© 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. Education Community Static Analysis: Fatigue

© 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. 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

© 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. 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.

© 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. 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

© 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. 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

© 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. 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

© 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. 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

© 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. 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

© 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. 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

© 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. 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

© 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. 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

© 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. 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

© 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. 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

© 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. 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 E (reapproved 2005) provides a standard practice for applying this method. The Fatigue Wizard in Autodesk® Simulation Multiphysics uses the Rainflow Counting Method.

© 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. 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)

© 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. 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.

© 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. 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.

© 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. 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

© 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. 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.

© 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. 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.

© 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. 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

© 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. 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