CH5 - Fatigue Algorithmsoss.jishulink.com/caenet/forums/upload/2010/02/27/191/... · Analysis...

Analysis Methods

Analysis

Details

fe-safe v5.2 Training Manual CH5-2

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 elastic-

plastic FEA results

Analysis

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Fatigue Algorithm Details

• 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

Analysis

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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

Analysis

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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

Analysis

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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’

Analysis

Details


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

Analysis

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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

Analysis

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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 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

Analysis

Details


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 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

Analysis

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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

Analysis

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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

Analysis

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Maximum Shear Strain


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 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

Analysis

Details


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



series of planes

• This algorithm tends to give conservative life estimates

for ductile metals, but can give unsafe life estimates for

brittle metals

Analysis

Details


Maximum Principal Stress


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

Analysis

Details


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



series of planes

• Fatigue analysis using principal stresses can give very

non-conservative results for most ductile metals

Analysis

Details


Brown-Miller Combined

Brown-Miller Combined Direct and Shear Stress analysis

Analysis

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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

Analysis

Details


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

Analysis

Details


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

Analysis

Details


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)

Analysis

Details


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

Analysis

Details


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

Analysis

Details


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

Analysis

Details


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

b

ff N )2(2

'

Analysis

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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

Analysis

Details


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)

Analysis

Details


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

Analysis

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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 re-

scaled nodal stresses

(continued)

Analysis

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FOS calculations (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)

Analysis

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• 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

Analysis

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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 0.01. Other FOS values

are calculated to a resolution of approximately 0.1.

Analysis

Details


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

Analysis

Details


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:

H

HH

B

AFRF

V

VV

B

AFRF

R

RR

B

AFRF

Horizontal FRF:

Veritical FRF:

Radial FRF:

Worst FRF: Worst of above 3 factors

Analysis

Details



• 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

Analysis

Details



• 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

Analysis

Details


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 strain-

life 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

Analysis

Details


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

Analysis

Details



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

Analysis

Details



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