Fatigue_ANSYS疲劳分析

Fatigue Analysis Using ANSYS

D. Alfred Hancq, Ansys Inc.

Contents

1) Introduction

2) Overview of Capabilities

3) Typical Use Cases

4) Additional Fatigue Resources

1. Introduction

It is estimated that 50-90% of structural failure is due to fatigue, thus there is

a need for quality fatigue design tools. However, at this time a fatigue tool is

not available which provides both flexibility and usefulness comparable to

other types of analysis tools. This is why many designers and analysts use

"in-house" fatigue programs which cost much time and money to develop. It

is hoped that these designers and analysts, given a proper library of fatigue

tools could quickly and accurately conduct a fatigue analysis suited to their

needs.

The focus of fatigue in ANSYS is to provide useful information to the

design engineer when fatigue failure may be a concern. Fatigue results can

have a convergence attached. A stress-life approach has been adopted for

conducting a fatigue analysis. Several options such as accounting for mean

stress and loading conditions are available.

2. Capabilities

A fatigue analysis can be separated into 3 areas: materials, analysis, and

results evaluation. Each area will be discussed in more detail below:

2.1 Materials

A large part of a fatigue analysis is getting an accurate description of the

fatigue material properties. Since fatigue is so empirical, sample fatigue

curves are included only for structural steel and aluminum materials. These

properties are included as a guide only with intent for the user to provide

his/her own fatigue data for more accurate analysis. In the case of

assemblies with different materials, each part will use its own fatigue

material properties just as it uses its own static properties (like modulus of

elasticity).

2.1.1 Stress-life Data Options/Features

• Fatigue material data stored as tabular alternating stress vs. life points.

• The ability to define mean stress dependent or multiple r-ratio curves if

the data is available.

• Options to have log-log, semi-log, or linear interpolation.

• Ability to graphically view the fatigue material data

• The fatigue data is saved in XML format along with the other static

material data.

• Figure 1 is a screen shot showing a user editing fatigue data in ANSYS.

Figure 1: Editing SN curves in ANSYS

2.2 Analysis

Fatigue results can be added before or after a stress solution has been

performed. To create fatigue results, a fatigue tool must first be inserted into

the tree. This can be done through the solution toolbar or through context

menus. The details view of the fatigue tool is used to define the various

aspects of a fatigue analysis such as loading type, handling of mean stress

effects and more. As seen in Figure 2, a graphical representation of the

loading and mean stress effects is displayed when a fatigue tool is selected

by the user. This can be very useful to help a novice understand the fatigue

loading and possible effects of a mean stress.

Figure 2: Fatigue tool information page in ANSYS

2.2.1 Loading

Fatigue, by definition, is caused by changing the load on a component over

time. Thus, unlike the static stress safety tools, which perform calculations

for a single stress, fatigue damage occurs when the stress at a point changes

over time. ANSYS can perform fatigue calculations for either constant

amplitude loading or proportional non-constant amplitude loading. A scale

factor can be applied to the base loading if desired. This option, located

under the “Loading” section in the details view, is useful to see the effects of

different finite element load magnitudes without having to re-run the stress

analysis.

• Constant amplitude, proportional loading: This is the classic, “back

of the envelope” calculation. Loading is of constant amplitude because

only 1 set of finite element stress results along with a loading ratio is

required to calculate the alternating and mean stress. The loading ratio is

defined as the ratio of the second load to the first load (LR = L2/L1).

Loading is proportional since only 1 set of finite element stress results is

needed (principal stress axes do not change over time). No cumulative

damage calculations need to be done. Common types of constant

amplitude loading are fully reversed (apply a load then apply an equal

and opposite load; a load ratio of –1) and zero-based (apply a load then

remove it; a load ratio of 0). Fully reversed, zero-based, or a specified

loading ratio can be defined in the details view under the “Loading”

section.

•

Non-constant amplitude, proportional loading: In this case, again

only 1 set of results are needed, however instead of using a single load

ratio to calculate the alternating and mean stress, the load ratio varies

over time. Think of this as coupling an FEM analysis with strain-gauge

results collected over a given time interval. Cumulative damage

calculations including cycle counting and damage summation need to be

done. A rainflow cycle counting method is used to identify stress

reversals and Miner’s rule is used to perform the damage summation.

The load scaling comes from an external data file provided by the user,

(such as the one in Figure 3) and is simply a list of scale factors.

Figure 3: Chart of loading history

Several sample load histories can be found in the “Load Histories”

directory under the “Engineering Data” folder. Setting the loading type

to “History Data” in the fatigue tool details view specifies non-constant

amplitude loading. Several analysis options are available for non-constant amplitude loading. Since rainflow counting is used, using a

“quick counting” technique substantially reduces runtime and memory.

