Roymech's Fatigue Calculator
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 Description:

Fatigue considerations are important because the consequent failure is generally sudden and at a stress level much lower than the ultimate stress. Fatigue properties of materials are generally determined by producing Wohler /SN Plots. These are simply plots with stress as the vertical axis and log (number of complete stress reversals) as the horizontal axis. A number of material specimens are tested and the points at which they break are plotted on the SN curve.
The fatigue strength is the maximum completely reversed stress under which a material will fail after it has experienced the stress for a specified number of cycles. (The strength is accompanied by the number of cycles).Fatigue Strength (fixed number of cycles) = Sn. It is a useful property of steel (and titanium) that when the stress level fall below a certain value the specimen is effectively never likely to fail. Generally other materials do not exhibit this effect. The Fatigue limit is the maximum completely reversed stress for which it is assumed that the material will never fail regardless of the number of cycles. Fatigue Limit = S'n
Experiments have shown little direct relationship between the fatigue limit and the yield strength, ductility etc. However some relationship between the fatigue limit and the tensile strength has been established for unnotched polished specimens tested using the rotating beam method. This method loads the specimens by reversed bending.
Purpose of calculation:
 Produce Wohler /SN Plots and Goodman Diagram Plot
 Determine cut off stress.
 Determine the fatigue strength of a material.
 Determine the fatigue limit.
 Determine the relationship between the fatigue limit and the tensile strength.
Calculation Reference
Many references have been considered in producing this calculation. I have named the calculation after the Roymech website in recognition of his great website.
 http://www.roymech.co.uk/Useful_Tables/Fatigue/Fatigue_index.html
 http://materials.open.ac.uk/mem/mem_mf.htm
 http://www.fatiguecalculator.com/
 Petersons Stress Concentration Factors
Calculation Procedure
1) Input Applied Stress
2) Define Material
 Material ultimate tensile strength.
 Material yield
 Type of loading
 Mean low cycle fatigue limit factor ('mean' represents a 50% survival limit).
 Number of cycles related to mean low cycle fatigue limit
 Mean high cycle fatigue limit factor ('mean' represents a 50% survival limit).
 Number of cycles related to mean high cycle fatigue limit
 Factor of safety
3) Calculate Low Cycle Fatigue Limit
 Fatigue limit at zero mean stress
 Allowable alternating stress  Soderberg (conservative)
 Allowable alternating stress  Goodman (steel, aluminium & titanium)
 Allowable alternating stress  Gerber (less conservative)
 Allowable alternating stress  Smith (cast iron & magnesium)
4) Determine Modifying Factors for High Cycle Fatigue Limit
Size Factor  The endurance limits of specimens have been observed to vary with their size. This is possibly related to the probability of a high stress interacting with a critical flaw within a certain volume, i.e., when the volume is large there is a higher probability of failure. Hence, when the size increases, the endurance decreases. Alternatively, since there appears to be a more pronounced size effect in reversed bending and/or torsion than in the reversed axial loading situation this suggests that the stress gradient at the surface is partially responsible for the size effect.
Surface finish factor.
 As Forged
 Hot Rolled
 Rough turned (peak to valley height 30μm)
 Turned/rough ground (peak to valley height 12μm)
 Fine turned (peak to valley height 6.5μm)
 Fine ground (peak to valley height 2.5μm)
 Lapped/rough polished (peak to valley height 1μm)
 Mirror polished
Probability of survival factor  The basic values are mean values implying a 50% survival rate. To enable determination of design strength values with a higher survival rate i.e. 90% upwards then the indicated strength values must be reduced.
 50.0000% 1,000
 90.0000% 0.897
 95.0000% 0.868
 99.0000% 0.814
 99.9000% 0.753
 99.9900% 0.702
 99.9990% 0.659
 99.9999% 0.620
Miscellaneous Factor  This factor is a general factor to allow for any other factors:
 corrosion
 electrolytic plating
 metal spraying
 cyclic frequency
 fretting corrosion
 radiation effects on materials.
Stress concentration factor  The theoretical stress concentration factor Kt of a section at subject to an internal stress resulting from a change of shape and/or geometry :
Kt = Highest value of stress at a discontinuity / Nominal stress at local minimum section
This value does not allow for the sensitivity of the material to stress concentrations.
Useful references for calculation of Kt :
 /repository/strength/stress/
 Machinery's Handbook 18th ed.
 Mechanical Engineers Data Book (J.Carvill)
 Machine DesignTheory & Practice A.D Deutschman, W.J Michels, C.E. Wilson
 The calculators in the links below (ETB and Stacie Glass)
Notch sensitivity factor  The material notch sensitivity value "q" is used to quantify the sensitivity of a material to local high stresses. The notch sensitivity of a material is a measure of how sensitive a material is to notches or geometric discontinuities.
 High notch sensitivity for Brittle/Hard Materials q=1.0
 Very perfect material is significantly damaged by addition of a notch
 Low Notch sensitivity for Soft Ductile Materials
 Material with a lot of flaws not damaged much by one more.
 Petersons estimate for steel
 Fatigue notch factor
5) Calculate High Cycle Fatigue Limit
Fatigue limit at zero mean stress
 Allowable alternating stress  Soderberg (conservative)
 Allowable alternating stress  Goodman (steel, aluminium & titanium)
 Allowable alternating stress  Gerber (less conservative)
 Allowable alternating stress  Smith (cast iron & magnesium)
6) Construct SN Diagram
 Use Excel curve fit functions for SN curve
 Calculate allowable alternating stress for known number of cycles
 Calculate allowable number of cycles for known alternating stress
7) Construct Goodman diagram
Calculation Reference
Petersons Stress Concentration Factors
 Find on Amazon.com  Find on Amazon.co.uk  Find on Amazon.fr  Find on Amazon.de  Find on Amazon.ca 
Machinery's Handbook 18th ed.
 Find on Amazon.com  Find on Amazon.co.uk  Find on Amazon.fr  Find on Amazon.de  Find on Amazon.ca 
Mechanical Engineers Data Book (J.Carvill)
 Find on Amazon.com  Find on Amazon.co.uk  Find on Amazon.fr  Find on Amazon.de  Find on Amazon.ca 
Machine DesignTheory & Practice A.D Deutschman, W.J Michels, C.E. Wilson
 Find on Amazon.com  Find on Amazon.co.uk  Find on Amazon.fr  Find on Amazon.de  Find on Amazon.ca 
The calculators in the links below (ETB and Stacie Glass)
 Find on Amazon.com  Find on Amazon.co.uk  Find on Amazon.fr  Find on Amazon.de  Find on Amazon.ca 
Version History
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 02 Feb 2010
 Submitted By:
 JohnDoyle[Admin]
 File Date:
 26 Jan 2010
 File Version:
 1.0
 File Size:
 121.82 Kb
 File Type:
 xlsx
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