Crack Paths 2006

Table 2. Experimental data

[o]

[o]

Mb,max

OM -

No

rad

N m

y ! max min ˆ ˆ D D

expˆD

Constant-amplitude loading

1 0 8.0; 10.0; 10.3 0.68 18.1

17.1 y 19.0

20.0 y 23.8

2 0 6.4; 7.4; 8.2; 9.8 0.96 21.9

3 0 5.3; 6.2; 7.2; 1.44 26.5

23.8 y 29.2

4 /2 8.9; 9.2; 9.6; 10.3 0.68 12.3

9.1 y 15.5

5 /2

8.3

0.98 8.4

7.3 y 9.5

6.4; 7.2

6 /2

1.42 10.2

6.4 y13.9

Variable-amplitude loading

7 -

18.4

’ 43.6/86.3 42.2y45.0/82.3 y 90.2

16.3

8 -

0 1.5

0.8y2.2

STRESSA N DS T R A I NC O M P U T A T I O N S

Stress and strain histories in an arbitrary point (x, y) of the specimen cross-section were

computed from bending and torsion momentsMb(t), Mt(t) considering the plastic strains.

Plasticity was included in the computation since the cyclic properties (K’, n’) of the

18G2Asteel reveal the appearance of the plastic strains even under low stress level ( %65.0 paH for Vaf= 204 MPa). The Chu [13] plasticity model of material behaviour

was applied to determine the strain-stress relation and the influence of loading history

on the strain state for each point of the specimen cross-section. For every increment of

bending 'Mb(t) and torsion 'Mt(t) moments the following quasi-static equilibrium

equations were solved by the trust-region method [14]

) , , (

0 ) ( ) , ( ' ' ³ t M d A t t A z U U W I , (21)

'

t M

'³

0 ) ( ,

y d A t y x

A z z V

b

zz(x, y, t+t)ízz(x, y, t) is the normal

zz(x, y, t) =

where the increment is defined as

stress increment for the finite element with the origin in the plane (x, y);

) is the

z(t,

shear stress increment for the finite element with the origin determined by the radius

2 2 U y x ; dA is the area of the finite element. Moreinformation about the stress and

strain computations are presented in [15].

E V A L U A T IAO NDDISCUSSION

The variable-amplitude torsion and bending were used to evaluate the damage

accumulation hypothesis. Calculated fatigue life T cal according to the failure criterion of

the maximumnormal stress applied under the variable-amplitude bending is closer to

the experimental fatigue life T exp

with the application of the Serensen-Kogayev

hypothesis than with the Palmgren-Miner one. Moreover, similar results were obtained