Page 401 - Biaxial Multiaxial Fatigue and Fracture

A Multiaxial Fatigue Life Criierion for Non-Symmetrical and Non-Proportional Elasto-Plastic ... 385

A SELECTIVE REVIEW OF STRAIN-BASED CRITERIA

Many mechanical components and structures are often subject to complex elasto-plastic strain
states, particularly at stress concentration zones such as notches. For a uniaxial stress state, in
the low and intermediate range of life, a fatigue life prediction may be obtained by the
Manson-Coffin equation:

6’
Ea =-1(2N,)b+&;(2NJ
E
where 0; and b are the fatigue strength coefficient and exponent respectively, E; and c are the
fatigue ductility coefficient and exponent respectively, and E is the Young modulus. Clearly,
the above relation is not able to take into account the effect of multiaxial loading. In the last
years different multiaxial fatigue life prediction methods have been proposed [IO] for assessing
the fatigue life under complex loads. Strain-based criteria are obtained by casting a multiaxial
strain state into an equivalent uniaxial strain. Some of the strain-based fatigue life prediction
methodologies are briefly reviewed in the following.

von Mises criterion

One of the most common equivalent strain-based criteria is the maximum octahedral shear
strain amplitude criterion. For a multiaxial strain state, this hypothesis defines an equivalent
strain amplitude through the relationship:

where E,,,~ and x,,, denote respectively normal and shear strain amplitudes and v is the
Poisson’s ratio. In the following, this criterion will be named after vonMises, even if the
original proposal by von Mises, currently employed in plasticity for determining the onset of
yielding, is based on the strain energy density of distortion. According to this approach, one
obtains a fatigue life prediction replacing into the Manson-Coffin relationship the axial strain
amplitude E, with the equivalent strain amplitude E,,,, , given by Eq. (2).
Let us consider two load states both having the same axial and shear strain amplitudes; in
the first state the strains are in-phase whereas in the second they are out-of-phase. The major
drawback resulting from the hypothesis of von Mises is that it produces the same equivalent
strain for both the in-phase and out-of-phase load states above. Consequently, both states
would result to the same fatigue life according to von Mises approach. Several experimental
results contradict this prediction, showing that, for strain controlled fatigue tests, the fatigue
life under out-of-phase loading is lower than the fatigue life under in-phase loading at the
same applied strain amplitudes.

ASME Code

The ASME Boiler and Pressure Vessel Code Procedure [l] is based on the von Mises
hypothesis. An equivalent strain range is defined through the relationship: