Fatigue Algorithm Input

Transcription

1 Methods

2 Fatigue Algorithm Input By default, fe-safe analyses stress datasets that contain elastic stresses The calculation of elastic-plastic stress-strains, where necessary, is performed in fe-safe using an elastic-plastic correction (using biaxial Neuber s Rule ) This elastic-plastic correction is applied to each node individually, and so it cannot allow for any stress redistribution effects in the FEA model Where stress redistribution may be significant, it is generally necessary to use an elastic-plastic FEA (The plasticity correction (Neuber s rule) is turned off in this case) Only the biaxial strain algorithms support elastic-plastic FEA results FOS, FRF, and Failure Rate for Target Lives calculations are not supported when using elasticplastic FEA results CH5-2

3 Fatigue Algorithm As can be seen in the menu, the Biaxial Strain Life and the Advanced Fatigue algorithms are applicable for both high (HCF) and low (LCF) cycle fatigue The Biaxial Stress Life algorithms are only applicable to HCF Several of the algorithms use critical plane (CP) methods CH5-3

4 Critical Plane Methods For many components subjected to combined direct and shear stresses, the phase relationship between the stresses is not constant In these cases it is not obvious which plane will experience the most severe combination of strains and hence the highest fatigue damage Critical plane methods resolve the strains onto a number of planes, and calculate the damage on each plane This form of analysis must be applied for criteria such as principal stress/strain, maximum shear stress/strain, and the Brown-Miller criterion, for complex strain signals with varying phase relationships. A 10º increment between planes is often used since this increment produces an error in calculated life of less than 2% compared with a 1º increment CH5-4

5 Mean Stress Corrections As was mentioned previously, the mean stress affects the fatigue life Thus, the equivalent stress or strain amplitude at at zero mean stress must be determined before the fatigue life is calculated Several mean stress corrections are available, including: Morrow Smith-Topper-Watson (STW) Goodman Gerber User defined None CH5-5

6 Use of S-N Curves To designate the S-N curves as the fatigue curves for an analysis, bring up the General FEA options dialog box found in the FEA Fatigue menu, and check the Use SN curves for stress-type analyses CH5-9

7 Maximum Principal Strain This is a critical plane multi-axial fatigue algorithm, using planes perpendicular to the surface If stress results from an elastic FEA are used, then a multi-axial elastic-plastic correction is used to calculate elastic-plastic stress-strains from these results Otherwise, elastic-plastic stress-strain dataset pairs are required, and the plasticity correction (i.e., Neuber s rule) is turned off CH5-10

8 Maximum Principal Strain (cont.) Fatigue lives are calculated on eighteen planes, spaced at 10º increments On each plane, The principal strains are used to calculate the time history of the strain normal to the plane Cycles of normal strain are extracted and corrected for the mean stress The fatigue life is calculated The fatigue life is the shortest life calculated for the series of planes Fatigue analysis using principal strains can give very non-conservative results for ductile metals However, this is the recommended algorithm for brittle metals CH5-11

9 Brown-Miller Algorithm This is a critical plane multi-axial fatigue algorithm, using planes perpendicular to the surface, and at 45º to the surface Principal strains are used to calculate the time history of the shear strain and the strain normal to the plane Fatigue cycles are extracted and corrected for mean normal stress If stress results from an elastic FEA are used, then a multi-axial elastic-plastic correction is used to calculate elastic-plastic stressstrains from these results Otherwise, elastic-plastic stress-strain dataset pairs are required, and the plasticity correction (i.e., Neuber s rule) is turned off CH5-12

10 Brown-Miller Algorithm (cont.) On each of three planes, fatigue lives are calculated on eighteen subsidiary planes, spaced at 10º increments On each plane, The principal strains are used to calculate the time history of the shear strain and the strain normal to the plane Cycles are extracted and corrected for the effect of the mean normal stress The fatigue life is calculated The fatigue life is the shortest life calculated for the series of planes The Brown-Miller algorithm is the preferred algorithm for most conventional metals at room temperature and is the default algorithm for most materials in the fe-safe materials data base CH5-13

11 Cast Iron This is a critical plane multi-axial fatigue algorithm, using planes perpendicular to the surface This algorithm is equally applicable to: Grey iron Compacted graphite (CG) iron Nodular (SG) iron CH5-14

12 Cast Iron (cont.) Fatigue lives are calculated on eighteen planes, spaced at 10º increments The normal strain on the plane is the damage parameter On each plane the fatigue cycles are: Extracted Corrected for plasticity using a biaxial Neuber s rule Corrected for mean-stress CH5-15

13 Maximum Shear Strain This is a critical plane multi-axial fatigue algorithm, using planes perpendicular to the surface, and at 45º to the surface Principal strains are used to calculate the time history of shear strain. Cycles of shear strain are calculated, and corrected for mean stress If stress results from an elastic FEA are used, then a multi-axial elastic-plastic correction is used to calculate elastic-plastic stressstrains from these results Otherwise, elastic-plastic stress-strain dataset pairs are required, and the plasticity correction (i.e., Neuber s rule) is turned off CH5-16

