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Basics for Fatigue Analysis of PipingSystem using Caesar II

Introduction:

Fatigue is the progressive and localized structural damage that occurs when a material is subjected tocyclic loading. Continued cycling of high stress concentrations may eventually cause a crack whichpropagates and results in leakages. This failure mechanism is called fatigue. Damage once done during

the fatigue process is cumulative and normally unrecoverable.Fatigue can be grouped in two classes; High cycle fatigue and low cycle fatigue.High cycle fatigue involves little or no plastic action. Therefore, it is stress-governed. Normally, a fatiguecurve (also called the SN curve) is generated for every material by experimental tests which correlatesapplied stress with the number of cycles to cause failure. For high-cycle fatigue, the analysis is performedto determine the endurance limit, which is actually a stress level that can be applied for an infinite number

of times without showing any failure. As a general rule no of cycles 10^5 is considered as demarcationpoint for high and low cycle fatigue.

The loading cycles applied in piping design are normally very few in the order of a few thousands. Thistype of fatigue is identified as low-cycle fatigue. For low-cycle fatigue, the applied stress normallyexceeds the yield strength of the material, which causes plastic instability in the specimen under test. Butwhen strain is used as the controlled variable, the results in low-cycle region are reliable as well asreproducible.

Sources of Fatigue:For Piping system, Cyclic loadings are primarily due to:

Thermal Expansion & Contraction

Vibration due to Occasional loading

Pressure variation within Piping system

Motion wave.

Due to Flow induced VibrationThe fatigue process is divided into three stages: crack initiation from the continued cycling of high stressconcentrations, crack propagation to critical size, and unstable rupture of the section.

Factors Affecting the Fatigue Behavior:The factors which affect the fatigue behaviour are listed below:

Type and Nature of Loading.

Size of Component and stress or strain Distribution.

Surface finish and Directional Properties.

Stress or Strain Concentration.

Mean stress or Strain.

Environmental Effects.

Metallurgical Factors and Material Properties.

Strain Rate and Frequency Effects.

Characteristics of Low Cycle Fatigue:

Characterized by high loads and a small no. of cycles before failure.

Here failure occurs only with stress levels in the plastic range, i.e. significant plastic strain occursduring each cycle.

The stresses which cause fatigue failure in the piping are the peak stresses.

In piping design, most of the loading cycles encountered would be of the low cycle type

Characteristics of High Cycle Fatigue:

Characterized by high no. of cycles (Preferable N>104) with relatively low stress levels and the

deformation is in elastic range.

This type of fatigue failure used in the design of rotating machinery.

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This type of fatigue results from strain cycles in the elastic range.

A stress level, endurance limit, may be applied an infinite times without failure, is calculated.

Failure Criteria:While preparing fatigue curves, the strains obtained in the tests are multiplied by one-half of the elasticmodulus to obtain pseudo stress amplitude. This pseudo stress is directly compared with the stressescalculated on the assumption of elastic behavior of piping. During piping stress analysis, a stress called

the alternating stress (Salt) is used which is defined as one-half of the calculated peak stress. Fatiguefailure can be prevented by ensuring that the number of load cycles (N) associated with a specificalternating stress is less than the number allowed in the SN curve or endurance curve. But in practicalservice conditions a piping system is subjected to alternating stresses of different magnitudes. Thesechanges in magnitudes make the direct use of the fatigue curves inapplicable since the curves are basedon constant-stress amplitude.

Fatigue tests of metallic materials and structures have provided the following main clues to the basicnature of fatigue:

Fatigue failure, or cracking under repeated stress much lower than the ultimate tensile strength, isshown in most metals and alloys that exhibit some ductility in static tests. The magnitude of theapplied alternating stress range is the controlling fatigue life parameter.

Failure depends upon the number of repetitions of a given range of stress rather than the total time

under load. The speed of loading is a factor of secondary importance, except at elevated temperatures.

Some metals, including ferrous alloys, have a safe range of stress. Below this stress, called the

endurance limit or fatigue limit, failure does not occur irrespective of the number of stress cycles.

Notches, grooves, or other discontinuities of section greatly decrease the stress amplitude that can besustained for a given number of cycles.

The range of stress necessary to produce failure in a fixed number of cycles usually decrease as themean tension stress of the loading cycle is increased.

Examination of fatigue fracture shows evidence of microscopic deformation, ever in the apparentlybrittle region of origin and propagates of the crack. The plastic deformation that accompanies aspreading fatigue crack is usually limited in extent to regions very near the crack.

Therefore, to make fatigue curves applicable for piping, some alternate approach is necessary.

One hypothesis asserts that the damage fraction of any stress level S, is linearly proportional to the Ratioof the number of cycles of operation at the stress level to the total number of cycles that wouldproduce failure at that stress level. This means that failure is predicted to occur ifU1.0 where U= Usage factor = (ni/Ni) for all stress levelsWhere, ni= number of cycles operating at stress level iNi= number of cycles to failure at stress level i as per material fatigue curve.

Analysis Requirement:If there are two or more types of stress cycles which produce significant stresses, their cumulative effectshall be evaluated as stipulated in Steps 1 through 6 below:1. Designate the specified number of times each type of stress cycle of types 1,2,3,,n, will be

Repeated during the life of the component as n1, n2, n3,., nn, respectively. In determining n1,n2, n3,., nn, consideration shall be given to the superposition of cycles of various origins whichproduce the greatest total alternating stress range. For example , if one type of stress cycle produce

1000 cycles of a stress variation from zero to +60,000 psi and another type of stress cycle produces10,000 cycles of a stress variation from zero to -50,000 psi, the two cycles to be considered areshown below:

cycle type 1: n1=1000 and Salt1= (60000+50000)/2

cycle type 2: n2=9000 and Salt2= (0+50000)/2

For each type of stress cycle, determine the alternating stress intensity Salt, which for our applicationis one half of the range between the expansion stress cycles (as shown above). These alternating stressintensities are designated as Salt1, Salt2, Saltn.

On the applicable design fatigue curve find the permissible number of cycles for each Salt computed.These are designated as N1, N2, .Nn.

For each stress cycle calculate the usage factor U1, U2, .Un where U1= n1/N1, U2=

n2/N2,..Un=nn/Nn.

Calculate the cumulative usage factor U as U=U1+U2+.+Un.

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The cumulative usage factor shall not exceed 1.0