Multiaxial fatigue and deformation including non-proportional hardening and variable amplitude loading effects

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 modeling, material properties and variations with hardness and microstructure, fatigue damage evolution, fatigue damage quantification parameters, cycle counting procedure, damage accumulation rule, and effects of multiaxial load non-proportionality on deformation and fatigue behaviors.;To evaluate the effect of hardness and microstructure on additional non-proportional hardening and fatigue behaviors, 1050 steel in normalized, quenched and tempered, and induction hardened conditions as well as 304L stainless steel were utilized. Constant amplitude in-phase and 90º out-of-phase strain-controlled axial-torsional cyclic tests were conducted. Reductions in the non-proportional cyclic hardening were observed as the microstructure of 1050 steel changed from pearlitic-ferritic with lower hardness to tempered martensite with higher hardness. Significant non-proportional cyclic hardening was also observed for 304L stainless steel with austenitic microstructure. Multiaxial data generated in this study as well as multiaxial deformation data of several materials 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. Similar fatigue life variation as a function of hardness of steels was found for in-phase and out-of-phase loadings, with higher ductility beneficial in low cycle fatigue (LCF) and higher strength beneficial in high cycle fatigue (HCF).;Multiaxial fatigue data were satisfactorily correlated for all hardness levels with the Fatemi-Socie parameter. Furthermore, in order to predict multiaxial fatigue life of steels in the absence of any fatigue data, the Roessle-Fatemi hardness method was used. 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.;Some 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 sensitivity to non-proportional loadings. Tubular specimens made of 1050 quenched and tempered (QT) steel with no non-proportional hardening and 304L stainless steel with significant non-proportional hardening were utilized. The 1050 QT steel was found to exhibit very similar stress responses under various multiaxial loading paths, whereas significant effects of loading sequence were observed on stress responses of 304L stainless steel. In-phase cycles with a random sequence of axial-torsional cycles on an equivalent strain circle were found to cause cyclic hardening levels similar to 90° out-of-phase loading of 304L stainless steel. In contrast, straining with a small increment of axial-torsional on an equivalent strain circle resulted in higher stress than for in-phase loading of 304L stainless steel, but the level of hardening was much lower than for 90° out-of-phase loading. Tanaka's non-proportionality parameter coupled with a Fredrick-Armstrong incremental plasticity model, and Kanazawa et al.'s empirical formulation as a representative of such empirical models were used to predict the stabilized stress response of the two materials under variable amplitude axial-torsional strain paths. While Kanazawa et al.'s empirical formulation could not distinguish between strain paths with random and incremental sequences of straining, resulting in significant over-prediction of stress for 304L stainless steel, consistent results between experimental observations and predictions were obtained by employing the plasticity model.;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 cycles with random sequences of axial-torsional within an equivalent strain circle, while resulting in higher stress response for 304L stainless steel, did not significantly affect fatigue life for either material. Experimentally observed failure planes for all strain paths in this study were in very 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 in this study. Fatigue damage for each counted cycle was evaluated using Fatemi-Socie damage parameter taking into consideration constitutive behavior effects and reflective of the material damage mechanisms. Linear cumulative fatigue damage was then employed to account for accumulation of damage. Fatigue lives for both materials under these strain paths were predicted satisfactorily employing this approach and either Bannantine-Socie or Wang-Brown cycle counting methods.;Finally, cracking behavior was analyzed for different materials investigated and under various loading conditions. Micro-cracks were observed to be around the maximum shear plane for in-phase and 90° out-of-phase loadings. It was also observed that the ratio of crack initiation life to total fatigue life as well as the crack growth rate depend on variety of factors including strain amplitude level, load non-proportionality, material ductility, and specimen geometry. It was also observed that cracks nucleate and grow on a wide range of planes around the critical plane depending on the load non-proportionality and strain level. Crack growth rates for in-phase and 90º out-of-phase loading were correlated well by Reddy-Fatemi effective strain-based intensity factor.