Hyperworks Fatigue

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Hosted HWU User Users can authorize their machines to use H-HWU licenses. view existing usage. Under such cyclical loading conditions. edit license configuration.Documentation: Product documentation is available for online view or download. manage authorized machines. remove already authorized machines. Alternately use the download links to download software-specific documentation. and Dang Van Criterion (Factor of Safety) approaches for predicting the life (number of loading cycles) of a structure under cyclical loading may be performed by using OptiStruct. and view license details here. Hosted HWU Admin Administrators can manage H-HWU users. The stress-life method works well in predicting fatigue life when the stress level in the structure falls mostly in the elastic range.0 » User's Guide » Fatigue Analysis » Fatigue Analysis Fatigue Analysis Fatigue analysis. using S-N (stress-life). the structure typically can withstand a large number of . If damage does occur. this is known as high-cycle fatigue. through fully reversed rotating bending tests. this is characterized as low-cycle fatigue. Figure 1: S-N data from testing When S-N testing data is presented in a log-log plot of alternating nominal stress amplitude Sa or range SR versus cycles to failure N. the S-N curve (and other fatigue properties) of a material is obtained from experiment. the relationship between S and N can be described by straight . It is necessary to consider if any fatigue damage will occur during the entire load history of the component. with plastic strains being considered as an important factor in the damage calculation. For low-cycle fatigue prediction. the fatigue endurance of the structure typically decreases significantly.000 loading cycles. defines a relationship between stress and number of cycles to failure. statistical characterization of the data should also be provided (certainty of survival is used to modify the S-N curve according to the standard error of the curve and a higher reliability level requires a larger certainty of survival).loading cycles. Due to the large amount of scatter that usually accompanies test results. The Dang Van criterion is used to predict if a component will fail in its entire load history. The generally accepted transition point between high-cycle and lowcycle fatigue is around 10. The appropriate FATDEF bulk data entry may be referenced from a fatigue subcase definition through the FATDEF Subcase Information entry. Typically. The conventional fatigue result that specifies the minimum fatigue cycles to failure is not applicable in such cases. the component cannot experience infinite life. Sections of a model on which fatigue analysis is to be performed must be identified on a FATDEF bulk DATA ENTRY . first developed by Wöhler. When the cyclical strains extend into plastic strain range. The Stress-Life (S-N) Approach S-N Curve The S-N curve. the strain-life (E-N) method is applied. on the life axis. a one or two segment idealization is used. S is the nominal stress range Nf are the fatigue cycles to failure b1 is the first fatigue strength exponent S1 is the fatigue strength coefficient The S-N approach is based on elastic cyclic loading. to numbers greater than 1000 cycles. Damage Model Palmgren-Miner's linear damage summation rule is used. Normally. inferring that the S-N curve should be confined. . This is commonly referred to as high-cycle fatigue. It is referenced through a Material ID (MID) which is shared by a structural material definition. Figure 2: One segment S-N curves in log-log scale for segment 1 (1) Where. Failure is predicted when: (2) Where.line segments. This ensures that no significant plasticity is occurring. S-N curve data is provided for a given material on a MATFAT bulk DATA ENTRY . it has been proved to work well for many applications. Then. Figure 3: Determine cycles using rainflow cycle counting method Parameters affecting rainflow cycle counting may be defined on a FATPARM bulk DATA ENTRY . Cycle counting will count the number of stress-strain hysteresis loops and keep track of their range/mean or maximum/minimum values. One way to understand “cycle counting” is as a changing stress-strain versus time signal. This procedure is repeated until the remaining data points are exhausted. three consecutive stress points (S1. the two points forming the cycle are discarded and the remaining points are connected to each other. However. . and S3) will define two consecutive ranges as S1 = |S1 S2| and S2 = |S2 . S2. A cycle from S1 to S2 is only extracted if S1 S2.S3| .Nif is the material’s fatigue life (number of cycles to failure) from its S-N curve at a combination of stress amplitude and means stress level i ni is the number of stress cycles at load level i Di is the cumulative damage under ni load cycle The linear damage summation rule does not take into account the effect of the load sequence on the accumulation of damage due to cyclic fatigue loading. Rainflow cycle counting is the most widely used cycle counting method. It requires that the stress time history be rearranged so that it contains only the peaks and valleys and it starts either with the highest peak or the lowest valley (whichever is greater in absolute magnitude). Once a