A finite element analysis of cracked square plates and bars under antiplane loading

Finite element analyses were carried out on cracked 20 mm square plates and bars ranging in thickness from 2.5 mm to a length of 60 mm. The crack extended from the middle of one side of the square to its centre, and was modelled as a narrow, parallel-sided notch with a semicircular tip. An antiplane loading was applied to the side containing the crack. An infinitely long bar under the antiplane loading used is in pure Mode III. It was found that the central portions of 40, 56 mm and 60 mm long bars were in pure Mode III, and also that K(III) was approximately constant. These central portions were therefore representative of an infinitely long bar. Towards the ends of a bar K(III) decreased. At the ends of a bar corner point effects meant that Mode II stress intensity factors and displacements were induced in the corner region. The size of the corner region was independent of bar length. In the 2.5, 5 and 10 mm thick plates out of plane bending means that the antiplane loading became a mixed Mode II and Mode III loading. At a centre line K(II) is zero by symmetry. Behaviour in the corner region was a function of plate thickness. For both plates and bars, as has been predicted theoretically, the ratio K(II) /K(III) tends to a constant value as a surface is approached. For a thickness of 20 mm, that is a 20-mm cube, behaviour represents a transition between plate and bar behaviour.