The plastic strain energy required for failure in low-cycle biaxial fatigue is estimated using the energy in uniaxial fatigue and assumptions from the theory of plasticity. A criterion for high-strain multiaxial fatigue of the form
is developed, where the equivalent stress amplitude Δσ and the equivalent plastic strain amplitude Δεp are based on the von Mises yield function of plasticity. The parameters K and c are assumed to depend on the mechanical properties of the material and to be functions of the stress ratio. These functions can be evaluated from uniaxial fatigue data and are compared with tests performed on thin-walled tubes of mild steel at different stress ratios. The proposed criterion seems to yield a promising approach for the low-cycle fatigue analysis of metals under biaxial states of stress.
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