cycle is extracted. Cycle Counting Cycle counting is used to extract discrete simple "equivalent" constant amplitude cycles from a random loading sequence. The appropriate FATPARM bulk DATA ENTRY may be referenced from a fatigue subcase definition through the FATPARM Subcase Information entry. and can be expressed as: Gerber: Goodman: (3) (4) Where. Various stress combination types are available with the default being “Absolute maximum principle stress”. The Gerber parabola and the Goodman line in Haigh's coordinates are widely used when considering mean stress influence. while “Signed von Mises stress” is recommended for ductile material. The sign on the signed parameters is taken from the sign of the Maximum Absolute Principal value. However. Mean stress Sm = (Smax + Smin) / 2 Stress amplitude Sa = (Smax . Parameters affecting stress combination may be defined on a FATPARM bulk data entry. The appropriate FATPARM bulk data entry may be referenced from a fatigue subcase definition through the FATPARM Subcase Information entry. and then used as equivalent nominal stress applied on the S-N curve. Tensile normal mean stresses are detrimental and compressive normal mean stresses are beneficial. Mean Stress Influence Generally S-N curves are obtained from standard experiments with fully reversed cyclic loading. at each time step. in terms of fatigue strength. the stress components need to be resolved into one combined value for each calculation point.Smin) / 2 Se is the stress range for fully reversed loading that is equivalent to the load case with a stress range SR and a mean stress Sm Su is ultimate strength The Gerber method treats positive and negative mean stress correction in the same way that mean stress always accelerates fatigue failure. Both methods give . Mean stress correction is used to take into account the effect of non-zero mean stresses.Equivalent Nominal Stress Since S-N theory deals with uniaxial stress. while the Goodman method ignores the negative means stress. In general “Absolute maximum principle stress” is recommended for brittle materials. the real fatigue loading could not be fully reversed and the normal mean stresses have significant effect on fatigue performance of components. The Strain-Life (E-N) Approach Monotonic Stress-Strain Behavior Relative to the current configuration. if the tensile means stress is greater than UTS. the damage will be greater than 1. respectively. In the whole process. Figure 5 shows the monotonic stress-strain curve in true stress-strain space.0.conservative result for compressive means stress. For the Goodman method. For Gerber method. no matter tensile or compressive. Figure 4: Haigh diagram and mean stress correction methods Parameters affecting mean stress influence may be defined on a FATPARM bulk DATA ENTRY .0. A Haigh diagram characterizes different combinations of stress amplitude and mean stress for a given number of cycles to failure. the true stress and strain relationship can be defined as: (5) (6) Where. the damage will be greater than 1. if the mean stress is greater than UTS. A is the current cross-section area. and and are the true stress and strain. l is the current specimen length. The appropriate FATPARM bulk data entry may be referenced from a fatigue subcase definition through the FATPARM Subcase Information entry. the stress continues . l0 is the initial specimen length. The Goodman method is recommended for brittle material while the Gerber method is recommended for ductile material. namely the elastic segment OA and plastic segment AC. is plastic strain. For most of materials.increasing to a large value until the specimen fails at C. Figure 5: Monotonic stress-strain curve The curve in Figure 5 is comprised of two typical segments. The segment OA keeps the linear relationship between stress and elastic strain following Hooke Law: (7) Where. E is elastic modulus and rewritten as: is elastic strain. the plastic strain can be expressed in terms of stress as: (10) The total strain induced by loading the specimen up to point B or D is the sum of plastic strain and elastic strain: (11) . The formula can also be (8) by expressing elastic strain in terms of stress. and n is work hardening coefficient. K is strength coefficient. the relationship between the plastic strain and the stress can be represented by a simple power law of the form: (9) Where. Similarly. it is called cyclic softening. as shown in Figure 7. there are four kinds of response. By placing these hysteresis loops in one coordinate system. Figure 6 illustrates the effect of cyclic hardening and cyclic softening where the first two hysteresis loops of two different materials are plotted. it is called cyclic hardening. as shown in the lower part of Figure 6. a series of hysteresis loops at steady state can be obtained. otherwise. Through specifying different strain ranges. In fact.Cyclic Stress-Strain Curve Material exhibits different behavior under cyclic load compared with that of monotonic load. Cyclic response of material can also be described by specifying the stress range and leaving strain unconstrained. it is called cyclic hardening. as shown in the upper part of Figure 6. the strain is constrained to change in fixed range. In both cases. •stable state •cyclically hardening •cyclically softening •softening or