Crack Paths 2009

initiate from this location. At very low ratios IUh (relatively thick plates) the stress

distribution across the thickness has a maximumin the vicinity of the free surface and

hence the preferred crack initiation site of thick plates is in this region.

In the last two decades the major progress in the analysis of three-dimensional

solutions is associated with the application of the finite element (FE) method. The finite

element results presented in various papers confirm the main features of the in-plane

stress distribution and provide a relatively easy way to analyze the effect of various

parameters. For example, Fig. 3 shows the m a x i m u mand minimumstress concentration

factors at the same critical location (x:i Rand y I 0) as a function of Poisson’s ratio,

v [13]. Despite the relatively small variation of the m a x i m u mstress concentration

factor from its plane stress or plane strain counterpart (SKF I 3), the variation of the

stresses across the plate thickness (or ratio of the maximumto minimumSCF) is

significantly affected by Poisson’s ratio, v, and can reach 50 percent for high values of

Poisson’s ratios.

Three-dimensional numerical investigations of elliptical holes

subjected to uniaxial tension showthat the difference between the solution of the plane

theory of elasticity and the corresponding three-dimensional solutions in terms of the

m a x i m u mSCF can reach 30 percent and the variation of SCF across the thickness up to

100 percent [13].

SCF

Tim“

I — First-order plate theory [10]

- — Finite element predictions [l3]

0.8 —I

0 Finite element [14]

1-4 ' ——— First-order plate theory [10]

1.3-

0-6-I T —

Z

SCF /scrmm m a x

12

0.4 -I

'

v I 0.3

_

O

1_1

0.2 -

_

O

1

.

.

.

.

.

.

.

0I

0.1

0.2

0.3

0.4

v

0.01

0.1

1

10

h/R

Fig~3~ M a x i m uamnd minimumStress

Fig.4. M a x i m ucmonstraint factor as a

Concentratlon factor at X I iR. Y I O as a

function of half-thickness to hole

function of Poisson’s ratio, v.

radius ratio.

To characterize the out-of-plane stress componentswe introduce the constraint factor

as a ratio of the out-of-plane stress, 62 to the sum of the in-plane stress components,

TZ :6Z/v(oX +oy).

(1)

The constraint factor is widely used to characterize the dominant stress state in plate

components [10-13] especially in fracture mechanics and composites where, the main

failure mechanisms, delamination, is often associated with the transverse stress

194