In quick counting, alternating and mean stresses are sorted into bins

before partial damage is calculated. Without quick counting, the data is

not sorted into bins until after

partial damages are found. The

accuracy of quick counting is

usually very good if a proper

number of bins is used when

counting. The default setting for

the number of bins can be set in

the Control Panel. Turning off

quick counting is not

recommended and in fact is not

a documented feature. To allow

quick counting to be turned off, set the variable “AllowQuickCounting”

to 1 in the Variable Manager. Another available option when conducting

a variable amplitude fatigue analysis is the ability to set the value used

for infinite life. In constant amplitude loading, if the alternating stress is

lower than the lowest alternating stress on the fatigue curve, ANSYS will

use the life at the last point. This provides for an added level of safety

because many materials do not exhibit an endurance limit. However, in

non-constant amplitude loading, cycles with very small alternating

stresses may be present and may incorrectly predict too much damage if

the number of the small stress cycles is high enough. To help control

this, the user can set the infinite life value that will be used if the

alternating stress is beyond the limit of the SN curve. Setting a higher

value will make small stress cycles less damaging if they occur many

times. The rainflow and damage matrix results can be helpful in

determining the effects of small stress cycles in your loading history.

The rainflow and damage matrices shown in Figure 4 illustrate the

possible effects of infinite life. Both damage matrices came from the

same loading (and thus same rainflow matrix), but the first damage

matrix was calculated with an infinite life if 1e6 cycles and the second

was calculated with an infinite life of 1e9 cycles.

Rainflow matrix for a

given load history.

Damage matrix with an infinite

life of 1e6 cycles. Total damage

is calculated to be .19 .

Damage matrix with an

infinite life of 1e9 cycles.

Total damage is calculated

to be .12 (37% less damage)

Figure 4: Effect of infinite life on fatigue damage

2.2.2 Load Effects

Fatigue material tests are usually conducted in a uniaxial loading under a

fixed or zero mean stress state. It is cost-prohibitive to conduct experiments

that capture all mean stress, loading, and surface conditions. Thus, empirical

relations are available if the fatigue data is not.

• Mean Stress correction. If the loading is other than fully reversed, a

mean stress exists and should be accounted for. Methods for handling

mean stress effects can be found in the “Options” section.

If experimental data at

different mean stresses or r-ratio’s exist, mean stress can

be accounted for directly

through interpolation between

material curves. If

experimental data is not

available, several empirical

options may be chosen

including Gerber, Goodman

and Soderberg theories which

use static material properties

(yield stress, tensile strength)

along with S-N data to account for any mean stress. In general, most

experimental data fall between the Goodman and Gerber theories with

the Soderberg theory usually being over conservative. The Goodman

theory can be a good choice for brittle materials with the Gerber theory

usually a good choice for ductile materials. As can be seen from the

screen shots in Figure 5, the Gerber theory treats negative and positive

mean stresses the same whereas Goodman and Soderberg do not apply

any correction for negative mean stresses. This is because although a

compressive mean stress can retard fatigue crack growth, ignoring a

negative mean is usually more conservative. The selected mean stress

theory is shown graphically in the display window as seen below. Note

that if an empirical mean stress theory is chosen and multiple SN curves

are defined, any mean stresses that may exist will be ignored when

querying the material data since an empirical theory was chosen. Thus if

you have multiple r-ratio SN curves and use the Goodman theory, the SN

curve at r=-1 will be used. In general it is not advisable to use an

empirical mean stress theory if multiple mean stress data exists.

Figure 5: The chosen mean stress theory is illustrated in the graphics window

• Multiaxial Stress Correction. Experimental test data is uniaxial

whereas stresses are usually multiaxial. At some point stress must be

converted from a multiaxial stress state to a uniaxial one. Von-Mises,

Max shear, Maximum principal stress, or any of the component stresses

can be used as the uniaxial stress value. In addition, a “signed” Von-Mises stress may be chosen where the Von-Mises stress takes the sign of

the largest absolute principal stress. This is useful to identify any

compressive mean stresses since several of the mean stress theories treat

positive and negative mean stresses differently. Setting the “Stress

Component” is done in the Options section in the fatigue tool detail view.

2.2.3 Miscellaneous Analysis options

Fatigue material property tests are usually conducted under very specific and

controlled conditions (eg. axial loading, polished specimens, .5 inch gauge

diameter). If the service part conditions differ from as tested, modification

factors can be applied to try to account for the difference. The fatigue

alternating stress is usually divided by this modification factor and can be

found in design handbooks. (Dividing the alternating stress is equivalent to

multiplying the fatigue strength by Kf.) The fatigue strength reduction factor

is defined by setting “Fatigue Strength Factor (Kf)” in the details view for

the fatigue tool. Note that this factor is applied to the alternating stress only

and does not affect the mean stress.

