Fatigue equation

The mechanical behaviour of asphalts is determined by resistance to tensile forces, known as resistance to fatigue cracking, and resistance to compressive forces, known as resistance to permanent deformation. The first is expressed by the relationship between tensile strain and number of loadings, known as the fatigue equation. The second is expressed by the relationship between compressive strain and number of loadings, known as the creep equation. 

If the correlation of the best-fit line is less than 0.9, it is recommended to increase the number of specimens. It is noted that the above equation is the logarithmic fatigue equation given in Section 7.7.1. 

The initial strain corresponding with a fatigue life of 10 cycles, e, is determined from the fatigue equation. 

The laboratory determination of the fatigue equation presupposes the existence of the appropriate device. 

The number of load repetitions for failure may be determined from fatigue equations by knowing the magnitude of the exerted strain, e. Similarly, from a fatigue equation, the allowable strain may be determined by knowing the number of load repetitions. A fatigue equation has the following mathematical expression ... 

Fatigue equations for asphalts have been developed by various organisations and research institutes and more information can be found in Section 7.7. 

Fatigue equations for hydraulically bound materials have also been developed however, limited information is available. As an example, the fatigue equation used by the Australia pavement design methodology (Austroads 2012) is as follows ... 

The above fatigue equation (criterion) is valid for cemented materials with moduli within the range 2000 to 10,000 MPa. 

The procedure for the determination of the thickness of the concrete slab is based on the two distress modes, as mentioned earlier, the flexural fatigue cracking of the slab and the subgrade/sub-base erosion. The two distress modes are expressed by two fatigue equations, provided in the reference manual, from which the allowable load repetitions can be calculated. 

Having estimated the stiffness moduli and knowing the thickness of each layer, the developed strain at critical interfaces can be calculated, from which, using fatigue equations, it is possible to estimate the remaining life of the pavement, in ESAL. 

Finally, when FWD measurements are available from which the developed strains at the critical interlayer can be determined, fatigue equations derived in relation to the tensile stain of the asphalt or the vertical strain of the subgrade criteria may also be used in PMS to predict the structural failure of the pavement, hence prolonging the pavement s life. 

Another important appHcation of LEFM is the rate of growth of a fatigue crack under cycHc loading. This is also controlled by the stress intensity factor through an equation of the following form (110) ... 

The constant, C, is proportional to the ductility of the material in tension the exponent, b, is near 0.5 for most materials over a wide temperature range. This equation applies usually in the range 1—10 cycles, and typical data are shown in Figure 4a (5). The exponent rises when creep or environmental interactions affect fatigue behavior. 

For high-cycle fatigue of uncracked components, where neither or. the yield stress, it is found empirically that the experimental data can be fitted to an equation of form... 

The fracture toughness for the steel is 200 MN m". The growth of the crack by fatigue may be represented approximately by the equation... 

In plastics, these correlative properties, together with those that can be used in design equations, generally are called engineering properties. They encompass a variety of situations over and above the basic static strength and rigidity requirements, such as impact, fatigue, flammability, chemical resistance, and temperature. 

Stiction, in mercury thermometers, 24 465 Stiff differential equation, 25 285 Stiffness loss, in fatigue, 16 187-188 of fibers, 11 181, 182 Stiffness values, of paper, 18-101 Stilbene(s), 25 181... 

As mentioned earlier, fatigue is the result of crack initiation and propagation. Crack growth under fatigue is estimated by the Paris equation ... 

Fatigue Properties of Candidate Metais. We assume that the fatigue crack growth law in the vessel material is described by the Paris equation [Eq. (5.48)] ... 

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