Crack Paths 2009

(a)

(b)

Figure 3. (a) Geometry of notched specimen made of AISI 1141 steel; (b) total strain amplitude

εzz,a for notch radius R=0.529 m mand nominal stress amplitude Sa=400 MPa

distribution

Table 1. Cyclic properties of AISI 1141 steel

()'/1'napaKσε=

c f f b f f a N N E ) 2 ( ' ) 2 ( / ' ε σ ε + ⋅ =

E,

'f-ε,

b-,

c-,

'fσ,

K’,

n',

State A F 200

GPa M P a 1296

1.026

-0.088

-0.686

M P a 1205

0.122

-

Q T 212

765

1.664

-0.041

-0.704

1133

0.134

The strain and stress distributions in the specimens were calculated using the 3D finite

element analysis applied in A N S Y Ssoftware. In computations a cyclic constitutive

model with non-linear hardening was applied. The material hardening was identified

from the cyclic hardening curve (from half-life hysteresis loops) expressed by the

Ramberg-Osgood

equation (Tab. 1).

(

)'/1'n

a pa σ ε =K

R E S U L TOSFC O M P U T A T I O N S

The current paper focuses on the analysis of influence of weight function on the fatigue

life. Because of this reason, for the analysis, the experimental data that concerns only

push-pull loading of smooth and notched specimens were selected. The same state of

loading applied to smooth and notched specimens allows narrowing the problem down

to nonlocal influence of inhomogeneous stress (strain) distribution. Problem of reducing

multiaxial stress (strain) state in notch specimens using fatigue criterion is omitted.

εa in the plane normal

Fatigue characteristic (εa-2Nf, Tab. 1) uses total strain amplitude

to the applied forces. Thus, the same parameter is used in the notched

specimens:

azz , , ε ε = , where εzz,a aeq

is total strain amplitude in direction of applied forces.

εeq,a is computed over the area of integration A and then

The equivalent strain amplitude

)(

2 ) / 2 (

n l r n e− r w = , to receive the non-local parameter

integrated, using weight function

aeq,ˆε.

This non-local parameter is used to calculated number of cycles to fatigue failure using

εa-2Nf

fatigue characteristic

(Ncal= Nf). To estimate the goodness of fit between

experimental Nexp and calculated Ncal fatigue lives the following estimators are used:

log

,

1

E E E E E

i j

j

ri

icail

m

r

E

)( i j N j E E N = = ∑ = 1 , std −

−

= +

)( i

2

2

2

,

(3)

∑ =

=

eq

m

std

r

m

e)x(p )(

1 (

,)

)(

1

1

i

436