hardening depending on strain range Which response will occur depends on its nature and initial condition of heat treatment. Generally. while the stress is allowed to change arbitrarily. the cyclic behavior of material will reach a steady state after a short time which generally occupies less than 10 percent of the material total life. If the strain range increases relative to the former cycle under fixed stress range. If the stress range increases relative to the former cycle under fixed strain range. the line connecting all the vertices of these hysteresis loops determine cyclic stress-strain curve which can be expressed in the similar form with monotonic stress-strain curve as: . it is called cyclic softening. otherwise. (b) Cyclic softening .Figure 6: Material cyclic response (a) Cyclic hardening. 12. This can be expressed with formulas: (13) (14) Expressing in terms of .Figure 7: Definition of stable stress-strain curve (12) Where. This implies that when the quantity is two times of . n' is strain cyclic hardening exponent. load reversal caused materials to exhibit anisotropic behavior. the stress-strain cycle will lie on the hysteresis loop. and substituting it into Eq. in terms of . the hysteresis loop formula can be deduced as: (15) . Based on experiment evidence. but with twice the magnitude. K' is cyclic strength coefficient. Massing put forward the hypothesis that a stressstrain hysteresis loop is geometrically similar to the cyclic stress strain curve. Hysteresis Loop Shape Bauschinger observed that after the initial load had caused plastic strain. Basquin observed the linear relationship between stress and fatigue life in log scale when the stress is limited. can be described by applying Basquin formula and Coffin-Manson formula: (19) Where. the other variable is the same with above. He found out that the total strain has more direct correlation with fatigue life. Two straight lines. Basquin rule can be rewritten as: (18) Where. which represent Basquin formula and CoffinManson rule respectively.18.Strain-Life Approach Almost a century ago. is elastic strain amplitude. is plastic strain amplitude. Later in the 1950s. is the total strain amplitude. applying the conditions: . is stress amplitude.17 and Eq. intersect at a point where elastic strain is equal to the plastic strain and the fatigue life predicted by the two methods is the same. Figure 8 illustrates three methods in log scale in stress-life space. c fatigue ductility exponent. which is the sum of the elastic strain and plastic stain. b fatigue strength exponent. The fatigue life at the intersection point is called transition life and can be calculated as: (20) by combining Eq. Coffin and Manson to consider both elastic strain and plastic strain contribution to the fatigue life. He put forward the following fatigue formula controlled by stress: (16) Where. fatigue strength coefficient. at the same time. By applying Hooke Law. therefore. fatigue ductility coefficient. Total strain amplitude. Coffin and Manson independently proposed that plastic strain may also be related with fatigue life by a simple power law: a (17) Where. Morrow combined the work of Basquin. otherwise. Figure 8: Strain-life curve in log scale Damage Accumulation Model In the E-N approach.(21) (22) Where. whereas in practice. When fatigue life is less than the transition life. Morrow is the first to consider the effect of mean stress through introducing the mean stress in fatigue strength coefficient by: 0 (23) Thus the entire fatigue life formula becomes: (24) Morrow's equation is consistent with the observation that mean stress . which is Palmgren-Miner's linear damage summation rule. Nt is the transition life. plastic strain plays the controlling role in life prediction. Mean Stress Influence The fatigue experiments carried out in the laboratory are always fully reversed. use the same damage accumulation model as the S-N approach. the mean stress is inevitable. thus the fatigue law established by the fully reversed experiments must be corrected before applied to engineering problems. elastic strain plays the key role. is the local strain. Neuber Correction Strain-life analysis is based on the fact that many critical locations such as notch roots have stress concentration. the maximum stress is given by: (25) By multiplying Eq. the Morrow approach provides more realistic results when the load is predominantly compressive. the damage parameter is modified as the product of the maximum stress and strain range in one cycle. However. and e is the nominal strain.19 with Eq. (27) (28 ) Where. if the plastic strain is present. the SWT method predicted conservative life for loads predominantly tensile. which will have obvious plastic deformation during the cyclic loading before fatigue failure. the concentration factors are introduced such as the local stress concentration factor . S is the nominal stress. focusing on this situation. whereas. and the local strain concentration factor . In order to derive the local stress from the nominal stress that is easier to obtain. In this case. Neuber introduced a theoretically elastic stress concentration factor Kt defined as: . When comparing the two methods. If nominal stress and local stress are both elastic. this method is called SWT in the following). Thereafter. is the