PSI - Issue 5

Jesús Toribio et al. / Procedia Structural Integrity 5 (2017) 1299–1303 Jesús Toribio et al./ Structural Integrity Procedia 00 (2017) 000 – 000

1300

2

Nomenclature a

crack depth

b

second dimension of the crack (modelled as an ellipse)

a / b

aspect ratio

( a / b ) 0

initial aspect ratio relative crack depth

a / t

( a / t ) 0 Δ a ( i )

initial relative crack depth crack advance at the point i Paris constant crack growth rate parameter to obtain K parameter F at the point i

Δ a {max}

maximum crack advance in the iterations

C

d a /d N

F

F ( i )

F {max}

maximum parameters F along the crack front angle characterizing a point at the crack front



i

crack front discrete point stress intensity factor SIF stress intensity factor range

K

Δ K

m Q

Paris exponent

parameter to obtain K

r

notch ratio

r / t

relative notch radius remote tensile stress

σ

t

plate thickness

w p

plate width

point over the crack front

2. Numerical modelling

A numerical model using Java programming language was performed to study the fatigue cracking paths associated with elliptical cracks placed at the corner ( quarter-elliptical corner cracks ) or at the surface ( semi-elliptical surface cracks ) in finite-thickness plates with a circular notch subjected to tension loading (Fig. 1). The crack front was characterized as a part of an ellipse of semi-axes a (crack depth) and b (crack length). Each point p over the crack front is defined by means of the angular parameter  , depending on the relationship between the semiaxes a and b of the ellipse (Fig. 2). In this paper, the SIF K solution provided by Newman et al . (1994) is used for the geometry and kind of loading shown in Figs. 1 and 2:

a Q   F

K



(1)

Function Q is given by the square of the complete elliptic integral of the second kind, depending only on the crack aspect ratio a / b , whereas function F does depend on the specific point at the crack front (coordinate  ) and on several dimensionless ratios: a / b , a / t , b / r , b / w , r / t , r / w . Eq. (1) is applicable in the case of corner cracks for: 0.2 < a / b < 2; a / t < 1; ( b + r )/ w < 0.6; 1 < r / t < 2; r / w = 1/16; 0 <  < π/2. For surface cracks, it is valid if: 0.2 < a / b < 2; a / t < 1; ( b + r )/ w < 0.6; 1 < r / t < 3.5; r / w = 1/16; - π/2 <  < π/2.