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1、Fatigue Analysis in the Ansys Workbench Environment D. Alfred Hancq, Ansys Inc., May 2003 Contents 1. Introduction 2. Materials 2.1. Stress-Life Data Options 3. Analysis 3.1. Loading 3.1.1. Constant Amplitude, Proportional Loading 3.1.2. Non-Constant Amplitude, Proportional Loading 3.1.3. Constant A
2、mplitude, Non-Proportional Loading 3.1.4. Non-Constant Amplitude, Non-Proportional Loading 3.2. Load Effects 3.2.1. Mean Stress Correction 3.2.2. Multiaxial Stress Correction 3.3. Miscellaneous Analysis Options 4. Results 4.1. Fatigue Life 4.2. Fatigue Damage 4.3. Factor of Safety 4.4. Stress Biaxia
3、lity 4.5. Equivalent Alternating Stress 4.6. Fatigue Sensitivity Chart 4.7. Rainflow Matrix Chart 4.8. Damage Matrix Chart 5. Typical Use Cases 5.1. Connecting Rod Under Fully Reversed Loading 5.2. Connecting Rod Under Random Loading 5.3. Universal Joint Under Combined Torsion and Bending 6. Additio
4、nal Fatigue Resources and Revision History 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, the availability of commercial fatigue tools is limited while the ones that are available are usually quite
5、expensive and difficult to use in the hands of a designer. It is hoped that these designers, given a proper library of fatigue tools, could quickly and accurately conduct a fatigue analysis suited to their needs in a friendly and well structured environment. Fatigue was initially introduced as a new
6、 capability at version 6.0. Its focus has been to provide useful information to the design engineer when fatigue failure may be a concern. Fatigue results can have a convergence attached. Currently, a stress-life approach has been adopted for conducting a fatigue analysis. Several options such as ac
7、counting for mean stress and loading conditions are available. A fatigue analysis can be separated into 3 areas: materials, analysis, and results evaluation. Each area will be discussed in more detail below: 2. Materials A large part of a fatigue analysis is getting an accurate description of the fa
8、tigue 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 assembl
9、ies 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 Stress-life Data Options/Features Fatigue material data stored as tabular alternating stress vs. life points. The ability to define mean st
10、ress 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
11、 user editing fatigue data w w w . b z f x w . c o m Figure 1: Editing SN curves 3. 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 toolba
12、r 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 fati
13、gue 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. w w w . b z f x w . c o m Figure 2: Fatigue tool information page 3.1 Loading Fatigue, by definition, is caused by changing the load on a component over ti
14、me. Thus, unlike static stress safety tools, which perform calculations for a single stress state, fatigue damage occurs when the stress at a point changes over time. There are essentially 4 classes of fatigue loading with the fatigue tool currently supporting the first 3: Constant amplitude, propor
15、tional loading Non-constant amplitude, proportional loading Constant Amplitude, non-proportional loading Non-constant amplitude, non-proportional loading w w w . b z f x w . c o m 3.1.1 Constant amplitude, proportional loading This is the classic, “back of the envelope” calculation. Loading is of co
16、nstant 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 el
17、ement stress results is needed (principal stress axes do not change over time). 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). Since the loading is
18、 proportional, the critical fatigue location can be ascertained by looking a single set of FEM results. Likewise, since there are only 2 loadings, no cycle counting or cumulative damage calculations need to be done. Figure 3: Chart showing constant amplitude, proportional loading w w w . b z f x w .