local stress. Smith. it can be rewritten as: (26) The SWT method will predict that no damage will occur when the maximum stress is zero or negative.25. Thus. which is not consistent with the reality. the elasticplastic strain results are essential for performing strain-life analysis. Neuber correction is the most popular practice to correct elastic analysis results into elastic-plastic results. Watson and Topper proposed a different method to account for the effect of mean stress by considering the maximum stress during one cycle (for convenience. the relationship between and no long holds. For a fully reversed cycle.effects are significant at low value of plastic strain and of little effect at high plastic strain. the local stress concentration factor is equal to the local strain concentration factor. notches and so on. but just to consider if any fatigue damage will occur during the entire load history of the component.30 as: (31) Where. the local stress instead of nominal stress is provided. e Dang Van Criterion (Factor of Safety) The Dang Van criterion is used to predict if a component will fail in its entire load history.31 together with the equations for the cyclic stress-strain curve and hysteresis loop. components may be required to last infinitely long. In certain physical systems.28 into Eq. fillets. It is not necessary to quantify the amount of fatigue damage. For example. If damage does occur. The main principle of the criterion is that the usual characterization of the fatigue cycle is replaced by the local loading path and so damaging loads can be distinguished.29. The general procedure of Dang Van fatigue analysis is: . this is a state of elastic shakedown if no damage occurs. is locally elastic stress and locally elastic strain obtained from elastic analysis. automobile components which undergo multiaxial cyclic loading at high rotational velocities (like propeller shafts) reach their high cycle fatigue limit within a short operating life. which implies the effect of the geometry in Eq. . .(29) Substitute Eq. This phenomenon takes place in the microscopic level and is localized to certain regions like grains which have undergone local plastic deformation in characteristic intracrystalline bands. the theoretical stress concentration factor Kt can be rewritten as: (30) Through linear static FEA. Fatigue crack initiation usually occurs at zones of stress concentration such as geometric discontinuities. thus you can set Kt as 1 and rewrite Eq. the component cannot experience infinite life.30 is removed. Fatigue analysis based on the Dang Van criterion is designed for this purpose.27 and Eq. the stress and strain at the presence of plastic strain. The conventional fatigue result that specifies the minimum fatigue cycles to failure is not applicable in such cases. Both and can be calculated from Eq. The Dang Van approach postulates a fatigue criterion using microscopic variables in the apparent stabilization state. Calculate . machined or forged. the component cannot experience infinite life.The Dang Van 3. If FOS is less than 1. . into a hydrostatic part the stabilized microscopic residual stress The expression is minimized with respect to and a deviatoric part .Calculate the deviatoric part of microscopic stress.1. It's presented on diagrams that categorize finish by means of qualitative terms such as polished.Calculate factor of safety (FOS): Where. as fatigue failures nucleate at the surface.Evaluate the macroscopic 2. Surface finish and treatment factors are considered to correct the fatigue analysis results. for each location at a different point in time. of Safety output can be requested using the FOS I/O options entry.Split stresses the macroscopic stress 3. Other Factors Affecting Fatigue Surface Condition (Finish and Treatment) Surface condition is an extremely important factor influencing fatigue strength. 5. OptiStruct Factor of Safety setup 1. based on the following equation: and maximized with respect to t. 4. 2. b and a are material constants. Surface finish correction factor Cfinish is used to characterize the roughness of the surface.The torsion fatigue limit and hydrostatic stress sensitivity values required for an FOS analysis can be set in the optional FOS continuation line on the MATFAT bulk DATA ENTRY .Factor criterion type can be selected on the FATPARM bulk DATA ENTRY . 0 * Cfinish (Ctreat = 2. If treatment type is SHOT-PEENED or COLD-ROLLED. Hathaway and Mark E. Fatigue Strength Reduction Factor In addition to the factors mentioned above. SHOT-PEENED. Elsevier. COLD-ROLLED are considered for surface treatment correction. loading type. In general cases. the total correction factor is Csur = Ctreat * Cfinish. size effect. Richard B.Figure 9*: Surface finish correction factor for steels (* Source: Yung-Li Lee. the stress at the transition point is also modified by multiplying by Csur. Fatigue testing and analysis: Theory and practice. Pan. Fatigue strength reduction factor Kf is introduced to account for the combined effect of all such corrections. Jwo. notch effect. then the total correction is Csur = 2. there are various others factors that could affect the fatigue strength of a structure.0). e. If treatment type is NITRIDED.g. Surface conditions may be defined on a PFAT bulk DATA ENTRY . 