Fatigue Crack Paths 2003

maximumtangential stress criterion (Erdogan and Sih [3]). Then, the propagation path

of the fatigue crack is perpendicular to the maximumprincipal stress. The same method

was applied earlier with reasonable success for different joint types, Nykänen et al.

[4,5,6,7,8].

Calculation of Fatigue Life

The fatigue life was calculated using the Paris-Erdogan relation as presented by Gurney

[9]. Paris' law for the crack growth rate is

da

m , dN =KΔ C

(1)

where da/dN is the crack growth rate per cycle, C and m are constants, and K is the

range of the stress intensity factor for the opening mode. The Paris law constants m = 3

and Cchar= 3×10-13 (Cmean = 1.7×10-13), with da/dN in mm/cycle and K in Nmm-3/2, are

recommended for the analysis of welded steel joints in Hobbacher [10], and are used in

this study. The characteristic Cchar-value given above corresponds to a 95% survival

probability. The threshold value of the stress intensity factor was omitted in these

simulations. Integrating Eq. 1 so that the variables, i.e., crack length, a, (using a/t

instead of a) and number of cycles, N, are separated produces

at

tC I

N =

tCI

N =

π σ

σ

σ

at

m

at

fi

fi

m

−

⎜ ⎜ ⎝ ⎛

⎟ ⎟ ⎠ ⎞

t

t

m

m

−

Δ ⋅ ⇒

at d t K

C

at

C

Δ

= ⎟ ⋅⋅ ⎞ ⎜ ⎝ ⎛ ⋅ ⋅ Δ ⋅ ⋅ = ⎟ ⎠ ⎞ ∫ dt t Y ⎜ ⎝ ⎛ ⋅⋅ ⎟ ⎠ ⎞ ⎠

⋅

− ⎜ ⎝ ⎛ ⋅ ⋅ Δ ⋅

(2)

∫

m

2 1 −

−

1

2

where ai and af are the initial and final crack lengths, respectively. The value of the

crack growth integral, I, depends on the geometry of the cracked body. In the numerical

integration of Esq. 1, which is carried out automatically by the FRANC2D/pLrogram

during the crack growth simulation, the final crack length aft was reached when the

increase in fatigue life was negligible.

R E S U L T S

MeanFatigue Strength

Several different models were analysed using the simulation program with a certain

stress range, , and thus the mean crack propagation life N was determined. The stress

range = ∗ m +∗∗ b ∗was then changed with Eq. 2 to correspond to a fatigue life

of two million cycles. Some of the predicted mean fatigue strengths,

are

mean,

presented in Table 1.

Theoretical Fatigue Class

Using the

mean-values given in Table 1 and Cchar = 3×10-13, the theoretical fatigue

class (FAT) for each case analysed can be determined. From Eq. 2, we can obtain the

following Eq. 3 for the FAT: