Manson-Coffin equation

At a small number of cycles (lcf), the stresses are large and the total strain is mainly determined by plastic deformation. In the LCF regime, a good approximation for the relation between plastic strain amplitude and cyclic life is given by the Coffin-Manson equation [32,94,95]. 

Coffln-Manson type equations are commonly used to predict the low-cycle fatigue life of solder. The general form of the Coffin-Manson equation is as follows ... 

When subjected to cyclic strains, ductile materials are found to fail either by Low Cycle Fatigue (when the life is given by the well known Coffin-Manson equation) or by Ratcheting Failure (when the life can be estimated by dividing the strain to failure by strain accumulation per cycle). Both LCF and RF act on the same material and so whichever occurs first causes failure. In this competitive mode of failure, the actual... 

At frequencies below 0.3 Hz, the slower ramp rates allow a greater extent of damage to occur, resulting in the acceleration of degradation. Then, the frequency-modified, Coffin-Manson equation becomes applicable ... 

Equation Coffin-Manson equation Basquin equation... 

Example 5. An example of modeling coupled failure mechanisms is the failure behavior model for components subjected to the coupling of fatigue and creep (Collins et al. 2009). For components subjected to only low-cycle fatigue, a Coffin-Manson model will approximate the failure behaviors quite well (Equation (14)). In equation (14), Ay is the TTF in cycles, A/ is the plastic strain range and both m and C are constants associated with material properties. 

Coffin-Manson predictions and test data. All predictions fall within 25% of the actual failure data. Subsequent creep-based analyses use the same fitting procedures and will produce separate fatigue life prediction equations for a given creep criterion and package type. 

From Table 7, it can also be observed that the larger the chip, the higher the stresses and the shorter the joint lifetime. This close correlation suggests that the stress value could be used as an indicator for lifetime estimation of ICA joints. An equation similar to the Coffin-Manson formula can then be proposed ... 

Isothermal fatigue predictions using the Coffin-Manson relationship have also been developed, but categorized according to the plastic strain levels to which the solder is exposed [88]. Guo et al. developed two equations to predict cycles to failure at 0.5 Hz, based upon a 50% load reduction criterion. The equations refer to two, tension-compression plastic strain ranges, Asp (%) ... 

Many empirical relations have been suggested to predict fatigue lifetimes, one of which is the Manson-Coffin equation. This and other relations have been widely used for metals and alloys (J. Pelleg). The Manson-Coffin relation for lifetime... 

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... 

Derive the S-N curve for the steel considered in sample problem 1. of Sect. 5.3 using Basquin and Manson-Coffin equations. To build the S-N curve the cyclic... 

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