Crack Paths 2012

than the method of damage accumulation which requires time-consuming calculations.

Determination of the critical plane with the method of variance is connected only with

the stress values, while the method of damage accumulation includes also characteristics

of the fatigue strength of the given material.

C O N C L U S I O N S

The presented calculation results in the specimens subjected to bending with torsion

loading allow to formulate the following conclusions:

1. The normalized values of the equivalent stress variance and damage accumulation

depending on the angle of the critical plane position α are different for different

combinations of loading.

2. The method of variance gives the results more similar to the experimental data for

the initiation plane position (stage I).

3. A better conformity of the calculated fatigue life with the experimental results was

obtained by means of the failure criterion of maximumshear stress in the critical

plane according to the maximumdamage.

Acknowledgements

This work was partly supported by the National Centre for Research and Development,

contract No. N R030065 06/2009.

R E F E R E N C E S

1. Bdkowski, W., Macha, E. (1992) Fatigue fracture plane under multiaxial random

loadings – prediction by variance of equivalent stress based on the maximumshear

and normal stresses, Mat.-wiss. U. Werkstofftech., 23, 82-94.

2. Łagoda, T., Macha, E., Bdkowski,W. (1999) A critical plane approach based on

energy concepts: application to biaxial random tension–compression high-cycle

fatigue regime, Int. J. Fatigue, 21(5), 431–443.

3. Karolczuk, A., Macha, E. (2005) Critical planes in multiaxial fatigue of materials,

monograph. Fortschritt-Berichte VDI, Mechanik/Bruchmechanik, reihe 18, nr. 298.

Düsseldorf: VDIVerlag, p. 204.

4. Carpinteri, A., Macha, E., Brighenti, R., Spagnoli, A. (1999) Expected principal

stress directions for multiaxial random loading - Part I, Theoretical aspects of the

weight function method, Int. J. Fatigue, 21, 83-88.

5. Marciniak, Z., Macha, E. (2010) Fatigue life of constructional steels under non

proportional bending with torsion, Opole University of Technology, Opole, p.170.

6. Marciniak, Z., Rozumek, D. & Macha, E. (2008) Fatigue lives of 18G2Aand

10HNAPsteels under variable amplitude and random non-proportional bending

with torsion loading, Int. J. of Fatigue, 30, 800-813.

7. Korn, G.A., Korn, T.M. (1968) Mathematical Handbook, Sec. Ed., M c Graw-Hill

BookCompany,N e wYork.

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