A reappraisal of transition elements in linear elastic fracture mechanics

This article offers a detailed comparison of the transition elements descri bed by P.P. Lynn and A.R. Ingraffea [International Journal for Numerical Me thods in Engineering 12, 1031-1036] and C. Manu [Engineering Fracture Mecha nics 24, 509-512]. The source of a numerical phenomenon in using Manu's tra nsition element (TE) is explained. The effect of eight-noded TEs with diffe rent quarter-point elements (QPE) on the calculated stress intensity factor s (SIFs) is investigated. Strain at the crack tip is shown to be singular f or any ray emanating from the crack tip within an eight-noded TE, but strai n has both r(-1/2) and r(-1) singularities, with r(-1/2) dominating for lar ge TEs. Semi-transition elements (STEs) are defined and shown to have a mar ginal effect on the calculated SIFs. Nine-noded transition elements are for mulated whose strain singularity is shown to be the same as that of eight-n oded TEs. Then the effect of eight-noded and nine-noded TEs with collapsed triangular QPEs, and rectangular and nonrectangular quadrilateral eight-nod ed and nine-noded QPEs, is studied, and nine-noded TEs are shown to behave exactly like eight-noded TEs with rectangular eight-noded and nine-noded QP Es and to behave almost the same with other QPEs. The layered transition el ements proposed by V. Murti and S.Valliapan [Engineering Fracture Mechanics 25, 237-258] are formulated correctly. The effect of layered transition el ements is shown by two numerical examples.