Fatigue Crack Paths 2003

Figures 5a and 5b illustrate the effect of overloading on subsequent crack propaga

tion rate for single overloading cycle and different values of A.

), then the case of brittle

Let us note that when KI tends to

*Ic K (or

n σ tends to

*cσ

fracture occurs. Let us remind that the first term of Eq. (36) dominates for stable crack

growth, and the second term is greater for the unstable growth. To formulate brittle

fracture condition, we can disregard the first term of Eq. (36) because

l K K ∂ ≈∂

<< ∂∂ σ

K ∂ σ

Kl l

d

d

so d

I

I

I I

(42)

.ld

It is justified in the case of load control (then dσ/dl≥ 0). Whenkinematic control

occurs, we have dσ/dl < 0 and it is necessary to consider the complete form of (49).

Rearranging Eq. (35) we can formulate the brittle fracture criterion in the following

form:

• crack propagation condition:

)p

(43)

(

n K= 1Kω − *Ic I

• unstable crack growth condition:

p n n p n pA ω ω

pK ω

( ) 1 ω

∂∂ ≥ Kl

d

1

−

⎥⎦⎤

I

0

*Ic

(44)

.

⎢⎣⎡

−

( ) 1

+ −

η

n

( ) 1 −

Figure 6 shows the graphic illustration of these equations.

a)

b)

Figure 5. The effect of a single overloading cycle on crack propagation rates: a) single

5.0 /*IcImax = K K

overloading cycle

9.0 K /*Ic = Kand subsequent cycles

, b) single

Imax

42.0 /*IcImax = K K ,

6.0 /*IcImax = K K

8.0 /*IcImax = K K

and

overloading cycle

9.0 = K Kwith subsequent / *Ic Imax

4.0 = K K . / *Ic Imax

cycles