How to predict fatigue life

DN Staff

December 17, 2001

9 Min Read
How to predict fatigue life

Purely static loading is rarely observed in modern engineering components or structures. By far, the majority of structures involve parts subjected to fluctuating or cyclic loads, often resulting in fatigue-caused structural failure. In fact, 80% to 95% of all structural failures occur through a fatigue mechanism. For this reason, design analysts must address the implications of repeated loads, fluctuating loads, and rapidly applied loads. As a result, fatigue analysis has become an early driver in the product development processes of a growing number of companies.

What is fatigue? Fatigue is failure under a repeated or varying load, never reaching a high enough level to cause failure in a single application. The fatigue process embraces two basic domains of cyclic stressing or straining, differing distinctly in character. In each domain, failure occurs by different physical mechanisms:

  1. Low-cycle fatigue-where significant plastic straining occurs. Low-cycle fatigue involves large cycles with significant amounts of plastic deformation and relatively short life. The analytical procedure used to address strain-controlled fatigue is commonly referred to as the Strain-Life, Crack-Initiation, or Critical Location approach.

  2. High-cycle fatigue-where stresses and strains are largely confined to the elastic region. High-cycle fatigue is associated with low loads and long life. The Stress-Life (S-N) or Total Life method is widely used for high-cycle fatigue applications-here the applied stress is within the elastic range of the material and the number of cycles to failure is large. While low-cycle fatigue is typically associated with fatigue life between 10 to 100,000 cycles, high-cycle fatigue is associated with life greater than 100,000 cycles.

Fatigue analysis refers to one of three methodologies: local strain or strain life, commonly referred to as the crack initiation method, which is concerned only with crack initiation (E-N, or sigma nominal); stress life, commonly referred to as total life (S-N, or nominal stress); and crack growth or damage tolerance analysis, which is concerned with the number of cycles until fracture.

Results of analysis from MSC.Nastran have been post-processed with MSC.Patran for identifying the potential fatigue hot spots. MSC. Fatigue can now be run directly using the results in the MSC. Patran database.

The method for calculating fatigue life is sometimes called the Five Box Trick, including material, loading, and geometry inputs, and analysis and results. The three main inputs for fatigue life analyses are processed using various life estimation tools depending on whether the analysis is for crack initiation, total life, or crack growth.

Material matters. When subjected to cyclic loading, materials behave differently than under monotonic loading. While monotonic material properties are the result of material tests where the load is steadily increased until a test coupon breaks, cyclic material properties are obtained from material stress where loading is reversed, then cycled until failure at various load levels. Different types of cyclic material properties are required depending on the type of fatigue analysis.

Because it can be difficult to gain access to measured cyclic properties, much effort has been expended finding ways of relating monotonic properties to cyclic properties. The approaches have all been empirical but do provide a means of estimating cyclic properties that are otherwise expensive to generate.

Carrying a heavy load. The proper specification of loading variation is extremely important to achieve an accurate fatigue life prediction. The loading can be defined in various manners and whether it is time-based, frequency-based or in the form of some sort of spectra depends on the type of fatigue analysis. When working with finite element models the loading can be force, pressure, temperature, displacement, or a number of other types. The time history used in a fatigue calculation must be a representation of the time variation in the loading applied in the FEA. For simple cases, this implies a force-time history corresponding to a time variation in the point loading used in the FEA. There are a number of different kinds of loading possible, each one requiring a different type of time history.

Find the right geometry. In the testing world, a fatigue test coupon can be described by the stress concentration factor, Kt. Typically, the fatigue failure point is located away from where stresses are measured. So the factor Kt is a geometry compensation factor that scales up the measured stresses for the failure point, based on geometry features such as bolt holes or notches. With a finite element model, local stresses and strains are known at all locations. Hence, Kt = 1 everywhere because there is no need to scale stresses for fatigue life calculations.

Transmission tunnel cover with spotwelds is modeled in MSC.Patran prior to running analysis in MSC.Fatigue. Modeling spotwelds is a particularly time consuming process made much faster through the automation features of the C-WELD element.

