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Definition of non-proportionality of strain path under multi-axial cyclic loading
Abstract
Based on the microstructural investigation of low cycle fatigue under multi-axial non-proportional loading of 316 L stainless steel, the distance within which dislocation moves freely was measured, while its distribution rule was analyzed. The quantitative relation between the macroscopic effective saturated stress and the statistical mean distance within which dislocations moves freely was given. The new definition of non-proportionality of loading path was presented on the basis of the statistical mean distance within which dislocation moves freely, which is considered as entering uniaxial cyclic constitutive equation to describe the stress and strain behavior under multiaxial loading.
Recent advances in micromechanisms of multiaxial fatigue under nonproportional loading are presented in the paper. The theory of additional hardening and its affecting factors are mainly discussed from the perspective of microstructure deformation. Finally, the ideas about the research of multiaxial fatigue micromechanisms under nonproportional loading are proposed.
Strain-controlled tension/torsion low cycle fatigue (LCF) tests of single crystal Ni-based superalloy, DD3, were carried out under non-proportional loadings based on orthogonal design at elevated temperatures, using thin-walled tube specimens with [001] orientation. Experimental variable factors were chosen to be strain range, strain path angle, tension/torsion phase angle, strain ratio and temperature. Results show that strain path angle, tension/torsion phase angle and equivalent strain range, are the main affected factors on multi-axial LCF life. Dividing diamond strain loading path into proportional loading and non-proportional loading segments, the equivalent strain range parameter to characterize the effects of non-proportional loading was proposed, and a strain triaxiality factor for single crystal superalloy was introduced to reflect the tension/torsion strain path angle on multiaxial fatigue life. A formula of cyclic plastic strain energy, which is composed of the equivalent strain range taking account of the effects of non-proportional loading path and the strain triaxiality factor, is put forward as failure parameter. Multiple linear regression analysis show that a power law of the failure parameter has a good correlation with the failure cycle, and all test data fall into a scatter band of the factor of 2.0.
Based on the time-dependent deformation behavior of solder alloy 63Sn-37Pb at room temperature, a damage-coupled unified visco-plastic multi-axial fatigue model and its failure criterion were proposed. In the evolution equation of damage for the model, the time-dependent effect of damage was taken into account. The model was used to predict the fatigue life under different loading paths. The comparison between the predicted and experimental results demonstrated that the time-dependent failure model can simulate the deformation behavior and predict the fatigue life well under different nonproportional strain paths.
A comprehensive yet relatively simple rate-independent constitutive model is presented. Most experimental observations such as strain amplitude effect, cross-hardening effect, erasure of memory property, etc., are simulated by the model. It is applicable to arbitrary complex non-proportional loading paths including cyclic loading. The material constants are comparatively few, and the procedure to determine them is outlined. The predictions of the model are compared to various experimental results and the agreement is found to be fairly good.