Crack Tip Element. A number of special crack tip finite elements have been
developed applicable to the displacement method, also the hybrid method has been
used in developing special crack tip elements. These special crack tip elements
contain a singularity off the strain field at the crack tip equal to the theoretical
singularity. For two-dimensional geometry the 8-node quadratic isoparametric
element can be made to simulate the 1//r singularity in stress. That is done
by placing the mid-side nodal coordinates on any side (connected to the crack
tip) at the quarter point .,.1i 'ent to the crack tip [40]. Lynn and Ingraffea [41]
have shown computation of SIF for isotropic material with high accuracy can be
achieved by placing mid-side nodes between quarter and mid-point of the elements
at the crack tip. This information further led to the development of the transition
element, which resulted in improved SIF calculations when the ratio of the quarter
point element and crack length is decreased.
Quadratic isoparametric elements with 20 nodes have proven to be excellent
elements for the calculation of SIF for elastic crack problems [31], when the mid-
side nodes are put near the crack tip at the quarter point. Also this element has
inverse square root ( ) singularity, which provides a stress field in agreement
with the theoretical stress singularity of linear fracture mechanics. While meshing
the model, the size of the element was of significant importance. Tarasovs [42]
has shown the effect of quarter point singular and transition element's size on
several SIF computation techniques. It was determined that computed SIF was not
sensitive to the singular element internal angle and size except for the quarter point
displacement technique and the displacement correlation technique. Therefore finer
mesh around the crack tip gives better results for the quarter point displacement
method.
Two-dimensional triangular elements [30], formed by collapsing one side of
rectangular elements, give better results for stress intensity factor. Also, it has