Research On Approximate Calculation Method For The Stress-Strain Response At Notch Tip Under Cyclic Loadings

The fatigue failure of the mechanical components is one of the most important problem in mechanical field, the current theories of the fatigue life prediction indicates that the crux is to obtain the stress-strain response at notch tip. Among the notch tip stress-strain analysis methods, the approximate calculation method for its easy to use and fast to calculate is accepted as a highest practical valuable method in engineering applications. In this paper, the research is performed for the notch tip stress-strain approximate calculation methods under uniaxial or multiaxial cycle loadings in proportional and non-proportional.After the comparison from the energy point of view of the three most typical applied nominal stress-strain and the actual notch root stress-strain relations methods: Neuber's rule, ESED method and thermodynamic method, an intrinsic link among the three methods is found. By introducing a parameter C_q , like the vibration damping, a unified expression is established for description the relations between the nominal stress-strain and the actual stress-strain at the notch tip, (?) is defined the thermodynamic energy dissipation coefficient during plastic deformation in a cycle loading, when ?? takes on different values, it corresponds respectively to the Neuber's rule, ESED method and thermodynamic method.A developed unified expression in the incremental form has been proposed, this equation combined with Jiang-Sehitoglu material constitutive model, a set of the notch tip stress-strain and its stress-strain increment equations can be obtained. By using the equations the notch tip stress-strain response path under non-proportional loading can be calculated. A computer program has been written in FORTRAN for a numerical solution of the equations.Finite element method was used to determine the location of the notch tip stress concentration and the notch's geometrical parameters: the true stress concentration factor, the true strain concentration factor and the theoretical stress concentration factor K_t . The experiments under four multiaxial loadings have been carried out for acquiring the strain response at notch tip, which is also be calculated by the proposed unified expression in Neuber's rule, ESED method and thermodynamic method, respectively, compared with the experimental results show that: Neuber's rule is usually overestimated the strain at the notch tip; ESED method usually underestimates the strain at the notch tip; thermodynamic method obtained a closest data to the experiments. It corresponds with the large number of the experimental and finite element method results that had been shown.