Critical plane approach to multiaxial variable amplitude fatigue loading

Yingyu Wang,Luca Susmel

doi:10.3221/igf-esis.33.38

Abstract

A new critical plane approach based on the modified Manson-Coffin curve method (MMCCM) is presented in this paper for predicting fatigue lifetime under variable amplitude (VA) multiaxial fatigue loading. The critical plane is assumed to coincide with that material plane experiencing the maximum variance of the resolved shear strain. Fatigue damage is hypothesized to be a function of both the amplitude of the resolved shear strain and the so-called critical plane stress ratio. The latter quantity depends on the mean value and the variance of the stress perpendicular to the critical plane as well as on the variance of the shear stress resolved along the direction experiencing the maximum variance of the resolved shear strain. Load cycles are counted from the resolved shear strain time history by using the classic rain flow counting method. Palmgren-Miner’s linear damage rule is applied to estimate cumulative fatigue damage. The accuracy and reliability of the proposed approach is checked by using several experimental data taken from the literature. The estimated fatigue lives based on the new approach are seen to be in sound agreement with the experimental results.

Highlights

Fatigue life prediction approaches based on the concept of the critical plane are generally accepted to be more accurate for multiaxial fatigue life estimation
The Maximum Variance Method (MVM) postulates that the critical plane can be defined as that plane containing the direction that experiences the maximum variance of the resolved shear stress
The present paper summarizes an attempt of extending the use of the Modified Manson-Coffin Curve Method (MMCCM) to those situations where complex variable amplitude loadings are involved

Summary

INTRODUCTION

Fatigue life prediction approaches based on the concept of the critical plane are generally accepted to be more accurate for multiaxial fatigue life estimation. The Maximum Variance Method (MVM) postulates that the critical plane can be defined as that plane containing the direction (passing through the assumed critical point) that experiences the maximum variance of the resolved shear stress. The MMCCM is suggested here as being applied in conjunction with the maximum variance method (MVM) to estimate fatigue lifetime by directly post-processing the strain state relative to that material plane containing the direction along which the variance of the resolved shear strain is maximized. Eq (13) makes it evident that the determination of the direction experiencing the maximum variance of the resolved shear strain is a conventional multi-variable optimization problem It can be satisfactorily solved by using the so-called Gradient Ascent Method [19]. Can be evaluated, at any instant, t, of the load history, through the following relationship:

EVALUATION OF STRAIN AND STRESS COMPONENTS RELATIVE TO THE CRITICAL PLANE

THE MMCCM TO ADDRESS THE VARIABLE AMPLITUDE PROBLEM

VALIDATION BY EXPERIMENTAL DATA

Resolved shear strain history