1. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Static Analysis: Fatigue

2. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Objectives This module will present the methods for estimating fatigue life using the Fatigue Wizard found in Autodesk® Simulation Multiphysics.  Two methods will be reviewed: Stress-Life and Strain-Life.  The Strain-Life method will be used for low-cycle fatigue situations having less than 10 4 cycles to failure.  The Stress-Life method will be used for high-cycle fatigue situations having more than 10 4 cycles to failure. Section II – Static Analysis Module 9 - Fatigue Page 2

3. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Fatigue  Fatigue is the progressive damage that occurs when a material is subjected to cyclic loading.  The loading and unloading of a mechanical component can lead to the initiation of a small crack that grows to a critical size and results in fracture.  Fatigue failures can occur when the stresses are significantly below the yield strength of the metal. Section II – Static Analysis Module 9 - Fatigue Page 3 The Fatigue Wizard in Autodesk® Simulation Multiphysics leads you through the steps needed to perform a fatigue analysis.

4. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Design Objectives  A mechanical component can be designed to meet one or more objectives.  It can be designed to carry a specific load (Figure 1) and/or it can be designed to achieve a specific life (Figure 2).  Fatigue calculations are associated with obtaining a specific life. time stress X failure Strength Figure 1 time stress X failure Figure2 Life Section II – Static Analysis Module 9 - Fatigue Page 4

5. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community High and Low Cycle Fatigue  High cycle fatigue involves stress levels significantly below the yield strength.  Low cycle fatigue involves stress levels near or greater than the yield strength of the material.  High cycle fatigue generally has cycles to failure of 10 4 or greater. Fatigue Life Estimation Methods Stress Life Strain Life Fatigue life determined using S-N Curve. Fatigue life is determined using the Basquin-Coffin- Manson Equations. High Cycle Fatigue Section II – Static Analysis Module 9 - Fatigue Page 5 Low Cycle Fatigue

6. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community High Cycle Fatigue Rotating Beam Fatigue Test  An alternating stress can be developed using a rotating beam test.  The stress is completely reversed, meaning that the stress alternates between tension and compression.  The test fixture uses a four point bending setup that removes shear from the test section.  Different stress levels are obtained by changing the load.  The cycles to failure at a specific load level are counted. Mott, R.L., Machine Elements in Mechanical Design, 3 rd Ed., Prentice-Hall, 1999 (p.145). Section II – Static Analysis Module 9 - Fatigue Page 6

7. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community High Cycle Fatigue Fatigue Strength  The fatigue strength is the stress level that a material can endure for N cycles.  A plot of fatigue strength versus the number of cycles to failure gives an S-N curve.  An S-N curve is often plotted on a Log-Log scale. S-N Curve for an Alloy Steel Cycles to Failure, N Section II – Static Analysis Module 9 - Fatigue Page 7

8. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community High Cycle Fatigue Endurance Limit  The stress level at which the material can withstand an infinite number of cycles is called the Endurance Limit.  Not all metals exhibit an Endurance Limit.  Ferrous metals typically exhibit an Endurance Limit.  Non-ferrous metals may not exhibit an Endurance Limit. S-N Curve for 4120 Alloy Steel Cycles to Failure S e, Endurance Limit Parts having stress levels below the endurance limit will have infinite life. Infinite Life Region Section II – Static Analysis Module 9 - Fatigue Page 8

9. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community High Cycle Fatigue Endurance Limit Modification Factors  The Endurance Limit is determined using specimens having smooth polished surfaces.  A variety of factors, including surface roughness, can reduce the Endurance Limit.  Factors effecting the endurance limit include: surface finish, size, environment, and type of test. Surface Finish Reduction Factors available in Autodesk® Simulation Multiphysics Section II – Static Analysis Module 9 - Fatigue Page 9

10. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community High Cycle Fatigue Alternating and Mean Stress Components  High cycle fatigue life estimation methods are based on the S-N curve.  The S-N curve is developed for completely reversed loading (zero mean stress).  A tension mean stress will reduce the fatigue life. Alternating Stress Mean Stress Section II – Static Analysis Module 9 - Fatigue Page 10

11. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community High Cycle Fatigue Mean Stress Interaction Equations Goodman Equation Gerber Equation  Several criteria are used to account for the reduction in fatigue life associated with a tensile mean stress.  Two common interaction equations are the Goodman equation and the Gerber Equation.  If these equations are used for infinite life design, the fatigue life, S(N), used in the equation is the endurance limit, Se. Section II – Static Analysis Module 9 - Fatigue Page 11

12. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community High Cycle Fatigue Mean Stress Interaction  The Fatigue Strength, S(N), can be found from the mean stress interaction equation, when there is a mean stress component.  Once S(N) is obtained, the number of cycles to failure is found using the S-N curve. Solving for S(N) yields Section II – Static Analysis Module 9 - Fatigue Page 12 Gerber Equation

13. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community High Cycle Fatigue Multicomponent Stress States  The S-N curve and associated mean and alternating stress components are developed for a single stress component.  The von Mises stress is used to determine an equivalent stress component when multi-axial stress components exist.  The equivalent mean and alternating stresses are then computed from the mean and alternating stress components. Section II – Static Analysis Module 9 - Fatigue Page 13

14. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community High Cycle Fatigue Complex Load Histories  The S-N curve is created using a sinusoidal stress.  Each cycle involves one stress reversal.  Complex load histories must be converted into a set of stress reversals having different amplitudes.  A cumulative damage law is then used to assess the combined effect of the stress reversals. Section II – Static Analysis Module 9 - Fatigue Page 14 The Rainflow Cycle Counting Method is a commonly used method for breaking a complex load history into a set of simple stress cycles. ASTM E1049-85(reapproved 2005) provides a standard practice for applying this method. The Fatigue Wizard in Autodesk® Simulation Multiphysics uses the Rainflow Counting Method.

15. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community High Cycle Fatigue Cumulative Damage Laws  All of the cycles from the Rainflow Counting Method use up some of the life of the component.  A cumulative damage law accounts for the effects of all of the cycles when assessing the life of the component. Section II – Static Analysis Module 9 - Fatigue Page 15 Miner’s Rule is the most commonly used Cumulative Damage Law and is used by the Fatigue Wizard. Miner’s Rule Number of stress cycles due to load cycle i NiNi Cycles to failure due to load cycle i (from S-N Curve)

16. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Low Cycle Fatigue Strain – Life Method Section II – Static Analysis Module 9 - Fatigue Page 16 E Stress Strain  The Strain-Life Method is used to determine the fatigue life in the low cycle fatigue regime.  This method is based on strain- controlled cyclic load tests carried out on axial fatigue test load frames.  A cyclic-stress-strain curve for a material loaded into the plastic strain region is shown in the figure.

17. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Low Cycle Fatigue Strain-Life Equations Fatigue ductility coefficient c Fatigue ductility exponent  The Basquin-Coffin-Manson equation for the total strain is used to determine the fatigue life.  The coefficients and exponents are determined experimentally. Basquin-Coffin-Manson Equation Fatigue strength coefficient b Fatigue strength exponent Section II – Static Analysis Module 9 - Fatigue Page 17 Experimental or approximate coefficients can be used with the Fatigue Wizard.

18. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Low Cycle Fatigue Total Strain Curve  The Basquin-Coffin-Manson equation is the sum of two effects.  The first curve is dominated by elastic strains (red).  The second curve is dominated by plastic strains (black).  The transition between low and high cycle fatigue is located at the intersection of the two curves. Plastic Strain Elastic Strain Section II – Static Analysis Module 9 - Fatigue Page 18

19. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Low Cycle Fatigue Neuber Method  The Basquin-Coffin-Manson equation requires a method for determining the total strain (sum of elastic and plastic components).  An elastic-plastic stress analysis could be performed.  As an alternative, the Neuber Method provides a method for estimating the total strain based on an elastic analysis.  If the Finite Element mesh is sufficiently fine to capture the stress concentration, the stress concentration factor, K t, can be set to one. Section II – Static Analysis Module 9 - Fatigue Page 19 Ramberg-Osgood Eq. Cyclic Stress-Strain Computed Real Iteratively solve for stress then find strain.

20. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Low Cycle Fatigue Mean Stress Effects  Two mean stress correction methods are used in the Fatigue Wizard:  1) Morrow and  2) Smith-Watson-Topper.  The Morrow method is best when the loading is predominately compressive.  The Smith-Watson-Topper method is best if the stress is predominately tensile. Section II – Static Analysis Module 9 - Fatigue Page 20 Morrow Smith-Watson-Topper Fatigue Life Estimates Determined by the Fatigue Wizard.

21. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Low Cycle Fatigue Cumulative Damage  The Rainflow Counting Method and Miner’s Cumulative Damage Rule discussed with respect to high-cycle fatigue are also used with low-cycle- fatigue.  The Rainflow Counting method uses data entered in the Fatigue Wizard’s Load Case History table. Section II – Static Analysis Module 9 - Fatigue Page 21

22. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Module Summary  This module has presented a summary of the methods used to estimate fatigue life using the Fatigue Wizard found in Autodesk® Simulation Multiphysics.  Two methods are available: Stress-Life and Strain-Life.  The Strain-Life method should be used for low-cycle fatigue situations having less than 10 4 cycles to failure.  The Stress-Life method can be used for high-cycle fatigue situations having more than 10 4 cycles to failure. Section II – Static Analysis Module 9 - Fatigue Page 22