14 Maximum Shear Strain (cont.) On each of three planes, fatigue lives are calculated on eighteen subsidiary planes, spaced at 10º increments On each plane, The principal strains are used to calculate the time history of the shear strain and normal stress Cycles of shear strain are extracted and corrected for the mean normal stress The fatigue life is calculated The fatigue life is the shortest life calculated for the series of planes This algorithm tends to give conservative life estimates for ductile metals, but can give unsafe life estimates for brittle metals CH5-17

15 Maximum Principal Stress This is a critical plane multi-axial fatigue algorithm, using planes perpendicular to the surface When using the local strain materials data to define the life curve, a cyclic plasticity correction is used to convert the elastic FEA stresses to elastic-plastic stress-strains Otherwise the life curve is defined by the S-N values defined in the materials database, and no plasticity correction is performed CH5-18

16 Maximum Principal Stress (cont.) Fatigue lives are calculated on eighteen planes, spaced at 10º increments On each plane, The principal stresses are used to calculate the time history of the stress normal to the plane Cycles are extracted and corrected for the mean stress The fatigue life is calculated The fatigue life is the shortest life calculated for the series of planes Fatigue analysis using principal stresses can give very non-conservative results for most ductile metals CH5-19

17 Brown-Miller Combined Brown-Miller Combined Direct and Shear Stress analysis CH5-20

18 Brown-Miller Combined (cont.) This algorithm can only be used when no plasticity occurs The life curve is defined as an S-N curve All nodes with lives beneath 1e6 are listed as they would probably experience plasticity and hence the algorithm would not be suitable This algorithm is as reliable as the Brown-Miller algorithm, but has the limitation that it can only be used for high cycle fatigue CH5-21

19 CPF Analysis Critical Plane Fatigue (CPF) Combined Direct and Shear Stress Analysis This algorithm is not recommended because as with all representative stress variables that have their sign defined by some criteria, there is a possibility of sign oscillation This occurs when the direct and shear contributions are approximately equal but the sign is opposite This is why using such representative stress values for fatigue analysis can cause spurious hot spots CH5-22

20 von Mises Life This algorithm is not recommended because as with all representative stress variables that have their sign defined by some criteria, there is a possibility of sign oscillation For the von Mises stress, this occurs when the hydrostatic stress is close to zero (i.e., the major two principal stresses are similar in magnitude and opposite) This is why using such representative stress values for fatigue analysis can cause spurious hot spots CH5-23

21 Dang Van Analysis The Dang Van model is an endurance criterion for analysis of high cycle fatigue (i.e., infinite life design) of components subject to complex multiaxial stresses The method calculates whether a component has infinite life, but does not calculate fatigue lives It is essentially a pass/fail analysis Two additional material parameters are required for Dang Van analyses (stress data for at least two different stress ratios) CH5-24

22 Uniaxial Strain Life The elastic-plastic strain amplitude is used to calculate the fatigue life This algorithm is provided for analyzing uniaxial stresses Uniaxial stresses rarely occur in practice The multiaxial algorithms are strongly recommended CH5-25

23 Uniaxial Strain Life (cont.) Elastic stresses are required for input Multiaxial methods are used to calculate elastic strains from elastic stresses A multiaxial elastic-plastic correction is used to derive the strain amplitudes and stress values needed in the equations CH5-26

24 Uniaxial Stress Life The stress amplitude is used to calculate the fatigue life This algorithm is provided for analyzing uniaxial stresses Uniaxial stresses rarely occur in practice The multiaxial algorithms are strongly recommended CH5-27

25 Uniaxial Stress Life (cont.) The fatigue life curve can either be a S-N curve or a stress-life curve derived from local strain materials data S-N Curve Defined by the S-N values in the materials database No plasticity correction is performed. When using the local materials strain data, the life curve is defined by the equation below, and a multiaxial cyclic plasticity correction is used to convert the elastic FEA stresses to elastic-plastic stress-strain 2 ' b f (2N f ) CH5-28

26 Fatigue Algorithm Recommendations In summary there are four criteria that can be recommended: Brown-Miller, with mean stress corrections, for ductile metals Principal (or axial) strain, with mean stress corrections, for brittle metals Cast iron, with mean stress corrections, for cast irons Dang Van for infinite life design CH5-29

27 Design Life There are three types of design life analyses that can be performed: Factor of Strength (FOS) calculations, which can be performed for any analysis other than the FRF calculations. A Fatigue Reserve Factor (FRF) analysis, which can be performed instead of a fatigue life analysis for Principal Stress or Principal Strain analyses A Failure Rate for Target Lives calculation, which is only available for the multi-axial calculations based upon strain-life materials data (i.e., it is not available for S-N curve analyses) CH5-30