2.3 Results Output

Several results for evaluating fatigue are available to the user. Some are

contour plots of a specific result over the model while others give

information about the most damaged point in the model(or the most

damaged point in the scope of the result). Outputs include fatigue life,

damage, factor of safety, stress biaxiality, fatigue sensitivity, rainflow

matrix, and damage matrix output. Each output will now be described in

detail.

• A contour plot of available life over the model. This result can be over

the whole model or scoped to a given part or surface. This result contour

plot shows the available life for the given fatigue analysis. If loading is of

constant amplitude, this represents the number of cycles until the part

will fail due to fatigue. If loading is non-constant, this represents the

number of loading blocks until failure. Thus if the given load history

represents one month of loading and the life was found to be 120, the

expected model life would be 120 months. In a constant amplitude

analysis, if the alternating stress is lower than the lowest alternating stress

defined in the S-N curve, the life at that point will be used. See section

2.2.1 for more information about the difference between constant and

non-constant amplitude loading.

• A contour plot of the fatigue damage at a given design life. Fatigue

damage is defined as the design life divided by the available life. This

result may be scoped. The default design life may be set through the

Control Panel.

• A contour plot of the factor of safety with respect to a fatigue failure at a

given design life. The maximum FS reported is 15. Like damage and

life, this result may be scoped. This calculation is iterative for non-constant amplitude loading and may substantially increase solve time.

• A stress biaxiality contour plot over the model. As mentioned

previously, material properties are uniaxial but stress results are usually

multiaxial. This result gives the user some idea of the stress state over

the model and how to interpret the results. Biaxiality indication is

defined as the principal stress smaller in magnitude divided by the larger

principal stress with the principal stress nearest zero ignored. A

biaxiality of zero corresponds to uniaxial stress, a value of –1

corresponds to pure shear, and a value of 1 corresponds to a pure biaxial

state. From the sample biaxiality plot shown below, most of the model is

under a pure shear or uniaxial stress. This is expected since a simple

torque has been applied at the top of the model. When using the

biaxiality plot along with the safety factor plot above, it can be seen that

the most damaged point occurs at a point of nearly pure shear. Thus it

would be desirable to use S-N data collected through torsional loading if

available. Of course collecting experimental data under different loading

conditions is cost prohibitive and not often done.

• A fatigue sensitivity plot. This plot shows how the fatigue results change

as a function of the loading at the critical location on the model. This

result may be scoped to parts or surfaces. Sensitivity may be found for

life, damage, or factory of safety.

The user may set the number of fill

points as well as the load variation

limits. For example, the user may

wish to see the sensitivity of the

model’s life if the load was 50% of

the current load up to if the load

150% of the current load. (The x-value of 1 on the graph corresponds

to the life at the current loading of

the model; The x-value at 1.5

corresponds to the critical fatigue

life if the finite element loads were 50% higher then they are currently,

etc…). Negative variations are allowed in order to see the effects of a

possible negative mean stress if the loading is not totally reversed.

Linear, Log-X, Log-Y, or Log-Log scaling can be chosen for chart

display. Default values for the sensitivity options may be set through the

Control Panel.

• A plot of the rainflow matrix for the critical location. This result is only

applicable for non-constant amplitude loading where rainflow counting is

needed. This result may be scoped. In this 3-D histogram, alternating

and mean stress is divided into bins and plotted. The Z-axis corresponds

to the number of counts for a given alternating and mean stress bin. This

result gives the user a measure of the composition of a loading history.

(Such as if most of the alternating stress cycles occur at a negative mean

stress.) From the rainflow matrix below, the user can see that most of the

alternating stresses have a positive mean stress and that bulk of the

smaller alternating stresses have a higher mean stress then the larger

alternating stresses.

• A plot of the damage matrix at the critical location on the model. This

result is only applicable for non-constant amplitude loading where

rainflow counting is needed. This result may be scoped. This result is

similar to the rainflow matrix except the %damage that each bin caused is

plotted as the Z-axis. As can be seen from the corresponding damage

matrix for the above rainflow matrix, in this particular case although

most of the counts occur at the lower stress amplitudes, most of the

damage occurs at the higher stress amplitudes.

3. Typical Use Cases

Scenario I, Connecting Rod under fully reversed loading: Here we have

a connecting rod in a compressor under fully reversed loading (load is

applied, removed, then applied in the opposite direction with a max loading

of 1000 pounds).