19、 c o m 3.1.2 Non-constant amplitude, proportional loading In this case, again only 1 set of FEM 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
20、results collected over a given time interval. Since the loading is proportional, the critical fatigue location can be ascertained by looking a single set of FEM results. However, the fatigue loading which causes the maximum damage cannot be easily seen and thus cumulative damage calculations includi
21、ng cycle counting (such as Rainflow) and damage summation (such as Miners rule) need to be done to determine the total amount of fatigue damage and which cycle combinations cause that damage. Figure 4: Chart showing non-constant amplitude, proportional loading Several sample load histories can be fo
22、und 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,
23、 using a “quick counting” technique substantially reduces runtime and memory. In quick counting, alternating and mean stresses are sorted into bins before partial w w w . b z f x w . c o m damage is calculated. Without quick counting, the data is not sorted into bins until after partial damages are
24、found. The accuracy of quick counting is usually very good if a proper number of bins are 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
25、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
26、alternating stress on the fatigue curve, the fatigue tool 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 a
27、nd 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 les
28、s 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 5 illustrate the possible effects of infinite life. Both damage matrices came from th
29、e 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. w w w . b z f x w . c o m Rainflow matrix for a given load history. Damage matrix with an infinite life of
30、 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 5: Effect of infinite life on fatigue damage w w w . b z f x w . c o m 3.1.3 Constant Amplitude, non-proportional loading In this case,
31、 there are exactly 2 load cases that need not be related by a scale factor. Thus, since there are 2 loads, the loading is of constant amplitude but non-proportional since the principal stress axes are free to change between these 2 load sets. Since the loading is of constant amplitude, no cycle coun
32、ting needs done. However, since the loading is non-proportional, the critical fatigue location may occur at a spatial location that is not easily identifiable by looking at either of the base loading stress states. The chart below illustrates a representative non-proportional fatigue loading a speci
33、fic location on the model. Note that each component of stress alternates between 2 values but there is no implied relation between different stress components. Figure 6: Fatigue tool with Non-Proportional loading This type of fatigue loading can describe common fatigue loadings such as: Alternating
34、between 2 distinct load cases (like a bending load and torsional load). w w w . b z f x w . c o m Applying an alternating load superimposed on a static load. Analyses where although the loading is proportional, the results are not. This happens under conditions where changing the direction or magnit
35、ude of the loads would cause a change in the relative stress distribution in the model. Situations where this effect may be important include nonlinear contact being present, existence of compression only surfaces, or the existence of bolt loads. Fatigue tools located under a solution branch are inh
36、erently applied to that single branch and thus can only handle proportional loading. In order to handle non-proportional loading, the fatigue tool must be able to span multiple solutions. This is accomplished by adding a fatigue tool under the solution combination folder that can indeed span multipl
37、e solution branches. In general, the results under a solution combination (both static and fatigue) will be based on a stress solution that is the linear combination of its selected environments. However, when non-proportional fatigue loading is selected, the stress solutions are not combined(superi
38、mposed) but treated as separate loadings for the fatigue analysis. Several things must be done to solve this type of fatigue problem. Exactly 2 environments must be selected under the solution combination folder and in addition the loading type in the fatigue tool must be selected as “Non- Proportio
39、nal” (This loading type is applicable to only fatigue tools under a solution combination). An example of how to set up and interpret a non- proportional constant amplitude fatigue analysis can be found in section 5, “Typical Use Cases”. w w w . b z f x w . c o m 3.1.4 Non-constant amplitude, non-pro
40、portional loading In this most general case, multiple (2) load cases are involved that have no relation to one another. Not only is the spatial location of critical fatigue life unknown, but also so is what combination of loads would cause the most damage. Thus, more advanced cycle counting is requi
41、red such as path independent peak methods or multiaxial critical plane methods. Currently the program does not support this type of fatigue loading. 3.2 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
42、conduct experiments that capture all mean stress, loading, and surface conditions. Thus, part of the duty of the fatigue tool is to convert the FEM stresses and fatigue loads into a form that can be used to query fatigue material data. 3.2.1 Mean Stress Correction If the loading is other than fully
43、reversed, a mean stress exists and may 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-ratios exist, mean stress can be accounted for directly through interpolation between material curves. If expe
44、rimental 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 Goodm
45、an 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 7, the Gerber theory treats negative and
46、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 gr
47、aphically 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 w w w . b z f x w . c o m ignored when querying the material data since an empirical theory was chosen. Thus if you have
48、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 7: The chosen mean stress theory is illustrated in the graphics window 3.2.2 Multiaxial Stress C
49、orrection Experimental test data is mostly 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 w w w . b z f x w . c o m 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 t