— A modification to Brown and Miller's critical plane approach is proposed to predict multiaxial fatigue life under both in-phase and out-of-phase loading conditions. The components of this modified parameter consist of the maximum shear strain amplitude and the maximum normal stress on the maximum shear strain amplitude plane. Additional cyclic hardening developed during out-of-phase loading is included in the normal stress term. Also, the mathematical formulation of this new parameter is such that variable amplitude loading can be accommodated. Experimental results from tubular specimens made of 1045 HR steel under in-phase and 90° out-of-phase axial-torsional straining using both sinusoidal and trapezoidal wave forms were correlated within a factor of about two employing this approach. Available Inconel 718 axial-torsional data including mean strain histories were also satisfactorily correlated using the aforementioned parameter.

A critical plane approach to multiaxial fatigue damage including out-of-phase loading

-A path-independent multiaxial fatigue damage criterion is proposed based on critical plane concepts: fatigue crack growth is controlled by the maximum shear strain, and an important secondary effect is due to the normal strain excursion over one reversal of the maximum shear strain. The effect of loading path on fatigue endurance is quantified by the normal strain excursion. Only one multiaxial material constant is required in the model which can be determined from uniaxial test data plus one torsional result. The parameter can be easily integrated with a shear strain-life relationship to predict low cycle fatigue lifetime. Experimental data of four different materials: En1 5R steel, I% Cr-Mo-V steel, 304 stainless steel, and 316 stainless steel at two temperatures were used to verify the criterion. It is shown that the proposed parameter can satisfactorily correlate test results for various proportional and non-proportional straining paths. NOMENCLATURE

A path-independent parameter for fatigue under proportional and non-proportional loading

Evaluation of an energy-based approach and a critical plane approach for predicting constant amplitude multiaxial fatigue life

A series of multiaxial low-cycle fatigue experiments was performed on 45 steel under non-proportional loading. The present evaluations of multiaxial low-cycle fatigue life were systematically analysed. A combined energy density and critical plane concept is proposed that considers different failure mechanisms for a shear-type failure and a tensile-type failure, and from which different damage parameters for the critical plane-strain energy density are proposed. For tensile-type failures in material 45 steel and shear-type failures in material 42CrMo steel, the new damage parameters permit a good prediction for multiaxial low-cycle fatigue failure under non-proportional loading. The currently used critical plane models are a special and simple form of the new model.

A critical plane-strain energy density criterion for multiaxial low-cycle fatigue life under non-proportional loading

In the paper three methods of determination of the expected fatigue fracture plane position under random triaxial stress state have been presented. They are: weight function method, variance method and damage cumulation method.



The weight function method for biaxial cyclic loadings has been analysed with digital simulation. The fatigue fracture plane position has been determined with mean values of the direction cosines of principal stress axes. Averaging has been done at angle values with use of weights. Eleven various weights have been presented and their usability has been analysed on the basis of experimental results obtained by Rotvel, and Nishihara-Kawamoto. The weights with good agreement of results of simulation tests and experiments have been shown.

Simulation investigations of the position of Fatigue Fracture Plane in materials with biaxial loads

The effects of out-of-phase or nonsychronous straining on low-cycle fatigue was investigated. Biaxial strains were imposed on thin-walled tubular 7075-T6 aluminum specimens by tension-compression and torsion. Phase angles of 0, 30, 45, 60, and 90 deg were applied between two strains. It was found that out-of-phase cycling has an effect on the failure mode in the low-cycle-fatigue range. An analysis based on the maximum total strain in three-dimensional strain is proposed for treating 'out-of-phase' straining conditions in low-cycle fatigue.

R. E. Frishmuth

Papers

The effects of out-of-phase biaxial-strain cycling on low-cycle fatigue