Strain-Life Curve

Once the analytical expression of the hysteresis loop has been derived, the following step is to infer the equation of the entire e-N curve or Wohler s curve. To this purpose, it is necessary to separate the two component of deformation, the elastic and the plastic one, as already done in Eq. (6.1). As to the elastic component Eg, it has been said in Sect. 5.2.2 that in 1910 Basquin [7] found a power law relationship with the cycles to failure N, see Eq. (5.22), so that in a log-log scale the elastic component of the S-N curve is a line. Later in the 50, Manson and Coffin [8-11] independently found that also the plastic component of the cyclic strain was related to life cycles N through a power law function, known as the Manson-Coffin relationship 

6 Strain-Based Fatigue Analysis Low Cycle Fatigue 

It must be kept in mind that both Eqs. (5.33) and (6.9) and therefore also their ratio 

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Figure 5-12. Plastic strain life curves of 316L stainless steel at 20°C in air and under vacuum.

Fig. 6.32 Total strain-life curve and its components plastic and elastic...

While fatigue data collected in the laboratory are generated using a fully reversed stress cycle, actual loading applications usually involve a nonzero mean stress. The mean stress can be compressive or zero and it affects the strain-life curve as shown schematically in Eig. 1.33. Mean stress has its largest effects in the high-cycle regime. Compressive means extend life and tensile means reduce it. 

Figure 1.33 The effect of mean stress on the strain-life curve.

Lepore, Marino, Xinhe Liu, Virginia Savage, Daniel Matalon, and Eliot L. Gardner. 19%. "Genetic Differences in A -Tetrahydrocannabinol-Induced Facilitation of Brain Stimulation Reward as Measured by a Rate-Frequency Curve-Shift Electrical Brain Stimulation Paradigm in Three Different Rat Strains." Life Sciences lPharmacology Letters) 25 PL365-72. 

Lepore M, Liu X, Savage V, Matalon D, Gardner E (1996) Genetic differences in delta 9-tetrahydrocannabinol-induced facilitation of brain stimulation reward as measured by a rate-frequency curve-shift electrical brain stimulation paradigm in three different rat strains. Life Sci 58 PL365-PL372... 

Si-C-0 fibers are prone to creep above 1100°C (Figure 14). The creep rate does not reach steady state prior to failure during tensile tests performed in argon. It decreases continuously with time, indicating that primary (or logarithmic) creep dominates the entire creep life of the fibers. The strain-time curves obey the following classical law ... 

Fig. 49. Fatigue life curves for some lilamenis of glassy metals. Full curves indicate ribbons and broken curves indicate wires. For further details and references see Table 7. The curves for the wires and the FeCr alloy have been measured in the bending mode with imposed surface strain. In order to represent the.se on the same stress scale this strain has been multiplied by their Young modulus. The bulk amorphous alloy has also been measured in the bending mode but with imposed bending stress.

Creep strain/time curves have been determined for a range of SiCf/SiC type composites, " for various types of SiC fibre and for other CFCMCs. However, the faetors eontrolling the creep properties of different composites have usually been diseussed by reference to only a few standard parameters, such as the minimum creep rate (Sm), and the creep rupture life (tf). For this reason, the present projeet seeks to demonstrate that evidence derived from analyses of creep curve shape is relevant to interpretation of the detailed manner in which specific material variables influence strain aecumulation and damage evolution during tensile creep of CFCMCs. 

Enhanced load-life curve for adhesively bonded single lap joints, showing regions of crack initiation Cl), stable crack growth (SCG), and fast crack growth (FG). The broken lines showing back-face strain as a function of number of cycles (Shenoy et al. 2009a)... 

Example 2.2 A polypropylene beam is 100 mm long, simply supported at each end and is subjected to a load W at its mid-span. If the maximum permissible strain in the material is to be 1.5%, calculate the largest load which may be applied so that the deflection of the beam does not exceed 5 mm in a service life of 1 year. For the beam / = 28 mm and the creep curves in Fig. 2.5 should be used. 

The only unknown on the right hand side is a value for modulus E. For the plastic this is time-dependent but a suitable value may be obtained by reference to the creep curves in Fig. 2.5. A section across these curves at the service life of 1 year gives the isochronous graph shown in Fig. 2.13. The maximum strain is recommended as 1.5% so a secant modulus may be taken at this value and is found to be 347 MN/m. This is then used in the above equation. 

A cylindrical polypropylene pressure vessel of 150 mm outside diameter is to be pressurised to 0.5 MN/m for 6 hours each day for a projected service life of 1 year. If the material can be described by an equation of the form s(t) = At" where A and n are constants and the maximum strain in the material is not to exceed 1.5% estimate a suitable wall thickness for the vessel on the assumption that it is loaded for 6 hours and unloaded for 18 hours each day. Estimate the material saved compared with a design in which it is assumed that the pressure is constant at 0.5 MN/m throughout the service life. The creep curves in Fig. 2.5 may be used. 

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