Crack Paths 2009

Evaluation of stresses on the entire ligament

Due to their nature Eqs. (3, 5) are valid only in the highly-stressed zone close to the

notch tip, and not in the nominal zones, where the influence of the notch can be

neglected. However, the range of applicability of the solution can be largely extended

by substituting the variable r with the following function:

+ Arc tan[(r — r0 )m]

f(r) : r0

(6)

This function has been already proposed in Refs [12-14] for uniaxially loaded notched

components of finite size.

By inserting f(r) according to Eq. (6) into Eq. (5) one obtains:

rzy (r,0) : Imp +m [1 _ % j

y(7)

1’1’1'0

l

E

RoundedV notches

E

2ot=l35°, a=10 m m

0 8

Eq‘ (7)

9 R=600mm,p=3 m m

Km=2.34, m=0.05, s;=0.235

2ot=l20°, a=10m m

5 R o u n d e dV notches \

AR=4OOmm,p=2.5 m m

(l6 5' 20t=90°, a=l0 m m

‘

Km=2.52, m=0.07, s3=0.29

§>

0 4 20t=60°, a=10 m m

EOR=1OOmm,p=2 m m

5 Km=2.75, m=0.105, s3=0.45

0'2 U notch, a=10m m

§OR=3Omm,p=O.l m m

5 Km=8.l2, rr|1=0.24l, s3=0i566

0

I

I

I I I I I I I

I

I I I I I I I

I

I I I I I I I

I I I I I I I ‘

I

II

.t

0.001

0.01

0.1

1

10

100

1000

Distance fromthe notch tip [mm]

Figure 4. Plot of the stress componentIn along the notch bisector line of U- and V

notches in a rounded bar and comparison with Eq. (7).

The value of m to be used in Eq. (7) can be easily determined by means of a simple

equilibrium equation on the net section:

990