2005) Surface treatment can improve the fatigue strength of components. The fatigue endurance limit FL will be modified by Csur as: FL' = FL * Csur. It is also possible to input a value to specify the surface treatment factor Ctreat. then the total correction is Csur = 1. The fatigue endurance limit FL will be modified by Kf as: FL' = FL / Kf .0. Surface conditions are then associated with sections of the model through the FATDEF bulk DATA ENTRY . It means you will ignore the effect of surface finish. NITRIDED. For two segment S-N curve.. Barekey. In the elastic part of the E-N formula. .The fatigue strength reduction factor may be defined on a PFAT bulk DATA ENTRY . If both Csur and Kf are specified. n is the total number of load cases Pk(t) and are. It may then be associated with sections of the model through the FATDEF bulk data entry. the time variation of the k-th load time history and the total stress tensor PFEA. respectively. It will remove small cycles (defined by a gate value) and intermediate points. The elastic part will be modified as well with the updated nominal fatigue limit. Setting Up a Fatigue Analysis Linear Superposition of Multiple FEA/Load Time History Load Cases When there are several load cases at the same time. Csur and Kf have similar influences on the E-N formula through its elastic part as on the S-N formula. a nominal fatigue endurance limit FL is calculated internally from the reversal limit of endurance Nc. The formula is: (32) Where.k and are. FL will be corrected if Csurand Kf are presented. the fatigue endurance limit FL will be modified as: FL' = FL * Csur / Kf. respectively. the k-th load magnitude and stress tensor from FE analysis Load Time History Compression This option is used to save calculation time. the principle of linear superposition will be used to combine all load cases together to determine the stress variation at each calculation point due to the combination of all loads. all of which vary independently of one another. adjacent turning points. This is shown by the sample above. . phase relationship will be maintained. will be removed from each channel. where the difference is less than the maximum range multiplied by relative gate value. In the first channel (top). However. when peaks and valleys occur on different channels at different times.Figure 10: Sample showing removal of small cycles When removing small cycles. while in the second channel (bottom). the points at time 4 and 5 will be removed when the absolute gate equals one. the points at time 1 and 2 will not be removed in order to keep the phase relationship between channels. it will not contribute in determining any stress cycle. but the computation time could be saved significantly. This mechanism is built in OptiStruct and is effective automatically. If any point on the load-time history is neither a peak nor valley point. For example. the left column in Fig 11 shows three load-time histories of three super-positioned loadcases. linear superposition is used. Such points could be screened out in the fatigue computation without losing the accuracy. Events and Sequences Fatigue loading is defined by scaling a static subcase with a load-time history. A fatigue sequence consists of a number of fatigue events and repeated instances of these events. After removing the intermediate points. A fatigue sequence can be made up of other sub . Fatigue Loads.Figure 11: Sample showing removal of intermediate points Removing intermediate points is another important mechanism to save computation time. respectively. A fatigue event consists of one or more static loadcases applied simultaneously in the same time duration scaled by load-time histories. For fatigue events with more than one static loadcase stress. the three load-time histories are obtained as in the right column. which can produce the same fatigue results as the left column. but use much less time. where a sequence of one or more fatigue loading events or other fatigue loading sequences is given. The appropriate FATSEQ bulk data entry may be referenced from a fatigue subcase definition through the FATSEQ Subcase Information entry. which can be defined in OptiStruct. you can define very complex events and sequences for fatigue analysis. where one or more fatigue loads (FATLOAD) are selected. « Fatigue Analysis Product: « Index » Multi-body Dynamics Simulation » . fatigue sequences defined in fatigue subcases (referred by FATSEQ) are the basic loading blocks. A fatigue loading event is defined by a FATEVNT bulk DATA ENTRY . The fatigue life results of these fatigue subcases are calculated as the number of repeats of the loading block. Below is an example of a "tree-like" fatigue sequence. where a static subcase and a load-time history are associated. A fatigue loading sequence is defined by a FATSEQ bulk DATA ENTRY . with FSEQ# identifying fatigue sequences and FEVN# identifying fatigue events: Figure 12: Example of a "tree-like" fatigue sequence Fatigue loading is defined by a FATLOAD bulk DATA ENTRY . In OptiStruct. In this way.fatigue sequences and/or fatigue events.      . Inc. All Rights Reserved.OptiStruct Stats: Was this document helpful to you? Yes No Altair | HyperWorks | PBS Works | ProductDesign | HiQube | solidThinking | TOGGLED | Altair Partner Alliance | Terms | Privacy © Copyright 2014 Altair Engineering.