Crack Paths 2012

Fatigue critical plane according to variance and cumulative

damagemethods under multiaxial loading

Z. Marciniak, D. Rozumek& E. Macha1

1 Opole University of Technology, ul. Proszkowska 76, 45-758 Opole, Poland

e-mails: z.marciniak@po.opole.pl, d.rozumek@po.opole.pl, e.macha@po.opole.pl

ABSTRACT.The paper presents comparison of fracture plane position gained from

experiment tests of specimens under multiaxial loading and theoretical ones from

calculation according to variance and cumulative damage methods. In the variance

method it is assumed that the plane in which the maximumvariance of the equivalent

stress appears is critical for a material and the fatigue fracture should be expected in

this plane. In the cumulative damage method as critical plane, the plane which suffered

the greatest damage during service loading is adopted. For both methods the equivalent

stress was calculated according to the fatigue failure criterion of maximumshear

stresses in the critical plane.

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

Under multiaxial random loading, the critical plane position can be determined by

means of one of the following methods:

- the method of variance,

- the method of damage accumulation,

- the method of weight functions.

The method of variance [1] relies on search of the maximumvariance of equivalent

stress (or another parameter) according to the selected fatigue failure criterion. The

plane where the variance reaches its maximumis assumed as the critical plane.

At present, the method of damage accumulation [2, 3] seems to be the most interesting

because of its close relation to the idea of critical plane. Here, the selected fatigue

failure criterion is applied for search of the plane of the maximumdamage, i.e. the plane

of the minimumfatigue life. This is an iterative method, so search of the critical plane

requires repetition of all the calculation algorithm manytimes.

The method of weight functions [4] relies on search of averaged positions of directions

of mean stress axes by suitable weight functions. The critical plane position is

determined in relation to those axes, taking into account a kind of the material (elastic

or intermediate). Under multiaxial service loadings and the failure

plastic, elastic-brittle,

criteria based on the critical plane, the algorithm presented in Fig. 1 is usually applied.

The algorithm is used for calculations of the fatigue life of materials under random

loadings with zero meanvalues [5].

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