Fatigue Crack Paths 2003

transformation between two Cartesian systems can be described in different ways, but

the direction cosines matrix is usually applied. On the other hand, such a matrix

includes nine dependent components, and averaging all the matrix elements is not

effective since the averaged matrix would not satisfy the conditions of transformation

[8]. Moreover, we are not able to select which three independent elements of the

direction cosines matrix should be averaged. The exact algorithm of average procedure

and calculation of Euler angles can be found in [4-5]. The aim of the present paper is to

verify whether the weight function method based on energy parameters can allow us to

determine the expected fatigue fracture plane position.

E X P E R I M E N TDAALT A

Fatigue tests were performed in the high cyclic fatigue regime on the smooth specimen

(Fig. 1) made of 18G2Asteel. Mechanical properties of 18G2Asteel were as follows,

yield stress: Re = 357 MPa, ultimate stress: Rm = 535 MPa, Young’s modulus: E = 210

GPa, Poisson’s ratio ν = 0.3, fatigue limit for fully reversed axial and torsion

respectively: σaf= 204 MPa, and τaf= 170 MPa, exponents of the fatigue curves for

fully reversed axial (σa-Nf) and torsion (τa-Nf) respectively: mσ=8.2 and mτ=8.2.

Figure 1. Specimen geometry.

The specimens were subjected to random bending, torsion and combined bending

with torsion for three values of the cross correlation coefficient (rσ= -0.01, 0.50, 1.00)

between courses of bending Mg(t) and torsional momentMs(t). Histories of loading with

normal probability distribution and narrow frequency band were generated in a

computer in the form of one block. The length of a loading block was equal to 33

minutes and 30 seconds. This block was repeated until to fatigue failure of specimen.

The moments of bending and torsion were recalculated to stress using the elastic model.

Fatigue tests were carried out for different ratio of maximum torsional stress to

maximumbending stress λσ= τmax/σmax (Table 1). As a result of fatigue test, the crack

line for each specimen was established on the basis of photos of specimen surface

(Fig.2). The photos of specimens were made using an optical microscope with

magnification of 60 times connected directly to the computer. Points representing

cracks were approximated to regression line using the least squares methods. The slope

coefficient of regression line was used to calculate the experimental value of angle αexp .