This study investigates fatigue damage and deformation behavior under multiaxial loading conditions, with the aim of evaluating reliable predictive models for life predictions. Life prediction for multiaxial variable amplitude loading involves a variety of issues to be considered. These include cyclic plasticity, material properties and variations with hardness and microstructure, fatigue damage evolution, fatigue damage quantification parameters, cycle counting procedure, damage accumulation rule, and effects of load non-proportionality.
To evaluate the effect of hardness and microstructure on additional non-proportional hardening and fatigue behaviors, 1050 steel in normalized, quenched and tempered (QT), and induction hardened conditions as well as 304L stainless steel were utilized. Reduction in the non-proportional cyclic hardening was observed as the 1050 steel changed from low hardness to higher hardness. Significant non-proportional cyclic hardening was observed for 304L stainless steel. Multiaxial data generated in this study as well as from literature suggest non-proportional cyclic hardening can be related to uniaxial cyclic hardening. Non-proportional hardening coefficients predicted from a proposed equation based on this observation were found to be in very good agreement with the experimental values in this study and from literature.
Multiaxial fatigue data for all hardness levels were satisfactorily correlated with the Fatemi-Socie parameter. In order to predict multiaxial fatigue life of steels in the absence of any fatigue data, the Roessle-Fatemi hardness method was extended to multiaxial loading. The applicability of the prediction method based on hardness was examined for several steels under a wide range of loading conditions. The great majority of the observed fatigue lives were found to be in good agreement with predicted lives.
Several discriminating multiaxial cyclic strain paths with incremental and random sequences were used to investigate fatigue and cyclic deformation behaviors of materials with low and high additional hardening resulting from non-proportional loadings. Tubular specimens made of 1050 QT steel and 304L stainless steel were utilized for this purpose. The 1050 QT steel was found to exhibit very similar stress response under various multiaxial loading paths, whereas significant effects of loading sequence were observed on stress response of 304L stainless steel. In-phase cycles with a random sequence of axial-torsional cycles on an equivalent strain circle caused cyclic hardening levels similar to 90° out-of-phase loading of 304L stainless steel. In contrast, straining with a gradual sequence resulted in much lower stress than for 90° out-of-phase loading. Tanaka’s non-proportionality parameter coupled with a Fredrick-Armstrong incremental plasticity model resulted in accurate prediction of the stabilized stress response. Kanazawa et al.’s empirical formulation as a representative of such empirical models could not distinguish between strain paths with random and incremental sequences of straining, resulting in significant over-prediction of stress for 304L stainless steel.
Contrary to common expectations, fatigue lives for 1050 QT steel with no non-proportional hardening were found to be more sensitive to non-proportionality of loadings as compared to 304L stainless steel with significant non-proportional hardening. In-phase loading cycles with random sequences of axial-torsion strain ratio within an equivalent strain circle did not significantly affect fatigue life for either material. Experimentally observed failure planes were in good agreements with predicted failure planes based on the Fatemi-Socie critical plane parameter. Bannantine-Socie and Wang-Brown cycle counting methods were utilized to identify loading cycles for variable amplitude strain paths. Fatigue damage for each counted cycle was evaluated using Fatemi-Socie damage parameter and linear cumulative fatigue damage was then employed to account for accumulation of damage. Fatigue lives for both materials under these discriminating strain paths were predicted satisfactorily employing this approach and either Bannantine-Socie or Wang-Brown cycle counting method.
Cracking behavior was analyzed for different materials investigated and under various loading conditions. Micro-cracks were observed to be around the maximum shear or critical plane. The ratio of crack initiation life to total fatigue life as well as the crack growth rate depended on a variety of factors including strain amplitude, load non-proportionality, material ductility, and specimen geometry. Crack growth rates for in-phase and 90° out-of-phase loading were correlated well by Reddy-Fatemi effective strain-based intensity factor.