Crack Paths 2009

models and multi-material systems. For crack-like geometries it was found experimentally

that the comer singularity has a strong influence on the fatigue crack growth behaviour [22].

In 2005 Kotousov, with reference to the first order plate theory, first identified and

investigated the out-of-plane singular modein a comerof arbitrary vertex angle subjected to

in-plane loading [23], see Fig. 50. This singular moderelates to the out-of-plane shear stress

components and is associated with Poisson’s effect. Fig. 6 illustrates the mechanism of

formation of this singular mode for a particular configuration: a sharp comer with zero

vertex angle (crack) subjected to anti-symmetric (shear) loading. Intuitively, such loading

will create compressive and tensile zones along two opposite free edges; and Poisson’s

effect will lead to a scissoring motion of the faces generating conditions similar to the

tearing modein fracture mechanics but symmetric with respect to the mid-plane of the plate

(see Fig.6). This intuitive analysis can be further verified if one considers the classical

asymptotic equations of the plane stress solution for a crack stressed in the shear mode

leading to the same general conclusion with regard to the out-of-plane displacements.

However, the plane stress theory of elasticity predicts infinite displacements at the crack tip

and cannot be utilised in the quantitative analysis of this singular mode, which is why,

presumably, this type of singularity has been overlooked in the past. It is clear that the same

mechanism or symmetric out-of-plane loading, which is less commonin practice, can

generate the out-of-plane singularities at other vertex angles.

'

>

Fig.5a In-plane singularity

Fig.5b Corner singularity

Fig-5%- gut'of'plane

singu am y

The strongest power of the singularity

(minimum value of )t, )t>0) for in-plane

normal and shear modes (mode I and II) as

well as for out-of-plane mode (0 - mode) is

shown in Fig. 7a. It can be realized that the

dependence of the strength of the singularity of

Compression

Tension

the out-of-plane mode is exactly the same as

for fracture mode III. However, there are

Fig.6 Crack and Poisson’s effect

essential differences between these two

singular modes, which will be discussed later in this paper.

The out-of-plane singular mode is coupled with the shear mode(mode II) and has

been recently investigated by Harding and Kotousov [24] and by Harding et al. [25].

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