• Import geometry and apply boundary conditions. Apply loading

corresponding to the maximum developed load of 1000 pounds.

• Insert fatigue tool.

• Specify fully reversed

loading to create

alternating stress cycles.

• Specify that this is a

stress-life fatigue

analysis. No mean

stress theory needs to be

specified since no mean

stress will exist (fully

reversed loading). Specify that Von-Mises stress will be used to

compare against fatigue material data.

• Specify a modification factor of .8 since material data represents a

polished specimen and the in-service component is cast.

• Perform stress and fatigue calculations (Solve command in context

menu).

• Plot factor of safety for a design life of 1,000,000 cycles.

• Find the sensitivity of available life with respect to loading. Specify a

minimum base load variation of 50% (an alternating stress of 500 lbs.)

and a maximum base load variation of 200% (an alternating stress of

2000 lbs.)

• Determine multiaxial stress state (uniaxial, shear, biaxial, or mixed) at

critical life location by inserting “biaxiality indicator” into fatigue

tool. The stress state near the critical location is not far from uniaxial

(.1~.2), which gives and added measure of confidence since the

material properties are uniaxial.

Scenario II, Connecting Rod under random loading: Here we have the

same connecting rod and boundary conditions but the loading is not of a

constant amplitude over time. Assume that we have strain gauge results that

were collected experimentally from the component and that we know that a

strain gauge reading of 200 corresponds to an applied load of 1,000 pounds.

• Conduct the static stress analysis as before using a load of 1,000

pounds.

• Insert fatigue tool.

• Specify fatigue loading as coming from a scale history and select

scale history file containing strain gauge results over time(ex.

Common

FilesAnsys IncEngineering DataLoad ).

Define the scale factor to be .005. (We must normalize the load

history so that the FEM load matches the scale factors in the load

history file).

1 FEM load1000lbs1 FEM load×==needed load scale factor1000lbs200 strain gauge200 strain gauge•

•

•

•

Specify a bin size of 32 (Rainflow and damage matrices will be of

dimension 32x32).

Specify Goodman theory to account for mean-stress effects. (The

chosen theory will be illustrated graphically in the graphics window.

Specify that a signed Von-Mises stress will be used to compare

against fatigue material data. (Use signed since Goodman theory

treats negative and positive mean stresses differently.)

Perform fatigue calculations (Solve command in context menu).

View rainflow and damage matrix.

• Plot life, damage, and factor of safety contours over the model at a

design life of 1000. (The fatigue damage and FS if this loading history

was experienced 1000 times). Thus if the loading history

corresponded to the loading experienced by the part over a month’s

time, the damage and FS will be at a design life of 1000 months. Note

that although a life of only 88 loading blocks is calculated, the needed

scale factor (since FS@1000=.61) is only .61 to reach a life of 1000

blocks.

•

•

•

•

Plot factor of safety as a function of the base load (fatigue sensitivity

plot, a 2-D XY plot).

Copy and paste to create another fatigue tool and specify that mean

stress effects will be ignored (SN-None theory) This will be done to

ascertain to what extent mean stress is affecting fatigue life.

Perform fatigue calculations.

View damage and factor of safety and compare results obtained when

using Goodman theory to get the extent of any possible mean stress

effect.

• Change bin size to 50, rerun analysis, and compare fatigue results to

verify that the bin size of 32 was of adequate size to get desired

precision for alternating and mean stress bins.

4. Additional fatigue resources

• Hancq, D.A., Walters, A.J., Beuth, J.L., “Development of an Object-Oriented Fatigue Tool”, Engineering with Computers, Vol 16, 2000,

pp. 131-144.

This paper gives details on both the underlying structure and

engineering aspects of the fatigue tool used by the DesignSpace

program.

• Bannantine, J., Comer, J., Handrock, J. “Fundamentals of Metal

Fatigue Analysis”, New Jersey, Prentice Hall (1990).

This is an excellent book that explains the fundamentals of fatigue to a

novice user. Many topics such as mean stress effects and rainflow

counting are topics in this book.

• Lampman, S.R. editor, “ASM Handbook: Volume 19, Fatigue and

Fracture”, ASM International (1996).

Good reference to have when conducting a fatigue analysis. Contains

papers on a wide variety of fatigue topics.

• U.S. Dept. of Defense, “MIL-HDBK-5H: “Metallic materials and

Elements for Aerospace Vehicle Structures”, (1998).

This publication distributed by the United States government gives

fatigue material properties of several common engineering alloys. It

is freely downloadable over the Internet from the NASA website.