The three methods used to predict life include total life (S-N), crack initiation (E-N), and crack growth. S-N analysis is relatively straightforward, being based on the nominal stress-life method using rainflow cycle counting and Palmgren-Miner linear damage summation. A range of analysis parameters may be selected, including Goodman or Gerber mean stress corrections, confidence parameters, manufacturing details (surface finish), and material heat treatments. Both component and material S-N curves may be accessed, with material S-N curves enabling material surface finish and treatment specification.

The S-N method is used in a variety of situations, including long life fatigue problems where there is little plasticity, and for components where crack inititation or crack growth modeling is not appropriate, such as non-ferrous materials, composites, welds, and plastics. The S-N method may be summarized as follows:

  1. By means of linear static FEA, derive the local stress time history from the load time histories, including superpositioning of multiple FEA/load time history load cases (or use stress time history directly from linear transient or forced vibration FE analysis). However, it is important to ensure that the S-N data applies to the situation being modeled; most S-N curves are for nominal stress, not local stress.

  2. Extract the fatigue cycles in the local stress time history by means of a rainflow algorithm.

  3. Assess the damage contribution of each cycle by referring to the selected damage curve.

  4. Linearly sum the damage associated with each cycle by using Miner's rule.

E-N analysis uses cyclic stress-strain modeling and Neuber's elastic-plastic correction (or modifications of Neuber's method such as Seeger-Beste or Merten-Dittman). A range of analysis parameters may be selected, including mean stress correction models, confidence parameters, manufacturing details (surface finish), and material heat treatments. Typically, the E-N method is used for components or metallic structures that are mostly defect-free and for locating where a crack could begin. The strain-life method in MSC. Fatigue may be summarized as follows:

  1. By means of linear static FEA, derive the local stress-strain time history from the load time histories, including superpositioning of multiple FEA/load time history load cases (or use stress-strain time history directly from linear transient or forced vibration FE analysis).

  2. Extract the fatigue cycles in the local stress time history by means of a rainflow algorithm.

  3. Make the elastic-plastic correction using the Neuber's, Merten-Dittman, or Seeger-Beste rule.

  4. Model the fatigue crack initiation process using hysteresis loop simulation based on the cyclic stress-strain curve.

  5. Assess the damage contribution of each closed hysteresis loop by referring to the selected damage curve. The damage curve selected is based on the mean stress correction model used-Smith-Watson-Topper or Morrow.

  6. Linearly sum the damage associated with each cycle by using Miner's rule.

Crack Growth analysis utilizes linear elastic fracture mechanics (LEFM) and cycle-by-cycle modeling of crack closure due to overloads, the effect of chemical environment, the loading rate, and history effects. The Crack Growth method is used for pre-cracked structures or structures that are presumed to be already cracked when manufactured, (such as welds), for pre-prediction of test programs to avoid tests of components in which cracks will not grow, and for planning inspection programs to ensure checks are made at the correct frequency.

The three methods are related to each other-the total number of cycles to failure (Nf) equals the number of cycles to initiate a crack (Ni) plus the number of cycles to grow the crack (Np). The three methods use different techniques with different degrees of accuracy. Note that in theory this equation is true, but in practice it seldom works when the three methods are applied to the same problem. In reality, it's unusual to utilize the three methods on the same problem, because different industries favor different design philosophies, which drive the analysis methods.

In addition to the three basic methodologies, MSC.Fatigue includes specialized modules based on the three basic approaches for analyzing:

  • Spot welds

  • Seam welds

  • Rotating structures

  • Vibration fatigue problems

  • Complex multi-axial loading problems

  • Powertrain and engine components using Factor of Safety calculations

  • Two-dimensional crack growth problems with NASA/FLAGRO

  • Fatigue test data and correlating with analytical data

Predicting fatigue life is a critical aspect of the design cycle because virtually every product manufactured will wear out or break down. The critical issues are whether the product/component/assembly will reach its expected life, and if damaged, whether the product/component/assembly will remain safely in service until the damage can be discovered and repaired. And as with most simulation analysis, the earlier fatigue analysis is deployed in the product development process, the more benefits will be realized, including safety and economic.

For example, fatigue analysis early in the design phase can locate areas that are likely to succumb to fatigue quickly, minimizing expensive and unnecessary prototypes and tests.

Access to fatigue information early in the design phase results in shorter time-to-market, improved product reliability, and customer confidence, as well as the elimination of costly recalls and premature product failures.


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