Crack Paths 2009

C R A CPKA T H SU N D EMRI X E D - M OLDOEA D I N G

Twoapproaches are developed for geometrical modeling of crack growth trajectories

for the inclined through thickness central cracks and the part-through surface flaw

respectively. The principal feature of such modeling is the determination of crack

growth direction and the definition of crack length increment in this direction.

Fracture damagezone concept

The crack growth from an inclined crack illustrates mixed-mode crack behavior on the

initial crack. As follows from experimental data for materials of different properties,

σθ max

θ∗

the

the angle of crack propagation

lies in the range between the curves corresponding to

maximum normal stress and theσ e

minimum effective stress criteria.

Therefore the most general empirical criterion is obtained by Shlyannikov [1] on the

basis of the limiting state theory of Pisarenko and Lebedev [2] and the fracture damage

zone size

()( ) ( ) χ θ σ χ θ σ θ 1 2 1 ∗ ∗ + − = e

(1)

θ

∗

max

χ σ σ = t c is the experimental constant and σt

in which

is the tension static strength,

(* θ2 σ

σc

is the compression static strength, σθ

* e θ1 σ

and

) maxθ

- are the crack growth

max

σe

directions in accordance to the

and the

) (

criteria respectively. For brittle

χ=0, while for plastic materials

χ=1.

materials

When applying any of fracture criteria to predict crack propagation, the point of

view being that the stress-strain characteristics are not determined at the crack tip itself,

but at some distance rc from it. To take advantage of equation (1), it is necessary to

define the sense of the radial distance rc . Many of the fracture mechanics theories are

based on a critical distance local to the crack tip. In the present work the critical

distance ahead of the crack tip is assumed to be located where the stress strain state rc

in the element reaches a certain critical value that can be measured from a uniaxial test.

l r c c δ = and crack growth rate model

Both relative fracture damage zone size (FDZ)

were introduced by Shlyannikov [1]

)(

( S W S S S ± − − +  ∗ 2 22 3 1 2 4 ) [ ] c p S

m t h t h 1

    

=

 

f n K K − ∆ σ

   

l σ δ

(2)

dl

   

(

)

2 2

δc

=

c W S

2 2

f f E * * 4 δ ε σ

2

,

2

− ∗ 3

dN

∗ ∗

2

ε σ

σσ

12

;

static loading







n σ α σ 2 f + + 1 n



cyclic

=

n f

W

=

f f

0

1

m

c

∗

+

c ∗

W

4 2

N

−

(

) f

( )

loading

yn

σ0

In these equations

is the yield stress,

is the true ultimate tensile stress, E is

f σ

modulus of elasticity,

is the fatigue ductility, σ is the fatigue strength coefficient, *fε *f

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