield safety factor rises in direct proportion to it.
- Get it right
- It must not exceed the tensile strength, or the tool reports an error. Use the 0.2 % proof stress if there is no clear yield point.
What this means: Test-specimen endurance limit (0 = estimate as…
- What it is
- The endurance limit of a polished rotating-beam test specimen of this material, before any corrections for the real part.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0 MPa to 1500 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The corrected endurance limit, and every fatigue safety factor, rises in proportion to it.
- Get it right
- Use 0 to let the tool estimate it from the tensile strength (a steel rule). Enter tested data where you have it.
Endurance correction factors
What this means: Surface factor
- What it is
- The correction to the endurance limit for the surface finish of the real part, such as ground, machined, hot rolled or as forged.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.8 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The corrected endurance limit is directly proportional to it.
- Get it right
- Read it for your finish and tensile strength from a fatigue design reference; rough surfaces lower it a lot.
What this means: Size factor
- What it is
- The correction to the endurance limit for the size of the section, because larger parts hold more flaws than a small test specimen.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 1.1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.85 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The corrected endurance limit is directly proportional to it.
- Get it right
- Base it on the diameter or effective size at the notch, not the largest size of the part.
What this means: Load factor
- What it is
- The correction to the endurance limit for the type of loading: bending, axial or torsion, compared with the rotating bending of the test.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The corrected endurance limit is directly proportional to it.
- Get it right
- Use 1 for bending. For axial or torsion loading take the value from your fatigue reference.
What this means: Temperature factor
- What it is
- The correction to the endurance limit for the operating temperature of the part.
- Units and format
- Enter a plain number with no unit. The form accepts 0.3 to 1.1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The corrected endurance limit is directly proportional to it.
- Get it right
- Use 1 near room temperature; take a value from material data for hot or cold service.
What this means: Reliability factor
- What it is
- The correction that lowers the average endurance limit so that the chosen share of parts, rather than half of them, will survive.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.868 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The corrected endurance limit is directly proportional to it.
- Get it right
- Use 1 for the average (50 % survival); pick the value for your required reliability from a fatigue reference.
Notch and load
What this means: Stress concentration factor
- What it is
- The theoretical stress concentration factor of the notch, shoulder, hole or groove: peak stress divided by nominal stress, for this geometry and load type.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2.2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher factor raises the fatigue notch factor and the notch stresses.
- Get it right
- Read it from stress concentration charts for the same load type (bending, axial or torsion) as the nominal stresses.
What this means: Notch radius
- What it is
- The radius at the root of the notch or fillet, used to work out how sensitive the material is to that notch.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.01 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger radius gives a higher notch sensitivity, so K_f moves closer to K_t.
- Get it right
- Use the same notch as the stress concentration factor; changing this radius here does not change K_t, so update both together.
What this means: Nominal maximum stress
- What it is
- The highest nominal stress in each load cycle at the section, worked out from the loads without the notch effect.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts -3000 MPa to 3000 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.
- Get it right
- Use nominal stress; the tool applies the notch factor itself. Enter compression as a negative value.
What this means: Nominal minimum stress
- What it is
- The lowest nominal stress in each load cycle at the section, without the notch effect. Together with the maximum it sets the alternating and mean stresses.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts -3000 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter compression as negative: a fully reversed cycle has a minimum equal to minus the maximum. It must not exceed the maximum.
What this means: Safety factor required
- What it is
- The smallest safety factor you accept, compared with the lower of the Goodman and yield safety factors.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 5. 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
- Use the factor your design code or company rules require for the consequence of failure.
What this means: Cycles required (if below infinite life)
- What it is
- The number of load cycles the part must survive. It is used only when the stress is above the corrected endurance limit, so the life is finite.
- Units and format
- Enter a number in cycles: cycles. The form accepts 1000 cycles or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000000 cycles as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Count cycles over the whole service life: cycles per hour or per revolution times the total hours or revolutions.
Method and formulas
- S_e = k_a k_b k_c k_d k_e S_e′.
- Neuber constant a = 0.0254 (2070 ÷ S_u)^1.8 mm; q = 1 ÷ (1 + a ÷ r); K_f = 1 + q(K_t − 1) (as the fatigue notch factor tool).
- σ_a = K_f (σ_max − σ_min) ÷ 2; σ_m = K_f (σ_max + σ_min) ÷ 2.
- Goodman n = 1 ÷ (σ_a ÷ S_e + σ_m ÷ S_u); Soderberg uses S_y; Gerber the parabola; yield n = S_y ÷ (σ_a + |σ_m|) (as the Goodman fatigue tool).
- Finite life: σ_ar = σ_a ÷ (1 − σ_m ÷ S_u); N from the S-N line through 0.9 S_u at 10³ and S_e at 10⁶ (as the S-N fatigue life tool).
- Example: S_e = 177.07 MPa and K_f = 1.9709 give σ_a 78.835 MPa, σ_m 118.25 MPa and a Goodman factor of 1.5569.
Limitations
- Correction factors and the S-N line are estimates; tested data for the material and finish govern.
- Uniaxial stress; combined stresses need an equivalent (von Mises) alternating and mean stress.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a shaft shoulder, hole or groove under cyclic load
- Find the life of a part that does not reach infinite life
- See how surface finish and notch radius affect fatigue
Who it is for
- Design engineers
- Reliability engineers
- Mechanical engineers
What you get
- Corrected endurance limit and fatigue notch factor
- Alternating and mean stresses
- Safety factors and finite life
Interpreting the result
- A larger notch radius and a better surface finish are usually the cheapest fatigue improvements.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 200–211, 280, 358. 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
How metal tires
In Metal Fatigue by the Numbers
What it covers: Why steel parts break under loads well below their strength: slip bands, crack starts, crack growth and final fracture, and how to read the story on a broken surface.
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.
Open the Fatigue Design Check (Corrected Endurance, Notch, Mean Stress, Life) calculator