Page 281 - Biaxial Multiaxial Fatigue and Fracture

BiaxiaVMultiaxial Fatigue and Fracture.
Andrea Carpinte.ri, Manuel de Freitas and Andrea Spagnoli (Eds.)
0 Elsevier Science Ltd. and ESIS. All rights reserved. 265

AN ANALYSIS OF ELASTO-PLASTIC STRAINS AND STRESSES IN NOTCHED
BODIES SUBJECTED TO CYCLIC NON-PROPORTIONAL LOADING PATHS

Andrzej BUCZYNSKI' and Grzegorz GLINKA'
' Warsaw University of Technology, Institute of Heavy Machinery Engineering,
ul. Narbutta 85,02-524 Warsaw, Poland
' University of Waterloo, Department of Mechanical Engineering, Waterloo,
Ontario N2L 3G1, Canada

ABSTRACT
Fatigue and durability analyses of machine components and structures require calculation of
elastic-plastic stresses and strains in notched bodies subjected to non-proportional loading
sequences. Analytical methods are seldom feasible even in the case relatively simple geometrical
configurations and therefore numerical methods are often employed. The numerical-analytical
method discussed below is based on the incremental relationships relating the fictitious elastic
and elastic-plastic Neuber type strain energy densities near the notch tip, and the material stress-
strain behavior simulated according to the Mroz-Garud cyclic plasticity model. The method
consists of a set of algebraic incremental equations that can be easily solved for elastic-plastic
stress and strain increments near a notch knowing the increments of the hypothetical elastic
notch tip stress history and the material stress-strain curve. The validation of the proposed model
against numerical data includes two non-proportional loading histories. In particular the basic
equations involving the equivalence of the strain energy density are carefully examined. Finally,
the numerical procedure for solving the basic set of equations is briefly described. The method is
particularly suitable for fatigue life analyses of notched bodies subjected to cyclic multiaxial
loading paths.

KEYWORDS

Elastic-plastic strains at notches, Multiaxial cyclic loading, Strain energy density
INTRODUCTION

Notches and other geometrical irregularities cause significant stress concentration. Such an
increase of stresses results often in localized near the notch tip plastic deformation, leading to
premature initiation of fatigue cracks. Therefore, the fatigue strength and durability estimations
of notched components require detail knowledge of stresses and strains in such regions. The
stress state in the notch tip region is in most cases multiaxial in nature. Axles and shafts may
experience, for example, combined out of phase torsion and bending loads. Although modem
Finite Element commercial software packages make possible to determine the notch tip stresses
in elastic and elastic plastic bodies for short loading histones, such methods are still impractical
in the case of long loading histories experienced by machines in service. A representative cyclic