Fatigue Crack Paths 2003

Identification of Fatigue Fracture Plane Positions with the

Expected Principal Stress Directions

A. Karolczuk and E. Macha

Technical University of Opole, Faculty of Mechanical Engineering, ul. Mikolajczyka 5,

45-271 Opole, Poland, e-mail: emac@po.opole.pl

ABSTRACT.Calculation of the material fatigue life under multiaxial random loading

needs, among others, application of the failure criteria based on the expected position

of critical planes. It is convenient to determine those positions in relation to the

principal stress or strain axis directions. In the paper the expected directions of the

principal stress under proportional and non-proportional loading have been determined

by averaging the instantaneous values of the Euler angles with use of special weight

functions. The known weight functions based on the stress parameters have not been

efficient for each loading or material. Thus, the authors considered new weight

functions based on the energy parameters. The presented forms of weight functions

were verified in tests of 18G2Asteel. It has been shown that the fatigue fracture plane

direction under multiaxial loading can be efficiently determined on the basis of an

averaged direction of the maximum principal stress including a suitable weight

function.

I N T R O D U C T I O N

Multiaxial fatigue tests prove that fatigue fracture plane orientations to a large degree

refer to the principal stress directions [1-2]. However, numerous models of fatigue crack

initiation and propagation for multiaxial loading do not take into account a change of

the principal stress axes. Averaged principal stress directions should be determined, and

the averaging procedure could be carried out to estimate the fatigue fracture plane

positions. The average procedure to calculate the expected fatigue fracture plane

positions has been proposed by Macha [3] and it is called the weight function method.

In this method, the directions of principal stress axes 123 at the instant time are

described by the three Euler angles ϕ, θ, ψ. The instant values of Euler angles are

averaged using suitable weight functions. Different weight functions based on stress

parameters have been already proposed [3-7]. In this paper, new weight functions based

on energy approach are proposed and verified on the basis of multiaxial fatigue tests

carried out on 18G2Asteel subjected to random bending, torsion and combined bending

with torsion. Three independent Euler angles were selected for average procedure to

avoid the problems with fulfilling a condition of orthogonal conversion. The principal

axes 123 system can be considered as a transformation of the X Y Zsystem. A