28 Factors of Strength The factor of strength (FOS) is the factor which, when applied to either the loading or to the elastic stresses in the finite element model, will produce the required design life at the node The FOS is calculated at each node, and the results are written as an additional value to the output file The FOS values can be plotted as contour plots This analysis can be selected when the Design Lives dialogue is opened by clicking on the Design Life button in the Fatigue from FEA dialogue CH5-31

29 Factors of Strength (cont.) The FOS at a node is calculated as follows: The calculated life is compared with the design life If the calculated life is lower than the design life, the elastic stresses at the node are scaled by a factor less than 1.0 If the calculated life is greater than the design life, the elastic stresses at the node are scaled by a factor greater than 1.0 The elastic stress history is recalculated using the rescaled nodal stresses (continued) CH5-32

30 FOS calculations (cont.) Factors of Strength (cont.) For local strain analysis, the cyclic plasticity model is used to recalculate the time history of elastic-plastic stress-strains. The fatigue life is then recalculated. For S-N curve analysis, the fatigue life is recalculated from the time history of the elastic stresses In the critical plane analysis, the critical plane orientation is re-calculated The process is repeated with different scale factors until The calculated life is within 5% of the design life, or The step change of 0.01 or.1 in the FOS value causes the design life to be bracketed, or The FOS exceeds the max. factor (default 2.0) or is less than the min. factor (default 0.5) CH5-33

31 Factors of Strength (cont.) The limits of the FOS values can be configured in the Band Definitions for FOS Calculations dialogue, which is found on the FOS tab of the General FEA options dialogue CH5-34

32 Factors of Strength (cont.) Band Definitions for FOS Calculations (cont.) The default limit values are: Maximum 2.0 (all FOS values higher than this will be written as 2.0) Maximum fine 1.5 Minimum fine 0.8 Minimum 0.5 (all FOS values lower than this will be written as 0.5) FOS values between the maximum and minimum fine factors are calculated to a resolution of approximately Other FOS values are calculated to a resolution of approximately 0.1. CH5-35

33 Fatigue Reserve Factor Analysis The Fatigue Reserve Factor (FRF) (sometimes referred to as the Fatigue Reliability Factor) is a linear scale factor obtained from a Goodman-type diagram The FRF analysis allows the user to specify an envelope of infinite life for the component as a function of stress/strain cycle amplitude and mean stress CH5-36

34 FRF Analysis (cont.) The ratio of the distance to the infinite life line and the distance to the cycle (Sa, Sm) is calculated for each extracted cycle, to produce four reserve factors: Horizontal FRF: FRF H A B H H Veritical FRF: Radial FRF: FRF V FRF R A B V V A B R R Worst FRF: Worst of above 3 factors CH5-37

35 FRF Analysis (cont.) The design life is specified in the Material Database Type and Algorithm Editing dialogue The design life is substituted into the life equation for the analysis type to calculate the amplitude that would cause failure at that design life CH5-38

36 FRF Analysis (cont.) When using an infinite life envelope, there are no issues with FRF analyses However, when designing for finite life, except in the case of constant amplitude loading, there are problems with FRF calculations Consider the case below. Currently, the smaller cycles are currently non-damaging. (Note that the endurance limit in the graph would already be reduced to 1/4 of the original value because of the presence of the larger cycles.) However, the FRF calculated for the larger cycles would not take into account that the smaller cycles would now be damaging if the loads were increased For this reason, it is strongly recommended that Factors of Strength (FOS) calculations be used, instead of FRFs CH5-39

37 Failure Rate for Target Lives This analysis combines the variability in the material fatigue strength and variability in the applied loading, to calculate a probability of failure for the life or lives specified It is only available for the multi-axial calculations based upon strainlife materials data (i.e., it is not available for S-N curve analyses) The analysis is configured in the Fatigue Rate for Target Lives dialogue, which is opened by clicking the Probability button in the Fatigue from FEA dialogue CH5-40

38 Failure Rate for Target Lives (cont.) The failure rate for target lives calculates the % probability of failure at the specified lives (user-defined life units) For each of the list of target lives, a contour plot will be created indicating the % probability of failure at that life This percentage can either be the % of components that will fail (Failure Rate) or the % that will survive (Reliability Rate) depending upon whether or not the check box Calculate Reliability rate instead of Failure Rate is checked CH5-41

39 Failure Rate for Target Lives (cont.) The failure rates are calculated as follows: The assumption is made that for failure rate analysis to be useful the component must fall in the elastic area of the strain-life curve A normal (Gaussian) distribution is applied to the variation in loading. The % standard deviation of loading is defined, representing the variability of the value of load amplitude relative to the amplitude defined. For non-constant amplitude loading the code derives an equivalent constant amplitude loading A Weibull distribution is applied to the material strength. This is defined by three parameters: The Weibull mean The Weibull slope The Weibull minimum parameter, Qmuf The overlap area of the normal distribution of loading and the Weibull distribution of fatigue strength is calculated for each of the target lives. This represents the probability of failure CH5-42

40 Failure Rate for Target Lives (cont.) CH5-43